integral of x(5x^2-7)^{9/2}

Lösung

\int x (5 x^{2} - 7)^{\frac{9}{2}} d x

\frac{1}{55} (5 x^{2} - 7)^{\frac{11}{2}} + C

Schritte zur Lösung

\int x (5 x^{2} - 7)^{\frac{9}{2}} d x

Wende U-Substitution an

= \int \frac{u ^{\frac{9}{2}}}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int u^{\frac{9}{2}} d u

Wende die Potenzregel an

= \frac{1}{10} \cdot \frac{2}{11} u^{\frac{11}{2}}

Setze in

u = 5 x^{2} - 7

ein

= \frac{1}{10} \cdot \frac{2}{11} (5 x^{2} - 7)^{\frac{11}{2}}

Vereinfache

\frac{1}{10} \cdot \frac{2}{11} (5 x^{2} - 7)^{\frac{11}{2}} : \frac{1}{55} (5 x^{2} - 7)^{\frac{11}{2}}

= \frac{1}{55} (5 x^{2} - 7)^{\frac{11}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{55} (5 x^{2} - 7)^{\frac{11}{2}} + C

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