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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2}{3} u^{\frac{3}{2}} - \frac{4}{5} u^{\frac{5}{2}} + C

Schritte zur Lösung

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

Multipliziere aus

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

\int \frac{u}{u} d u = \frac{2}{3} u^{\frac{3}{2}}

\int \frac{2 u ^{2}}{u} d u = \frac{4}{5} u^{\frac{5}{2}}

= \frac{2}{3} u^{\frac{3}{2}} - \frac{4}{5} u^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} u^{\frac{3}{2}} - \frac{4}{5} u^{\frac{5}{2}} + C

Graph

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\int_{- \infty}^{15} r e^{\frac{r}{5}} d r

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