What is the integral from 0 to 1/6 of xln(6x) ?

The integral from 0 to 1/6 of xln(6x) is -1/144

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integral from 0 to 1/6 of xln(6x)

\int_{0}^{\frac{1}{6}} x ln (6 x) d x

- \frac{1}{144}

Solution steps

\int_{0}^{\frac{1}{6}} x ln (6 x) d x

Apply Integration By Parts

: [\frac{1}{2} (x^{2} ln (6 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{6}}

= [\frac{1}{2} (x^{2} ln (6 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{6}}

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

= [\frac{1}{2} (x^{2} ln (6 x) - 2 \cdot \frac{x ^{2}}{4})]_{0}^{\frac{1}{6}}

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

= [\frac{1}{2} (x^{2} ln (6 x) - \frac{x ^{2}}{2})]_{0}^{\frac{1}{6}}

Compute the boundaries:

- \frac{1}{144}

= - \frac{1}{144}

y = x + 1, (- 1, 4)

x \to \infty lim (i^{x})

f (x) = (x^{3} + 5) (x^{3} + x + 1)

\int \frac{3}{x ln ( 2 x )} d x

\int 1 d x^{2}

What is the integral from 0 to 1/6 of xln(6x) ?
The integral from 0 to 1/6 of xln(6x) is -1/144