Question

Integrate the function: $\frac{x}{e^{x^2}}$

Answer 1

Let x2 = t

∴ 2xdx = dt

$\Rightarrow \int \frac{x}{e^{x^2}}dx=\frac{1}{2}\int\frac{1}{e^t}dt$

= $\frac{1}{2}\int e^{-t}dt$

= $\frac{1}{2}\bigg(\frac{e^{-t}}{-1}\bigg)+C$

= $-\frac{1}{2}e^{-x{^2}}+C$

= $\frac{-1}{2e^{x^2}}+C$