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Beliebt Rechnen >

integral of (4x^2)/(\sqrt[3]{1-x)}

Lösung

\int \frac{4 x ^{2}}{3 1 - x} d x

Lösung

4 (- \frac{3}{2} x^{2} (1 - x)^{\frac{2}{3}} - 3 (- \frac{3}{8} (1 - x)^{\frac{8}{3}} + \frac{3}{5} (1 - x)^{\frac{5}{3}})) + C

Schritte zur Lösung

\int \frac{4 x ^{2}}{3 1 - x} d x

Entferne die Konstante:

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

= 4 \cdot \int \frac{x ^{2}}{3 1 - x} d x

Wende die partielle Integration an

= 4 (- \frac{3}{2} x^{2} (1 - x)^{\frac{2}{3}} - \int - 3 x (1 - x)^{\frac{2}{3}} d x)

\int - 3 x (1 - x)^{\frac{2}{3}} d x = 3 (- \frac{3}{8} (1 - x)^{\frac{8}{3}} + \frac{3}{5} (1 - x)^{\frac{5}{3}})

= 4 (- \frac{3}{2} x^{2} (1 - x)^{\frac{2}{3}} - 3 (- \frac{3}{8} (1 - x)^{\frac{8}{3}} + \frac{3}{5} (1 - x)^{\frac{5}{3}}))

Füge eine Konstante zur Lösung hinzu

= 4 (- \frac{3}{2} x^{2} (1 - x)^{\frac{2}{3}} - 3 (- \frac{3}{8} (1 - x)^{\frac{8}{3}} + \frac{3}{5} (1 - x)^{\frac{5}{3}})) + C

Graph

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