BITSAT2019MathematicsIndefinite IntegrationActual
The integral ∫ 1 + x - 1 x e x + 1 x d x is equal to
Options
- Ax - 1 e x + 1 x + C
- Bx e x + 1 x + C
- Cx + 1 e x + 1 x + C
- D- x e x + 1 x + C
Correct answer
B. x e x + 1 x + C
Step-by-step solution
We have, I = ∫ 1 + x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x 1 - 1 x 2 e x + 1 x d x I = ∫ e x + 1 x d x + x e x + 1 x - ∫ e x + 1 x d x I = x e x + 1 x + C