integral of (sqrt(49-x^2))/(x^4)

Lösung

\int \frac{49 - x ^{2}}{x ^{4}} d x

- \frac{49 - x ^{2}}{3 x ^{3}} + \frac{49 - x ^{2}}{147 x} + C

Schritte zur Lösung

\int \frac{49 - x ^{2}}{x ^{4}} d x

Wende die partielle Integration an

= - \frac{49 - x ^{2}}{3 x ^{3}} - \int \frac{1}{3 x ^{2} - x ^{2} + 49} d x

\int \frac{1}{3 x ^{2} - x ^{2} + 49} d x = - \frac{49 - x ^{2}}{147 x}

= - \frac{49 - x ^{2}}{3 x ^{3}} - (- \frac{49 - x ^{2}}{147 x})

Vereinfache

= - \frac{49 - x ^{2}}{3 x ^{3}} + \frac{49 - x ^{2}}{147 x}

Füge eine Konstante zur Lösung hinzu

= - \frac{49 - x ^{2}}{3 x ^{3}} + \frac{49 - x ^{2}}{147 x} + C

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