What is the integral from 1 to 3 of 2xln(x) ?

The integral from 1 to 3 of 2xln(x) is -4+9ln(3)

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integral from 1 to 3 of 2xln(x)

\int_{1}^{3} 2 x ln (x) d x

- 4 + 9 ln (3)

Decimal

5.88751 \dots

Solution steps

\int_{1}^{3} 2 x ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{3} x ln (x) d x

Apply Integration By Parts

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

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

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

Compute the boundaries:

- 2 + \frac{9}{2} ln (3)

= 2 (- 2 + \frac{9}{2} ln (3))

Simplify

= - 4 + 9 ln (3)

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What is the integral from 1 to 3 of 2xln(x) ?
The integral from 1 to 3 of 2xln(x) is -4+9ln(3)