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Beliebt Rechnen >

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

Lösung

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

Lösung

arctan (x^{2} - 1) - arcsec (x) - \frac{1}{2} sin (2 arcsec (x)) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - 2}{x ^{3} x ^{2} - 1} : \frac{1}{x x ^{2} - 1} - \frac{2}{x ^{3} x ^{2} - 1}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{x x ^{2} - 1} d x = arctan (x^{2} - 1)

\int \frac{2}{x ^{3} x ^{2} - 1} d x = arcsec (x) + \frac{1}{2} sin (2 arcsec (x))

= arctan (x^{2} - 1) - (arcsec (x) + \frac{1}{2} sin (2 arcsec (x)))

Vereinfache

= arctan (x^{2} - 1) - arcsec (x) - \frac{1}{2} sin (2 arcsec (x))

Füge eine Konstante zur Lösung hinzu

= arctan (x^{2} - 1) - arcsec (x) - \frac{1}{2} sin (2 arcsec (x)) + C

Graph

Beliebte Beispiele

integral of (x^3-4x+3)/(x+5)

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