int {x{e^{{x^2}}}} dx = | vedclass

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Question

(B) Let $I = \int {x{e^{{x^2}}}} dx$.Substitute ${x^2} = t$,then differentiating both sides with respect to $x$,we get $2x dx = dt$,which implies $x d

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let $I = \int {x{e^{{x^2}}}} dx$.Substitute ${x^2} = t$,then differentiating both sides with respect to $x$,we get $2x dx = dt$,which implies $x dx = \frac{dt}{2}$.Substituting these into the integral,we get $I = \int {{e^t} \cdot \frac{dt}{2}} = \frac{1}{2} \int {{e^t} dt}$.Integrating with respect to $t$,we get $I = \frac{1}{2} {e^t} + c$.Substituting back $t = {x^2}$,we get $I = \frac{{{e^{{x^2}}}}}{2} + c$.

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

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