AP EAMCET20225 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual
The value of e^ ⁻¹ x (1+x+x^2 ) 1+x^2 d x is
Options
- A⁻¹ x+c
- Be^ ⁻¹ x +c
- Ce^ ⁻¹ x -x+c
- Dx e^ ⁻¹ x +c
Correct answer
D. x e^ ⁻¹ x +c
Step-by-step solution
Let aligned & I= (e^ ⁻¹ x (1+x^2 ) (1+x^2 ) d x+e^ ⁻¹ x x (1+x^2 ) ) & I= (e^ ⁻¹ x +e^ ⁻¹ x x 1+x^2 ) d x aligned As we know, aligned & d (e^ ⁻¹ x )=e^ ⁻¹ x (d ( ⁻¹ x ) ) & d (e^ ⁻¹ x )=e^ ⁻¹ x ( 1 1+x^2 ) aligned So, aligned & I= (e^ ⁻¹ x d x+x d (e^ ⁻¹ x ) ) & I= d d x (x e^ ⁻¹ x ) d x+c aligned I=x e^ ⁻¹ x +c