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

Lösung

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

divergiert

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{2 ln ( x ) - ln ^{2} ( x )}{x} d x = ln^{2} (x) - \frac{ln ^{3} ( x )}{3}

= [ln^{2} (x) - (ln^{2} (x) - \frac{ln ^{3} ( x )}{3})]_{0}^{1}

Vereinfache

[ln^{2} (x) - (ln^{2} (x) - \frac{ln ^{3} ( x )}{3})]_{0}^{1} : [\frac{1}{3} ln^{3} (x)]_{0}^{1}

= [\frac{1}{3} ln^{3} (x)]_{0}^{1}

Berechne die Grenzen:

divergiert

= divergiert

\int_{1}^{2} - 4 t^{- 4} d t

\int_{0}^{2} (x^{4} - 8 x) d x

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

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

\int_{0}^{l n (x)} y e^{z} d z