integral from 1 to e^4 of (4ln(x))/x

Lösung

\int_{1}^{e^{4}} \frac{4 ln ( x )}{x} d x

32

Schritte zur Lösung

\int_{1}^{e^{4}} \frac{4 ln ( x )}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{e^{4}} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{4} u d u

Wende die Potenzregel an

= 4 [\frac{u ^{2}}{2}]_{0}^{4}

Berechne die Grenzen:

8

= 4 \cdot 8

Vereinfache

= 32

\int_{- 2}^{1} (3 - y) - (y^{2} + 1) d y

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