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

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

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integral of ln(x/y)

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

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

Solution steps

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

Apply Integration By Parts

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

\int 1 d x = x

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

Add a constant to the solution

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