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.