x e^ x^2 dx = - Vidyadip

MCQ

$\int {x{e^{{x^2}}}} dx = $

A
$ - \frac{{{e^{{x^2}}}}}{2} + c$
✓
$\frac{{{e^{{x^2}}}}}{2} + c$
C
$\frac{{{e^x}}}{2} + c$
D
$ - \frac{{{e^x}}}{2} + c$

✓

Answer

Correct option: B.

$\frac{{{e^{{x^2}}}}}{2} + c$

b
(b) $I = \int {x{e^{{x^2}}}dx} $$ = \frac{1}{2}\int {{e^t}dt = \frac{{{e^{{x^2}}}}}{2}} + c$.
{Put ${x^2} = t$ ==> $2xdx = dt$}

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