I have to approximate the following integral, using Simpson's Composite $1/3$ Rule: $\displaystyle \int\limits_{0}^1 \mathrm{\frac{e^{2x}}{\sqrt[5]{x^2}}}\,\mathrm{d}x$. The only problem is that the integral is improper and when I compute it at the value $0$, I get $\frac 1 0$ which is impossible. I can do a change of variable, only I'm not sure how to do it.
How can I change the variable in order to make the integral a proper one?
You can transform the improper integral into a proper integral using the change of variables $x = t^{5/2}$.
Then
$$\int_{0}^{1}\frac{\exp(2x)}{x^{2/5}}dx =\frac{5}{2}\int_{0}^{1}t^{1/2}\exp(2t^{5/2})dt $$