For what values of M does this integral converge?

[nonaa]

For what values of M does this integral converge?

$$\int_{-\infty}^{0}\frac{x.e^x}{(1-e^{2x})^M}dx$$


My pathetic attempt for solution ended here:

$$\frac{2x.e^x}{2.(-1)^M(e^{2x}-1)^M}.x^{M-1}\stackrel{x\rightarrow0}{\longrightarrow}\frac{(-1)^M}{2}$$

$$M-1<1, M<2$$

Am I going in the right direction? And what to do if $$x\rightarrow\infty$$?

 

[tiny-tim]

Welcome to PF!

Hi nonaa! Welcome to PF!

No, you're misreading the question.

It means for what values of M is the whole integral finite.

 

[nonaa]

Hi, I'm here for almost a day but you people are so nice and helpful :) I'm glad I've found this forum :)

And how to do this? I've never solved such type of problems before. Would you give me a little hint?