integral of 1/2 x+2/3 x^2

Lösung

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

\frac{x ^{2}}{4} + \frac{2 x ^{3}}{9} + C

Schritte zur Lösung

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

\int \frac{1}{2} x d x = \frac{x ^{2}}{4}

\int \frac{2}{3} x^{2} d x = \frac{2 x ^{3}}{9}

= \frac{x ^{2}}{4} + \frac{2 x ^{3}}{9}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{4} + \frac{2 x ^{3}}{9} + C

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