Shalyt/ASyMOB-Algebraic_Symbolic_Mathematical_Operations_Benchmark huggingface dataset:
Problem: Evaluate
$ \lim_{x \to \infty} \left(A \cdot x - A \cdot J \cdot x^2 \cdot \ln\left(1 + \frac{ 1 }{ J \cdot x }\right)\right)^{B} $
Assume A,B,J are real and positive.
Answer (LaTeX): \left(\frac{A}{2 J}\right)^{B}
Answer (SymPy): (A/(2*J))**B
Problem: Evaluate
$ \lim_{x \to 0^+} J \cdot \left( \frac{\tan(A \cdot x)}{A \cdot x} \right)^{\frac{ H }{3 \cdot B \cdot x^2}} $
Assume A,B,J,H are real and positive.
Answer (LaTeX): J e^{\frac{A^{2} H}{9 B}}
Answer (SymPy): J*e**((A**2*H)/((9*B)))
Problem: Evaluate 
$ \lim_{x \to 0} \left| J \cdot \left( \frac{-\sin(A \cdot x)}{A \cdot x} \right)^{\frac{1}{4 \cdot B \cdot x^2}} \right| $
Assume A,B,J are real and positive.
Answer (LaTeX): \left( e^{-\frac{A^2}{6B}} \right)^{\frac{1}{4}} \left| J \right|
Answer (SymPy): (exp(-A**2 / (6 * B)))**Rational(1, 4) * Abs(J)
Problem: Integrate
$ \int B \cdot \sin(J \cdot x)^4 \cdot \cos(J \cdot x)^6 dx $
Assume B,J are real and positive.
Answer (LaTeX): \frac{\frac{B \sin{\left(2 J x \right)}}{512} - \frac{B \sin{\left(4 J x \right)}}{256} - \frac{B \sin{\left(6 J x \right)}}{1024} + \frac{B \sin{\left(8 J x \right)}}{2048} + \frac{B \sin{\left(10 J x \right)}}{5120} + \frac{J x \left(256 A + 3 B\right)}{256}}{J}
Answer (SymPy): (3*B*x)/256 + (B*sin(2*J*x))/(512*J) - (B*sin(4*J*x))/(256*J) - (B*sin(6*J*x))/(1024*J) + (B*sin(8*J*x))/(2048*J) + (B*sin(10*J*x))/(5120*J)
Problem: Solve the following integral. Assume A,B,G,H are real and positive.
$ \int \frac{A \cdot \sqrt[5]{x} + B \cdot x^{4/5} + H \cdot x^{6/5}}{x \left(G+x^{2/5}\right)}   dx $
Answer (LaTeX): \frac{5}{4} \left(\frac{4 A \tan ^{-1}\left(\frac{\sqrt[5]{x}}{\sqrt{G}}\right)}{\sqrt{G}}+2 x^{2/5} (B-H G)+2 G (H G-B) \log
   \left(G+x^{2/5}\right)+H x^{4/5}\right)
Answer (SymPy): (5/4)*(H*x**(4/5) + ((2*(x**(2/5)*(B - H*G)) + (4*(A*atan(x**(1/5)/(sqrt(G)))))/(sqrt(G))) + 2*(G*(-B + H*G)*log(G + x**(2/5), E))))
Problem: Solve the following integral. Assume A,B,J are real and positive.

$ \int \frac{A }{ B \cdot \sin ^7(J \cdot x) \cdot \cos (J \cdot x)}   dx $
Answer (LaTeX): -\frac{A \left(2 \csc ^6(J x)+3 \csc ^4(J x)+6 \csc ^2(J x)+12 (\log (\cos (J x))-\log (\sin (J x)))\right)}{12 B J}
Answer (SymPy): -A*(-12*log(sin(J*x)) + 12*log(cos(J*x)) + 2*(1/(sin(J*x)))**6 + 3*(1/(sin(J*x)))**4 + 6*(1/(sin(J*x)))**2)/(12*B*J)
Problem: Solve the following integral. Assume A,B,J are real and positive.

$ \int -\frac{2 \cdot A \cdot \sqrt{4 \cdot B + (J \cdot x)^2}}{ (J \cdot x)^4}   dx $
Answer (LaTeX): \frac{A \left(4 B+J^2 x^2\right)^{3/2}}{6 B J^4 x^3}
Answer (SymPy): A*(4*B + J**2*x**2)**(3/2)/(6*B*J**4*x**3)
Problem: Solve the following integral. Assume A,B,J are real and positive.

