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Beliebt Rechnen >

integral of ((x+4))/((x+1)^2)

Lösung

\int \frac{( x + 4 )}{( x + 1 ) ^{2}} d x

Lösung

ln ∣ x + 1 ∣ - \frac{3}{x + 1} + C

Schritte zur Lösung

\int \frac{x + 4}{( x + 1 ) ^{2}} d x

Wende U-Substitution an

= \int \frac{u + 3}{u ^{2}} d u

Multipliziere aus

\frac{u + 3}{u ^{2}} : \frac{1}{u} + \frac{3}{u ^{2}}

= \int \frac{1}{u} + \frac{3}{u ^{2}} 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 \frac{1}{u} d u + \int \frac{3}{u ^{2}} d u

\int \frac{1}{u} d u = ln ∣ u ∣

\int \frac{3}{u ^{2}} d u = - \frac{3}{u}

= ln ∣ u ∣ - \frac{3}{u}

Setze in

u = x + 1

ein

= ln ∣ x + 1 ∣ - \frac{3}{x + 1}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ - \frac{3}{x + 1} + C

Graph

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