solve the integral from 0 to 1 of lnx1x21 I am have extreme
solve the integral from 0 to 1 of (ln(x+1))/(x^2+1). I am have extreme difficulty in solving this. I have tried everything from trig substitutions to creative \"U\" substitutions, none of which have gotten me anywhere. If anyone can figure this one out, it would be GREATLY appreciated. I can easily get the answer using a the Wolfram Alpha calculator, but it can provide no steps on how it got that answer. (the answer is (pi)ln(2)/8))
Solution
put x = tan
dx= sec^2 d
so, integral
I = ln(tan+1) *sec^2 d/(tan^2 + 1)
I = ln(tan+1) d from 0 to /4
now apply king that is upper limit + lower limit -x = x
I = integral ln(tan(/4 - )+1)
I = integral ln(2/(1+tan))
I = integral ln(2) - I with the limit = 0 from = /4
2I = /4 ln(2)
I = /8 ln(2)
