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Integration of ln(x) with x i.e. ∫ ln(x) dx = _______.

1. x·ln(x) − x + Constant
2. x − ln(x) + Constant
3. x·ln(x) + x + Constant
4. ln(x) − x + Constant

Correct answer: x·ln(x) − x + Constant

Solution

The correct option is derived from integration by parts, where we let u = ln(x) and dv = dx. This results in the formula x·ln(x) - x, plus a constant of integration, which accurately represents the indefinite integral of ln(x).

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