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Beliebt Rechnen >

integral of (4+x^2)/(x^3)

Lösung

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

Lösung

- \frac{2}{x ^{2}} + ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{4 + x ^{2}}{x ^{3}} : \frac{4}{x ^{3}} + \frac{1}{x}

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{2}{x ^{2}} + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{x ^{2}} + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

(dQ)/(dt)=3-(3Q)/(1000)

\frac{d Q}{d t} = 3 - \frac{3 Q}{1000}

limit as x approaches-1 of sqrt(|x|-x)

x \to - 1 lim (∣ x ∣ - x)

(2x+5)y^'+10y=10(2x+5)

(2 x + 5) y^{^{'}} + 10 y = 10 (2 x + 5)

sum from n=0 to infinity of 3/(5^n)

n = 0 \sum \infty \frac{3}{5 ^{n}}

integral of (x^2-2x)

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