int x^2 e^{x^3} d x= . . . . . . . | vedclass

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Question

(A) To evaluate the integral $I = \int x^2 e^{x^3} dx$,we use the method of substitution.Let $u = x^3$.Then,differentiating both sides with respect to

Vedclass · Accepted Answer

$\frac{1}{3} e^{x^3}+c$

Vedclass · Answer

(A) To evaluate the integral $I = \int x^2 e^{x^3} dx$,we use the method of substitution.Let $u = x^3$.Then,differentiating both sides with respect to $x$,we get $du = 3x^2 dx$,which implies $x^2 dx = \frac{1}{3} du$.Substituting these into the integral,we have:$I = \int e^u \cdot \frac{1}{3} du$$I = \frac{1}{3} \int e^u du$$I = \frac{1}{3} e^u + c$Substituting back $u = x^3$,we get:$I = \frac{1}{3} e^{x^3} + c$.Thus,the correct option is $A$.

$\int x^2 e^{x^3} d x=$ . . . . . . .

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