$ \int \left(\frac{B \cdot (4 \cdot A + J \cdot x)}{J \cdot x - 4 \cdot A}\right)^{\frac{ 3 }{ 2 }}   dx $
Answer (LaTeX): \frac{B \sqrt{\frac{B (4 A+J x)}{J x-4 A}} \left(\sqrt{4 A+J x} (J x-20 A)+24 A \sqrt{J x-4 A} \tanh ^{-1}\left(\frac{\sqrt{4
   A+J x}}{\sqrt{J x-4 A}}\right)\right)}{J \sqrt{4 A+J x}}
Answer (SymPy): B*sqrt(-B*(4*A + J*x)/(4*A - J*x))*(24*A*sqrt(-4*A + J*x)*atanh(sqrt(4*A + J*x)/sqrt(-4*A + J*x)) + (-20*A + J*x)*sqrt(4*A + J*x))/(J*sqrt(4*A + J*x))
Problem: Solve the following integral. Assume A,B,J,G are real and positive.

$ \int \frac{ -A }{B \cdot (J \cdot x)^2 \cdot \left(3 \cdot G + (J \cdot x)^3\right)^{\frac{ 5 }{ 3 }} }   dx $
Answer (LaTeX): \frac{A \left(J^3 x^3+2 G\right)}{6 B J^2 G^2 x \left(J^3 x^3+3 G\right)^{2/3}}
Answer (SymPy): A*(J**3*x**3 + 2*G)/(6*B*J**2*G**2*x*(J**3*x**3 + 3*G)**(2/3))
Problem: Solve the following integral. Assume A,B,J,G,H are real and positive.

$ \int \frac{\sqrt{4 \cdot A \cdot x - 5 \cdot B} + 4 \cdot J \cdot x}{5 \cdot G \cdot \sqrt[4]{4 \cdot A \cdot x - 5 \cdot B} + H \cdot (4 \cdot A \cdot x - 5 \cdot B)^{\frac{3}{4}}}   dx $
Answer (LaTeX): \frac{\frac{\sqrt{H} \left(20 A^2 H^2 x+375 J G^2 \sqrt{4 A x-5 B}+5 B H \left(12 J H \sqrt{4 A x-5 B}-5 A H+25 J G\right)+A H
   \left(12 J H x \sqrt{4 A x-5 B}-75 G \sqrt{4 A x-5 B}-100 J G x\right)\right)}{\sqrt[4]{4 A x-5 B}}-75 \sqrt{5} \sqrt{G}
   \left(-A G H+B J H^2+5 J G^2\right) \tan ^{-1}\left(\frac{\sqrt{H} \sqrt[4]{4 A x-5 B}}{\sqrt{5} \sqrt{G}}\right)}{15 A^2
   H^{7/2}}
Answer (SymPy): (75*sqrt(5)*sqrt(G)*(4*A*x - 5*B)**(1/4)*(A*G*H - B*J*H**2 - 5*J*G**2)*atan(sqrt(5)*sqrt(H)*(4*A*x - 5*B)**(1/4)/(5*sqrt(G))) + sqrt(H)*(20*A**2*H**2*x + A*H*(-100*J*G*x + 12*J*H*x*sqrt(4*A*x - 5*B) - 75*G*sqrt(4*A*x - 5*B)) + 5*B*H*(-5*A*H + 25*J*G + 12*J*H*sqrt(4*A*x - 5*B)) + 375*J*G**2*sqrt(4*A*x - 5*B)))/(15*A**2*H**(7/2)*(4*A*x - 5*B)**(1/4))
Problem: Solve the following integral. Assume A,B,J are real and positive.

$ \int \frac{3 \cdot A \cdot \csc ^7(2 \cdot J \cdot x) \sec (2 \cdot J \cdot x)}{ B }   dx $
Answer (LaTeX): -\frac{A \left(2 \csc ^6(2 J x)+3 \csc ^4(2 J x)+6 \csc ^2(2 J x)+12 (\log (\cos (2 J x))-\log (\sin (2 J x)))\right)}{8 B J}
Answer (SymPy): -A*(-12*log(sin(2*J*x)) + 12*log(cos(2*J*x)) + 2*csc(2*J*x)**6 + 3*csc(2*J*x)**4 + 6*csc(2*J*x)**2)/(8*B*J)
Problem: Solve the following integral. Assume A,J are real and positive.

$ \int \frac{ A }{ (\sin(8 \cdot J \cdot x))^5 }   dx $
Answer (LaTeX): -\frac{A \left(\csc ^4(4 J x)+6 \csc ^2(4 J x)-\sec ^4(4 J x)-6 \sec ^2(4 J x)+24 (\log (\cos (4 J x))-\log (\sin (4 J
   x)))\right)}{512 J}
Answer (SymPy): -A*(-24*log(sin(4*J*x)) + 24*log(cos(4*J*x)) + csc(4*J*x)**4 + 6*csc(4*J*x)**2 - sec(4*J*x)**4 - 6*sec(4*J*x)**2)/(512*J)
Problem: Solve the following integral. Assume A,B,J are real and positive.

