Trigonometriske funktioner

$\int\sin(u)\;du=-\cos(u)$

$\int\cos(u)\;du=\sin(u)$

$\int\tan(u)\;du=\ln(\operatorname{sec}(u))=-\ln(\cos(u))$

$\int\cot(u)\;du=\ln(\sin(u))$

$\int \operatorname{sec}(u)\;du=\ln(\operatorname{sec}(u)+\tan(u))=\ln \left(\tan \left(\frac{u}{2}+\frac{\pi}{4}\right)\right)$

$\int \operatorname{csc}(u)\;du=\ln \left(\operatorname{csc}(u)-\cot(u)\right)=\ln(\tan(\frac{u}{2}))$

$\int \operatorname{sec}^2(u)\;du=\tan(u)$

$\int \operatorname{csc}^2(u)\;du=-\cot(u)$

$\int \tan^2(u)\;du=\tan(u)-u$

$\int \cot^2(u)\;du=-\cot(u)-u$

$\int \sin^2(u)\;du=\frac{u}{2}-\frac{\sin(2u)}{4}=\frac{1}{2}\left(u-\sin(u)·\cos(u)\right)$

$\int \cos^2(u)\;du=\frac{u}{2}+\frac{\sin(2u)}{4}=\frac{1}{2}\left(u+\sin(u)·\cos(u)\right)$

$\int \operatorname{sec}(u)·\tan(u)\;du=\operatorname{sec}(u)$

$\int \operatorname{csc}(u)·\cot(u)\;du=-\operatorname{csc}(u)$

Se hyperbolske integraler (sinh, cosh, tanh, coth, sech, csch) her