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Beliebt Rechnen >

integral of (t+7)e^{2t+3}

Lösung

\int (t + 7) e^{2 t + 3} d t

Lösung

\frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3} + C

Schritte zur Lösung

\int (t + 7) e^{2 t + 3} d t

Wende die partielle Integration an

= \frac{1}{2} e^{2 t + 3} (t + 7) - \int \frac{1}{2} e^{2 t + 3} d t

\int \frac{1}{2} e^{2 t + 3} d t = \frac{1}{4} e^{2 t + 3}

= \frac{1}{2} e^{2 t + 3} (t + 7) - \frac{1}{4} e^{2 t + 3}

Vereinfache

\frac{1}{2} e^{2 t + 3} (t + 7) - \frac{1}{4} e^{2 t + 3} : \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3}

= \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{2 t + 3} t + \frac{13}{4} e^{2 t + 3} + C

Graph

Beliebte Beispiele

derivative of sqrt(5)x+sqrt(6x)

\frac{d}{d x} (5 x + 6 x)

fläche y^2-7x=1,x-y=1

a re a y^{2} - 7 x = 1, x - y = 1

integral of 6e^5

\int 6 e^{5} d x

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\frac{d}{d x} ((x - 1) (x^{2} + x + 1))

derivative of-2ln(-x)

\frac{d}{d x} (- 2 ln (- x))