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

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

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integral from 1 to 3 of xln(x)

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

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

Decimal Notation

2.94375 \dots

Solution steps

\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}

= [\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}

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

Compute the boundaries:

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

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

\int \frac{4 - 32 x}{25 - 16 x ^{2}} d x

\frac{d}{d x} (8 + 4 x)

\int x x x d x

f (x) = 8 (x - \frac{1}{x})^{3}, at x = 2

n = 0 \sum \infty (3 x)^{n}

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