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Beliebt Rechnen >

integral of (4-7x)\sqrt[3]{x}

Lösung

\int (4 - 7 x) 3 x d x

Lösung

3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}} + C

Schritte zur Lösung

\int (4 - 7 x) 3 x d x

Wende die partielle Integration an

= 3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - \int - \frac{21}{4} x^{\frac{4}{3}} d x

\int - \frac{21}{4} x^{\frac{4}{3}} d x = - \frac{9}{4} x^{\frac{7}{3}}

= 3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - (- \frac{9}{4} x^{\frac{7}{3}})

Vereinfache

3 x^{\frac{4}{3}} - \frac{21}{4} x^{\frac{7}{3}} - (- \frac{9}{4} x^{\frac{7}{3}}) : 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}}

= 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}}

Füge eine Konstante zur Lösung hinzu

= 3 x^{\frac{4}{3}} - 3 x^{\frac{7}{3}} + C

Graph

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