integral of 8x^4+4x^3-6x^2-4x+5

Lösung

\int 8 x^{4} + 4 x^{3} - 6 x^{2} - 4 x + 5 d x

\frac{8 x ^{5}}{5} + x^{4} - 2 x^{3} - 2 x^{2} + 5 x + C

Schritte zur Lösung

\int 8 x^{4} + 4 x^{3} - 6 x^{2} - 4 x + 5 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 8 x^{4} d x + \int 4 x^{3} d x - \int 6 x^{2} d x - \int 4 x d x + \int 5 d x

\int 8 x^{4} d x = \frac{8 x ^{5}}{5}

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

\int 6 x^{2} d x = 2 x^{3}

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

\int 5 d x = 5 x

= \frac{8 x ^{5}}{5} + x^{4} - 2 x^{3} - 2 x^{2} + 5 x

Füge eine Konstante zur Lösung hinzu

= \frac{8 x ^{5}}{5} + x^{4} - 2 x^{3} - 2 x^{2} + 5 x + C

\int + 50 x d x

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