integral from 0.5 to 1 of (ln(x))/(4x)

Lösung

\int_{0.5}^{1} \frac{ln ( x )}{4 x} d x

- 0.06005 \dots

Schritte zur Lösung

\int_{0.5}^{1} \frac{ln ( x )}{4 x} d x

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{0.5}^{1} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= \frac{1}{4} \cdot \int_{- 0.69314 \dots}^{0} u d u

Wende die Potenzregel an

= \frac{1}{4} [\frac{u ^{2}}{2}]_{- 0.69314 \dots}^{0}

Vereinfache

= 0.25 [0.5 u^{2}]_{- 0.69314 \dots}^{0}

Berechne die Grenzen:

- 0.24022 \dots

= 0.25 (- 0.24022 \dots)

Vereinfache

= - 0.06005 \dots

\int_{1}^{x} x^{4} + 1 d x

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