integral of x^2(2x^3+4)

Lösung

\int x^{2} (2 x^{3} + 4) d x

\frac{1}{3} x^{3} (2 x^{3} + 4) - \frac{x ^{6}}{3} + C

Schritte zur Lösung

\int x^{2} (2 x^{3} + 4) d x

Wende die partielle Integration an

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

= \frac{1}{3} x^{3} (2 x^{3} + 4) - \frac{x ^{6}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} (2 x^{3} + 4) - \frac{x ^{6}}{3} + C

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