Mathematics

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


ANSWER

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


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
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