Integration is the basic operation in integral calculus.
Pengintegralan atau integrasi merupakan operasi dasar dalam kalkulus integral.
More detail may be found on the following pages for the lists of integrals: List of integrals of rational functions List of integrals of irrational algebraic functions List of integrals of trigonometric functions List of integrals of inverse trigonometric functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of Gaussian functions Gradshteyn, Ryzhik, Geronimus, Tseytlin, Jeffrey, Zwillinger, and Moll's (GR) Table of Integrals, Series, and Products contains a large collection of results.
Daftar integral yang lebih detail dapat dilihat pada halaman-halaman berikut Daftar integral dari fungsi rasional Daftar integral dari fungsi irrasional Daftar integral dari fungsi trigonometri Daftar integral dari fungsi trigonometri terbalik Daftar integral dari fungsi hiperbolik Daftar integral dari fungsi hiperbolik terbalik Daftar integral dari fungsi eksponensial Daftar integral dari fungsi logaritmik Daftar integral dari fungsi Gaussian ∫ a f ( x )
a x d x1 a e a x + C \,dx={\frac {1}{a}}e^{ax}+C} ∫ f ′ ( x ) e f ( x )
d xa ∫ f ( x ) d x ( a konstan) }a{\mbox{ konstan)}}\,\!}
d xe x ∑ k1 n ( − 1 ) k − 1 d k − 1 f ( x ) d x k − 1 + C \left(f\left(x\right)-\left(-1\right)^{n}{\frac {d^{n}f\left(x\right)}{dx^{n}}}\right)\,dx}=e^{x}\sum _{k=1}^{n}{\left(-1\right)^{k-1}{\frac {d^{k-1}f\left(x\right)}{dx^{k-1}}}}+C} (if n is a positive integer) ∫ e − x ( f ( x ) − d n f ( x )
[ f ( x ) ] n f ′ ( x ) d x[ f ( x ) ] n + 1 n + 1 + C (untuk n ≠ − 1 ) f'(x)\,dx={[f(x)]^{n+1} \over n+1}+C\qquad {\mbox{(untuk }}n\neq -1{\mbox{)}}\,\!} ∫ f ′ ( x )
xln ⁡ | sinh ⁡ x | + C , for x ≠ 0 }x\neq 0} ∫ sech ⁡ x d xarctan ⁡ ( sinh ⁡ x ) + C x\,dx=\arctan(\sinh x)+C} ∫ csch x d xln ⁡ | coth ⁡ x − csch ⁡ x | + Cln ⁡ | tanh ⁡ x 2 | + C , for x ≠ 0 \,x\,dx=\ln \left|\operatorname {coth} x-\operatorname {csch} x\right|+C=\ln
d xx a r c c o s ( x ) − 1 − x 2 + C }}+C} ∫ arctan ⁡ x d xx arctan ⁡ x − 1 2 ln ⁡ | 1 + x 2 | + C \,dx=x\,\arctan {x}-{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C} ∫ arccot ⁡ x d xx arccot ⁡ x + 1 2 ln ⁡ | 1 + x 2 | + C {x}\,dx=x\,\operatorname {arccot} {x}+{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C} ∫ arcsec ⁡ ( x )
Then ∫ | f ( x ) | d xsgn ⁡ ( f ( x ) )
[ f ( x ) + g ( x ) ] d x∫ f ( x )
d xx Ei ⁡ ( x )
d xf ( x ) ∫ g ( x )
x∑ n1 ∞ n − n (1.29128 59970 6266 … ) ∫ 0 1 x x d x− ∑ n1 ∞ ( − n )
Integral tersebut di antaranya ∫ 0 1 x − x d x∑ n1 ∞ n − n (1 , 29128599706266 … ) ∫ 0 1 x x d x− ∑ n1 ∞ ( − n )
− n (0.78343 05107 1213 … ) \int _{0}^{1}x^{-x}\,dx&=\sum _{n=1}^{\infty }n^{-n}&&(=1.29128\,59970\,6266\dots )\\[6pt]\int _{0}^{1}x^{x}\,dx&=-\sum _{n=1}^{\infty }(-n)^{-n}&&(=0.78343\,05107\,1213\dots )\end{aligned}}} attributed to Johann Bernoulli.
− n (0 , 78343051071213 … ) \int _{0}^{1}x^{-x}\,dx&=\sum _{n=1}^{\infty }n^{-n}&&(=1,29128599706266\dots )\\\int _{0}^{1}x^{x}\,dx&=-\sum _{n=1}^{\infty }(-n)^{-n}&&(=0,78343051071213\dots )\end{aligned}}} Integral Kalkulus Fungsi gamma tidak komplit Jumlah tak terbatas Daftar limit Daftar deret matematikal Integrasi simbolik M. Abramowitz and I.A. Stegun, editors.
Table of Integrals, Series, and Products.
Table of Integrals, Series, and Products, seventh edition.
Yuri A. Brychkov (Ю. А. Брычков), Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas.
Yu.A. Brychkov (Ю.А. Брычков), Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas.
Meyer Hirsch, Integraltafeln oder Sammlung von Integralformeln (Duncker und Humblot, Berlin, 1810)
Meyer Hirsch, Integraltafeln, oder, Sammlung von Integralformeln (Duncker und Humblot, Berlin, 1810)
Meyer Hirsch, Integral Tables Or A Collection of Integral Formulae (Baynes and son, London, 1823)
Meyer Hirsch, Integral Tables, Or, A Collection of Integral Formulae (Baynes and son, London, 1823)
A short table of integrals - revised edition (Ginn & co., Boston, 1899)
A short table of integrals – revised edition (Ginn & co., Boston, 1899)
Paul's Online Math Notes A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals Definite Integrals Math Major: A Table of Integrals O'Brien, Francis J. Jr.
Paul's Online Math Notes A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals Definite Integrals Math Major: A Table of Integrals Diarsipkan 2012-10-30 di Archive.is O'Brien, Francis J. Jr.
Rule-based Integration Precisely defined indefinite integration rules covering a wide class of integrands Mathar, Richard J. (2012).
Derived integrals of exponential and logarithmic functions Rule-based Mathematics Precisely defined indefinite integration rules covering a wide class of integrands Mathar, Richard J. (2012).
Victor Hugo Moll, The Integrals in Gradshteyn and Ryzhik Integration examples for Wolfram Alpha wxmaxima gui for Symbolic and numeric resolution of many mathematical problems The Single Most Overpowered Integration Technique in Existence.
V. H. Moll, The Integrals in Gradshteyn and Ryzhik Integration examples for Wolfram Alpha wxmaxima gui for Symbolic and numeric resolution of many mathematical problems Diarsipkan 2011-03-20 di Wayback Machine.