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Popular >

integral of 1-ln(y)

Solution

\int 1 - ln (y) d y

Solution

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

Popular Examples

integral of 1/(sqrt(-8-4x^2-12x))

\int \frac{1}{- 8 - 4 x ^{2} - 12 x} d x

integral of x/(5-5x^3)

\int \frac{x}{5 - 5 x ^{3}} d x

integral of e^{-0.06t}

\int e^{- 0.06 t} d t

integral of (xy^2)

\int (x y^{2}) d x

integral of sin(10pi)t

\int sin (10 π) t d t

Frequently Asked Questions (FAQ)

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