integral of ln(x+sqrt((x^2-1)))

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

p a r i t y ln (sec (x) + tan (x))

\int 1 + 9 sin^{2} (3 x) d x

x \to 0 lim (\frac{( x ^{2} - 4 x )}{x})

\int - e^{x} (x + 1) d x

in v erse l a pl a ce \frac{1}{s ^{2} + s ^{2}}