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

= 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

\frac{x d y}{d x} + y = e^{- x}

9 y^{^{''}} + 6 y^{^{'}} + 6 y = 0

\int_{3}^{4} 15 x (x - 2)^{4} d x

\int 2 x^{2} e^{- x} d x

x^{2} e^{2 x}