What is the integral from 1/3 to 5 of 12xln(3x) ?

The integral from 1/3 to 5 of 12xln(3x) is 12(-56/9+25/2 ln(15))

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integral from 1/3 to 5 of 12xln(3x)

\int_{\frac{1}{3}}^{5} 12 x ln (3 x) d x

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

Decimal Notation

331.54086 \dots

Solution steps

\int_{\frac{1}{3}}^{5} 12 x ln (3 x) d x

Take the constant out:

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

= 12 \cdot \int_{\frac{1}{3}}^{5} x ln (3 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (3 x) - \int \frac{x}{2} d x]_{\frac{1}{3}}^{5}

= 12 [\frac{1}{2} x^{2} ln (3 x) - \int \frac{x}{2} d x]_{\frac{1}{3}}^{5}

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

= 12 [\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4}]_{\frac{1}{3}}^{5}

Compute the boundaries:

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

= 12 (- \frac{56}{9} + \frac{25}{2} ln (15))

\int tan^{2} (x co) s^{3} x d x

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

\int e^{x + 3 e^{x}} d x

\frac{d ^{2} y}{d x ^{2}} - 9 y = 0

\frac{\partial}{\partial x} (a - b x - \frac{c}{y} + d \frac{x}{y})

What is the integral from 1/3 to 5 of 12xln(3x) ?
The integral from 1/3 to 5 of 12xln(3x) is 12(-56/9+25/2 ln(15))