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Beliebt Rechnen >

integral of x^3-3x^2+7x^{-2}+e^x

Lösung

\int x^{3} - 3 x^{2} + 7 x^{- 2} + e^{x} d x

Lösung

\frac{x ^{4}}{4} - x^{3} - \frac{7}{x} + e^{x} + C

Schritte zur Lösung

\int x^{3} - 3 x^{2} + 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 x^{3} d x - \int 3 x^{2} d x + \int 7 x^{- 2} d x + \int e^{x} d x

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

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

= \frac{x ^{4}}{4} - x^{3} - \frac{7}{x} + e^{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - x^{3} - \frac{7}{x} + e^{x} + C

Graph

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