Question:
Evaluate the following integrals:
$\int \sin ^{5} x \cos x d x$
Solution:
Assume $\sin x=t$
$d(\sin x)=d t$
$\cos x d x=d t$
$\therefore$ Substituting $t$ and $d t$ in given equation we get
$\Rightarrow \int \mathrm{t}^{5} \mathrm{dt}$
$\Rightarrow \frac{t^{6}}{6}+c$
But $t=\sin x$
$\Rightarrow \frac{\sin ^{6} x}{6}+c$
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