integral of (-7/(x-4)+6/(x-3))

Lösung

\int (- \frac{7}{x - 4} + \frac{6}{x - 3}) d x

- 7 ln ∣ x - 4 ∣ + 6 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int - \frac{7}{x - 4} + \frac{6}{x - 3} 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{7}{x - 4} d x + \int \frac{6}{x - 3} d x

\int \frac{7}{x - 4} d x = 7 ln ∣ x - 4 ∣

\int \frac{6}{x - 3} d x = 6 ln ∣ x - 3 ∣

= - 7 ln ∣ x - 4 ∣ + 6 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - 7 ln ∣ x - 4 ∣ + 6 ln ∣ x - 3 ∣ + C

\int \frac{( lo g _{e} ( x ) ) ^{2}}{x} d x

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