integral from 1 to e^x of 8ln(x)

Lösung

\int_{1}^{e^{x}} 8 ln (x) d x

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

Schritte zur Lösung

\int_{1}^{e^{x}} 8 ln (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{1}^{e^{x}} ln (x) d x

Wende die partielle Integration an

= 8 [x ln (x) - \int 1 d x]_{1}^{e^{x}}

\int 1 d x = x

= 8 [x ln (x) - x]_{1}^{e^{x}}

Berechne die Grenzen:

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

= 8 (e^{x} x - e^{x} + 1)

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\int_{0}^{π} 1 - cos (2 x) d x

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\int_{0}^{2} 1 - x^{2} d x