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

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

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integral of (ln(x^2))

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

2 x ln (x) - 2 x + C

Solution steps

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

Apply Integration By Parts

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

\int 2 d x = 2 x

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 2 x ln (x) - 2 x

Add a constant to the solution

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