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

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

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integral of ln(2x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

\int 2 d x = 2 x

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

Simplify

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

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

Add a constant to the solution

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

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