What is the integral of (6ln(4x))/5 ?

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

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integral of (6ln(4x))/5

\int \frac{6 ln ( 4 x )}{5} d x

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

Solution steps

\int \frac{6 ln ( 4 x )}{5} d x

Take the constant out:

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

= \frac{6}{5} \cdot \int ln (4 x) d x

Apply Integration By Parts

: x ln (4 x) - \int 1 d x

= \frac{6}{5} (x ln (4 x) - \int 1 d x)

\int 1 d x = x

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

Add a constant to the solution

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

- 2 sin (x)

f (x) = x^{5} - 3 x + 4

\frac{e ^{x}}{x + 1}

x \to 1 lim (∣ x - 1 ∣)

\frac{d}{d x} (\frac{x - 2}{x})

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