What is the integral of ln((6x)^2) ?

The integral of ln((6x)^2) is 2xln(6x)-2x+C

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integral of ln((6x)^2)

\int ln ((6 x)^{2}) d x

2 x ln (6 x) - 2 x + C

Solution steps

\int ln ((6 x)^{2}) d x

Apply Integration By Parts

: x ln (36 x^{2}) - \int 2 d x

= x ln (36 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (36 x^{2}) - 2 x

Simplify

ln (36 x^{2}) : 2 ln (6 x)

= 2 x ln (6 x) - 2 x

Add a constant to the solution

= 2 x ln (6 x) - 2 x + C

\int \frac{1}{sin ^{2} ( x )} d x

4 y^{^{''}} + 20 y^{^{'}} + 25 y = 0

y = e^{x}, y = 0, x = 0, x = ln (3)

\int e^{x} 8 - e^{x} d x

\frac{d}{d a} (sin^{4} (a) - cos^{4} (a) + cos^{2} (a))

What is the integral of ln((6x)^2) ?
The integral of ln((6x)^2) is 2xln(6x)-2x+C