原始関数の一覧
∫ cos  x d x = sin  x + C {\displaystyle \int \cos x\,dx=\sin x+C}
∫ − sin  x d x = cos  x + C {\displaystyle \int -\sin x\,dx=\cos x+C}
∫ sec 2  x d x = tan  x + C {\displaystyle \int \sec ^{2}x\,dx=\tan x+C}
∫ − csc 2  x d x = cot  x + C {\displaystyle \int -\csc ^{2}x\,dx=\cot x+C}
∫ sec  x tan  x d x = sec  x + C {\displaystyle \int \sec x\tan x\,dx=\sec x+C}
∫ − csc  x cot  x d x = csc  x + C {\displaystyle \int -\csc x\cot x\,dx=\csc x+C}
∫ tan  x d x = − ln  ( cos  x ) + C {\displaystyle \int \tan x\,dx=-\ln(\cos x)+C}
∫ cot  x d x = ln  ( sin  x ) + C {\displaystyle \int \cot x\,dx=\ln(\sin x)+C}
∫ 1 x a + b x d x = 1 a ln  ( a + b x − a a + b x + a ) + C , a > 0 {\displaystyle \int {\frac {1}{x{\sqrt {a+bx}}}}\,dx={\frac {1}{\sqrt {a}}}\ln \left({\frac {{\sqrt {a+bx}}-{\sqrt {a}}}{{\sqrt {a+bx}}+{\sqrt {a}}}}\right)+C,a>0} = 2 − a arctan  a + b x − a + C , a < 0 {\displaystyle ={\frac {2}{\sqrt {-a}}}\arctan {\sqrt {\frac {a+bx}{-a}}}+C,a<0}
∫ 1 x n a + b x d x = − 1 a ( n − 1 ) a + b x x n − 1 − ( 2 n − 3 ) b 2 a ( n − 1 ) ∫ 1 x n − 1 a + b x d x , n ≠ 1 {\displaystyle \int {\frac {1}{x^{n}{\sqrt {a+bx}}}}\,dx={\frac {-1}{a(n-1)}}{\frac {\sqrt {a+bx}}{x^{n-1}}}-{\frac {(2n-3)b}{2a(n-1)}}\int {\frac {1}{x^{n-1}}}{\sqrt {a+bx}}dx,n\neq 1}