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

Asked by  | 16th Jan, 2010, 08:11: PM

Expert Answer:

Dear Student

log(1+x2)/(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

 

Answered by  | 17th Jan, 2010, 11:53: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.