Evaluate the integral .

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Evaluate the integral ∫sin⁡4x dx\displaystyle \int \sin^{4}x\,dx. (a) Rewrite sin⁡4x\sin^{4}x in terms of multiple–angle trigonometric functions and obtain a simplified integrand. (b) Hence calculate ∫sin⁡4x dx\displaystyle \int \sin^{4}x\,dx, writing the result with the constant of integration +C+C."

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