Integrals containing trigonometric functions.

$\displaystyle \int \tan u \; du$ $\displaystyle = \ln \vert \sec u \vert + C.$ (B..34)
$\displaystyle \int\cot u du$ $\displaystyle = \ln \vert \sin u \vert + C.$ (B..35)
$\displaystyle \int \sec u \; du$ $\displaystyle = \ln \vert \sec u + \tan u \vert + C.$ (B..36)
$\displaystyle \int \csc u \; du$ $\displaystyle = \ln \vert \csc u - \cot u \vert + C.$ (B..37)
$\displaystyle \int \sec^2 u \; du$ $\displaystyle = \tan u + C.$ (B..38)
$\displaystyle \int \csc^2 u \; du$ $\displaystyle = - \cot u + C.$ (B..39)
$\displaystyle \int \sin^n u \; du$ $\displaystyle = -\frac 1n \sin^{n-1} u \; \cos u + \frac{n - 1}{n} \int \sin^{n - 2} u \; du$ (B..40)
$\displaystyle \int \cos^n u \; du$ $\displaystyle = \frac 1n \cos^{n - 1} u \; \sin u + \frac{n - 1}{n} \int \cos^{n - 2} u \; du$ (B..41)
$\displaystyle \int \tan^n u \; du$ $\displaystyle = \frac{1}{n - 1} \tan^{n - 1} u - \int \tan^{n - 2} u \; du$ (B..42)
$\displaystyle \int \cot^n u \; du$ $\displaystyle = - \frac {1}{n - 1} \cot^{n - 1} u - \int \cot^{n - 2} u \; du$ (B..43)
$\displaystyle \int \sec^n u \; du$ $\displaystyle = \frac{1}{n - 1} sec^{n - 2} u \tan u + \frac{n - 2}{n - 1} \int \sec^{n - 2} u \; du$ (B..44)
$\displaystyle \int \csc^n u \; du$ $\displaystyle = -\frac{1}{n - 1} \csc^{n - 2} u \cot u + \frac{n - 2}{n - 1} \int \csc^{n - 2} u \; du.$ (B..45)

Noah Dana-Picard 2007-12-28