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

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

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integral of ln((2x)^2)

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

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

Solution steps

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

Apply Integration By Parts

= x ln (4 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (4 x^{2}) - 2 x

Simplify

ln (4 x^{2}) : 2 ln (2 x)

= 2 x ln (2 x) - 2 x

Add a constant to the solution

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

\int \frac{1}{7 x ^{2} - 14 x + 28} d x

y = \frac{4}{x - 2}

\int e^{s i n (t)} cos (t) d t

\int 7 x + 3 d x

n = 1 \sum \infty \frac{n ^{2} x ^{4 n}}{5 ^{4 n}}

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