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

Lösung

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

2 ln ∣ x ∣ + 2 x + x + C

Schritte zur Lösung

\int \frac{2 + x + x}{x} d x

Multipliziere aus

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

= \int \frac{2}{x} + \frac{1}{x} + 1 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{1}{x} d x + \int 1 d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{1}{x} d x = 2 x

\int 1 d x = x

= 2 ln ∣ x ∣ + 2 x + x

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + 2 x + x + C

\int \frac{3 x + 2}{x ^{2} - 3 x + 2} d x

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