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

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

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integral of ln((3x)^2)

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

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

Solution steps

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

Apply Integration By Parts

: x ln (9 x^{2}) - \int 2 d x

= x ln (9 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (9 x^{2}) - 2 x

Simplify

ln (9 x^{2}) : 2 ln (3 x)

= 2 x ln (3 x) - 2 x

Add a constant to the solution

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

f (x) = (x + 3) (5 x^{2} - 7 x)

\int \frac{- 8 x ^{2} + 16 x + 8}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\int_{1}^{7} x - 1 d x

\int \frac{ln ( ln ( 3 x ) )}{3 x} d x

x \to 3 lim (5 x^{3} - 3 x + x - 6)

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