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Beliebt Rechnen >

integral of (5x^4-8x^3+9x^2-2x+7)

Lösung

\int (5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7) d x

Lösung

x^{5} - 2 x^{4} + 3 x^{3} - x^{2} + 7 x + C

Schritte zur Lösung

\int 5 x^{4} - 8 x^{3} + 9 x^{2} - 2 x + 7 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 x^{4} d x - \int 8 x^{3} d x + \int 9 x^{2} d x - \int 2 x d x + \int 7 d x

\int 5 x^{4} d x = x^{5}

\int 8 x^{3} d x = 2 x^{4}

\int 9 x^{2} d x = 3 x^{3}

\int 2 x d x = x^{2}

\int 7 d x = 7 x

= x^{5} - 2 x^{4} + 3 x^{3} - x^{2} + 7 x

Füge eine Konstante zur Lösung hinzu

= x^{5} - 2 x^{4} + 3 x^{3} - x^{2} + 7 x + C

Graph

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