Question

Integral of (x^2)/(e^x^3)

Answer 1

$I=\displaystyle\int\frac{x^2}{e^{x^3}}\,\mathrm dx$

Substitute $y=x^3$ and $\mathrm dy=3x^2\,\mathrm dx$. Then

$I=\displaystyle\frac13\int\frac{\mathrm dy}{e^y}=-\frac1{3e^y}+C=-\frac1{3e^{x^3}}+C$