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

Lösung

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

x^{5} - \frac{x ^{4}}{2} + \frac{3 x ^{2}}{2} - 4 x + C

Schritte zur Lösung

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

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

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

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

\int 4 d x = 4 x

= x^{5} - \frac{x ^{4}}{2} + \frac{3 x ^{2}}{2} - 4 x

Füge eine Konstante zur Lösung hinzu

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

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