Evaluate integral of 2 natural log of x with respect to x

$\int 2 \ln (x) d x$

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int \ln (x) d x$

Integrate by parts using the formula $\int u d v = u v - \int v d u$ , where $u = \ln (x)$ and $d v = 1$ .

$2 (\ln (x) x - \int x \frac{1}{x} d x)$

Simplify.

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Combine $x$ and $\frac{1}{x}$ .

$2 (\ln (x) x - \int \frac{x}{x} d x)$

Cancel the common factor of $x$ .

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Cancel the common factor.

$2 (\ln (x) x - \int \frac{x}{x} d x)$

Divide $1$ by $1$ .

$2 (\ln (x) x - \int 1 d x)$

Since $1$ is constant with respect to $x$ , move $1$ out of the integral.

$2 (\ln (x) x - (x + C))$

Simplify.

$2 (\ln (x) x - x) + C$

Evaluate integral of 2 natural log of x with respect to x

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