Homework Soursesolve the integral from 0 to 1 of lnx1x21 I found according
solve the integral from 0 to 1 of (ln(x+1))/(x^2+1). I found, according to the wolfram alpha calculator, that the answer is (pi)(ln(2))/8. I have no clue what steps were taken to achieve this answer, so any help is greatly appreciated.
Solution
ln(x+1)/(x^2+1) dx
let x+1=t
dx=dt
=lnt/(t^2-2t) dt
=1/2lnt[-1/t+1/(t-2)]dt
=1/2[-lnt/t dt+lnt/(t-2)dt]
integrating this we get the answer
