integral of (10x^3-4x^2+2x-1)

Lösung

\int (10 x^{3} - 4 x^{2} + 2 x - 1) d x

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

Schritte zur Lösung

\int 10 x^{3} - 4 x^{2} + 2 x - 1 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 10 x^{3} d x - \int 4 x^{2} d x + \int 2 x d x - \int 1 d x

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

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