integral of (7+x+x^2)

Lösung

\int (7 + x + x^{2}) d x

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

Schritte zur Lösung

\int 7 + 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 7 d x + \int x d x + \int x^{2} d x

\int 7 d x = 7 x

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

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

= 7 x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 7 x + \frac{x ^{2}}{2} + \frac{x ^{3}}{3} + C

\int_{1}^{e^{x}} ln (x) d x

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