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Beliebt Rechnen >

integral of e^xsech(x)

Lösung

\int e^{x} sech (x) d x

Lösung

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

Schritte zur Lösung

\int e^{x} sech (x) d x

Wende U-Substitution an

= \int sech (ln (u)) d u

Wende die partielle Integration an

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

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

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

Setze in

u = e^{x}

ein

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

Vereinfache

e^{x} sech (ln (e^{x})) - (sech (ln (e^{x})) arcsech (sech (ln (e^{x}))) + 2 arcsin (\frac{1}{2} sech (ln (e^{x})) + 1)) : e^{x} sech (x) - sech (x) arcsech (sech (x)) - 2 arcsin (\frac{1}{2} sech (x) + 1)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (3x+3)/(x^2+8x+16)

\int \frac{3 x + 3}{x ^{2} + 8 x + 16} d x

integral of 1/(sqrt(-x^2-8x))

\int \frac{1}{- x ^{2} - 8 x} d x

integral of 1 (xsin(x))

\int \frac{d}{1} (x sin (x)) d x

integral of (x+3)/x

\int \frac{x + 3}{x} d x

integral of-x^2+2x+8

\int - x^{2} + 2 x + 8 d x