What is the integral from 1/5 to 7 of 14xln(5x) ?

The integral from 1/5 to 7 of 14xln(5x) is 14(-306/25+49/2 ln(35))

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integral from 1/5 to 7 of 14xln(5x)

\int_{\frac{1}{5}}^{7} 14 x ln (5 x) d x

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

Decimal Notation

1048.12438 \dots

Solution steps

\int_{\frac{1}{5}}^{7} 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}}^{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}

= 14 [\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}

= 14 [\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)

= 14 (- \frac{306}{25} + \frac{49}{2} ln (35))

- sec (x) + 2 sec^{3} (x)

\int 4 sin (2 x) - 3 cos (6 x) d x

\int_{0}^{\frac{π}{3}} 49 sin^{2} (x) d x

\int \frac{x ^{3} - 1}{( 2 x ^{4} - 8 x ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (2 cos (x) + cos^{2} (x))

What is the integral from 1/5 to 7 of 14xln(5x) ?
The integral from 1/5 to 7 of 14xln(5x) is 14(-306/25+49/2 ln(35))