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Beliebt Rechnen >

integral of (x^4+10x^3)/(2x^2)

Lösung

\int \frac{x ^{4} + 10 x ^{3}}{2 x ^{2}} d x

Lösung

\frac{1}{2} (\frac{x ^{3}}{3} + 5 x^{2}) + C

Schritte zur Lösung

\int \frac{x ^{4} + 10 x ^{3}}{2 x ^{2}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{x ^{4} + 10 x ^{3}}{x ^{2}} d x

\frac{x ^{4} + 10 x ^{3}}{x ^{2}} = x^{2} + 10 x

= \frac{1}{2} \cdot \int x^{2} + 10 x 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

= \frac{1}{2} (\int x^{2} d x + \int 10 x d x)

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

\int 10 x d x = 5 x^{2}

= \frac{1}{2} (\frac{x ^{3}}{3} + 5 x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (\frac{x ^{3}}{3} + 5 x^{2}) + C

Graph

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