integral of (-3/(x+2)-4/(x+5))

Lösung

\int (- \frac{3}{x + 2} - \frac{4}{x + 5}) d x

- 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣ + C

Schritte zur Lösung

\int - \frac{3}{x + 2} - \frac{4}{x + 5} 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{3}{x + 2} d x - \int \frac{4}{x + 5} d x

\int \frac{3}{x + 2} d x = 3 ln ∣ x + 2 ∣

\int \frac{4}{x + 5} d x = 4 ln ∣ x + 5 ∣

= - 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣

Füge eine Konstante zur Lösung hinzu

= - 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣ + C

\int \frac{1}{sin ^{2} ( 3 x )} + 3 d x

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\int (x + 17) 34 x + x^{2} d x

\int \frac{2}{( x - 3 ) ^{4}} d x