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Beliebt Rechnen >

integral of (x^2+sqrt(x)+1/x)

Lösung

\int (x^{2} + x + \frac{1}{x}) d x

Lösung

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

Schritte zur Lösung

\int x^{2} + 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^{2} d x + \int x d x + \int \frac{1}{x} d x

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative f(x)=5x^2-5x+9

d er i v a t i v e f (x) = 5 x^{2} - 5 x + 9

derivative of-9x^3+27x+7x-66

\frac{d}{d x} (- 9 x^{3} + 27 x + 7 x - 66)

tangent 3sqrt(x),\at x=4

t an g e n t 3 x, at x = 4

integral of 5tan^3(x)sec^3(x)

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

integral from 1 to 4 of 1/(sqrt(x))

\int_{1}^{4} \frac{1}{x} d x