What is the integral from 1/5 to 7 of 12xln(5x) ?

The integral from 1/5 to 7 of 12xln(5x) is 12(-306/25+49/2 ln(35))

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integral from 1/5 to 7 of 12xln(5x)

\int_{\frac{1}{5}}^{7} 12 x ln (5 x) d x

12 (- \frac{306}{25} + \frac{49}{2} ln (35))

Decimal Notation

898.39233 \dots

Solution steps

\int_{\frac{1}{5}}^{7} 12 x ln (5 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}{5}}^{7} x ln (5 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

= 12 [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

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

= 12 [\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}]_{\frac{1}{5}}^{7}

Compute the boundaries:

- \frac{306}{25} + \frac{49}{2} ln (35)

= 12 (- \frac{306}{25} + \frac{49}{2} ln (35))

\int \frac{- 1}{1 + x ^{2}} d x

\frac{d}{d x} (\frac{ln ( 2 x )}{5 x})

\int cos^{2} (\frac{1}{2} x) d x

\int \frac{x ^{2} - 5 x + 6}{x ^{2} + 4} d x

\frac{\partial}{\partial x} ((\frac{y}{x})^{\frac{3}{4}})

What is the integral from 1/5 to 7 of 12xln(5x) ?
The integral from 1/5 to 7 of 12xln(5x) is 12(-306/25+49/2 ln(35))