integral from 0 to 1 of x^{-0.5}ln(x)

Lösung

\int_{0}^{1} x^{- 0.5} ln (x) d x

- 4

Schritte zur Lösung

\int_{0}^{1} x^{- 0.5} ln (x) d x

Vereinfache

x^{- 0.5} ln (x) : \frac{ln ( x )}{x}

= \int_{0}^{1} \frac{ln ( x )}{x} d x

Wende die partielle Integration an

= [2 x ln (x) - \int \frac{2}{x} d x]_{0}^{1}

\int \frac{2}{x} d x = 4 x

= [2 x ln (x) - 4 x]_{0}^{1}

Berechne die Grenzen:

- 4

= - 4

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