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Beliebt Rechnen >

integral of (z^4)/(\sqrt[3]{7+z^5)}

Lösung

\int \frac{z ^{4}}{3 7 + z ^{5}} d z

Lösung

\frac{3}{10} (7 + z^{5})^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{z ^{4}}{3 7 + z ^{5}} d z

Wende U-Substitution an

= \int \frac{1}{5 3 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int \frac{1}{3 u} d u

Wende die Potenzregel an

= \frac{1}{5} \cdot \frac{3}{2} u^{\frac{2}{3}}

Setze in

u = 7 + z^{5}

ein

= \frac{1}{5} \cdot \frac{3}{2} (7 + z^{5})^{\frac{2}{3}}

Vereinfache

\frac{1}{5} \cdot \frac{3}{2} (7 + z^{5})^{\frac{2}{3}} : \frac{3}{10} (7 + z^{5})^{\frac{2}{3}}

= \frac{3}{10} (7 + z^{5})^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{10} (7 + z^{5})^{\frac{2}{3}} + C

Graph

Beliebte Beispiele

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