The indefinite integral ∫ e e x x e x ⋅ ln ⁡ x + 1 x d x simplifies to (where, c is the constant of integration)

Question

The indefinite integral ∫ e e x x e x ⋅ ln ⁡ x + 1 x d x simplifies to (where, c is the constant of integration), x ln ⁡ ln ⁡ x + c, e e x + c, e e x x + c, e e x ⋅ ln ⁡ x + c

MARKS App · Accepted Answer

Given integral is I = ∫ e e x ⋅ e x ⋅ ln ⁡ x + e e x x d x Let, e e x = f x and ln ⁡ x = g x ∴ I = ∫ f ' x g x + f x g ' x d x = f x · g x + c = e e x ⋅ ln ⁡ x + c

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