Solving Integrals by Trigonometric substitution/Basic trigonometric integrals

This module contains a list of basic trigonometric integrals.

Integrals of Sine

$\int \sin cxdx=-\frac{1}{c}\cos cx$

$\int {\sin }^{n}cxdx=-\frac{{\sin }^{n-1}cx\cos cx}{nc}+\frac{n-1}{n}\int {\sin }^{n-2}cxdx\text{(for }n>0\text{)}$

Integrals of Cosine

$\int \cos cxdx=\frac{1}{c}\sin cx$

$\int {\cos }^{n}cxdx=-\frac{{\cos }^{n-1}cx\sin cx}{nc}+\frac{n-1}{n}\int {\cos }^{n-2}cxdx\text{(for }n>0\text{)}$

Integrals of Tangent

$\int \tan cxdx=-\frac{1}{c}\ln |\cos cx|$

$\int {\tan }^{n}cxdx=\frac{1}{c(n-1)}{\tan }^{n-1}cx-\int {\tan }^{n-2}cxdx\text{(for }n\ne 1\text{)}$

Integrals of Secant

$\int \sec cxdx=\frac{1}{c}\ln |\sec cx+\tan cx|$

$\int {\sec }^{n}cxdx=\frac{{\sec }^{n-1}cx\sin cx}{c(n-1)}+\frac{n-2}{n-1}\int {\sec }^{n-2}cxdx\text{ (for }n\ne 1\text{)}$

Integrals of Cosecant

$\int \csc cxdx=-\frac{1}{c}\ln |\csc cx+\cot cx|$

$\int {\csc }^{n}cxdx=-\frac{{\csc }^{n-1}cx\cos cx}{c(n-1)}+\frac{n-2}{n-1}\int {\csc }^{n-2}cxdx\text{ (for }n\ne 1\text{)}$

Integrals of Cotangent

$\int \cot cxdx=\frac{1}{c}\ln |\sin cx|$

$\int {\cot }^{n}cxdx=-\frac{1}{c(n-1)}{\cot }^{n-1}cx-\int {\cot }^{n-2}cxdx\text{(for }n\ne 1\text{)}$

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