integral from 0 to 10 of (ln(x))/x

Lösung

\int_{0}^{10} \frac{ln ( x )}{x} d x

divergiert

Schritte zur Lösung

\int_{0}^{10} \frac{ln ( x )}{x} d x

Wende die partielle Integration an

= [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{10}

\int \frac{1 - ln ( x )}{x} d x = - \frac{( 1 - ln ( x ) ) ^{2}}{2}

= [ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{10}

Vereinfache

[ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{10} : [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{10}

= [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{10}

Berechne die Grenzen:

divergiert

= divergiert

\int_{- 2}^{2} (x^{2} + 2) d x

\int_{- 5}^{10} e^{- 0.05 x} d x

\int_{- 2}^{1} 2 - y - y^{2} d y

\int_{0}^{l n (2 x)} sin (5 e^{t}) d t

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