Question

Which strategy should I use for this integral?

Answer 1

\[\Large \int\limits_{}^{}\frac{ dx }{ \sqrt{e^x-1} }\]

Answer 2

\[I=\int\limits \frac{ 1 }{ \sqrt{e^x-1} }dx\]
put \[\sqrt{e^x-1}=t,e^x=1+t^2,e^x dx=2tdt,dx=\frac{ 2t }{ 1+t^2 }dt\]

Answer 3

i think now the problem is easy.

Answer 4

\[\int\limits \frac{ dx }{ a^2+x^2 }=\frac{ 1 }{ a }\tan^{-1} \frac{ x }{ a }\]

Answer 5

you got it.

Answer 6

Yes, I got it, thank you for showing me how to do this!

Answer 7

yw