AP EAMCET20224 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual
If ∫ e x x x + x d x = e x A x + B x + C + K , then A + B + C =
Options
- A- 2
- B2
- C4
- D- 4
Correct answer
B. 2
Step-by-step solution
I = ∫ e x x x + x d x Let x = t 1 2 x d x = d t i.e. I = 2 ∫ e t t 2 + t d t = 2 ∫ t 2 e t d t + 2 ∫ t e t d t = 2 t 2 e t - 2 ∫ 2 t e t d t + 2 ∫ t e t d t = 2 t 2 e t - 2 ∫ t e t d t = 2 t 2 e t - 2 t e t - ∫ e t d t = 2 t 2 e t - 2 t e t + 2 e t + C ' = e x 2 x - 2 x + 2 + C ' Hence, A + B + C = 2