What is the integral from 1 to 2 of xlog_{2}(x) ?

The integral from 1 to 2 of xlog_{2}(x) is -3/(4ln(2))+2

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integral from 1 to 2 of xlog_{2}(x)

\int_{1}^{2} x lo g_{2} (x) d x

- \frac{3}{4 ln ( 2 )} + 2

Decimal

0.91797 \dots

Solution steps

\int_{1}^{2} x lo g_{2} (x) d x

Apply Integration By Parts

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

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

\int \frac{x}{2 ln ( 2 )} d x = \frac{x ^{2}}{4 ln ( 2 )}

= [\frac{1}{2} x^{2} lo g_{2} (x) - \frac{x ^{2}}{4 ln ( 2 )}]_{1}^{2}

Compute the boundaries:

- \frac{3}{4 ln ( 2 )} + 2

= - \frac{3}{4 ln ( 2 )} + 2

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What is the integral from 1 to 2 of xlog_{2}(x) ?
The integral from 1 to 2 of xlog_{2}(x) is -3/(4ln(2))+2