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Beliebt Rechnen >

integral of (5x+4)\sqrt[5]{1+8x+5x^2}

Lösung

\int (5 x + 4) 5 1 + 8 x + 5 x^{2} d x

Lösung

\frac{5}{12} (1 + 8 x + 5 x^{2})^{\frac{6}{5}} + C

Schritte zur Lösung

\int (5 x + 4) 5 1 + 8 x + 5 x^{2} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int 5 u d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{5}{6} u^{\frac{6}{5}}

Setze in

u = 1 + 8 x + 5 x^{2}

ein

= \frac{1}{2} \cdot \frac{5}{6} (1 + 8 x + 5 x^{2})^{\frac{6}{5}}

Vereinfache

\frac{1}{2} \cdot \frac{5}{6} (1 + 8 x + 5 x^{2})^{\frac{6}{5}} : \frac{5}{12} (1 + 8 x + 5 x^{2})^{\frac{6}{5}}

= \frac{5}{12} (1 + 8 x + 5 x^{2})^{\frac{6}{5}}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{12} (1 + 8 x + 5 x^{2})^{\frac{6}{5}} + C

Graph

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