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

\begin{array}{1 1}(A)\;\frac{1}{3}e^{x^3}+C\qquad(B)\;\frac{1}{3}e^{x^2}+C\\(C)\;\frac{1}{2}e^{x^3}+C\qquad(D)\;\frac{1}{2}e^{x^2}+C\end{array}

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  • (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
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$
Correct Answer is A


answered Feb 7, 2013 by meena.p
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