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

Lösung

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

Ei (2 ln (1)) - Ei (ln (1))

Schritte zur Lösung

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

Multipliziere aus

\frac{x - 1}{ln ( x )} : \frac{x}{ln ( x )} - \frac{1}{ln ( x )}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

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

\int_{x}^{y} \frac{1}{x ^{2}} d x

\int_{0}^{0.2} x d x

\int_{0}^{π} t cos (t) sin (t) d t

\int_{- π}^{π} (sin (2 x))^{2} d x