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

Lösung

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

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int u - 1 d u

Wende die Summenregel an:

\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

Setze in

u = x - 2

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

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

t an g e n t f (x) = 9 - x, at x = 0

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

in v erse l a pl a ce \frac{6}{s ^{2} ( 7 s + 1 )}

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