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

= 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

x \to 1 - lim (\frac{2 - x}{x - 1})

x \to \infty - lim (\frac{( 8 x ^{3} + 6 x + 7 )}{( 6 x - 7 )})

f (x) = \frac{x + 3}{2}

\int x^{2} (2 x - 4)^{5} d x

\frac{d}{d x} (\frac{( ln ( x ) )}{x})