Inhalt

A.9. Integrale mit $u^{2} - a^{2}$

Übliche reelle Bedingungen: $a > 0$ , $∣ u ∣ \geq a$ ; falls die Wurzel im Nenner steht, $∣ u ∣ > a$ , und falls $u$ unten vorkommt, $u \neq = 0$ .

Formel

\int u^{2} - a^{2} d u = \frac{u}{2} u^{2} - a^{2} - \frac{a ^{2}}{2} ln u + u^{2} - a^{2} + C

$ln u + u^{2} - a^{2} + C$

Details ansehen →

Formel

\int u^{2} u^{2} - a^{2} d u = \frac{u}{8} (2 u^{2} - a^{2}) u^{2} - a^{2} - \frac{a ^{4}}{8} ln u + u^{2} - a^{2} + C

$ln u + u^{2} - a^{2} + C$

Details ansehen →

Formel

\int \frac{u ^{2} - a ^{2}}{u} d u = u^{2} - a^{2} - a arcsec \frac{u}{a} + C

Details ansehen →

Formel

\int \frac{u ^{2} - a ^{2}}{u ^{2}} d u = - \frac{u ^{2} - a ^{2}}{u} + ln u + u^{2} - a^{2} + C

Details ansehen →

Formel

\int \frac{d u}{u ^{2} - a ^{2}} = ln u + u^{2} - a^{2} + C

Details ansehen →

Formel

\int \frac{u ^{2} d u}{u ^{2} - a ^{2}} = \frac{u}{2} u^{2} - a^{2} + \frac{a ^{2}}{2} ln u + u^{2} - a^{2} + C

$ln u + u^{2} - a^{2} + C$

Details ansehen →

Formel

\int \frac{d u}{u ^{2} u ^{2} - a ^{2}} = \frac{u ^{2} - a ^{2}}{a ^{2} u} + C

Details ansehen →

Formel

\int \frac{d u}{( u ^{2} - a ^{2} ) ^{3/2}} = - \frac{u}{a ^{2} u ^{2} - a ^{2}} + C

Details ansehen →