What is the integral of-ln(y) ?

The integral of-ln(y) is -yln(y)+y+C

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integral of-ln(y)

\int - ln (y) d y

- y ln (y) + y + C

Solution steps

\int - ln (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int ln (y) d y

Apply Integration By Parts

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

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

\int 1 d y = y

= - (y ln (y) - y)

Simplify

= - y ln (y) + y

Add a constant to the solution

= - y ln (y) + y + C

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