• Source: 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



sin
⁡
x


{\displaystyle \sin x}

is any trigonometric function, and



cos
⁡
x


{\displaystyle \cos x}

is its derivative,




∫
a
cos
⁡
n
x

d
x
=


a
n


sin
⁡
n
x
+
C


{\displaystyle \int a\cos nx\,dx={\frac {a}{n}}\sin nx+C}


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


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



B
(
a
,
b
)


{\displaystyle B(a,b)}

one can write




Integrals with symmetric limits






Integral over a full circle






See also


Trigonometric integral




References

Kata Kunci Pencarian:

• Integral Dirichlet
• List of integrals of trigonometric functions
• List of integrals of inverse trigonometric functions
• Trigonometric functions
• List of trigonometric identities
• Lists of integrals
• Inverse trigonometric functions
• Trigonometric substitution
• List of integrals of inverse hyperbolic functions
• Outline of trigonometry
• List of calculus topics