integral of (3-x)/(2x+1)

Lösung

\int \frac{3 - x}{2 x + 1} d x

- \frac{1}{2} x + \frac{7}{4} ln ∣ 2 x + 1 ∣ + C

Schritte zur Lösung

\int \frac{3 - x}{2 x + 1} d x

Lange Division

\frac{3 - x}{2 x + 1} : - \frac{1}{2} + \frac{7}{2 ( 2 x + 1 )}

= \int - \frac{1}{2} + \frac{7}{2 ( 2 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{1}{2} d x + \int \frac{7}{2 ( 2 x + 1 )} d x

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

\int \frac{7}{2 ( 2 x + 1 )} d x = \frac{7}{4} ln ∣ 2 x + 1 ∣

= - \frac{1}{2} x + \frac{7}{4} ln ∣ 2 x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} x + \frac{7}{4} ln ∣ 2 x + 1 ∣ + C

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