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

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

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integral of ln(y^2)

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

2 y ln (y) - 2 y + C

Solution steps

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

Apply Integration By Parts

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

\int 2 d y = 2 y

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

Apply log rule

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

assuming

x \geq 0

= 2 y ln (y) - 2 y

Add a constant to the solution

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