integral of (x^2+1)(2x-3)

Lösung

\int (x^{2} + 1) (2 x - 3) d x

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

Schritte zur Lösung

\int (x^{2} + 1) (2 x - 3) d x

Wende die partielle Integration an

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

\int 2 (\frac{x ^{3}}{3} + x) d x = \frac{x ^{4}}{6} + x^{2}

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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