what is the integration of log(1+x) divided by (1+x2)

Dear Student

log(1+x^2_)/(1+x2)

Put x = tany

so, dx = sec²y dy

and 1+tan²y =sec²y

==> Integral changes to   log (sec²y) dy = 2log sec y

Integral log (x) = x ln(x) - x + C. and derivative of secy= secy tan y

==>Integral 2 log sec y  dy

= 2[ sec y ln(sec y) -sec y + C] / (secy tany)

y= arc tan(x)

Regards

Team

Topperlearning