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Beliebt Rechnen >

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

Lösung

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

Lösung

x + 2 ln ∣ x ∣ - \frac{1}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= x + 2 ln ∣ x ∣ - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= x + 2 ln ∣ x ∣ - \frac{1}{x} + C

Graph

Beliebte Beispiele

derivative f(x)=ln((20+2x)^4)

d er i v a t i v e f (x) = ln ((20 + 2 x)^{4})

y^'=0.05y-48000

y^{^{'}} = 0.05 y - 48000

integral of (cos(pi/(x^{12)}))/(x^{13)}

\int \frac{cos ( \frac{π}{x ^{12}} )}{x ^{13}} d x

derivative sqrt(4(x+2)^3)

d er i v a t i v e 4 (x + 2)^{3}

integral of a/(s^2-a^2)

\int \frac{a}{s ^{2} - a ^{2}} d s