integral of e^{(a+b)x}

Lösung

\int e^{(a + b) x} d x

e^{(a + b) x} x - \frac{e ^{x (a + b)} x ( a + b ) - e ^{x (a + b)}}{a + b} + C

Schritte zur Lösung

\int e^{(a + b) x} d x

Wende die partielle Integration an

= e^{(a + b) x} x - \int e^{(a + b) x} (a + b) x d x

\int e^{(a + b) x} (a + b) x d x = \frac{e ^{x (a + b)} x ( a + b ) - e ^{x (a + b)}}{a + b}

= e^{(a + b) x} x - \frac{e ^{x (a + b)} x ( a + b ) - e ^{x (a + b)}}{a + b}

Füge eine Konstante zur Lösung hinzu

= e^{(a + b) x} x - \frac{e ^{x (a + b)} x ( a + b ) - e ^{x (a + b)}}{a + b} + C

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