How Do You Solve This Complex Integration Problem?

[mahmud_dbm]

I need some help with an Integration. Here's the equation

I = $\int_0^∞ \frac {x^{n+1}} {1 + x^n} ⋅ e^{-x^2/{2 \sigma^2}}$

I have tried to solve the equation by simplifying first like
let, $\frac x {\sqrt 2 \sigma} = v$, so the $x = v \sqrt 2 \sigma$
then, $dx = \sqrt 2 \sigma d v$
Also, let ${\sqrt 2 \sigma} = m, and \ 1+n = p$

Finally, the integration is simplified as follows

I = $m^{p+1} \int_0^∞ \frac {e^{-v^2}⋅ v^p} {{1 + v^{p - 1} m^{p - 1}}} dv$

Now i don't know what to do from here!
Thank you in advance for your attention to to this post.
I would appreciate any help.

 

[Mark44]

I need some help with an Integration. Here's the equation

I = $\int_0^∞ \frac {x^{n+1}} {1 + x^n} ⋅ e^{-x^2/{2 \sigma^2}}$

I have tried to solve the equation by simplifying first like
let, $\frac x {\sqrt 2 \sigma} = v$, so the $x = v \sqrt 2 \sigma$
then, $dx = \sqrt 2 \sigma d v$
Also, let ${\sqrt 2 \sigma} = m, and \ 1+n = p$

Finally, the integration is simplified as follows

I = $m^{p+1} \int_0^∞ \frac {e^{-v^2}⋅ v^p} {{1 + v^{p - 1} m^{p - 1}}} dv$

Now i don't know what to do from here!
Thank you in advance for your attention to to this post.
I would appreciate any help.

I would start with integration by parts, with $u = \frac{x^n}{1 + x^n}$ and $dv = xe^{-x^2/{2 \sigma^2}} dx$. I don't guarantee that this would work, but that's what I would start with.

Also, in future threads, please don't delete the Homework Template. Its use is required.