integral of (1+x)^2

Lösung

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

x + x^{2} + \frac{x ^{3}}{3} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 1 d x = x

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

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

= x + x^{2} + \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= x + x^{2} + \frac{x ^{3}}{3} + C

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x \to 1 lim (8)

x \to 0 lim (\frac{2 sin ( 3 x )}{x})

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