integral of (2+cos(x))/x

Lösung

\int \frac{2 + cos ( x )}{x} d x

2 ln ∣ x ∣ + Ci (x) + C

Schritte zur Lösung

\int \frac{2 + cos ( x )}{x} d x

Multipliziere aus

\frac{2 + cos ( x )}{x} : \frac{2}{x} + \frac{cos ( x )}{x}

= \int \frac{2}{x} + \frac{cos ( x )}{x} d x

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{2}{x} d x + \int \frac{cos ( x )}{x} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{cos ( x )}{x} d x = Ci (x)

= 2 ln ∣ x ∣ + Ci (x)

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + Ci (x) + C

\frac{d}{d j} (6 i + 8 j)

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