MHT CET20227 Aug 2022Morning ShiftMathematicsIndefinite IntegrationActual
e^x (2+e^x ) (e^x+1 ) d x= (where C is a constant of integration.)
Options
- Ae^x+1 e^x+2 +C
- B( e^x+2 e^x+1 )+C
- C( e^x+1 e^x+2 )+C
- D( e^x e^x+2 )+C
Correct answer
C. ( e^x+1 e^x+2 )+C
Step-by-step solution
aligned & e^x (2+e^x ) (e^x+1 ) d x & = d t (t+2)(t+1) = ( -1 t+2 + 1 t+1 ) d t & =- |t+2|+ |t+1|+c & = | t+1 t+2 |+c & = | e^x+1 e^x+2 |+c aligned