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Beliebt Rechnen >

integral of (2z-3)/(7z-10)

Lösung

\int \frac{2 z - 3}{7 z - 10} d z

Lösung

\frac{2}{7} z - \frac{20}{49} - \frac{1}{49} ln ∣ 7 z - 10 ∣ + C

Schritte zur Lösung

\int \frac{2 z - 3}{7 z - 10} d z

Multipliziere aus

\frac{2 z - 3}{7 z - 10} : \frac{2 z}{7 z - 10} - \frac{3}{7 z - 10}

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 z}{7 z - 10} d z - \int \frac{3}{7 z - 10} d z

\int \frac{2 z}{7 z - 10} d z = \frac{2}{49} (7 z - 10 + 10 ln ∣ 7 z - 10 ∣)

\int \frac{3}{7 z - 10} d z = \frac{3}{7} ln ∣ 7 z - 10 ∣

= \frac{2}{49} (7 z - 10 + 10 ln ∣ 7 z - 10 ∣) - \frac{3}{7} ln ∣ 7 z - 10 ∣

Vereinfache

\frac{2}{49} (7 z - 10 + 10 ln ∣ 7 z - 10 ∣) - \frac{3}{7} ln ∣ 7 z - 10 ∣ : \frac{2}{7} z - \frac{20}{49} - \frac{1}{49} ln ∣ 7 z - 10 ∣

= \frac{2}{7} z - \frac{20}{49} - \frac{1}{49} ln ∣ 7 z - 10 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{2}{7} z - \frac{20}{49} - \frac{1}{49} ln ∣ 7 z - 10 ∣ + C

Graph

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