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Popular >

integral of ln(1/x)

Solution

integral

ln (\frac{1}{x})

Solution

- x ln (x) + x + C

Solution steps

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

Apply Integration By Parts

: - x ln (x) - \int - 1 d x

= - x ln (x) - \int - 1 d x

\int - 1 d x = - x

= - x ln (x) - (- x)

Simplify

= - x ln (x) + x

Add a constant to the solution

= - x ln (x) + x + C

Graph

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Frequently Asked Questions (FAQ)

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