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

The integral of (ln(y))^2 is yln^2(y)-2(yln(y)-y)+C

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integral of (ln(y))^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 2 ln (y) d y = 2 (y ln (y) - y)

= y ln^{2} (y) - 2 (y ln (y) - y)

Add a constant to the solution

= y ln^{2} (y) - 2 (y ln (y) - y) + C

(x^{2} - 1) (x^{2} - 4), x = 0, x = 5

x 4 - x^{2}, 0

x + y

\frac{d}{d x} (4 x (x^{2} + 1))

y = \frac{1}{x}, x = 2, y = - 1

What is the integral of (ln(y))^2 ?
The integral of (ln(y))^2 is yln^2(y)-2(yln(y)-y)+C