$ \int \cos (2 \cdot J \cdot x) \left(A \cdot (J \cdot x)^3+3 \cdot B \right)   dx $
Answer (LaTeX): \frac{2 \sin (2 J x) \left(A J x \left(2 J^2 x^2-3\right)+6 B\right)+3 A \left(2 J^2 x^2-1\right) \cos (2 J x)}{8 J}
Answer (SymPy): ((2*A*J*x*(2*J**2*x**2 - 3) + 12*B)*sin(2*J*x) + 3*A*(2*J**2*x**2 - 1)*cos(2*J*x))/(8*J)
Problem: Use factoring to calculate the following limit.
Assume A,B,J are real and positive.
$ \lim_{x \rightarrow \frac{K}{J}} \frac{(J \cdot x)^{4 \cdot B} - K^{4 \cdot B}}{A \cdot \left((J \cdot x)^{5 \cdot B}- K^{5 \cdot B}\right)} $
Answer (LaTeX): \frac{4 K^{-B}}{5 A}
Answer (SymPy): 4/(5*A*K**B)
Problem: Calculate the following limit.
Assume A,B,J are real and positive.
$ \lim_{x \to 0} \frac{B - B \cdot \cos (10 \cdot J \cdot x)}{A \cdot \cos ^2(6 \cdot J \cdot x) - A} $
Answer (LaTeX): -\frac{25 B}{18 A}
Answer (SymPy): -25*B/(18*A)
Problem: Calculate the following limit.
Assume A,B,J are real and positive.
$ \lim_{x\to 1} \frac{A \cdot (J \cdot x)^2 + 11 \cdot A \cdot J \cdot x - 12 \cdot A}{B \cdot \log (J \cdot x)} $
Answer (LaTeX): \frac{13 A}{B}
Answer (SymPy): 13*A/B
Problem: Calculate the following limit.
Assume A,J are real and A>1.

$ \lim\limits_{x\to+\infty} 4^{-\frac{1}{J \cdot x}} \left(\frac{(4 \cdot A)^{J \cdot x} + (6 \cdot A)^{J \cdot x} }{ A }\right)^{\frac{1}{J \cdot x}} $
Answer (LaTeX): 6 A
Answer (SymPy): 6*A
Problem: Calculate the following integral. 
Assume A,B, J are real and positive.
$\int_{2 \cdot B}^{\infty} 3 \cdot A \cdot (J \cdot x)^2 e^{- (J \cdot x)^3}  dx$
Answer (LaTeX): \frac{A e^{-8 B^3 J^3}}{J}
Answer (SymPy): A/(J*e**(8*B**3*J**3))
Problem: Evaluate the indefinite integral. 
Assume A, J are real and positive.
$\int A \cdot \tan ^3(J \cdot x) \sec ^9(J \cdot x)   dx$
Answer (LaTeX): \frac{A \sec ^9(J x) \left(9 \sec ^2(J x)-11\right)}{99 J}
Answer (SymPy): A*(9*sec(J*x)**2 - 11)*sec(J*x)**9/(99*J)
Problem: Evaluate the indefinite integral.
Assume A, J are real and positive.
$\int 208 \cdot A \cdot \cos ^4(16 \cdot J \cdot x)  dx$
Answer (LaTeX): \frac{13 A (192 J x+8 \sin (32 J x)+\sin (64 J x))}{32 J}
Answer (SymPy): 13*A*(192*J*x + 8*sin(32*J*x) + sin(64*J*x))/(32*J)
Problem: Evaluate the integral.
Assume A, B, J, G are real and positive.
$ \int \frac{-38 \cdot A+10 \cdot B \cdot (J \cdot x)^2 - 48 \cdot J \cdot G \cdot x}{(J \cdot x)^3 - 5 (J \cdot x)^2 - 8 \cdot J \cdot x+48} dx $
Answer (LaTeX): \frac{2 \left(\frac{7 (19 A-80 B+96 G)}{J x-4}+(19 A+200 B-72 G) \log (4-J x)+(-19 A+45 B+72 G) \log (J x+3)\right)}{49 J}
Answer (SymPy): 2*(133*A - 560*B + 672*G + (J*x - 4)*((-19*A + 45*B + 72*G)*log(J*x + 3) + (19*A + 200*B - 72*G)*log(-J*x + 4)))/(49*J*(J*x - 4))
Problem: Evaluate the integral.
Assume A,B,J are real and positive.
$ \int A \cdot e^{J \cdot x} \sqrt{64 \cdot B-e^{2 \cdot J \cdot x}} dx$
Answer (LaTeX): \frac{A \left(e^{J x} \sqrt{64 B-e^{2 J x}}+64 B \tan ^{-1}\left(\frac{e^{J x}}{\sqrt{64 B-e^{2 J x}}}\right)\right)}{2 J}
Answer (SymPy): A*(64*B*atan(e**(J*x)/sqrt(64*B - e**(2*J*x))) + e**(J*x)*sqrt(64*B - e**(2*J*x)))/(2*J)
Problem: Evaluate the following limit.
Assume A,B,J are real and positive.
$\lim_{x \to 0} \frac{-\frac{9}{2} \cdot B^2 (J \cdot x)^6 + 3 \cdot B \cdot J^3 \cdot x^3 + e^{-3 \cdot B \cdot (J \cdot x)^3}-1}{12 \cdot A \cdot (J \cdot x)^9} $
Answer (LaTeX): -\frac{3 B^3}{8 A}
Answer (SymPy): -3*B**3/(8*A)
Problem: Solve the following first-order differential equation:
Assume A,B,J,G are real and positive.
$ A \cdot \frac{dy}{dx} + 2 \cdot B \cdot y = J \cdot e^{-x}, \quad y(0) = G .$
Answer (LaTeX): \frac {e^{-\frac{2 B x}{A}} \left(J \left(-e^{x \left(\frac{2 B}{A}-1\right)}\right)+A G-2 B
   G+J\right)}{A-2 B}
Answer (SymPy): (A*G - 2*B*G + J + J*(-e**x*((-A + 2*B)/A)))/(e**(2*B*x/A)*(A - 2*B))
Problem: Consider the differential equation 
$A \cdot \frac{dy}{dx} = B \cdot x \cdot y$. 
Find the value of $y(\sqrt{2})$ given that $y(0) = 2 \cdot J$.
Assume A,B,J are real and positive.
Answer (LaTeX): 2 J e^{\frac{B}{A}}
Answer (SymPy): 2*J*e**(B/A)
Problem: Evaluate the following limit:
$ \lim_{x \to \infty} \sqrt{-B + H \cdot (J \cdot x)^2 + 2 \cdot J \cdot G \cdot x}-\sqrt{3 \cdot A + H \cdot (J \cdot x)^2} $
Assume A,B,J,G,H are real and positive.
Answer (LaTeX): \frac{G}{\sqrt{H}}
Answer (SymPy): G/sqrt(H)
Problem: Evaluate $\lim\limits_{x\to \frac{4 \cdot B}{ J }} \frac{A \cdot (J \cdot x - 4 \cdot B)}{\sqrt{J \cdot x}-2 \sqrt{ B }} $.

