What is the integral of 5xln(4x) ?

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

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integral of 5xln(4x)

\int 5 x ln (4 x) d x

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

Solution steps

\int 5 x ln (4 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 (4 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (4 x) - \int \frac{x}{2} d x

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

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

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

Add a constant to the solution

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

f (x) = x^{2} + 3 x - 7

\frac{\partial}{\partial s} (- 3 s^{2} + t^{2})

y^{^{'}} = y + 3

\int \frac{1}{x ^{2} + 6 x} d x

\frac{d}{d x} (e^{1 x})

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