Question:
Evaluate the following integrals:
$\int \sin ^{5} x \cos x d x$
Solution:
Let $\sin x=t$
Then $d(\sin x)=d t=\cos x d x$
Put $t=\sin x$ and $d t=\cos x d x$ in above equation
$\int \sin ^{5} x \cos x d x=\int t^{5} d t$
$=\frac{t^{6}}{6}+c\left(\right.$ since $\int x^{n} d x=\frac{x^{n+1}}{n+1}+c$ for any $\left.c \neq-1\right)$
$=\frac{\sin ^{6} x}{6}+c$
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