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Beliebt Rechnen >

integral of (3x^{1/2}+x^4)

Lösung

\int (3 x^{\frac{1}{2}} + x^{4}) d x

Lösung

2 x^{\frac{3}{2}} + \frac{x ^{5}}{5} + C

Schritte zur Lösung

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

\int 3 x^{\frac{1}{2}} d x = 2 x^{\frac{3}{2}}

\int x^{4} d x = \frac{x ^{5}}{5}

= 2 x^{\frac{3}{2}} + \frac{x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

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

Graph

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