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Beliebt Rechnen >

integral of (x^2-17x+4)/(x+7)

Lösung

\int \frac{x ^{2} - 17 x + 4}{x + 7} d x

Lösung

\frac{( x + 7 ) ^{2}}{2} - 31 (x + 7) + 172 ln ∣ x + 7 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} - 17 x + 4}{x + 7} d x

Wende U-Substitution an

= \int \frac{u ^{2} - 31 u + 172}{u} d u

Multipliziere aus

\frac{u ^{2} - 31 u + 172}{u} : u - 31 + \frac{172}{u}

= \int u - 31 + \frac{172}{u} 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 31 d u + \int \frac{172}{u} d u

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

\int 31 d u = 31 u

\int \frac{172}{u} d u = 172 ln ∣ u ∣

= \frac{u ^{2}}{2} - 31 u + 172 ln ∣ u ∣

Setze in

u = x + 7

ein

= \frac{( x + 7 ) ^{2}}{2} - 31 (x + 7) + 172 ln ∣ x + 7 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( x + 7 ) ^{2}}{2} - 31 (x + 7) + 172 ln ∣ x + 7 ∣ + C

Graph

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