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

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

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integral of ln(r^2)

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

2 r ln (r) - 2 r + C

Solution steps

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

Apply Integration By Parts

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

\int 2 d r = 2 r

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

Apply log rule

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

assuming

x \geq 0

= 2 r ln (r) - 2 r

Add a constant to the solution

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