What is the integral from 1/2 to 5 of 14xln(2x) ?

The integral from 1/2 to 5 of 14xln(2x) is 14(-99/16+25/2 ln(10))

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integral from 1/2 to 5 of 14xln(2x)

\int_{\frac{1}{2}}^{5} 14 x ln (2 x) d x

14 (- \frac{99}{16} + \frac{25}{2} ln (10))

Decimal Notation

316.32739 \dots

Solution steps

\int_{\frac{1}{2}}^{5} 14 x ln (2 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}{2}}^{5} x ln (2 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x]_{\frac{1}{2}}^{5}

= 14 [\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x]_{\frac{1}{2}}^{5}

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

= 14 [\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}]_{\frac{1}{2}}^{5}

Compute the boundaries:

- \frac{99}{16} + \frac{25}{2} ln (10)

= 14 (- \frac{99}{16} + \frac{25}{2} ln (10))

(3 x^{2} y + x y^{2}) d x + (x^{3} + x^{2} y) d y = 0

\int_{5}^{6} \frac{x}{x ^{2} + 4 x + 20} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{x}

\frac{d}{d x} (- 8 e^{- 8 x})

\frac{\partial}{\partial r} (r^{2} + s^{2})

What is the integral from 1/2 to 5 of 14xln(2x) ?
The integral from 1/2 to 5 of 14xln(2x) is 14(-99/16+25/2 ln(10))