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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

\int 1 d x = x

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

Berechne die Grenzen:

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

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

Beliebte Beispiele

integral from 1 to 6 of 3/t

\int_{1}^{6} \frac{3}{t} d t

integral from 1 to 2 of 2xe^{x^2}

\int_{1}^{2} 2 x e^{x^{2}} d x

integral from 0 to s of 9e^x

\int_{0}^{s} 9 e^{x} d x

integral from 0 to 3 of (2x^2-1)

\int_{0}^{3} (2 x^{2} - 1) d x

integral from 0 to t of x^5

\int_{0}^{t} x^{5} d x