What is the integral from 1/7 to 3 of 16xln(7x) ?

The integral from 1/7 to 3 of 16xln(7x) is 16(-110/49+9/2 ln(21))

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integral from 1/7 to 3 of 16xln(7x)

\int_{\frac{1}{7}}^{3} 16 x ln (7 x) d x

16 (- \frac{110}{49} + \frac{9}{2} ln (21))

Decimal

183.28724 \dots

Solution steps

\int_{\frac{1}{7}}^{3} 16 x ln (7 x) d x

Take the constant out:

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

= 16 \cdot \int_{\frac{1}{7}}^{3} x ln (7 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

= 16 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

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

= 16 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{3}

Compute the boundaries:

- \frac{110}{49} + \frac{9}{2} ln (21)

= 16 (- \frac{110}{49} + \frac{9}{2} ln (21))

\int_{0}^{4} 17 d x

\int_{1}^{t} \frac{37}{x ^{3}} d x

y^{^{'}} = - x^{2} - \frac{1}{x} \cdot y

\int \frac{1}{1 - 64 x ^{2}} d x

\int \frac{2 x + 3}{x ^{3} + x ^{2} - 2 x} d x

What is the integral from 1/7 to 3 of 16xln(7x) ?
The integral from 1/7 to 3 of 16xln(7x) is 16(-110/49+9/2 ln(21))