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Beliebt Rechnen >

integral of ((sqrt(x)-5)^2-x)^2

Lösung

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

Lösung

50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x + C

Schritte zur Lösung

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

Multipliziere aus

(x - 5)^{2} - x : - 10 x + 25

= \int (- 10 x + 25)^{2} d x

Multipliziere aus

(- 10 x + 25)^{2} : 100 x - 500 x + 625

= \int 100 x - 500 x + 625 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 100 x d x - \int 500 x d x + \int 625 d x

\int 100 x d x = 50 x^{2}

\int 500 x d x = \frac{1000}{3} x^{\frac{3}{2}}

\int 625 d x = 625 x

= 50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x

Füge eine Konstante zur Lösung hinzu

= 50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x + C

Graph

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