Originally Posted by
shawsend Write it as:
$\displaystyle \int x^{-3/2}-x^{-3/2} e^{-x} dx$
then use parts on the second one to get the expression $\displaystyle \frac{e^{-x}}{\sqrt{x}}$, then use the substitution $\displaystyle w=\sqrt{x}$ on that expression to get it in terms of $\displaystyle \int_0^{\infty}e^{-w^2}dw=\frac{\sqrt{\pi}}{2}$. May have to take limits since it's indeterminate at zero. Mathematica returns $\displaystyle 2\sqrt{\pi}$ but I haven't worked out all the steps so fix it if I left some kinks ok.