int e^{x^2} x , dx is equal to | vedclass

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(B) To evaluate the integral $I = \int e^{x^2} x \, dx$,we use the method of substitution.Let $t = x^2$.Then,differentiating both sides with respect t

Vedclass · Accepted Answer

$\frac{1}{2} e^{x^2}$

Vedclass · Answer

(B) To evaluate the integral $I = \int e^{x^2} x \, dx$,we use the method of substitution.Let $t = x^2$.Then,differentiating both sides with respect to $x$,we get $dt = 2x \, dx$,which implies $x \, dx = \frac{1}{2} dt$.Substituting these into the integral:$I = \int e^t \cdot \frac{1}{2} dt$$I = \frac{1}{2} \int e^t \, dt$$I = \frac{1}{2} e^t + C$Substituting back $t = x^2$,we get:$I = \frac{1}{2} e^{x^2} + C$.Thus,the correct option is $B$.

$\int e^{x^2} x \, dx$ is equal to

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