integral from 0 to a of x/(a^2-x^2)

Lösung

\int_{0}^{a} \frac{x}{a ^{2} - x ^{2}} d x

divergiert

Schritte zur Lösung

\int_{0}^{a} \frac{x}{a ^{2} - x ^{2}} d x

Wende U-Substitution an

= \int_{a^{2}}^{0} - \frac{1}{2 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int_{a^{2}}^{0} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} [ln ∣ u ∣]_{a^{2}}^{0}

Berechne die Grenzen:

divergiert

= divergiert

\int_{0}^{\frac{3 π}{4}} x^{3} sin (2 x) d x

\int_{y}^{e} \frac{ln ( x )}{x} d x

\int_{4}^{\infty} \frac{1}{x ^{4}} d x

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

\int_{0}^{\frac{1}{2}} t d t