integral of x-(x^2-2)

Lösung

\int x - (x^{2} - 2) d x

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

Schritte zur Lösung

\int x - (x^{2} - 2) d x

Vereinfache

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

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