What is the integral of (ln(6x))^2 ?

The integral of (ln(6x))^2 is xln^2(6x)-2(xln(6x)-x)+C

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integral of (ln(6x))^2

\int (ln (6 x))^{2} d x

x ln^{2} (6 x) - 2 (x ln (6 x) - x) + C

Solution steps

\int (ln (6 x))^{2} d x

Apply Integration By Parts

: x ln^{2} (6 x) - \int 2 ln (6 x) d x

= x ln^{2} (6 x) - \int 2 ln (6 x) d x

\int 2 ln (6 x) d x = 2 (x ln (6 x) - x)

= x ln^{2} (6 x) - 2 (x ln (6 x) - x)

Add a constant to the solution

= x ln^{2} (6 x) - 2 (x ln (6 x) - x) + C

\frac{d y}{d x} = k \cdot y^{2}

\int sin^{5} (x) cos^{7} (x) d x

\frac{d y}{d x} = \frac{1}{1 + x}

\int 2 m (E - \frac{1}{2} k x^{2}) d x

f (x) = - 12 x^{2} + 400 x - 3800

What is the integral of (ln(6x))^2 ?
The integral of (ln(6x))^2 is xln^2(6x)-2(xln(6x)-x)+C