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Beliebt Rechnen >

integral of x^2(5x-3)

Lösung

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

Lösung

\frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{5 x ^{3}}{3} d x = \frac{5 x ^{4}}{12}

= \frac{1}{3} x^{3} (5 x - 3) - \frac{5 x ^{4}}{12}

Multipliziere aus

\frac{1}{3} x^{3} (5 x - 3) : \frac{5}{3} x^{4} - x^{3}

= \frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{3} x^{4} - x^{3} - \frac{5 x ^{4}}{12} + C

Graph

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