Definite integral substitution method ∫ [2T / (1 + T)] DT =?

Definite integral substitution method ∫ [2T / (1 + T)] DT =?

∫ [2t/(1+t)]dt
= ∫ [2(1+t) -2]/(1+t) dt
=∫ (2- 2/(1+t) ) dt
= 2t- ln|1+t|+C