KCET2016MathematicsIndefinite Integration
The value of ( e^ x (x² ⁻¹ x+ ⁻¹ x+1 ) x²+1 d x ) is equal to
Options
- A( e^ x ⁻¹ x+c )
- B( ⁻¹ (e^ x )+c )
- C( ⁻¹ (x^ e )+c )
- D( e^ ⁻¹ x +c )
Correct answer
A. ( e^ x ⁻¹ x+c )
Step-by-step solution
Given that, ( I= e^ x (x² ⁻¹ x+ ⁻¹ x+1 ) x²+1 d x ) ( = e^ x ( (x²+1 ) ⁻¹ x+1 x²+1 ) d x ) ( = e^ x ( ⁻¹ x+ 1 x²+1 ) d x ) Since ( e^ x [f(x)+f^ (x) ] d x=e^ x f(x) ) So, ( I=e^ x ⁻¹ x+c )