MHT CET202618 April 2026Morning ShiftMathematicsIndefinite IntegrationActual
(x+1) ,dx x(1+xe^x) =
Options
- A| xe^x 1+xe^x | + c
- B| 1+xe^x xe^x | + c
- C| (x+1)e^x xe^x | + c
- D| (x+1)e^x 1+xe^x | + c
Correct answer
A. | xe^x 1+xe^x | + c
Step-by-step solution
Let I = x+1 x(1+xe^x) dx Multiplying the numerator and the denominator by e^x : I = (x+1)e^x xe^x(1+xe^x) dx Let xe^x = t Differentiating both sides with respect to x : (1 e^x + x e^x) dx = dt (x+1)e^x dx = dt Substituting these into the integral: I = dt t(1+t) Using partial fractions: I = ( 1 t - 1 1+t ) dt I = |t| - |1+t| + c I = | t 1+t | + c Substituting t = xe^x back into the expression: I = | xe^x 1+xe^x | + c Answer: | xe^x 1+xe^x | + c