What is the integral from 1/5 to 3 of 8xln(5x) ?

The integral from 1/5 to 3 of 8xln(5x) is 8(-56/25+9/2 ln(15))

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integral from 1/5 to 3 of 8xln(5x)

\int_{\frac{1}{5}}^{3} 8 x ln (5 x) d x

8 (- \frac{56}{25} + \frac{9}{2} ln (15))

Decimal Notation

79.56980 \dots

Solution steps

\int_{\frac{1}{5}}^{3} 8 x ln (5 x) d x

Take the constant out:

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

= 8 \cdot \int_{\frac{1}{5}}^{3} 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}}^{3}

= 8 [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{3}

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

= 8 [\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}]_{\frac{1}{5}}^{3}

Compute the boundaries:

- \frac{56}{25} + \frac{9}{2} ln (15)

= 8 (- \frac{56}{25} + \frac{9}{2} ln (15))

ln (e)

\int x^{\frac{3}{4}} d x

y^{^{''}} + 289 y = sec (17 x)

f (x) = 2 x^{5} - 3 e^{6 x}

\int_{0}^{1} x^{2} - x d x

What is the integral from 1/5 to 3 of 8xln(5x) ?
The integral from 1/5 to 3 of 8xln(5x) is 8(-56/25+9/2 ln(15))