integral from 1 to e^x of 2ln(t)

Lösung

\int_{1}^{e^{x}} 2 ln (t) d t

2 (x e^{x} - e^{x} + 1)

Schritte zur Lösung

\int_{1}^{e^{x}} 2 ln (t) d t

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{e^{x}} ln (t) d t

Wende die partielle Integration an

= 2 [t ln (t) - \int 1 d t]_{1}^{e^{x}}

\int 1 d t = t

= 2 [t ln (t) - t]_{1}^{e^{x}}

Berechne die Grenzen:

x e^{x} - e^{x} + 1

= 2 (x e^{x} - e^{x} + 1)

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