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

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

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integral of 3(2x-2)ln(x-2)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

\int x d x = \frac{x ^{2}}{2}

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

Add a constant to the solution

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

\int 3 x + 1 d x

a re a x^{2} - 4 x + 1, - x + 5

x \to 2 lim (15)

x + y \cdot y^{^{'}} = 0

t an g e n t f (x) = (3 x - 1)^{2}, at x = 1

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