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

Lösung

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

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

Schritte zur Lösung

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

\int 1 d x = x

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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