How Do You Integrate Functions with Polynomial and Rational Powers?

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Hi how to solve this type of integrals

{t^{k+n}}/{(1+qt)(1+t)^{2k+3}}dt

here n is natural number if some one know how to solve it without n also it is okay.
 
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Hi raghavendar24! :smile:

(try using the X2 tag just above the Reply box :wink:)

The easiest way is probably to substitute u = 1+t, so that it becomes a sum of terms like 1/(a + bu)ur,

and then use integration by parts on each term. :smile:
 
Hi, thanks for reply,


yeah if we substitute the transformation 1+u=t,

the integral tourns out as

Integrate[(u-1)^{k+n}/(1-q+bq)u^{2k+3},{u,1,2}]

i am unable to solve it once again just using integral by parts
 
oops!

raghavendar24 said:
Integrate[(u-1)^{k+n}/(1-q+bq)u^{2k+3},{u,1,2}]

i am unable to solve it once again just using integral by parts
uhh? :confused: oh-oooh :redface:
tiny-tim said:
The easiest way is probably to substitute u = 1+t, so that it becomes a sum of terms like 1/(a + bu)ur,

and then use integration by parts on each term. :smile:

oops! sorry! I meant use partial fractions. :blushing:

Is that easier? :smile:
 
Hie,


unable to break it through partail fractions, so can i get any alternative idea to solve it
 
How to solve the integral


t^{k+1}/(1+qt)^{2k+2}dt, t from 0 to 1
 
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