Find int log x , dx. | vedclass

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Question

(B) To evaluate the integral $\int \log x \, dx$,we use the method of integration by parts.Integration by parts formula is given by $\int u \cdot v \,

Vedclass · Accepted Answer

$x \log x - x + C$

Vedclass · Answer

(B) To evaluate the integral $\int \log x \, dx$,we use the method of integration by parts.Integration by parts formula is given by $\int u \cdot v \, dx = u \int v \, dx - \int \left( \frac{du}{dx} \int v \, dx \right) dx$.Let $u = \log x$ and $v = 1$.Then,$\frac{du}{dx} = \frac{1}{x}$ and $\int v \, dx = \int 1 \, dx = x$.Substituting these into the formula:$\int \log x \cdot 1 \, dx = (\log x) \cdot x - \int \left( \frac{1}{x} \cdot x \right) dx$$= x \log x - \int 1 \, dx$$= x \log x - x + C$.

Find $\int \log x \, dx$.

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