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Beliebt Rechnen >

integral of sqrt(1-4x)

Lösung

\int 1 - 4 x d x

Lösung

- \frac{1}{6} (1 - 4 x)^{\frac{3}{2}} + C

Schritte zur Lösung

\int 1 - 4 x d x

Wende U-Substitution an

= \int - \frac{u}{4} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{4} \cdot \int u d u

Wende die Potenzregel an

= - \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 1 - 4 x

ein

= - \frac{1}{4} \cdot \frac{2}{3} (1 - 4 x)^{\frac{3}{2}}

Vereinfache

- \frac{1}{4} \cdot \frac{2}{3} (1 - 4 x)^{\frac{3}{2}} : - \frac{1}{6} (1 - 4 x)^{\frac{3}{2}}

= - \frac{1}{6} (1 - 4 x)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6} (1 - 4 x)^{\frac{3}{2}} + C

Graph

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