I read from theoretical physics lecture notes the following: http://theory.physics.helsinki.fi/~fymmi/Luennot4_1-9.pdf
$$\Gamma(p)\Gamma(q)=4\int_0^\infty dr r^{2p+2q+1}e^{-r^2}\int_0^{\pi/2}d\varphi \cos^{2p-1}\varphi\sin^{2q-1}\varphi$$
Is it possible to put that dr just after the integral as I have understood that the function is in between the integral sing and dr?
As long as it remains clear what is and is not being integrated, it should be fine.