Integral of statistical mechanics

[alejandrito29]

Hello, i need solve de following integral

\int ^{\infty}_0 \frac{x^3}{e^x+1} dx

i tried with the fermi function but the factor e^x is different to e^{x-\eta}, and with the gamma function but the factor e^x+1 is different to e^x-1.

Help please

 

[Dick]

Hello, i need solve de following integral

\int ^{\infty}_0 \frac{x^3}{e^x+1} dx

i tried with the fermi function but the factor e^x is different to e^{x-\eta}, and with the gamma function but the factor e^x+1 is different to e^x-1.

Help please

The Bose and Fermi forms are related by 1/(e^x+1)-1/(e^x-1)=2/(e^(2x)-1). I know you know the Fermi form. You should be able to find the Bose form from there.