- #1
mahmud_dbm
- 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.
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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