What is the integral of (1-ln(y)) ?

The integral of (1-ln(y)) is 2y-yln(y)+C

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integral of (1-ln(y))

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

2 y - y ln (y) + C

Solution steps

\int 1 - ln (y) d y

Apply Integration By Parts

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

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

\int - 1 d y = - y

= y (1 - ln (y)) - (- y)

Simplify

y (1 - ln (y)) - (- y) : 2 y - y ln (y)

= 2 y - y ln (y)

Add a constant to the solution

= 2 y - y ln (y) + C

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