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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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\int \frac{200}{20 - 3 x} d x

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x \to 1 lim (x^{3} + 1)

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x \to \infty lim (5 \cdot x)

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\int \frac{1}{( 1 + x ) x} d x