What is the integral of ln^3(2x) ?

The integral of ln^3(2x) is xln^3(2x)-3(xln^2(2x)-2(xln(2x)-x))+C

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integral of ln^3(2x)

\int ln^{3} (2 x) d x

x ln^{3} (2 x) - 3 (x ln^{2} (2 x) - 2 (x ln (2 x) - x)) + C

Solution steps

\int ln^{3} (2 x) d x

Apply Integration By Parts

: x ln^{3} (2 x) - \int 3 ln^{2} (2 x) d x

= x ln^{3} (2 x) - \int 3 ln^{2} (2 x) d x

\int 3 ln^{2} (2 x) d x = 3 (x ln^{2} (2 x) - 2 (x ln (2 x) - x))

= x ln^{3} (2 x) - 3 (x ln^{2} (2 x) - 2 (x ln (2 x) - x))

Add a constant to the solution

= x ln^{3} (2 x) - 3 (x ln^{2} (2 x) - 2 (x ln (2 x) - x)) + C

\frac{1}{x - 3}

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

x y^{^{'}} - (1 + x) y = x y^{2}

x \to 1 lim (\frac{x - 1}{x + 24 - 5})

\frac{\partial}{\partial x} (2 x + 4)

What is the integral of ln^3(2x) ?
The integral of ln^3(2x) is xln^3(2x)-3(xln^2(2x)-2(xln(2x)-x))+C