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

Lösung

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

\frac{1}{4} (x + 1 - ln (4 ∣ x + 1 ∣)) + \frac{3}{4} ln ∣ 4 x + 4 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 3}{4 x + 4} : \frac{x}{4 x + 4} + \frac{3}{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}{4 x + 4} d x + \int \frac{3}{4 x + 4} d x

\int \frac{x}{4 x + 4} d x = \frac{1}{4} (x + 1 - ln (4 ∣ x + 1 ∣))

\int \frac{3}{4 x + 4} d x = \frac{3}{4} ln ∣ 4 x + 4 ∣

= \frac{1}{4} (x + 1 - ln (4 ∣ x + 1 ∣)) + \frac{3}{4} ln ∣ 4 x + 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} (x + 1 - ln (4 ∣ x + 1 ∣)) + \frac{3}{4} ln ∣ 4 x + 4 ∣ + C

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