Mathematics

# Integrate with respect to $x$:$2x^{2}e^{x^{2}}$

##### SOLUTION

Consider the given integral.

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

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

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

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

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

Therefore,

$I=\dfrac{2}{3}\int{{{e}^{t}}}dt$

$I=\dfrac{2}{3}\left( {{e}^{t}} \right)+C$

Thus,

$I=\dfrac{2}{3}\left( {{e}^{{{x}^{3}}}} \right)+C$

Hence, this is the answer.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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