The integral ∫ 1 + x - 1 x e x + 1 x d x is equal to

Question

The integral ∫ 1 + x - 1 x e x + 1 x d x is equal to, x - 1 e x + 1 x + C, x e x + 1 x + C, x + 1 e x + 1 x + C, - x e x + 1 x + C

MARKS App · Accepted Answer

We have, I = ∫ 1 + x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x - 1 x e x + 1 x d x I = ∫ e x + 1 x d x + ∫ x 1 - 1 x 2 e x + 1 x d x I = ∫ e x + 1 x d x + x e x + 1 x - ∫ e x + 1 x d x I = x e x + 1 x + C

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