What is the integral of 8ln(3x) ?

The integral of 8ln(3x) is 8(xln(3x)-x)+C

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integral of 8ln(3x)

\int 8 ln (3 x) d x

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

Solution steps

\int 8 ln (3 x) d x

Take the constant out:

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

= 8 \cdot \int ln (3 x) d x

Apply Integration By Parts

: x ln (3 x) - \int 1 d x

= 8 (x ln (3 x) - \int 1 d x)

\int 1 d x = x

= 8 (x ln (3 x) - x)

Add a constant to the solution

= 8 (x ln (3 x) - x) + C

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