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List of integrals of trigonometric functions

From Wikipedia, the free encyclopedia

List of integrals of trigonometric functions
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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.[1]

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.

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Integrands involving only sine

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Integrands involving only cosine

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Integrands involving only tangent

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Integrands involving only secant

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Integrands involving only cosecant

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Integrands involving only cotangent

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Integrands involving both sine and cosine

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

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Integrands involving both sine and tangent

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Integrand involving both cosine and tangent

Integrand involving both sine and cotangent

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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

References

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