The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals. For the special antiderivatives involving trigonometric functions, see Trigonometric integral.
Generally, if the function
is any trigonometric function, and
is its derivative,

In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
Integrands involving only sine[edit]


















Integrands involving only cosine[edit]

















Integrands involving only tangent[edit]






Integrands involving only secant[edit]
- See Integral of the secant function.






Integrands involving only cosecant[edit]






Integrands involving only cotangent[edit]





Integrands involving both sine and cosine[edit]
An integral that is a rational function of the sine and cosine can be evaluated using Bioche's rules.






















![{\displaystyle {\begin{aligned}\int {\frac {\sin ^{2}x}{1+\cos ^{2}x}}\,dx&={\sqrt {2}}\operatorname {arctangant} \left({\frac {\tan x}{\sqrt {2}}}\right)-x\qquad {\mbox{(for x in}}]-{\frac {\pi }{2}};+{\frac {\pi }{2}}[{\mbox{)}}\\&={\sqrt {2}}\operatorname {arctangant} \left({\frac {\tan x}{\sqrt {2}}}\right)-\operatorname {arctangant} \left(\tan x\right)\qquad {\mbox{(this time x being any real number }}{\mbox{)}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99bc35b310db277a8b20f736913c8178097758b6)






Integrands involving both sine and tangent[edit]







Integrals in a quarter period[edit]

Integrals with symmetric limits[edit]





Integral over a full circle[edit]


See also[edit]