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Beliebt Rechnen >

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

Lösung

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

Lösung

x + ln ∣ x ∣ + \frac{6}{x} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( x - 2 ) ( x + 3 )}{x ^{2}} : 1 + \frac{1}{x} - \frac{6}{x ^{2}}

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= x + ln ∣ x ∣ - (- \frac{6}{x})

Vereinfache

= x + ln ∣ x ∣ + \frac{6}{x}

Füge eine Konstante zur Lösung hinzu

= x + ln ∣ x ∣ + \frac{6}{x} + C

Graph

Beliebte Beispiele

derivative of 7sqrt(2)cos(x)

\frac{d}{d x} (72 cos (x))

extreme f(w)= w/(w+d/w)

e x t re m e f (w) = \frac{w}{w + \frac{d}{w}}

integral of x/(\sqrt[3]{x+2)}

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

(\partial)/(\partial x)(x^3+4x^2y+2y^3)

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 2 y^{3})

tangent f(x)= 2/(x-1),(3,1)

t an g e n t f (x) = \frac{2}{x - 1}, (3, 1)