hey guys i have doubt in this question;;;;plz help me;;;;

integrate1/t(1+t^2)^2

Splitting as partial fractions,we get

1/t-t/1+t²-t/(1+t²)² whose integral is lnt-(1/2)ln(1+t²)+1/2(1+t²)

put t=tanx

dx/tanx sec^2x

cos^3(x) /sinx dx

cotx dx +cos x sinx dx

log sinx -(1/4)cos2x

log sin tan^-1(t) -(1/4)cos2tan^-1(t)

cheers

much simpler one

now put 1/t as z and integrate easily to get the same answer