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Beliebt Rechnen >

integral of sqrt(x)+1/x

Lösung

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

Lösung

\frac{2}{3} x^{\frac{3}{2}} + ln ∣ x ∣ + C

Schritte zur Lösung

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{2}{3} x^{\frac{3}{2}} + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (5x-(x^3)/2+(ARyx^2)/2+C)

\int (5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C) d x

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\int \frac{8}{x ^{3} + 4 x} d x

integral of tan^5(x/3)

\int tan^{5} (\frac{x}{3}) d x

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\int x^{3} ln (9 x) d x

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