Question

I need Help

Answer 1

How to solve integral:
\[\int\limits dx \frac{ x^{3} }{ e^{x}-1 }\]

Answer 2

\[\int\limits \frac{ x ^{3} }{ e ^{x}-1 }dx=\int\limits \frac{ x ^{3}e ^{-x}dx }{1-e ^{-x} }\]
i think you can integrate by parts.

Answer 3

i think i don't., can you help me how it works???

Answer 4

it's same

Answer 5

what is \((\ln(1-e^{-x}))'\) ?

Answer 6

well there is no anti derivative for integrand in terms of preliminary functions, u must use series i think

Answer 7

if \(x>0\) by gemetric series\[\frac{x^3}{e^x-1}= \frac{ x ^{3}e ^{-x} }{1-e ^{-x} }=x^3 e^{-x} \sum_{n=0}^{\infty} e^{-nx}\] it is easy now to integrating