integral of (x+5)/(x+4)

Lösung

\int \frac{x + 5}{x + 4} d x

ln ∣ x + 4 ∣ + x + C

Schritte zur Lösung

\int \frac{x + 5}{x + 4} d x

\frac{x + 5}{x + 4} = \frac{1}{x + 4} + 1

= \int \frac{1}{x + 4} + 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}{x + 4} d x + \int 1 d x

\int \frac{1}{x + 4} d x = ln ∣ x + 4 ∣

\int 1 d x = x

= ln ∣ x + 4 ∣ + x

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 4 ∣ + x + C

\int (x^{2} + 8) (x - 8) d x

\int \frac{2 x ^{4} - x ^{3} - x + 1}{x ^{3} - 1} d x

\int \frac{30}{2 x + 4} d x

\int x (2 x - 5)^{5} d x

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