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Beliebt Rechnen >

integral of (sqrt(a^2+x^2))/(x^4)

Lösung

\int \frac{a ^{2} + x ^{2}}{x ^{4}} d x

Lösung

- \frac{a ^{2} + x ^{2}}{3 x ^{3}} - \frac{a ^{2} + x ^{2}}{3 a ^{2} x} + C

Schritte zur Lösung

\int \frac{a ^{2} + x ^{2}}{x ^{4}} d x

Wende die partielle Integration an

= - \frac{a ^{2} + x ^{2}}{3 x ^{3}} - \int - \frac{1}{3 x ^{2} x ^{2} + a ^{2}} d x

\int - \frac{1}{3 x ^{2} x ^{2} + a ^{2}} d x = \frac{a ^{2} + x ^{2}}{3 a ^{2} x}

= - \frac{a ^{2} + x ^{2}}{3 x ^{3}} - \frac{a ^{2} + x ^{2}}{3 a ^{2} x}

Füge eine Konstante zur Lösung hinzu

= - \frac{a ^{2} + x ^{2}}{3 x ^{3}} - \frac{a ^{2} + x ^{2}}{3 a ^{2} x} + C

Graph

Beliebte Beispiele

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