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# Choose the correct answer in $\Large \int \normalsize x^2e^{x^3}\;dx$ equals

Toolbox:
• (i)Method of substitution: Let us consider $\int f(x) dx.$ If we substitude f(x) as t, then $f'(x)dx=dt$ Hence the integral function become $\int t.dt$
Given $I=\int x^2e^{x^3}dx$

Let $x^3=t.$

on differentiating with respect to x

$3x^2dx=dt.$

$x^2dx=\frac{dt}{3}$

Now substituting t and dt we get

$I=\int e^t.dt/3=\frac{1}{3}\int e^t.dt$

On integrating we get

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

Now substituting for t we get

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