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

The integral of (x-2)ln(x) is ln(x)((x^2)/2-2x)-1/2 ((x^2)/2-4x)+C

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integral of (x-2)ln(x)

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

ln (x) (\frac{x ^{2}}{2} - 2 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 4 x) + C

Solution steps

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

Apply Integration By Parts

: ln (x) (\frac{x ^{2}}{2} - 2 x) - \int \frac{1}{2} (x - 4) d x

= ln (x) (\frac{x ^{2}}{2} - 2 x) - \int \frac{1}{2} (x - 4) d x

\int \frac{1}{2} (x - 4) d x = \frac{1}{2} (\frac{x ^{2}}{2} - 4 x)

= ln (x) (\frac{x ^{2}}{2} - 2 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 4 x)

Add a constant to the solution

= ln (x) (\frac{x ^{2}}{2} - 2 x) - \frac{1}{2} (\frac{x ^{2}}{2} - 4 x) + C

4 x^{2} + y^{2} = 25, (2, 3)

70 x^{- 5}

\int \frac{x ^{2}}{( a + b x ^{3} ) ^{2}} d x

x \to 0 + lim ((tan (7 x))^{x})

(2 y^{2} + 3 x) d x + 4 x y d y = 0

What is the integral of (x-2)ln(x) ?
The integral of (x-2)ln(x) is ln(x)((x^2)/2-2x)-1/2 ((x^2)/2-4x)+C