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Beliebt Rechnen >

integral of x^2(e^{x^3}+3x+2)

Lösung

\int x^{2} (e^{x^{3}} + 3 x + 2) d x

Lösung

\frac{1}{3} e^{x^{3}} + \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

Schritte zur Lösung

\int x^{2} (e^{x^{3}} + 3 x + 2) d x

Multipliziere aus

x^{2} (e^{x^{3}} + 3 x + 2) : e^{x^{3}} x^{2} + 3 x^{3} + 2 x^{2}

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

\int e^{x^{3}} x^{2} d x = \frac{1}{3} e^{x^{3}}

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

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

= \frac{1}{3} e^{x^{3}} + \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} e^{x^{3}} + \frac{3 x ^{4}}{4} + \frac{2 x ^{3}}{3} + C

Graph

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