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Beliebt Rechnen >

integral of 10-(14-2(16-2x)^{1/2})

Lösung

\int 10 - (14 - 2 (16 - 2 x)^{\frac{1}{2}}) d x

Lösung

- \frac{2}{3} (16 - 2 x)^{\frac{3}{2}} + 2 (16 - 2 x) + C

Schritte zur Lösung

\int 10 - (14 - 2 (16 - 2 x)^{\frac{1}{2}}) d x

Wende U-Substitution an

= \int - u^{\frac{1}{2}} + 2 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int u^{\frac{1}{2}} d u + \int 2 d u

\int u^{\frac{1}{2}} d u = \frac{2}{3} u^{\frac{3}{2}}

\int 2 d u = 2 u

= - \frac{2}{3} u^{\frac{3}{2}} + 2 u

Setze in

u = 16 - 2 x

ein

= - \frac{2}{3} (16 - 2 x)^{\frac{3}{2}} + 2 (16 - 2 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{3} (16 - 2 x)^{\frac{3}{2}} + 2 (16 - 2 x) + C

Graph

Beliebte Beispiele

integral of x^4-8x^2+16

\int x^{4} - 8 x^{2} + 16 d x

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x \to - 3 lim (\frac{x}{( x + 3 ) ^{4}})

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y^{^{''}} - k y = k x e^{- x}

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