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Beliebt Rechnen >

integral y=12(x-1)^2(x+2)

Lösung

integral

y = 12 (x - 1)^{2} (x + 2)

Lösung

3 x^{4} - 18 x^{2} + 24 x + C

Schritte zur Lösung

\int 12 (x - 1)^{2} (x + 2) d x

Entferne die Konstante:

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

= 12 \cdot \int (x - 1)^{2} (x + 2) d x

Wende die partielle Integration an

= 12 ((x + 2) (\frac{x ^{3}}{3} - x^{2} + x) - \int \frac{x ^{3}}{3} - x^{2} + x d x)

\int \frac{x ^{3}}{3} - x^{2} + x d x = \frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2}

= 12 ((x + 2) (\frac{x ^{3}}{3} - x^{2} + x) - (\frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2}))

Vereinfache

12 ((x + 2) (\frac{x ^{3}}{3} - x^{2} + x) - (\frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{x ^{2}}{2})) : 3 x^{4} - 18 x^{2} + 24 x

= 3 x^{4} - 18 x^{2} + 24 x

Füge eine Konstante zur Lösung hinzu

= 3 x^{4} - 18 x^{2} + 24 x + C

Graph

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