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

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

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integral of (ln(3x))^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 2 ln (3 x) d x = 2 (x ln (3 x) - x)

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

Add a constant to the solution

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

f (θ) = cos^{2} (θ)

x^{2} y^{^{'}} - x y = x^{4} cos (2 x), y (π) = \frac{π}{4}

\int \frac{6 x}{( 5 + 3 x ^{2} ) ^{4}} d x

x, 5 x, - x + 4

\frac{d y}{d x}, y = x^{9}

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