What is the integral of (x^2-5x+6)/(x-2) ?

The integral of (x^2-5x+6)/(x-2) is 1/2 (x-2)^2-x+2+C

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integral of (x^2-5x+6)/(x-2)

\int \frac{x ^{2} - 5 x + 6}{x - 2} d x

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

Solution steps

\int \frac{x ^{2} - 5 x + 6}{x - 2} d x

Apply u-substitution

: \int u - 1 d u

= \int u - 1 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u - \int 1 d u

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

\int 1 d u = u

= \frac{u ^{2}}{2} - u

Substitute back

u = x - 2

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

Simplify

\frac{( x - 2 ) ^{2}}{2} - (x - 2) : \frac{1}{2} (x - 2)^{2} - x + 2

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

Add a constant to the solution

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

\int \frac{( x + 5 )}{3 x + 9} d x

f (x) = 9 - x, at x = 0

x \to - 1 lim (3 x^{2} + 2 x - 1)

\frac{6}{s ^{2} ( 7 s + 1 )}

\int 10 x (4 x^{2} - 1)^{9} d x

What is the integral of (x^2-5x+6)/(x-2) ?
The integral of (x^2-5x+6)/(x-2) is 1/2 (x-2)^2-x+2+C