What is the integral of ln(2x^3) ?

The integral of ln(2x^3) is x(ln(2)+3ln(x))-3x+C

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integral of ln(2x^3)

\int ln (2 x^{3}) d x

x (ln (2) + 3 ln (x)) - 3 x + C

Solution steps

\int ln (2 x^{3}) d x

Apply Integration By Parts

: x ln (2 x^{3}) - \int 3 d x

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

\int 3 d x = 3 x

= x ln (2 x^{3}) - 3 x

Simplify

ln (2 x^{3}) : 3 ln (x) + ln (2)

= x (ln (2) + 3 ln (x)) - 3 x

Add a constant to the solution

= x (ln (2) + 3 ln (x)) - 3 x + C

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What is the integral of ln(2x^3) ?
The integral of ln(2x^3) is x(ln(2)+3ln(x))-3x+C