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Beliebt Rechnen >

integral of (x+7)e^{0.1x+2}

Lösung

\int (x + 7) e^{0.1 x + 2} d x

Lösung

10 e^{0.1 x + 2} x - 30 e^{0.1 x + 2} + C

Schritte zur Lösung

\int (x + 7) e^{0.1 x + 2} d x

Multipliziere aus

(x + 7) e^{0.1 x + 2} : e^{0.1 x + 2} x + 7 e^{0.1 x + 2}

= \int e^{0.1 x + 2} x + 7 e^{0.1 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^{0.1 x + 2} x d x + \int 7 e^{0.1 x + 2} d x

\int e^{0.1 x + 2} x d x = 10 e^{0.1 x + 2} x - 100 e^{0.1 x + 2}

\int 7 e^{0.1 x + 2} d x = 70 e^{0.1 x + 2}

= 10 e^{0.1 x + 2} x - 100 e^{0.1 x + 2} + 70 e^{0.1 x + 2}

Vereinfache

= 10 e^{0.1 x + 2} x - 30 e^{0.1 x + 2}

Füge eine Konstante zur Lösung hinzu

= 10 e^{0.1 x + 2} x - 30 e^{0.1 x + 2} + C

Graph

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