What is the integral from 1 to 16 of sqrt(x)ln(x) ?

The integral from 1 to 16 of sqrt(x)ln(x) is -28+512/3 ln(2)

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integral from 1 to 16 of sqrt(x)ln(x)

\int_{1}^{16} x ln (x) d x

- 28 + \frac{512}{3} ln (2)

Decimal Notation

90.29711 \dots

Solution steps

\int_{1}^{16} 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}^{16}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{16}

\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}^{16}

Compute the boundaries:

- 28 + \frac{512}{3} ln (2)

= - 28 + \frac{512}{3} ln (2)

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What is the integral from 1 to 16 of sqrt(x)ln(x) ?
The integral from 1 to 16 of sqrt(x)ln(x) is -28+512/3 ln(2)