integral of 1/x-1/(x+6)

Lösung

\int \frac{1}{x} - \frac{1}{x + 6} d x

ln ∣ x ∣ - ln ∣ x + 6 ∣ + C

Schritte zur Lösung

\int \frac{1}{x} - \frac{1}{x + 6} 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} d x - \int \frac{1}{x + 6} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{1}{x + 6} d x = ln ∣ x + 6 ∣

= ln ∣ x ∣ - ln ∣ x + 6 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln ∣ x + 6 ∣ + C

\int y 2 + 10 y - 25 y^{2} d y

d er i v a t i v e \frac{( x + 1 ) ^{2}}{( x - 1 ) ( x + 2 )}

x \to \infty lim (x (x - x^{2} - 4))

t an g e n t 2 \frac{1}{x}, at x = 3

\int \frac{9 x ^{2} - 1}{x} d x