Integral of statistical mechanics

[alejandrito29]

Hello, i need solve de following integral

[tex] \int ^{\infty}_0 \frac{x^3}{e^x+1} dx [/tex]

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

Help please

 

[Dick]

Hello, i need solve de following integral

[tex] \int ^{\infty}_0 \frac{x^3}{e^x+1} dx [/tex]

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

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.