What is the integral of ln(6x^3) ?

The integral of ln(6x^3) is x(ln(6)+3ln(x))-3x+C

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integral of ln(6x^3)

\int ln (6 x^{3}) d x

x (ln (6) + 3 ln (x)) - 3 x + C

Solution steps

\int ln (6 x^{3}) d x

Apply Integration By Parts

: x ln (6 x^{3}) - \int 3 d x

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

\int 3 d x = 3 x

= x ln (6 x^{3}) - 3 x

Simplify

ln (6 x^{3}) : 3 ln (x) + ln (6)

= x (ln (6) + 3 ln (x)) - 3 x

Add a constant to the solution

= x (ln (6) + 3 ln (x)) - 3 x + C

f (x) = x \cdot e^{x}

f (- 1) = (5 p + 4)^{40}

\int \frac{t}{1 - t} d t

x \to - 3 lim (- 2 x - 3)

What is the integral of ln(6x^3) ?
The integral of ln(6x^3) is x(ln(6)+3ln(x))-3x+C