View source for Solving Integrals by Trigonometric substitution/Basic trigonometric integrals

This module contains a list of basic trigonometric integrals.
== Integrals of Sine ==

: <math>\int\sin cx\;dx = -\frac{1}{c}\cos cx\,\!</math>

: <math>\int\sin^n cx\;dx = -\frac{\sin^{n-1} cx\cos cx}{nc} + \frac{n-1}{n}\int\sin^{n-2} cx\;dx \qquad\mbox{(for }n>0\mbox{)}\,\!</math>

== Integrals of Cosine ==

: <math>\int\cos cx\;dx = \frac{1}{c}\sin cx\,\!</math>

: <math>\int\cos^n cx\;dx = -\frac{\cos^{n-1} cx\sin cx}{nc} + \frac{n-1}{n}\int\cos^{n-2} cx\;dx \qquad\mbox{(for }n>0\mbox{)}\,\!</math>


== Integrals of Tangent ==

: <math>\int\tan cx\;dx = -\frac{1}{c}\ln|\cos cx|\,\!</math>

: <math>\int\tan^n cx\;dx = \frac{1}{c(n-1)}\tan^{n-1} cx-\int\tan^{n-2} cx\;dx \qquad\mbox{(for }n\neq 1\mbox{)}\,\!</math>

== Integrals of Secant ==

:<math>\int \sec{cx} \, dx = \frac{1}{c}\ln{\left| \sec{cx} + \tan{cx}\right|}</math>

:<math>\int \sec^n{cx} \, dx = \frac{\sec^{n-1}{cx} \sin {cx}}{c(n-1)} \,+\, \frac{n-2}{n-1}\int \sec^{n-2}{cx} \, dx \qquad \mbox{ (for }n \ne 1\mbox{)}\,\!</math>

== Integrals of Cosecant ==

:<math>\int \csc{cx} \, dx = -\frac{1}{c}\ln{\left| \csc{cx} + \cot{cx}\right|}</math>

:<math>\int \csc^n{cx} \, dx = -\frac{\csc^{n-1}{cx} \cos{cx}}{c(n-1)} \,+\, \frac{n-2}{n-1}\int \csc^{n-2}{cx} \, dx \qquad \mbox{ (for }n \ne 1\mbox{)}\,\!</math>

== Integrals of Cotangent ==

: <math>\int\cot cx\;dx = \frac{1}{c}\ln|\sin cx|\,\!</math>

: <math>\int\cot^n cx\;dx = -\frac{1}{c(n-1)}\cot^{n-1} cx - \int\cot^{n-2} cx\;dx \qquad\mbox{(for }n\neq 1\mbox{)}\,\!</math>


{{Wikipedia|List_of_integrals_of_trigonometric_functions}}

{{Subject|Solving Integrals by Trigonometric substitution}}