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.

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]

also:
also:
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also:
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Integrands involving both sine and tangent[edit]

Integrand involving both cosine and tangent[edit]

Integrand involving both sine and cotangent[edit]

Integrand involving both cosine and cotangent[edit]

Integrand involving both secant and tangent[edit]

Integrand involving both cosecant and cotangent[edit]

Integrals in a quarter period[edit]

Integrals with symmetric limits[edit]

Integral over a full circle[edit]

See also[edit]

References[edit]