How Do You Integrate Functions with Polynomial and Rational Powers?

[raghavendar24]

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.

 

[tiny-tim]

Hi raghavendar24!

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

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

and then use integration by parts on each term.

 

[raghavendar24]

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

 

[tiny-tim]

oops!

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? oh-oooh …

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

and then use integration by parts on each term.

oops! sorry! I meant use partial fractions.

Is that easier? ​

 

[raghavendar24]

Hie,


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

 

[raghavendar24]

How to solve the integral


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