What is the integral of 3xln(6x) ?

The integral of 3xln(6x) is 3(1/2 x^2ln(6x)-(x^2)/4)+C

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integral of 3xln(6x)

\int 3 x ln (6 x) d x

3 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4}) + C

Solution steps

\int 3 x ln (6 x) d x

Take the constant out:

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

= 3 \cdot \int x ln (6 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (6 x) - \int \frac{x}{2} d x

= 3 (\frac{1}{2} x^{2} ln (6 x) - \int \frac{x}{2} d x)

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

= 3 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 3 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4}) + C

\int \frac{ln ( x + a )}{x + a} d x

x \to + (- 2) lim (- 4 x + a)

\int x^{4} sin (x^{5}) d x

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

x \to 2 lim (x^{2} + 3 x + 9)

What is the integral of 3xln(6x) ?
The integral of 3xln(6x) is 3(1/2 x^2ln(6x)-(x^2)/4)+C