integral of (8+sqrt(x)+x)/x

Lösung

\int \frac{8 + x + x}{x} d x

8 ln ∣ x ∣ + 2 x + x + C

Schritte zur Lösung

\int \frac{8 + x + x}{x} d x

Multipliziere aus

\frac{8 + x + x}{x} : \frac{8}{x} + \frac{1}{x} + 1

= \int \frac{8}{x} + \frac{1}{x} + 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{8}{x} d x + \int \frac{1}{x} d x + \int 1 d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int \frac{1}{x} d x = 2 x

\int 1 d x = x

= 8 ln ∣ x ∣ + 2 x + x

Füge eine Konstante zur Lösung hinzu

= 8 ln ∣ x ∣ + 2 x + x + C

x \to 1 - lim (arcsin (x))

x \to \frac{π}{3} lim (sin (3 x))

x \to \infty lim (x^{2} - 3)

d er i v a t i v e 7 x^{4}

\int (sin (x))^{3} (cos (x))^{2} d x