What is the integral of ln(2/x) ?

The integral of ln(2/x) is xln(2/x)+x+C

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integral of ln(2/x)

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

x ln (\frac{2}{x}) + x + C

Solution steps

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

Apply Integration By Parts

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

\int - 1 d x = - x

= x ln (\frac{2}{x}) - (- x)

Simplify

= x ln (\frac{2}{x}) + x

Add a constant to the solution

= x ln (\frac{2}{x}) + x + C