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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
$\int x^{2} e^{x^{3}} d x$ equals
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Answer

Let $I=\int x^{2} e^{x^{3}} d x$ 
Also, let x3 = t, $\Rightarrow$ 3x2dx = dt
Thus,
$\Rightarrow I=\frac{1}{3} \int e^{t} d t$ 
$=\frac{1}{3}\left(e^{t}\right)+C$ 
$=\frac{1}{3}\left(e^{x^{3}}\right)+C$

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