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

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

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integral of ln^2(2/x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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What is the integral of ln^2(2/x) ?
The integral of ln^2(2/x) is xln^2(2/x)+2(xln(2/x)+x)+C