x 2 e x 3 d x equals:

Question

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

Smart Achievers · Accepted Answer

(1)

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

Explanation :

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

$Put$ $x^{3} = t$

$\Rightarrow$ $3 x^{2} d x = d t$

$\Rightarrow$ $x^{2} d x = \frac{1}{3} d t$

$∴$ $I = \frac{1}{3} \int e^{t} d t$

$\Rightarrow$ $I = \frac{1}{3} e^{t} + C$

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

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