Pathria 7.4 integrals for calculation of mean phonon drift velocity.

Clear[f]
f[x_] = (1 + a x)^3 ;
$Assumptions = a ∈ Reals ;
i1 = Integrate[x/f[x], {x, -1, 1}]
i2 = Integrate[1/f[x], {x, -1, 1}]

Integrals for equation 12 (mean momentum)

i3= Integrate[ x^3 /(E^(a x)-1), {x, 0, Infinity}]
i4 = Integrate[ Cos[theta]Sin[theta](1 - b Cos[theta])^(-4), {theta, 0, Pi}]

integrals for equation 13 (mean energy)

i5 = Integrate[ Sin[theta](1 - b Cos[theta])^(-4), {theta, 0, Pi}]