List of integrals of trigonometric functions

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Trigonometry
Outline History Usage Functions (sin, cos, tan, inverse) Generalized trigonometry
Reference
Identities Exact constants Tables Unit circle
Laws and theorems
Sines Cosines Tangents Cotangents Pythagorean theorem
Calculus
Trigonometric substitution Integrals (inverse functions) Derivatives Trigonometric series
Mathematicians
Hipparchus Ptolemy Brahmagupta al-Hasib al-Battani Regiomontanus Viète de Moivre Euler Fourier
v t e

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 ${\displaystyle \sin x}$ is any trigonometric function, and ${\displaystyle \cos x}$ is its derivative,

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

In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.