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Beliebt Rechnen >

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

Lösung

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

Lösung

x - 3 ln ∣ x ∣ - \frac{2}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d x = x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

= x - 3 ln ∣ x ∣ - \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

= x - 3 ln ∣ x ∣ - \frac{2}{x} + C

Graph

Beliebte Beispiele

derivative of-6/((x-1^4))

\frac{d}{d x} (- \frac{6}{( x - 1 ) ^{4}})

integral of e^{x-2x}sin(x)

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

y^{''}+4y^'+4y=x^2+e^{-2x}

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} + e^{- 2 x}

integral from 0 to 4 of 1/((x-4)^2)

\int_{0}^{4} \frac{1}{( x - 4 ) ^{2}} d x

integral of (4-ln(x+3))/(x+3)

\int \frac{4 - ln ( x + 3 )}{x + 3} d x