What is the integral from 1/5 to 3 of 14xln(5x) ?

The integral from 1/5 to 3 of 14xln(5x) is 14(-56/25+9/2 ln(15))

integral from 1/5 to 3 of 14xln(5x)

\int_{\frac{1}{5}}^{3} 14 x ln (5 x) d x

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

Decimal

139.24716 \dots

Solution steps

\int_{\frac{1}{5}}^{3} 14 x ln (5 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}{5}}^{3} x ln (5 x) d x

Apply Integration By Parts

= 14 [\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}

= 14 [\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)

= 14 (- \frac{56}{25} + \frac{9}{2} ln (15))

d er i v a t i v e y = x^{5} ln (x)

x \to 0 lim (\frac{2 8 ^{x} - 1}{x})

d er i v a t i v e (arcsin (5 x + 5))^{8}

x \to - 2 lim ((x + 4)^{3})

\frac{d}{d x} (30 x^{4} - 80 x^{3} + 60 x^{2} - 10)

What is the integral from 1/5 to 3 of 14xln(5x) ?
The integral from 1/5 to 3 of 14xln(5x) is 14(-56/25+9/2 ln(15))