- #1
nonaa
- 17
- 0
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?
\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?
