What is the integral from 0 to 1/13 of xln(13x) ?

The integral from 0 to 1/13 of xln(13x) is -1/676

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integral from 0 to 1/13 of xln(13x)

\int_{0}^{\frac{1}{13}} x ln (13 x) d x

- \frac{1}{676}

Solution steps

\int_{0}^{\frac{1}{13}} x ln (13 x) d x

Apply Integration By Parts

: [\frac{1}{2} (x^{2} ln (13 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{13}}

= [\frac{1}{2} (x^{2} ln (13 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{13}}

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

= [\frac{1}{2} (x^{2} ln (13 x) - 2 \cdot \frac{x ^{2}}{4})]_{0}^{\frac{1}{13}}

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

= [\frac{1}{2} (x^{2} ln (13 x) - \frac{x ^{2}}{2})]_{0}^{\frac{1}{13}}

Compute the boundaries:

- \frac{1}{676}

= - \frac{1}{676}

y^{^{''}} - 12 y^{^{'}} + 45 y = 0

\frac{d}{d x} ((x - sin (x)) (x + cos (x)))

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

\int e^{x} \frac{1}{x} d x

cos (x y)

What is the integral from 0 to 1/13 of xln(13x) ?
The integral from 0 to 1/13 of xln(13x) is -1/676