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]
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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
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
Summarize
Perspective
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
References
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