integral of (8+x+7x^2+e^x)

Lösung

\int (8 + x + 7 x^{2} + e^{x}) d x

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

Schritte zur Lösung

\int 8 + x + 7 x^{2} + e^{x} 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 8 d x + \int x d x + \int 7 x^{2} d x + \int e^{x} d x

\int 8 d x = 8 x

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

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

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

= 8 x + \frac{x ^{2}}{2} + \frac{7 x ^{3}}{3} + e^{x}

Füge eine Konstante zur Lösung hinzu

= 8 x + \frac{x ^{2}}{2} + \frac{7 x ^{3}}{3} + e^{x} + C

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