What is the integral of (ln(5x))^2 ?

The integral of (ln(5x))^2 is xln^2(5x)-2(xln(5x)-x)+C

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integral of (ln(5x))^2

\int (ln (5 x))^{2} d x

x ln^{2} (5 x) - 2 (x ln (5 x) - x) + C

Solution steps

\int (ln (5 x))^{2} d x

Apply Integration By Parts

: x ln^{2} (5 x) - \int 2 ln (5 x) d x

= x ln^{2} (5 x) - \int 2 ln (5 x) d x

\int 2 ln (5 x) d x = 2 (x ln (5 x) - x)

= x ln^{2} (5 x) - 2 (x ln (5 x) - x)

Add a constant to the solution

= x ln^{2} (5 x) - 2 (x ln (5 x) - x) + C

\int \frac{( 17 x + 3 )}{( 4 x + 1 ) ( x - 1 )} d x

x \to 0 lim (x^{2} ln (x))

\frac{d}{d x} (\frac{1}{5 sin ( x )} + \frac{csc ( x )}{4})

\frac{d}{d x} (x - sin^{2} (x) - 4 x y e^{x y^{2}})

x y^{^{'}} + 4 y = \frac{( 2 e ^{- 4 x} )}{x ^{3}}

What is the integral of (ln(5x))^2 ?
The integral of (ln(5x))^2 is xln^2(5x)-2(xln(5x)-x)+C