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Beliebt Rechnen >

integral of 11+5e^{6-3x}-16

Lösung

\int 11 + 5 e^{6 - 3 x} - 16 d x

Lösung

- 5 x - \frac{5}{3} e^{- 3 x + 6} + C

Schritte zur Lösung

\int 11 + 5 e^{6 - 3 x} - 16 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 11 d x + \int 5 e^{6 - 3 x} d x - \int 16 d x

\int 11 d x = 11 x

\int 5 e^{6 - 3 x} d x = - \frac{5}{3} e^{6 - 3 x}

\int 16 d x = 16 x

= 11 x - \frac{5}{3} e^{6 - 3 x} - 16 x

Vereinfache

= - 5 x - \frac{5}{3} e^{- 3 x + 6}

Füge eine Konstante zur Lösung hinzu

= - 5 x - \frac{5}{3} e^{- 3 x + 6} + C

Graph

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