integral of x*arcsec(x)

Lösung

\int x \cdot arcsec (x) d x

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

Schritte zur Lösung

\int x arcsec (x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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