What is the integral from 1 to 25 of sqrt(x)ln(x) ?

The integral from 1 to 25 of sqrt(x)ln(x) is -496/9+500/3 ln(5)

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integral from 1 to 25 of sqrt(x)ln(x)

\int_{1}^{25} x ln (x) d x

- \frac{496}{9} + \frac{500}{3} ln (5)

Decimal

213.12854 \dots

Solution steps

\int_{1}^{25} x ln (x) d x

Apply Integration By Parts

: [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{25}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{25}

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

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}]_{1}^{25}

Compute the boundaries:

- \frac{496}{9} + \frac{500}{3} ln (5)

= - \frac{496}{9} + \frac{500}{3} ln (5)

f (x) = \frac{x}{x}

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = 8 x

\int 5 x^{2} e^{- x} d x

\frac{d}{d x} (sin (5 π x))

\frac{d}{d x} (12 ln (\frac{x}{20}))

What is the integral from 1 to 25 of sqrt(x)ln(x) ?
The integral from 1 to 25 of sqrt(x)ln(x) is -496/9+500/3 ln(5)