List of integrals of trigonometric functions

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

• where and .

Integrands involving only cosine

Integrands involving only tangent

Integrands involving only secant

Integrands involving only cosecant

Integrands involving only cotangent

Integrands involving both sine and cosine

An integral that is a rational function of the sine and cosine can be evaluated using Bioche's rules.

Integrands involving both sine and tangent

Integrand involving both cosine and tangent

Integrand involving both sine and cotangent

Integrand involving both cosine and cotangent

Integrand involving both secant and tangent

Integrand involving both cosecant and cotangent

Integrals in a quarter period

Using the beta function one can write

Using the modified Struve functions and modified Bessel functions one can write

Integrals with symmetric limits

Integral over a full circle

See also

• Trigonometric integral

References