Question

Find y in \[y=\int\limits_{0}^{\infty}\frac{1}{x^5(e^{\frac{k}{x}}-1)}dx\]

Answer 1

integrate by parts?

Answer 2

trig subs might work, but x would need to be like
ln(tan^2x)^-1
making it overly complicated once you need to solve back for the original answer, and finding the derivative

not sure

Answer 3

\[\frac{d(e^{k/x}-1)^{-1}}{dx}=\frac{-1}{(e^{k/x}-1)^{2}}(ke^{k/x})(\frac{-1}{x^2})\]
If you use the exponetial in parts as the bit that you differentiate, it will generate new problems. If you use \[1/x^5\], the 5 will grow.

Answer 4

So parts looks hopeless.