Check convergence of these improper integrals:
a) $\displaystyle \int_{0}^{+\infty}x^{17}e^{-\sqrt{x}}\mbox{d}x$
b) $\displaystyle \int_{0}^{1}\frac{\sin x}{x^{3/2}} \mbox{d}x$
c) $\displaystyle \int_{0}^{1}\frac{1}{\sqrt[3]{1-x^3}} \mbox{d}x$
I know comparision test and Dirichlet test. But still have troubles using them. Any hints for these examples? I want to practise.