Trigonometric Reduction Formulas

Reference > Calculus: Integration

Description

\(\int {sin}^{n}x \,dx=-\frac{1}{n}{sin}^{n-1}x\cos{x}+\frac{n-1}{n}\int {sin}^{n-2}x \,dx\)

\(\int {cos}^{n}x \,dx=\frac{1}{n}{cos}^{n-1}x\sin{x}+\frac{n-1}{n}\int {cos}^{n-2}x \,dx\)

\(\int {tan}^{n}x \,dx=\frac{1}{n-1}{tan}^{n-1}x-\int {tan}^{n-2}x \,dx\)

\(\int {cot}^{n}x \,dx=-\frac{1}{n-1}{cot}^{n-1}x-\int {cot}^{n-2}x \,dx\)

\(\int {sec}^{n}x \,dx=\frac{1}{n-1}{sec}^{n-2}x\tan{x}+\frac{n-2}{n-1}\int {sec}^{n-2}x \,dx\)

\(\int {csc}^{n}x \,dx=-\frac{1}{n-1}{csc}^{n-2}x\cot{x}+\frac{n-2}{n-1}\int {csc}^{n-2}x \,dx\)