intigrate w.r.t x

Asked by sumahr | 20th Dec, 2009, 07:45: PM

Expert Answer:

Put x = tan θ, dx = sec2θ dθ

log(1+x2)dx = sec2θ log(1+tan2θ)dθ = sec2θ log (sec2θ) dθ

= 2sec2θ log (sec θ) dθ

Integrating by parts,

= 2[tanθ log (secθ) - tanθtanθ dθ

= 2[tanθ log (secθ) - (sec2θ - 1) dθ

= 2[tanθ log (secθ) - (tanθ - θ) + c

= 2{[x log (x2+1)] - (x - tan-1x)} + c

Regards,

Team,

TopperLearning.

 

 

Answered by  | 21st Dec, 2009, 12:28: AM

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