What is the integral of x^{-2}ln(x) ?

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

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integral of x^{-2}ln(x)

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

- \frac{ln ( x )}{x} - \frac{1}{x} + C

Solution steps

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

Apply Integration By Parts

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

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

= - \frac{ln ( x )}{x} - \frac{1}{x}

Add a constant to the solution

= - \frac{ln ( x )}{x} - \frac{1}{x} + C

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