integral of (sqrt(1-x^2))/(x^3)

Lösung

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

- \frac{1 - x ^{2}}{2 x ^{2}} + \frac{1}{4} (ln - x^{2} + 1 + 1 - ln - x^{2} + 1 - 1) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1}{2 x - x ^{2} + 1} d x = - \frac{1}{4} (ln - x^{2} + 1 + 1 - ln - x^{2} + 1 - 1)

= - \frac{1 - x ^{2}}{2 x ^{2}} - (- \frac{1}{4} (ln - x^{2} + 1 + 1 - ln - x^{2} + 1 - 1))

Vereinfache

= - \frac{1 - x ^{2}}{2 x ^{2}} + \frac{1}{4} (ln - x^{2} + 1 + 1 - ln - x^{2} + 1 - 1)

Füge eine Konstante zur Lösung hinzu

= - \frac{1 - x ^{2}}{2 x ^{2}} + \frac{1}{4} (ln - x^{2} + 1 + 1 - ln - x^{2} + 1 - 1) + C

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