Let t=sinx⇒ dt=cosxdx ∫sin^3xcosx dx =∫t^3 dt =t^44+c where c is the constant of integration. =sin^4x4+c ...

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Integration by Substitution

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Question

Solve: $\int {sin}^{3} x cos x d x$

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Solution

Let $t = sin x \Rightarrow d t = cos x d x$
$\int {sin}^{3} x cos x d x$
$= \int t^{3} d t$
$= \frac{t^{4}}{4} + c$ where $c$ is the constant of integration.
$= \frac{{sin}^{4} x}{4} + c$

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