Question
$\int x^{2} e^{x^{3}} d x$ equals
✓
Answer
Let $I=\int x^{2} e^{x^{3}} d x$
Also, let $x^3 = t, $
$\Rightarrow 3x^2dx = dt$
Thus,
$\Rightarrow I=\frac{1}{3} \int e^{t} d t$
$=\frac{1}{3}\left(e^{t}\right)+C$
$=\frac{1}{3}\left(e^{x^{3}}\right)+C$
Also, let $x^3 = t, $
$\Rightarrow 3x^2dx = dt$
Thus,
$\Rightarrow I=\frac{1}{3} \int e^{t} d t$
$=\frac{1}{3}\left(e^{t}\right)+C$
$=\frac{1}{3}\left(e^{x^{3}}\right)+C$
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