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Beliebt Rechnen >

integral of (x^2+2x-10)^{2/3}(5x+5)

Lösung

\int (x^{2} + 2 x - 10)^{\frac{2}{3}} (5 x + 5) d x

Lösung

\frac{3}{2} (x^{2} + 2 x - 10)^{\frac{5}{3}} + C

Schritte zur Lösung

\int (x^{2} + 2 x - 10)^{\frac{2}{3}} (5 x + 5) d x

Wende U-Substitution an

= \int \frac{5 u ^{\frac{2}{3}}}{2} d u

Entferne die Konstante:

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

= \frac{5}{2} \cdot \int u^{\frac{2}{3}} d u

Wende die Potenzregel an

= \frac{5}{2} \cdot \frac{3}{5} u^{\frac{5}{3}}

Setze in

u = x^{2} + 2 x - 10

ein

= \frac{5}{2} \cdot \frac{3}{5} (x^{2} + 2 x - 10)^{\frac{5}{3}}

Vereinfache

\frac{5}{2} \cdot \frac{3}{5} (x^{2} + 2 x - 10)^{\frac{5}{3}} : \frac{3}{2} (x^{2} + 2 x - 10)^{\frac{5}{3}}

= \frac{3}{2} (x^{2} + 2 x - 10)^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} (x^{2} + 2 x - 10)^{\frac{5}{3}} + C

Graph

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