1. ## integration

{integrat from 0 to 1} (x^n) /(x+5) dx
integrat from 0 to 1} (x^(n+1) )/(x+5) dx
I think we have to use integration by parts but how many times or there is another way
I appreciate any help
Thank you all

2. Use long division.

3. what do you mean by long division?
using several integration by parts

4. Review partial fractions.

5. Originally Posted by koko2009

{integrat from 0 to 1} (x^n) /(x+5) dx
integrat from 0 to 1} (x^(n+1) )/(x+5) dx
I think we have to use integration by parts but how many times or there is another way
I appreciate any help
Thank you all
I suggest you first consider simple concrete cases like n = 0, 1 and 2. Then you might make better sense of the help you have been given and see why integration by parts is not going to be much help.

6. Let u= x+ 5 and then use the Binomial expansion of $(u- 5)^n$.