Assume A,B,J are real and positive.
Answer (LaTeX): 4 A \sqrt{B}
Answer (SymPy): 4*A*sqrt(B)
Problem: Evaluate $\int_0^{4 \cdot B}  (2 \cdot A \cdot x - \sqrt{(4 \cdot B \cdot J)^2 - (J \cdot x)^2}) dx$.

Assume A,B,J are real and positive.
Answer (LaTeX): 4 B^2 (4 A-\pi  J)
Answer (SymPy): 4*B**2*(4*A - J*pi)
Problem: Evaluate the series $\sum\limits_{x=1}^\infty \frac{ A }{B \cdot (J + x) (J +x+2)} $.

Assume A,B,J are real and positive.
Answer (LaTeX): \frac{A (2 J+3)}{2 B (J+1) (J+2)}
Answer (SymPy): A*(2*J + 3)/(2*(J + 2)*B*(J + 1))
Problem: Evaluate the limit $\lim\limits_{x \to 0} \frac{(A \cdot x+1)^{\frac{1}{A \cdot x}}-e}{B \cdot x} $.

Assume A,B are real and positive.
Answer (LaTeX): -\frac{e A}{2 B}
Answer (SymPy): -A*e/(2*B)
Problem: Evaluate the series $\sum\limits_{n=0}^\infty \frac{ \left(\frac{1}{2 \cdot B}\right)^{A \cdot (2 n+1)}}{J \cdot (2 n+1)} $.

Assume A,B,J are real and positive.
Answer (LaTeX): \frac{\tanh ^{-1}\left(2^{-A} \left(\frac{1}{B}\right)^A\right)}{J}
Answer (SymPy): atanh((1/(2*B))**A)/J
Problem: Evaluate the limit
$\lim\limits_{n\to\infty}\sum\limits_{k=0}^{n-1}\frac{ A }{B \cdot \sqrt{J \cdot n^2-k^2}}$

Assume A,B, J are real and positive - and $J \ge 1$.
Answer (LaTeX): \frac{A}{B} \arcsin\left(\frac{1}{\sqrt{J}}\right)
Answer (SymPy): A*asin(1/sqrt(J))/B
Problem: Evaluate the iterated integral $\int_0^1dy\int_y^1 e^{-A \cdot (J \cdot x)^2} + B \cdot e^{J \cdot x} dx$.

