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List of integrals of trigonometric functions

These 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.

Contents

Integrands involving only sineEdit

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Integrands involving only cosineEdit

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Integrands involving only tangentEdit

 
 
 
 
 
 

Integrands involving only secantEdit

See Integral of the secant function.
 
 
 
 
 
 

Integrands involving only cosecantEdit

 
 
 
 
 
 

Integrands involving only cotangentEdit

 
 
 
 

Integrands involving both sine and cosineEdit

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

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Integrands involving both sine and tangentEdit

 
 

Integrand involving both cosine and tangentEdit

 

Integrand involving both sine and cotangentEdit

 

Integrand involving both cosine and cotangentEdit

 

Integrand involving both secant and tangentEdit

 

Integrand involving both cosecant and cotangentEdit

 

Integrals in a quarter periodEdit

 

Integrals with symmetric limitsEdit

 
 
 
 
 

Integral over a full circleEdit

 

See alsoEdit

ReferencesEdit