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Beliebt Rechnen >

integral of sech(ln(x))

Lösung

\int sech (ln (x)) d x

Lösung

x sech (ln (x)) - sech (ln (x)) arcsech (sech (ln (x))) - 2 arcsin (\frac{1}{2} sech (ln (x)) + 1) + C

Schritte zur Lösung

\int sech (ln (x)) d x

Wende die partielle Integration an

= x sech (ln (x)) - \int - sech (ln (x)) tanh (ln (x)) d x

\int - sech (ln (x)) tanh (ln (x)) d x = sech (ln (x)) arcsech (sech (ln (x))) + 2 arcsin (\frac{1}{2} sech (ln (x)) + 1)

= x sech (ln (x)) - (sech (ln (x)) arcsech (sech (ln (x))) + 2 arcsin (\frac{1}{2} sech (ln (x)) + 1))

Vereinfache

= x sech (ln (x)) - sech (ln (x)) arcsech (sech (ln (x))) - 2 arcsin (\frac{1}{2} sech (ln (x)) + 1)

Füge eine Konstante zur Lösung hinzu

= x sech (ln (x)) - sech (ln (x)) arcsech (sech (ln (x))) - 2 arcsin (\frac{1}{2} sech (ln (x)) + 1) + C

Graph

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