Assume A,B,J are real and positive.
Answer (LaTeX): \frac{2 A B \left(e^J (J-1)+1\right)-e^{-A J^2}+1}{2 A J^2}
Answer (SymPy): (e**(A*J**2)*(2*A*B*(e**J*(J - 1) + 1) + 1) - 1)/(2*A*J**2*e**(A*J**2))
Problem: What is the integral of $ 2 \cdot A \cdot x - B \cdot x^{7 \cdot J} \tan ^{-1}(3 \cdot G) $

Assume A,B,J,G are real and positive.
Answer (LaTeX): x \left(A x-\frac{B x^{7 J} \tan ^{-1}(3 G)}{7 J+1}\right)
Answer (SymPy): x*((A*x*(7*J + 1) - B*x**(7*J)*atan(3*G))/(7*J + 1))
Problem: What is the integral of
$ A + B \cdot J \cdot x + \cosh (2 \cdot G) \cdot (J \cdot x)^{3 \cdot H} $

Assume A,B,J,G,H are real and positive.
Answer (LaTeX): A x+\frac{1}{2} B J x^2+\frac{x \cosh (2 G) (J x)^{3 H}}{3 H+1}
Answer (SymPy): x*(2*(J*x)**(3*H)*cosh(2*G) + (2*A + B*J*x)*(3*H + 1))/(2*(3*H + 1))
Problem: What is the integral of $12 \cdot A + 6 \cdot B \cdot \cosh (J \cdot x)$

Assume A,B,J are real and positive.
Answer (LaTeX): 12 A x+\frac{6 B \sinh (J x)}{J}
Answer (SymPy): 12*A*x + 6*B*sinh(J*x)/J
Problem: What is the integral of 
$ 4 \cdot (B \cdot x)^{7 \cdot J} + G \cdot \sin (H + A \cdot x) $

Assume A,B,J,G,H are real and positive.
Answer (LaTeX): \frac{4 A x (B x)^{7 J}-(7 J+1) G \cos (H+A x)}{7 J A+A}
Answer (SymPy): (4*A*x*(B*x)**(7*J) - G*(7*J + 1)*cos(H + A*x))/(A*(7*J + 1))
Problem: What is the integral of
$ 2 x + 2 \cdot B \cdot x^{2 \cdot J}+\frac{x}{G \cdot x + H \cdot x \cdot e^{A \cdot x}} $.

Assume A,B,J,G,H are real and positive.
Answer (LaTeX): x \left(x+\frac{2 B x^{2 J}}{2 J+1}\right)-\frac{\log \left(G A \left(G+H e^{A x}\right)\right)}{G A}+\frac{\log \left(e^{A
   x}\right)}{G A}
Answer (SymPy): (G*A*x*((x*(2*J + 1) + 2*B*x**(2*J))/(2*J + 1)) + log(e**(A*x)) - log(G*A*(G + H*e**(A*x))))/(G*A)
Problem: What is the integral of 
$ B \cdot \log (3 \cdot H \cdot x) \cos (J \cdot \log (\sin (3))) - A \cdot x $

Assume A,B,J,H are real and positive.
Answer (LaTeX): B x (\log (3 H x)-1) \cos (J \log (\sin (3)))-\frac{A x^2}{2}
Answer (SymPy): -A*x**2/2 + B*x*(log(3*H*x) - 1)*cos(J*log(sin(3)))
Problem: What is the integral of
$ 3 \cdot A \cdot x - 4 \cdot B \cdot (H \cdot x)^2 \cdot \cos (J \cdot x + 3 \cdot G) $

Assume A,B,J,G,H are real and positive.
Answer (LaTeX): \frac{3 A x^2}{2}-\frac{8 B H^2 x \cos (J x+3 G)}{J^2}-\frac{4 B H^2 \left(J^2 x^2-2\right) \sin (J x+3 G)}{J^3}
Answer (SymPy): (3*A*J**3*x**2 - 16*B*J*H**2*x*cos(J*x + 3*G) - 8*B*H**2*(J**2*x**2 - 2)*sin(J*x + 3*G))/(2*J**3)
Problem: What is the integral of 
$ A \cdot \tan ^{-1}(B \cdot x) + J \cdot \log (G \cdot \tanh (3 \cdot H))-3 $

Assume A,B,J,G,H are real and positive.
Answer (LaTeX): -\frac{A \log \left(B^2 x^2+1\right)}{2 B}+A x \tan ^{-1}(B x)+x (J \log (G \tanh (3 H))-3)
Answer (SymPy): A*x*atan(B*x) - A*log(B**2*x**2 + 1)/(2*B) + x*(J*log(G*tanh(3*H)) - 3)
Problem: What is the integral of
$ A \cdot (J \cdot x + 4 \cdot G) \cdot (3 \cdot J \cdot x + 4 \cdot G) e^{B \cdot x \cdot (J \cdot x + 4 \cdot G)^2} $

