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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x + 2 ∣ + \frac{1}{x + 2} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 1}{x ^{2} + 4 x + 4} : \frac{x}{x ^{2} + 4 x + 4} + \frac{1}{x ^{2} + 4 x + 4}

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

\int \frac{x}{x ^{2} + 4 x + 4} d x = ln ∣ x + 2 ∣ + \frac{2}{x + 2}

\int \frac{1}{x ^{2} + 4 x + 4} d x = - \frac{1}{x + 2}

= ln ∣ x + 2 ∣ + \frac{2}{x + 2} - \frac{1}{x + 2}

Vereinfache

= ln ∣ x + 2 ∣ + \frac{1}{x + 2}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 2 ∣ + \frac{1}{x + 2} + C

Graph

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