Mathematics

# Evaluate the given integral.$\int { 2{ x }^{ 2 }{ e }^{ { x }^{ 3 } } } dx$

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

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

Let $t={x}^{3}\Rightarrow\,dt=3{x}^{2}\,dx$

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

$=\dfrac{2}{3}{e}^{t}+c$

$=\dfrac{2}{3}{e}^{{x}^{3}}+c$   ......where $t={x}^{3}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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