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Beliebt Rechnen >

integral of (u-1)/(u^2)

Lösung

\int \frac{u - 1}{u ^{2}} d u

Lösung

ln ∣ u ∣ + \frac{1}{u} + C

Schritte zur Lösung

\int \frac{u - 1}{u ^{2}} d u

Multipliziere aus

\frac{u - 1}{u ^{2}} : \frac{1}{u} - \frac{1}{u ^{2}}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{u} d u = ln ∣ u ∣

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

= ln ∣ u ∣ - (- \frac{1}{u})

Vereinfache

= ln ∣ u ∣ + \frac{1}{u}

Füge eine Konstante zur Lösung hinzu

= ln ∣ u ∣ + \frac{1}{u} + C

Graph

Beliebte Beispiele

integral from 0 to infinity of xe^{-x^2}

\int_{0}^{\infty} x e^{- x^{2}} d x

(\partial)/(\partial y)(1/(x-y))

\frac{\partial}{\partial y} (\frac{1}{x - y})

inverselaplace 2

in v erse l a pl a ce 2

tangent f(x)= 9/(x^2+5)

t an g e n t f (x) = \frac{9}{x ^{2} + 5}

taylor cos^2(x),0

t a y l or cos^{2} (x), 0