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Beliebt Rechnen >

integral of (1-u^2)/(u+u^3)

Lösung

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

Lösung

ln ∣ u ∣ - ln u^{2} + 1 + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{u} d u = ln ∣ u ∣

\int \frac{2 u}{u ^{2} + 1} d u = ln u^{2} + 1

= ln ∣ u ∣ - ln u^{2} + 1

Füge eine Konstante zur Lösung hinzu

= ln ∣ u ∣ - ln u^{2} + 1 + C

Graph

Beliebte Beispiele

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