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Beliebt Rechnen >

integral of x(5x^2+x^{1/2})

Lösung

\int x (5 x^{2} + x^{\frac{1}{2}}) d x

Lösung

\frac{5 x ^{4}}{4} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (5 x^{2} + x^{\frac{1}{2}}) d x

Multipliziere aus

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

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

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{5 x ^{4}}{4} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{4}}{4} + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

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