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

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

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