Assume A,B,J,G are real and positive.
Answer (LaTeX): \frac{A e^{B x (J x+4 G)^2}}{B}
Answer (SymPy): A*e**(B*x*(J*x + 4*G)**2)/B
Problem: What is the integral of

$ -A \cdot e^{3 \cdot B \cdot x} \cdot \sin \left(J \cdot e^{3 \cdot B \cdot x}\right) $

Assume A,B,J are real and positive.
Answer (LaTeX): \frac{A \cos \left(J e^{3 B x}\right)}{3 B J}
Answer (SymPy): A*cos(J*e**(3*B*x))/(3*B*J)
Problem: If $\log_{(2 \cdot A)} x - 2 \cdot J \cdot \log _{(2 \cdot A)} y = 2 \cdot B$, determine $y$, as a function of $x$

Assume A,B,J are real and positive.
Answer (LaTeX): e^{\frac{\log (x)-2 B \log (2 A)}{2 J}}
Answer (SymPy): e**((-2*B*log(2*A) + log(x))/(2*J))
Problem: If $f(x)=2 \cdot A \cdot x+ B $ and $g(f(x)) = 4 \cdot J \cdot x^{2}+ G$, determine an expression for $g(x)$.

Assume A,B,J,G are real and positive.
Answer (LaTeX): \frac{J (x-B)^2}{A^2}+G
Answer (SymPy): G + J*(-B + x)**2/A**2
Problem: Solve the following integral. Assume A,B,J are real and B>0.

$\int_0^{\frac{\pi}{2 \cdot J}} \frac{A \cdot x \cdot \sin(2 \cdot J \cdot x)}{B + \cos^2(2 \cdot J \cdot x)}   dx$
Answer (LaTeX): \frac{A\pi}{4J^2\sqrt{B}} \arctan\!\frac{1}{\sqrt{B}}
Answer (SymPy): A*pi*atan(1/sqrt(B))/(4*sqrt(B)*J**2)
Problem: Solve the following integral. Assume A,B,J,G are real and positive.

$\int_{1}^{2} \frac{A \cdot e^{J \cdot x} \cdot (J \cdot x - 1)}{J \cdot x \cdot \left(B \cdot e^{J \cdot x} + J \cdot G \cdot x\right)}   dx$ 
Answer (LaTeX): -\frac{A \log \left(\frac{2 (e B+G)}{e^2 B+2 G}\right)}{B J}
Answer (SymPy): -A*log((2*(B*E + G))/(B*E**2 + 2*G), E)/(B*J)
Problem: Solve the following integral. Assume A,B,J are real and positive.

Solve the following integral:
$\int_{0}^{\pi} A \cdot \log(B \cdot (\sin(x))^{ J })   dx$
Answer (LaTeX): A \pi \log\left(\frac{B}{2^J}\right)
Answer (SymPy): A*(pi*log(B/(2**J), E))
Problem: Evaluate the following hypergeometric function. Assume A,B are real numbers. Return a closed-form symbolic answer.

$ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 2 \end{array}; (-A)^{B} \right) $
Answer (LaTeX): -(-A)^{-B} \log \left(1-(-A)^B\right)
Answer (SymPy): log(1 - (-A)**B, E)/((-A)**B)
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer.

$ {}_2F_1\left( \begin{array}{c} 1 ,1 \\ 3 \end{array}; -2 \cdot (A^{B}) \right) $
Answer (LaTeX): \frac{1}{2} A^{-2 B} \left(\left(2 A^B+1\right) \log \left(2 A^B+1\right)-2
   A^B\right)
Answer (SymPy): (-2*(A**B) + (2*(A**B) + 1)*log(2*(A**B) + 1, E))/(2*(A**B)**2)
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B,G,H are real numbers. Return a closed-form symbolic answer.

$ {}_8F_7\left( \begin{array}{c} 1,1,1, A , B , 1, G, H \\ 2,2, H, G, B, 1,  A \end{array}; -1 \right) $
Answer (LaTeX): \frac{\pi ^2}{12}
Answer (SymPy): pi**2/12
Problem: Evaluate the following hypergeometric function. Assume the parameters: x,A,B,G,H are real numbers. Return a closed-form symbolic answer.

$ {}_3F_2\left( \begin{array}{c} -1,-A, -B \\ -H, -G \end{array}; x \right) $
Answer (LaTeX): 1-\frac{A B x}{H G}
Answer (SymPy): 1 - A*(B*x)/(H*G)
Problem: Solve the following integral. Assume the parameters: A,B,J are real numbers. Return a closed-form symbolic answer.

