What is the integral of ln(-1/5 x) ?

The integral of ln(-1/5 x) is xln(-1/5 x)-x+C

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integral of ln(-1/5 x)

\int ln (- \frac{1}{5} x) d x

x ln (- \frac{1}{5} x) - x + C

Solution steps

\int ln (- \frac{1}{5} x) d x

Apply Integration By Parts

: x ln (- \frac{1}{5} x) - \int 1 d x

= x ln (- \frac{1}{5} x) - \int 1 d x

\int 1 d x = x

= x ln (- \frac{1}{5} x) - x

Add a constant to the solution

= x ln (- \frac{1}{5} x) - x + C

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What is the integral of ln(-1/5 x) ?
The integral of ln(-1/5 x) is xln(-1/5 x)-x+C