What is the integral from 1/5 to 7 of 10xln(5x) ?

The integral from 1/5 to 7 of 10xln(5x) is 10(-306/25+49/2 ln(35))

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integral from 1/5 to 7 of 10xln(5x)

\int_{\frac{1}{5}}^{7} 10 x ln (5 x) d x

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

Decimal Notation

748.66027 \dots

Solution steps

\int_{\frac{1}{5}}^{7} 10 x ln (5 x) d x

Take the constant out:

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

= 10 \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}

= 10 [\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}

= 10 [\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)

= 10 (- \frac{306}{25} + \frac{49}{2} ln (35))

f (t) = sin (5 t)

\int 125 x^{2} cos (5 x) d x

\frac{\partial}{\partial u} (u^{2} v^{3})

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

\int x^{5} x^{3} + 4 d x

What is the integral from 1/5 to 7 of 10xln(5x) ?
The integral from 1/5 to 7 of 10xln(5x) is 10(-306/25+49/2 ln(35))