integral from 0 to ln(y) of e^{x+y}

Lösung

\int_{0}^{l n (y)} e^{x + y} d x

e^{y} (y - 1)

Schritte zur Lösung

\int_{0}^{l n (y)} e^{x + y} d x

e^{y + x} = e^{y} e^{x}

= \int_{0}^{l n (y)} e^{y} e^{x} d x

Entferne die Konstante:

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

= e^{y} \cdot \int_{0}^{l n (y)} e^{x} d x

Nutze das gemeinsame Integral :

\int e^{x} d x = e^{x}

= e^{y} [e^{x}]_{0}^{l n (y)}

Berechne die Grenzen:

y - 1

= e^{y} (y - 1)

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