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

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

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integral of ln^2(2x)

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

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

Solution steps

\int ln^{2} (2 x) 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

\frac{d}{d u} (uv)

x \to 0 lim (- \frac{sin ( x )}{3 x})

\int x x + 9 d x

x \to - 1 lim (x^{2} - 5 x + 6)

\frac{\partial}{\partial y} (3 x^{2} - 3 y)

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