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Beliebt Rechnen >

integral of ((4x-3))/(x+1)

Lösung

\int \frac{( 4 x - 3 )}{x + 1} d x

Lösung

4 (x + 1) - 7 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{4 x - 3}{x + 1} d x

Wende U-Substitution an

= \int \frac{4 u - 7}{u} d u

Multipliziere aus

\frac{4 u - 7}{u} : 4 - \frac{7}{u}

= \int 4 - \frac{7}{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 4 d u - \int \frac{7}{u} d u

\int 4 d u = 4 u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

= 4 u - 7 ln ∣ u ∣

Setze in

u = x + 1

ein

= 4 (x + 1) - 7 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 4 (x + 1) - 7 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches 0 of-(e^{1/x})

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

derivative f(x)=2x^2+3

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

derivative of x^{(1/3})

\frac{d}{d x} (x^{(\frac{1}{3})})

integral of (x^2)/((x+2)^2(x+4)^2)

\int \frac{x ^{2}}{( x + 2 ) ^{2} ( x + 4 ) ^{2}} d x

integral of (2x)/(x^2-2)

\int \frac{2 x}{x ^{2} - 2} d x