Question

I have the following integral:

Answer 1

\[I_{n} = \int\limits_{0}^{1}\frac{ x^{n} }{ 1+x } dx\]

Answer 2

and i also have to prove that:

Answer 3

ok i wanna solve it

Answer 4

\[n I_{n} = \frac{ 1 }{ 2 } - \int\limits_{0}^{1} \frac{ x^{n} }{ (1+x)^{2} }\]

Answer 5

and dx of course. :)

Answer 6

i think it looked better when you used integration by parts, but we couldn t get \[x^{n}\]at the numerator.

Answer 7

i was thinking about trying to write \[\frac{ 1 }{ 2 }\] as \[\int\limits_{0}^{1} \] from something and then try to bring it to the final form.