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Beliebt Rechnen >

integral of e^{2x}-x^2-1

Lösung

\int e^{2 x} - x^{2} - 1 d x

Lösung

\frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x + C

Schritte zur Lösung

\int e^{2 x} - x^{2} - 1 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 e^{2 x} d x - \int x^{2} d x - \int 1 d x

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

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

\int 1 d x = x

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{2 x} - \frac{x ^{3}}{3} - x + C

Graph

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