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Beliebt Rechnen >

integral of sqrt(t)+sin(t)-e^{-2t}

Lösung

\int t + sin (t) - e^{- 2 t} d t

Lösung

\frac{2}{3} t^{\frac{3}{2}} - cos (t) + \frac{1}{2} e^{- 2 t} + C

Schritte zur Lösung

\int t + sin (t) - e^{- 2 t} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t d t + \int sin (t) d t - \int e^{- 2 t} d t

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

\int sin (t) d t = - cos (t)

\int e^{- 2 t} d t = - \frac{1}{2} e^{- 2 t}

= \frac{2}{3} t^{\frac{3}{2}} - cos (t) - (- \frac{1}{2} e^{- 2 t})

Vereinfache

= \frac{2}{3} t^{\frac{3}{2}} - cos (t) + \frac{1}{2} e^{- 2 t}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} t^{\frac{3}{2}} - cos (t) + \frac{1}{2} e^{- 2 t} + C

Graph

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