How to find this integral

1. Jun 2, 2010

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 with out n also it is okay.

2. Jun 4, 2010

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)ur,

and then use integration by parts on each term.

3. Jun 4, 2010

raghavendar24

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

4. Jun 4, 2010

tiny-tim

oops!

uhh? oh-oooh
oops! sorry! I meant use partial fractions.

Is that easier?

5. Jun 8, 2010

raghavendar24

Hie,

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

6. Jun 11, 2010

raghavendar24

How to solve the integral

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