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
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