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

The integral of (ln(2x))^2 is xln^2(2x)-2(xln(2x)-x)+C

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integral of (ln(2x))^2

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

x ln^{2} (2 x) - 2 (x ln (2 x) - x) + C

Solution steps

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

Apply Integration By Parts

: x ln^{2} (2 x) - \int 2 ln (2 x) d x

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

\int 2 ln (2 x) d x = 2 (x ln (2 x) - x)

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

Add a constant to the solution

= x ln^{2} (2 x) - 2 (x ln (2 x) - x) + C

x \to - 3 lim (\frac{2}{x + 2})

\int x (x + 3) d x

\frac{x}{x - 6}

f (x) = (x^{3} + 1) e^{x}

\int_{1}^{3} (x^{2} + 2 x - 2) d x

What is the integral of (ln(2x))^2 ?
The integral of (ln(2x))^2 is xln^2(2x)-2(xln(2x)-x)+C