i need the full solutions of the integrals that lead to these equations:

Question

mean speed of molecules in a gas:
vavg= sqrt(8RT/PiM)

average of the square of speeds:
(v^2)avg= 3RT/M

fraction of molecules with speed:
4PI*(M/2PiRT)^(3/2)*e^(-Mv^2/RT)(deltav)

the general integral given is integral from 0 to infinity of v*P(v) where P(v)=4Pi*(M/2PiRT)^(3/2)*v^2*e^(-Mv^2/RT)

Answer 1

Look for this classic book in your school library. It used to be available in paperback:
http://www.amazon.com/Mathematical-Theory-Non-uniform-Gases-Conduction/dp/052140844X