∫ex-1 dx =

Let I=∫ex−1 dx​Put ex−1=t2 ​⇒exdx=2t dt⇒ ​dx=2t1+t2dt​I=∫t.2t1+t2dt​    = ∫ 2t21+t2dt​    =∫2t2+2−21+t2dt​     =2∫t2+11+t2dt−2∫11+t2dt​     =2t−2tan−1t+c​     =2ex−1 −tan−1ex−1 +c