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Beliebt Rechnen >

integral of (2x^2+6sqrt(x)-5x)/(3x^2)

Lösung

\int \frac{2 x ^{2} + 6 x - 5 x}{3 x ^{2}} d x

Lösung

\frac{1}{3} (2 x - \frac{12}{x} - 5 ln ∣ x ∣) + C

Schritte zur Lösung

\int \frac{2 x ^{2} + 6 x - 5 x}{3 x ^{2}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{2 x ^{2} + 6 x - 5 x}{x ^{2}} d x

Multipliziere aus

\frac{2 x ^{2} + 6 x - 5 x}{x ^{2}} : 2 + \frac{6}{x ^{\frac{3}{2}}} - \frac{5}{x}

= \frac{1}{3} \cdot \int 2 + \frac{6}{x ^{\frac{3}{2}}} - \frac{5}{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

= \frac{1}{3} (\int 2 d x + \int \frac{6}{x ^{\frac{3}{2}}} d x - \int \frac{5}{x} d x)

\int 2 d x = 2 x

\int \frac{6}{x ^{\frac{3}{2}}} d x = - \frac{12}{x}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{1}{3} (2 x - \frac{12}{x} - 5 ln ∣ x ∣)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (2 x - \frac{12}{x} - 5 ln ∣ x ∣) + C

Graph

Beliebte Beispiele

derivative y=-csc(x)-cos(x)

d er i v a t i v e y = - csc (x) - cos (x)

2 y^{^{''}} + 8 y = 0

integral from-infinity to-1 of e^{2x}

\int_{- \infty}^{- 1} e^{2 x} d x

integral of 6x^2-3x^3

\int 6 x^{2} - 3 x^{3} d x

fläche x+y=7,x=0,y=0

a re a x + y = 7, x = 0, y = 0