Mathematics

# $\int x ^ { 2 } e ^ { x ^ { 3 } } d x$ equals

$\dfrac { 1 } { 3 } e ^ { x ^ { 3 } } + C$

##### SOLUTION
To find : $\int x^{2}e^{x^{3}}dx,$ let I $= \int x^{2}e^{x^{3}}dx$

Put $x^{3} = t$

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

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

$= \dfrac{1}{3}\int e^{t}dt = \dfrac{1}{3}e^{t}+c$

$= \dfrac{1}{3}e^{x^{3}}+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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