What is the integral from 1/5 to 3 of 4xln(5x) ?

The integral from 1/5 to 3 of 4xln(5x) is 4(-56/25+9/2 ln(15))

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integral from 1/5 to 3 of 4xln(5x)

\int_{\frac{1}{5}}^{3} 4 x ln (5 x) d x

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

Decimal Notation

39.78490 \dots

Solution steps

\int_{\frac{1}{5}}^{3} 4 x ln (5 x) d x

Take the constant out:

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

= 4 \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}

= 4 [\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}

= 4 [\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)

= 4 (- \frac{56}{25} + \frac{9}{2} ln (15))

n = 1 \sum \infty \frac{7}{1 0 ^{n}}

f (x) = 2 x^{3} + 36 x^{2} + 192 x + 8

x \to 0 + lim (\frac{e ^{x}}{1 - e ^{- x}})

\frac{d}{d x} (4 e^{6 x})

f (x) = sin (3 x + 1)

What is the integral from 1/5 to 3 of 4xln(5x) ?
The integral from 1/5 to 3 of 4xln(5x) is 4(-56/25+9/2 ln(15))