MHT CET202124 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
d x e^x+e^ -x +2 =
Options
- A1 e ^ 2 x +1 + c
- B-1 e ^ x +1 + c
- C1 e ^ x + c
- D-1 e ^ x + c
Correct answer
B. -1 e ^ x +1 + c
Step-by-step solution
Let aligned I & = d x e^x+e^ -x +2 & = d x e^x+ 1 e^x +2 = e^x d x e^ 2 x +2 e^x+1 = e^x (e^x+1 )^2 d x aligned Put e ^ x +1= t e ^ x dx = dt I= d t t^2 = t^2 d t= t⁻¹ -1 +c= -1 t +c= -1 e^x+1 +c