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Beliebt Rechnen >

integral of (5x-3)/(x+1)

Lösung

\int \frac{5 x - 3}{x + 1} d x

Lösung

5 (x + 1) - 8 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{5 x - 3}{x + 1} d x

Wende U-Substitution an

= \int \frac{5 u - 8}{u} d u

Multipliziere aus

\frac{5 u - 8}{u} : 5 - \frac{8}{u}

= \int 5 - \frac{8}{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 5 d u - \int \frac{8}{u} d u

\int 5 d u = 5 u

\int \frac{8}{u} d u = 8 ln ∣ u ∣

= 5 u - 8 ln ∣ u ∣

Setze in

u = x + 1

ein

= 5 (x + 1) - 8 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 5 (x + 1) - 8 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

derivative f(x)= 4/(3x^2)

d er i v a t i v e f (x) = \frac{4}{3 x ^{2}}

integral of (x^2e^x)/((x+2)^2)

\int \frac{x ^{2} e ^{x}}{( x + 2 ) ^{2}} d x

integral of-(18)/(x^{19)}

\int - \frac{18}{x ^{19}} d x

(dx)/(dt)-x/(t-1)=t^2+2

\frac{d x}{d t} - \frac{x}{t - 1} = t^{2} + 2

limit as x approaches 0 of ((1+x)^2-1)/x

x \to 0 lim (\frac{( 1 + x ) ^{2} - 1}{x})