MHT CET202415 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
(1+x- 1 x ) e ^ x+ 1 x ~d x is equal to
Options
- A(x-1) e ^ x+ 1 x + c , where c is a constant of integration.
- Bx e ^ x+ 1 x + c , where c is a constant of integration.
- C(x+1) e ^ x+ 1 x + c , where c is a constant of integration.
- D-x e ^ x+ 1 x + c , where c is a constant of integration.
Correct answer
B. x e ^ x+ 1 x + c , where c is a constant of integration.
Step-by-step solution
aligned & (1+x-x⁻¹ ) e ^ x+x⁻¹ ~d x & = [x e ^ x+x⁻¹ (1- 1 x^2 )+ e ^ x+x⁻¹ ] d x & =x e ^ x+x⁻¹ + c [ [x f ^ (x)+ f (x) ] d x=x f (x)+ c ] aligned