What is the integral of ln(1/(x^2)) ?

The integral of ln(1/(x^2)) is -2xln(x)+2x+C

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integral of ln(1/(x^2))

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int - 2 d x = - 2 x

= - x ln (x^{2}) - (- 2 x)

Simplify

- x ln (x^{2}) - (- 2 x) : - 2 x ln (x) + 2 x

= - 2 x ln (x) + 2 x

Add a constant to the solution

= - 2 x ln (x) + 2 x + C

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What is the integral of ln(1/(x^2)) ?
The integral of ln(1/(x^2)) is -2xln(x)+2x+C