I need some help with an Integration

  • #1
17
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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.
 
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Answers and Replies

  • #2
34,687
6,394
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.
 

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