integral of (4x^5+1)x^4

Lösung

\int (4 x^{5} + 1) x^{4} d x

\frac{2 x ^{10}}{5} + \frac{x ^{5}}{5} + C

Schritte zur Lösung

\int (4 x^{5} + 1) x^{4} d x

Multipliziere aus

(4 x^{5} + 1) x^{4} : 4 x^{9} + x^{4}

= \int 4 x^{9} + 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 4 x^{9} d x + \int x^{4} d x

\int 4 x^{9} d x = \frac{2 x ^{10}}{5}

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

= \frac{2 x ^{10}}{5} + \frac{x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{10}}{5} + \frac{x ^{5}}{5} + C

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