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Beliebt Rechnen >

integral ((3x+10))/((x-2))

Lösung

integral

\frac{( 3 x + 10 )}{( x - 2 )}

Lösung

3 (x - 2) + 16 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{3 x + 10}{x - 2} d x

Wende U-Substitution an

= \int \frac{3 u + 16}{u} d u

Multipliziere aus

\frac{3 u + 16}{u} : 3 + \frac{16}{u}

= \int 3 + \frac{16}{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 3 d u + \int \frac{16}{u} d u

\int 3 d u = 3 u

\int \frac{16}{u} d u = 16 ln ∣ u ∣

= 3 u + 16 ln ∣ u ∣

Setze in

u = x - 2

ein

= 3 (x - 2) + 16 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= 3 (x - 2) + 16 ln ∣ x - 2 ∣ + C

Graph

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