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Beliebt Rechnen >

integral of x(9x^2-5)^{3/2}

Lösung

\int x (9 x^{2} - 5)^{\frac{3}{2}} d x

Lösung

\frac{1}{45} (9 x^{2} - 5)^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (9 x^{2} - 5)^{\frac{3}{2}} d x

Wende U-Substitution an

= \int \frac{u ^{\frac{3}{2}}}{18} d u

Entferne die Konstante:

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

= \frac{1}{18} \cdot \int u^{\frac{3}{2}} d u

Wende die Potenzregel an

= \frac{1}{18} \cdot \frac{2}{5} u^{\frac{5}{2}}

Setze in

u = 9 x^{2} - 5

ein

= \frac{1}{18} \cdot \frac{2}{5} (9 x^{2} - 5)^{\frac{5}{2}}

Vereinfache

\frac{1}{18} \cdot \frac{2}{5} (9 x^{2} - 5)^{\frac{5}{2}} : \frac{1}{45} (9 x^{2} - 5)^{\frac{5}{2}}

= \frac{1}{45} (9 x^{2} - 5)^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{45} (9 x^{2} - 5)^{\frac{5}{2}} + C

Graph

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