$ \int \frac{ A }{ B + (x \cdot J)^3 }   dx $
Answer (LaTeX): -\frac{A \left(\log \left(B^{2/3}-\sqrt[3]{B} J x+J^2 x^2\right)-2 \log \left(\sqrt[3]{B}+J x\right)+2 \sqrt{3} \tan
   ^{-1}\left(\frac{1-\frac{2 J x}{\sqrt[3]{B}}}{\sqrt{3}}\right)\right)}{6 B^{2/3} J}
Answer (SymPy): -A*(-2*log(B**(1/3) + J*x) + log(B**(2/3) - B**(1/3)*J*x + J**2*x**2) + 2*sqrt(3)*atan(sqrt(3)*(B**(1/3) - 2*J*x)/(3*B**(1/3))))/(6*B**(2/3)*J)
Problem: Solve the following integral. Assume A,B are positive integers.

$ \int \frac{(2 \cdot A + (2 \cdot A - B) \cdot x^{B}) \cdot x^{A - 1}}{2 \cdot (1 + x^{B} + x^{2 \cdot A}) \cdot \sqrt{1 + x^{B}}} dx $
Answer (LaTeX): \tan ^{-1}\left(\frac{\left x^A}{\sqrt{x^B+1}}\right)
Answer (SymPy): atan(x**A/(sqrt(x**B + 1)))
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B,G are real numbers. Return a closed-form symbolic answer.

$ {}_2F_1\left( \begin{array}{c} A, G \\ A \end{array}; -B \right) $
Answer (LaTeX): (B+1)^{-G}
Answer (SymPy): (B+1)**(-G)
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B are real numbers. Return a closed-form symbolic answer.

$ {}_1F_1\left( \begin{array}{c} A \\ A \end{array}; B \right) $
Answer (LaTeX): e^B
Answer (SymPy): E**B
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B,G are real numbers. Return a closed-form symbolic answer.

$ {}_2F_1\left( \begin{array}{c} A, -2 \\ 2+G \end{array}; B \right) $
Answer (LaTeX): -\frac{(-A-1) A B^2}{(G+2) (G+3)}-\frac{2 A B}{G+2}+1
Answer (SymPy): 1 - (2*A*B)/(2+G) + (B**2 * A * (A+1))/((2+G)*(3+G))
Problem: Evaluate the following hypergeometric function. Assume the parameters: A,B,G, H are real numbers. Return a closed-form symbolic answer.

