int x^{2} e^{x^{3}} d x equals | vedclass

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Question

(C) Let $I = \int x^{2} e^{x^{3}} d x$. Substitute $t = x^{3}$,then differentiate both sides with respect to $x$: $dt = 3x^{2} dx$,which implies $x^{2

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let $I = \int x^{2} e^{x^{3}} d x$. Substitute $t = x^{3}$,then differentiate both sides with respect to $x$: $dt = 3x^{2} dx$,which implies $x^{2} dx = \frac{1}{3} dt$. Substituting these into the integral: $I = \int e^{t} \cdot \frac{1}{3} dt$ $I = \frac{1}{3} \int e^{t} dt$ Integrating $e^{t}$ gives $e^{t}$: $I = \frac{1}{3} e^{t} + C$ Substituting back $t = x^{3}$: $I = \frac{1}{3} e^{x^{3}} + C$. Thus,the correct option is $C$.

$\int x^{2} e^{x^{3}} d x$ equals

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