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Beliebt Rechnen >

integral of (2x^{5/2}-8x^2)x^{-5/2}

Lösung

\int (2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} d x

Lösung

2 x - 16 x^{\frac{1}{2}} + C

Schritte zur Lösung

\int (2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} d x

Vereinfache

(2 x^{\frac{5}{2}} - 8 x^{2}) x^{- \frac{5}{2}} : \frac{2 x ^{\frac{5}{2}} - 8 x ^{2}}{x ^{\frac{5}{2}}}

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

Multipliziere aus

\frac{2 x ^{\frac{5}{2}} - 8 x ^{2}}{x ^{\frac{5}{2}}} : 2 - \frac{8}{x ^{\frac{1}{2}}}

= \int 2 - \frac{8}{x ^{\frac{1}{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 2 d x - \int \frac{8}{x ^{\frac{1}{2}}} d x

\int 2 d x = 2 x

\int \frac{8}{x ^{\frac{1}{2}}} d x = 16 x^{\frac{1}{2}}

= 2 x - 16 x^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 x - 16 x^{\frac{1}{2}} + C

Graph

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