$ {}_3F_1\left( \begin{array}{c} (A + 1), -2, (H + 3) \\ (2 + G) \end{array}; \frac{B}{2} \right) $
Answer (LaTeX): \frac{(A+1) (A+2) B^2 (H+3) (H+4)}{4 (G+2) (G+3)}-\frac{(A+1) B (H+3)}{G+2}+1
Answer (SymPy): (-(A + 1)*B*(H + 3) / (G + 2) + ((( (B**2) * ((H + 3)*(H + 4)))*(A + 2))*(A + 1)) / ((4*((G + 2)*(G + 3)))) ) + 1
Problem: Solve the following differential equation:
$ B \cdot x \cdot y' + B \cdot y = A \cdot x \cdot \sin(x), y(\pi) = G $
Assume the parameters: A,B,G are real numbers.
Answer (LaTeX): \frac{A \sin (x)+A (-x) \cos (x)-\pi  A+\pi  B G}{B x}
Answer (SymPy): (-A*pi + A*sin(x) + B*G*pi + A*(-x)*cos(x)) / (B*x)
Problem: Solve the following differential equation:
$ A \cdot y' = B \cdot e^{J \cdot x} \cdot y , y(H) = G $
Assume the parameters: A,B,G,H,J are real numbers.
Answer (LaTeX): G e^{\frac{B e^{J x}}{A J}-\frac{B e^{H J}}{A J}}
Answer (SymPy): G*e**(B*(-e**(H*J) + e**(J*x))/(A*J))
Problem: Solve the following differential equation:
$ A \cdot y' = 2 \cdot B \cdot x \cdot y^2 - G \cdot y , y(H) = J $
Assume the parameters: A,B,G,H,J are real numbers.
Answer (LaTeX): \frac{G^2 J e^{\frac{G H}{A}}}{-2 B G H J e^{\frac{G x}{A}}+2 B G J x e^{\frac{G
   H}{A}}+2 A B J e^{\frac{G H}{A}}-2 A B J e^{\frac{G x}{A}}+G^2 e^{\frac{G
   x}{A}}}
Answer (SymPy): G**2*J*e**(G*H/A)/(2*A*B*J*e**(G*H/A) - 2*A*B*J*e**(G*x/A) - 2*B*G*H*J*e**(G*x/A) + 2*B*G*J*e**(G*H/A)*x + G**2*e**(G*x/A))
Problem: Solve the following differential equation:
$ A \cdot y' = B \cdot x \cdot y^{G+1} - y , y(H) = J $
Assume the parameters: A,B,G,H,J are real numbers.
Answer (LaTeX): \left(\frac{J^{-G} e^{\frac{G (x-H)}{A}} \left(-A B J^G-B G H J^G+G\right)+A B+B G
   x}{G}\right)^{-1/G}
Answer (SymPy): ((B*J**G*(A + G*x) - e**(G*(-H + x) / A)*(A*B*J**G + B*G*H*J**G - G)) / (G*J**G))**(-1/G)
Problem: Solve the following differential equation:
$ A \cdot y' = \frac{(B+1) \cdot x \cdot y + G \cdot y^2}{x^2} , y(H) = J $
Assume the parameters: A,B,G,H,J are real numbers.
Answer (LaTeX): \frac{H J (A-B-1) x^{\frac{A+B+1}{A}}}{-G J x H^{\frac{B+1}{A}}+G H J
   x^{\frac{B+1}{A}}+x (A-B-1) H^{\frac{A+B+1}{A}}}
Answer (SymPy): H*x**((A + B + 1)/A)*J*(A - B - 1) / (G*H*J*x**((B + 1)/A) - G*H**((B + 1)/A)*J*x + H**((A + B + 1)/A)*x*(A - B - 1))
Problem: Solve the following differential equation:
$ y' = A \cdot e^{-G \cdot x} - 2 \cdot B \cdot y , y(H) = J $
Assume the parameters: A,B,G,H,J are real and positive numbers.
Answer (LaTeX): \frac{e^{-2 B x} \left(A \left(-e^{H (2 B-G)}\right)+A e^{x (2 B-G)}-G J e^{2 B
   H}+2 B J e^{2 B H}\right)}{2 B-G}
Answer (SymPy): (A*e**(x*(2*B - G)) + 2*B*J*e**(2*B*H) - G*J*e**(2*B*H) + A*(-e**(H*(2*B - G)))) / (e**(2*B*x)*(2*B - G))
Problem: Solve the following differential equation:
$ A \cdot y' = 3 \cdot x^2 \cdot \left( B + y^2 \right) , y(H) = J $
Assume the parameters: A,B,G,H,J are real and positive numbers.
Answer (LaTeX): \sqrt{B} \tan \left(\frac{A \tan ^{-1}\left(\frac{J}{\sqrt{B}}\right)-\sqrt{B}
   H^3+\sqrt{B} x^3}{A}\right)
Answer (SymPy): sqrt(B)*tan((A*atan(J/sqrt(B)) - sqrt(B)*H**3 + sqrt(B)*x**3)/A)
Problem: Solve the following differential equation:
$ A \cdot y' = \frac{2 \cdot G \cdot (A \cdot y + B \cdot x)}{x} , y(H) = J $
Assume the parameters: A,B,G,H,J are real and positive numbers.
Answer (LaTeX): -\frac{H^{-2 G} \left(A J x^{2 G}-2 A G J x^{2 G}+2 B G x H^{2 G}-2 B G H x^{2
   G}\right)}{A (2 G-1)}
Answer (SymPy): (2*A*G*J*x**(2*G) - A*J*x**(2*G) + 2*B*G*H*x**(2*G) - 2*B*G*H**(2*G)*x)/(H**(2*G)*A*(2*G - 1))
Problem: Solve the following differential equation:
$ A \cdot y' = \frac{ (A \cdot y + B \cdot x)}{x} , y(H) = J $
Assume the parameters: A,B,H,J are real and positive numbers.
Answer (LaTeX): \frac{x (A J+B H \log (x)-B H \log (H))}{A H}
Answer (SymPy): x*(A*J - B*H*log(H) + B*H*log(x))/(A*H)
Problem: Solve the following differential equation:
$ A \cdot y' = \left(\frac{x}{G}\right)^{B} , y(H) = J $
Assume the parameters: A,B,G,H,J are real and positive numbers.
Answer (LaTeX): \frac{G^{-B} \left(A J G^B+A B J G^B-H^{B+1}+x^{B+1}\right)}{A (B+1)}
Answer (SymPy): (A*B*G**B*J + A*G**B*J - H**(B + 1) + x**(B + 1))/(G**B*A*(B + 1))
Problem: Solve the following differential equation:
$ A \cdot y' = G \cdot x - 2 \cdot B \cdot x \cdot y , y(H) = J $
Assume the parameters: A,B,G,H,J are real and positive numbers.
Answer (LaTeX): \frac{e^{-\frac{B x^2}{A}} \left(G \left(-e^{\frac{B H^2}{A}}\right)+G e^{\frac{B
   x^2}{A}}+2 B J e^{\frac{B H^2}{A}}\right)}{2 B}
Answer (SymPy): (2*B*J*e**(B*H**2/A) + G*e**(B*x**2/A) + G*(-e**(B*H**2/A)))/(2*B*e**(B*x**2/A))