If ∫ e x x x + x d x = e x A x + B x + C + K , then A + B + C =

Question

If ∫ e x x x + x d x = e x A x + B x + C + K , then A + B + C =, - 2, 2, 4, - 4

MARKS App · Accepted Answer

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

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