In integral calculus, the trigonometric functions are involved in integration but the integrals of trigonometric functions cannot be evaluated directly and it requires some special rules to find the integrals of them. The following are some standard trigonometric integration formulas with proofs.

The list of fundamental integral rules of trigonometric functions with proofs.

$\displaystyle \int{\sin{x}\,}dx$ $\,=\,$ $-\cos{x}+c$

$\displaystyle \int{\cos{x}\,}dx$ $\,=\,$ $\sin{x}+c$

$\displaystyle \int{\sec^2{x}\,}dx$ $\,=\,$ $\tan{x}+c$

$\displaystyle \int{\csc^2{x}\,}dx$ $\,=\,$ $-\cot{x}+c$

$\displaystyle \int{\sec{x}\tan{x}\,}dx$ $\,=\,$ $\sec{x}+c$

$\displaystyle \int{\csc{x}\cot{x}\,}dx$ $\,=\,$ $-\csc{x}+c$

$\displaystyle \int{\operatorname{cosec}{x}\cot{x}\,}dx$ $\,=\,$ $-\operatorname{cosec}{x}+c$

The list of advanced trigonometric integration formulas with proofs.

$\displaystyle \int{\sec{x}}\,dx$ $\,=\,$ $\log_{e}{|\sec{x}+\tan{x}|}+c$

$\displaystyle \int{\csc{x}}\,dx$ $\,=\,$ $\log_{e}{|\csc{x}-\cot{x}|}+c$

$\displaystyle \int{\operatorname{cosec}{x}}\,dx$ $\,=\,$ $\log_{e}{|\operatorname{cosec}{x}-\cot{x}|}+c$

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved