Someone can give me a link where I can find the solution step by step of the following integrals. Otherwise,if there is someone so kind to solve them.
$$dN(v)=4\pi N(\frac{m}{2\pi kT})^{\frac{3}{2}}e^{\frac{-mv^{2}}{2kT}}v^{2}dv$$
$$\int_{0}^{\infty }vdN(v)=\frac{2}{\sqrt{\pi }}v_{p}$$ $$\sqrt{\int_{0}^{\infty }v^{2}dN(v)}=\sqrt{\frac{3}{2}}v_{p}$$
Thank you a lot for your help!