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

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 5 d x = 5 x

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

Füge eine Konstante zur Lösung hinzu

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

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