What is the integral from 2 to 3 of 6xln(x) ?

The integral from 2 to 3 of 6xln(x) is 6(-2ln(2)-5/4+9/2 ln(3))

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integral from 2 to 3 of 6xln(x)

\int_{2}^{3} 6 x ln (x) d x

6 (- 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3))

Decimal Notation

13.84476 \dots

Solution steps

\int_{2}^{3} 6 x ln (x) d x

Take the constant out:

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

= 6 \cdot \int_{2}^{3} x ln (x) d x

Apply Integration By Parts

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

= 6 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{2}^{3}

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

= 6 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{2}^{3}

Compute the boundaries:

- 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3)

= 6 (- 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3))

\frac{d}{d θ} (cos (θ) + i sin (θ))

x \to 0 lim (7)

\int \frac{5 x ^{5}}{x} d x

\int x^{2} + 6 x + 5 d x

\frac{d y}{d x} = 3 y + x^{2} + 2

What is the integral from 2 to 3 of 6xln(x) ?
The integral from 2 to 3 of 6xln(x) is 6(-2ln(2)-5/4+9/2 ln(3))