What is the integral of ln^2(x-9) ?

The integral of ln^2(x-9) is ln^2(x-9)(x-9)-2(xln(x-9)-9ln(x-9)-x+9)+C

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integral of ln^2(x-9)

\int ln^{2} (x - 9) d x

ln^{2} (x - 9) (x - 9) - 2 (x ln (x - 9) - 9 ln (x - 9) - x + 9) + C

Solution steps

\int ln^{2} (x - 9) d x

Apply u-substitution

: \int ln^{2} (u) d u

= \int ln^{2} (u) d u

Apply Integration By Parts

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

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

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

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

Substitute back

u = x - 9

= (x - 9) ln^{2} (x - 9) - 2 ((x - 9) ln (x - 9) - (x - 9))

Expand

(x - 9) ln (x - 9) - (x - 9) : x ln (x - 9) - 9 ln (x - 9) - x + 9

= ln^{2} (x - 9) (x - 9) - 2 (x ln (x - 9) - 9 ln (x - 9) - x + 9)

Add a constant to the solution

= ln^{2} (x - 9) (x - 9) - 2 (x ln (x - 9) - 9 ln (x - 9) - x + 9) + C

ln (x^{2}) - \frac{1}{x ^{2}} - 5

y^{3} = 126 - x^{3}, at x = 5

\frac{d}{d x} (2^{3} e^{2})

\int \frac{x ^{2}}{a x ^{2} - b} d x

\frac{d}{d x} (arctan^{2} (6 x))

What is the integral of ln^2(x-9) ?
The integral of ln^2(x-9) is ln^2(x-9)(x-9)-2(xln(x-9)-9ln(x-9)-x+9)+C