What is the integral from 1/2 to 5 of 12xln(2x) ?

The integral from 1/2 to 5 of 12xln(2x) is 12(-99/16+25/2 ln(10))

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integral from 1/2 to 5 of 12xln(2x)

\int_{\frac{1}{2}}^{5} 12 x ln (2 x) d x

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

Solution steps

\int_{\frac{1}{2}}^{5} 12 x ln (2 x) d x

Take the constant out:

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

= 12 \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}

= 12 [\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}

= 12 [\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)

= 12 (- \frac{99}{16} + \frac{25}{2} ln (10))

\frac{3}{x}

x \to 1 lim (\frac{1}{x} + 1)

y^{^{''}} + 9 y = 26 e^{2 x}

\int_{0}^{5} π (2 3 y)^{2} d y

\frac{2 s}{1 + 2 s}

What is the integral from 1/2 to 5 of 12xln(2x) ?
The integral from 1/2 to 5 of 12xln(2x) is 12(-99/16+25/2 ln(10))