For what values of M does this integral converge?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{-\infty}^{0}\frac{x.e^x}{(1-e^{2x})^M}dx[/tex]

My pathetic attempt for solution ended here:

[tex]\frac{2x.e^x}{2.(-1)^M(e^{2x}-1)^M}.x^{M-1}\stackrel{x\rightarrow0}{\longrightarrow}\frac{(-1)^M}{2}[/tex]

[tex]M-1<1, M<2[/tex]

Am I going in the right direction? And what to do if [tex]x\rightarrow\infty[/tex]?

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# For what values of M does this integral converge?

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