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Beliebt Rechnen >

integral of x^3sqrt(1+(3x^2)^2)

Lösung

\int x^{3} 1 + (3 x^{2})^{2} d x

Lösung

\frac{1}{54} (1 + 9 x^{4})^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{3} 1 + (3 x^{2})^{2} d x

Wende U-Substitution an

= \int \frac{u}{36} d u

Entferne die Konstante:

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

= \frac{1}{36} \cdot \int u d u

Wende die Potenzregel an

= \frac{1}{36} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 1 + (3 x^{2})^{2}

ein

= \frac{1}{36} \cdot \frac{2}{3} (1 + (3 x^{2})^{2})^{\frac{3}{2}}

Vereinfache

\frac{1}{36} \cdot \frac{2}{3} (1 + (3 x^{2})^{2})^{\frac{3}{2}} : \frac{1}{54} (1 + 9 x^{4})^{\frac{3}{2}}

= \frac{1}{54} (1 + 9 x^{4})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{54} (1 + 9 x^{4})^{\frac{3}{2}} + C

Graph

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