integral from 0 to 2 of 1/(ln(x))

Lösung

\int_{0}^{2} \frac{1}{ln ( x )} d x

Ei (ln (1)) + Ei (ln (2)) - Ei (0)

Schritte zur Lösung

\int_{0}^{2} \frac{1}{ln ( x )} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 1

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{1} \frac{1}{ln ( x )} d x + \int_{1}^{2} \frac{1}{ln ( x )} d x

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

\int_{1}^{2} \frac{1}{ln ( x )} d x = Ei (ln (2)) - Ei (0)

= Ei (ln (1)) + Ei (ln (2)) - Ei (0)

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\int_{1}^{3} 2 x - 1 d x