integral of ((8x^3)/3-3x^2+5)

Lösung

\int (\frac{8 x ^{3}}{3} - 3 x^{2} + 5) d x

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

Schritte zur Lösung

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

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

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

\int 5 d x = 5 x

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

Füge eine Konstante zur Lösung hinzu

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

\int 8 x 8 x^{2} + 16 d x

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