What is the integral from 0 to y of ln(y) ?

The integral from 0 to y of ln(y) is yln(y)-y

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integral from 0 to y of ln(y)

\int_{0}^{y} ln (y) d y

y ln (y) - y

Solution steps

\int_{0}^{y} ln (y) d y

Apply Integration By Parts

: [y ln (y) - \int 1 d y]_{0}^{y}

= [y ln (y) - \int 1 d y]_{0}^{y}

\int 1 d y = y

= [y ln (y) - y]_{0}^{y}

Compute the boundaries:

y ln (y) - y

= y ln (y) - y

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\int_{1}^{4} \frac{x ^{3} - 6 x + 5}{x} d x

\int_{1}^{2} \frac{x e ^{\frac{x}{y}}}{y ^{2}} d y

What is the integral from 0 to y of ln(y) ?
The integral from 0 to y of ln(y) is yln(y)-y