What is the integral from 1 to 9 of sqrt(y)ln(y) ?

The integral from 1 to 9 of sqrt(y)ln(y) is 36ln(3)-104/9

integral from 1 to 9 of sqrt(y)ln(y)

\int_{1}^{9} y ln (y) d y

36 ln (3) - \frac{104}{9}

Decimal

27.99448 \dots

Solution steps

\int_{1}^{9} y ln (y) d y

Apply Integration By Parts

= [\frac{2}{3} y^{\frac{3}{2}} ln (y) - \int \frac{2}{3} y^{\frac{1}{2}} d y]_{1}^{9}

\int \frac{2}{3} y^{\frac{1}{2}} d y = \frac{4}{9} y^{\frac{3}{2}}

= [\frac{2}{3} y^{\frac{3}{2}} ln (y) - \frac{4}{9} y^{\frac{3}{2}}]_{1}^{9}

Compute the boundaries:

36 ln (3) - \frac{104}{9}

= 36 ln (3) - \frac{104}{9}

\frac{\partial}{\partial x} (\frac{x}{sin ( 2 x + 3 y + z ^{2} )})

\frac{\partial}{\partial u} (3 v cos (u))

\frac{d}{d x} (ln ((x^{2} + 4)^{5}))

x \to 4 lim (\frac{( 2 )}{x - 4})

x \to 2 - lim (\frac{2 x}{x ^{2} - 4})

What is the integral from 1 to 9 of sqrt(y)ln(y) ?
The integral from 1 to 9 of sqrt(y)ln(y) is 36ln(3)-104/9