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

\int (\frac{( x ^{m} - x ^{n} ) ^{2}}{x}) d x

\frac{\partial}{\partial y} (4 x^{2} + 2 x y + y^{2} - 8)

\frac{d}{d x} (x^{5} e^{x y} + 3 x)

f (x) = tan (5 x)

∣ 3 x ∣, x^{2} - 4