JEE Main2013MathematicsIndefinite IntegrationActual
If x^2-x+1 x^2+1 e^ ⁻¹ x d x=A(x) e^ ⁻¹ x +C , then A(x) is equal to :
Options
- A-x
- Bx
- C1-x
- D1+x
Correct answer
B. x
Step-by-step solution
Let I = x^2-x+1 x^2+1 e^ ⁻¹ x d x Put x= t - cosec ^2 t d t=d x Now, 1+ ^2 t= cosec ^2 t I = e^t ( ^2 t- t+1 ) (1+ ^2 t ) (- cosec ^2 t ) d t aligned & =- e^t ( cosec ^2 t- t ) d t & = e^t ( t- cosec ^2 t ) d t & =e^t t+ C & =e^ ⁻¹ x (x)+ C A (x) e^ ⁻¹ x + C A (x) & =x aligned