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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{8}{5} x^{\frac{5}{2}} - \frac{8}{7} x^{\frac{7}{2}} + C

Schritte zur Lösung

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

Multipliziere aus

x^{\frac{3}{2}} (4 - 4 x) : 4 x^{\frac{3}{2}} - 4 x^{\frac{5}{2}}

= \int 4 x^{\frac{3}{2}} - 4 x^{\frac{5}{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 4 x^{\frac{3}{2}} d x - \int 4 x^{\frac{5}{2}} d x

\int 4 x^{\frac{3}{2}} d x = \frac{8}{5} x^{\frac{5}{2}}

\int 4 x^{\frac{5}{2}} d x = \frac{8}{7} x^{\frac{7}{2}}

= \frac{8}{5} x^{\frac{5}{2}} - \frac{8}{7} x^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{8}{5} x^{\frac{5}{2}} - \frac{8}{7} x^{\frac{7}{2}} + C

Graph

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