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Beliebt Rechnen >

integral of sqrt(x)(14x^2+x)

Lösung

\int x (14 x^{2} + x) d x

Lösung

4 x^{\frac{7}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (14 x^{2} + x) d x

Multipliziere aus

x (14 x^{2} + x) : 14 x^{\frac{5}{2}} + x^{\frac{3}{2}}

= \int 14 x^{\frac{5}{2}} + 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 14 x^{\frac{5}{2}} d x + \int x^{\frac{3}{2}} d x

\int 14 x^{\frac{5}{2}} d x = 4 x^{\frac{7}{2}}

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

= 4 x^{\frac{7}{2}} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 4 x^{\frac{7}{2}} + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

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