不定積分
{\displaystyle \int {\frac {1}{\sin x}}\,dx=\ln \left|\tan {\frac {x}{2}}\right|+C.}
∫ 1 sin 2  x d x = − 1 tan  x + C . {\displaystyle \int {\frac {1}{\sin ^{2}x}}\,dx=-{\frac {1}{\tan x}}+C.}
∫ 1 cos  x d x = 1 2 ln  1 + sin  x 1 − sin  x + C . {\displaystyle \int {\frac {1}{\cos x}}\,dx={\frac {1}{2}}\ln {\frac {1+\sin x}{1-\sin x}}+C.}
∫ 1 cos 2  x d x = tan  x + C . {\displaystyle \int {\frac {1}{\cos ^{2}x}}\,dx=\tan x+C.}
∫ 1 tan  x d x = ln  | sin  x | + C . {\displaystyle \int {\frac {1}{\tan x}}\,dx=\ln |\sin x|+C.}
∫ arctan  x d x = x arctan  x − 1 2 ln  ( 1 + x 2 ) + C . {\displaystyle \int \arctan x\,dx=x\arctan x-{\frac {1}{2}}\ln(1+x^{2})+C.}