integral of (1+x^3)^2

Lösung

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

x + \frac{x ^{4}}{2} + \frac{x ^{7}}{7} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int 1 + 2 x^{3} + x^{6} 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 1 d x + \int 2 x^{3} d x + \int x^{6} d x

\int 1 d x = x

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

\int x^{6} d x = \frac{x ^{7}}{7}

= x + \frac{x ^{4}}{2} + \frac{x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= x + \frac{x ^{4}}{2} + \frac{x ^{7}}{7} + C

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