Mr. Integral
Math notes/Calculus II/Integration Methods

Integrating Trigonometric Powers — Cheat sheet

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Core rule

Odd sine: save sin⁡x dx\sin x\,dx, use u=cos⁡xu=\cos x. Odd cosine: save cos⁡x dx\cos x\,dx, use u=sin⁡xu=\sin x. Both even: use half-angle identities.

Watch for

Track minus signs, frequency factors and intervals avoiding trigonometric poles. Tangent/secant patterns use 1+tan⁡2x=sec⁡2x1+\tan^2x=\sec^2x.