Integrate with respect to $x$ :
$2 x^{3} e^{x^{2}}$

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Solution

$\int 2 x^{3} e^{x^{2}} d x$
$= \int 2 x^{2} x e^{x^{2}} d x$
putting $x^{2} = t$
$\Rightarrow 2 x d x = d t$
$= \int t . e^{t} d t$
$= t e^{t} - \int e^{t} d t$
$= t e^{t} - e^{t} + c$
$= (x^{2} - 1) e^{x^{2}} + c$

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