integral of 2x+3-x^2

Lösung

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

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

Schritte zur Lösung

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

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

\int 3 d x = 3 x

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

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

Füge eine Konstante zur Lösung hinzu

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