integral of x^3(1/x+6x^2)

Lösung

\int x^{3} (\frac{1}{x} + 6 x^{2}) d x

\frac{x ^{3}}{3} + x^{6} + C

Schritte zur Lösung

\int x^{3} (\frac{1}{x} + 6 x^{2}) d x

Multipliziere aus

x^{3} (\frac{1}{x} + 6 x^{2}) : x^{2} + 6 x^{5}

= \int x^{2} + 6 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 x^{2} d x + \int 6 x^{5} d x

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

\int 6 x^{5} d x = x^{6}

= \frac{x ^{3}}{3} + x^{6}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + x^{6} + C

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