What is the integral of 5xln(6x) ?

The integral of 5xln(6x) is 5(1/2 x^2ln(6x)-(x^2)/4)+C

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integral of 5xln(6x)

\int 5 x ln (6 x) d x

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

Solution steps

\int 5 x ln (6 x) d x

Take the constant out:

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

= 5 \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

= 5 (\frac{1}{2} x^{2} ln (6 x) - \int \frac{x}{2} d x)

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

= 5 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 5 (\frac{1}{2} x^{2} ln (6 x) - \frac{x ^{2}}{4}) + C

y = x^{3} + 4

\frac{d}{d x} (cos^{2} (sin (5 e^{x} - 1 6^{x})))

\int \frac{1}{t ^{3}} d t

\frac{\partial}{\partial x} ((x) cos (x) cos (y))

y^{^{'}} = \frac{sec ( y )}{( x - 4 ) ^{2}}

What is the integral of 5xln(6x) ?
The integral of 5xln(6x) is 5(1/2 x^2ln(6x)-(x^2)/4)+C