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Beliebt Rechnen >

integral of 3e^{(3t)/2}t

Lösung

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

Lösung

2 e^{\frac{3 t}{2}} t - \frac{4}{3} e^{\frac{3 t}{2}} + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende die partielle Integration an

= 3 (\frac{2}{3} e^{\frac{3 t}{2}} t - \int \frac{2}{3} e^{\frac{3 t}{2}} d t)

\int \frac{2}{3} e^{\frac{3 t}{2}} d t = \frac{4}{9} e^{\frac{3 t}{2}}

= 3 (\frac{2}{3} e^{\frac{3 t}{2}} t - \frac{4}{9} e^{\frac{3 t}{2}})

Vereinfache

3 (\frac{2}{3} e^{\frac{3 t}{2}} t - \frac{4}{9} e^{\frac{3 t}{2}}) : 2 e^{\frac{3 t}{2}} t - \frac{4}{3} e^{\frac{3 t}{2}}

= 2 e^{\frac{3 t}{2}} t - \frac{4}{3} e^{\frac{3 t}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 e^{\frac{3 t}{2}} t - \frac{4}{3} e^{\frac{3 t}{2}} + C

Graph

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