integral from 1/2 to 1 of (ln(x))/(4x)

Lösung

\int_{\frac{1}{2}}^{1} \frac{ln ( x )}{4 x} d x

- \frac{ln ^{2} ( 2 )}{8}

Dezimale

- 0.06005 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \frac{1}{4} \cdot \int_{- l n (2)}^{0} u d u

Wende die Potenzregel an

= \frac{1}{4} [\frac{u ^{2}}{2}]_{- l n (2)}^{0}

Berechne die Grenzen:

- \frac{ln ^{2} ( 2 )}{2}

= \frac{1}{4} (- \frac{ln ^{2} ( 2 )}{2})

Vereinfache

= - \frac{ln ^{2} ( 2 )}{8}

\int_{6}^{10} \frac{y}{y ^{2} - 2 y - 3} d y

\int_{0}^{1} π (x^{2} + 1) d x

\int_{- 1}^{0} \frac{3 e ^{\frac{1}{x}}}{x ^{3}} d x

\int_{1}^{4} (x - (x - 2)^{2}) d x

\int_{\frac{π}{4}}^{\frac{3 π}{4}} 1