MHT CET202015 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual
e^ ⁻¹ x (1+ x 1+x² ) d x
Options
- A( x 2 ) e^ ⁻¹ x +c
- Bx e^ ⁻¹ x +c
- C( 1 2 ) e^ ⁻¹ x +c
- De^ ⁻¹ x +c
Correct answer
B. x e^ ⁻¹ x +c
Step-by-step solution
Let I= e^ ⁻¹ x (1+ x 1+x² ) d x aligned I &= e^ ⁻¹ x ( 1+x²+x 1+x² ) d x Put ⁻¹ x &=t x= t and 1 1+x² d x=d t I &= e^ t (1+ ² t+ t ) d t e^ t ( t+ ² t ) d t &=e^ t t+c=x e^ ⁻¹ x +c aligned