Question:
Write a value of $\int x^{2} \sin x^{3} d x$.
Solution:
let $x^{3}=t$
Differentiating on both sides we get,
$3 \mathrm{x}^{2} \mathrm{dx}=\mathrm{dt}$
$x^{2} d x=\frac{1}{3} d t$
substituting above equation in $\int x^{2} \sin x^{3} d x$ we get,
$=\int \frac{1}{3} \sin t d t$
$=-\frac{1}{3} \cos t+c$
$=-\frac{1}{3} \cos x^{3}+c$
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