SOLUTION: From a Putnam competition: Evaluate the integral {{{int(ln(x+1)/(x^2+1), dx, 0,1)}}}.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: From a Putnam competition: Evaluate the integral {{{int(ln(x+1)/(x^2+1), dx, 0,1)}}}.      Log On


   

Question 1033411: From a Putnam competition:
Evaluate the integral int%28ln%28x%2B1%29%2F%28x%5E2%2B1%29%2C+dx%2C+0%2C1%29.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Since dtan%5E-1%28x%29+=+dx%2F%281%2Bx%5E2%29,
.
Let w+=+tan%5E-1%28x%29. ==> tanw = x. Now if x = 0, w = 0, and when x = 1, w+=+pi%2F4.
==> .
Now
=
=
=.
But by using the substitution z+=+pi%2F4+-+w on the left integral.
Hence