What is the integral from 1/7 to 3 of 14xln(7x) ?

The integral from 1/7 to 3 of 14xln(7x) is 14(-110/49+9/2 ln(21))

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integral from 1/7 to 3 of 14xln(7x)

\int_{\frac{1}{7}}^{3} 14 x ln (7 x) d x

14 (- \frac{110}{49} + \frac{9}{2} ln (21))

Decimal Notation

160.37634 \dots

Solution steps

\int_{\frac{1}{7}}^{3} 14 x ln (7 x) d x

Take the constant out:

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

= 14 \cdot \int_{\frac{1}{7}}^{3} x ln (7 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

= 14 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

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

= 14 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{3}

Compute the boundaries:

- \frac{110}{49} + \frac{9}{2} ln (21)

= 14 (- \frac{110}{49} + \frac{9}{2} ln (21))

\frac{\partial}{\partial x} (\frac{5 y}{x ^{2} + 1})

\frac{d}{d x} (\frac{x + 1}{1 - x})

\int_{- 3}^{3} (\frac{27}{2} - \frac{3}{2} x^{2}) d x

x \to 0 - lim (\frac{x - 2}{x ^{2} - 4})

\frac{( q x + r )}{( s x + t )}

What is the integral from 1/7 to 3 of 14xln(7x) ?
The integral from 1/7 to 3 of 14xln(7x) is 14(-110/49+9/2 ln(21))