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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Graph

Beliebte Beispiele

y^'=-100y+101cos(t)+99sin(t),y(0)=1

y^{^{'}} = - 100 y + 101 cos (t) + 99 sin (t), y (0) = 1

integral of (1/x-2/(9x^2+1))

\int (\frac{1}{x} - \frac{2}{9 x ^{2} + 1}) d x

derivative of (5x+1^3)

\frac{d}{d x} ((5 x + 1)^{3})

slopeintercept (9.1)(6.5)

s l o p e in t erce pt (9.1) (6.5)

integral of 3/y-1/(y+3)

\int \frac{3}{y} - \frac{1}{y + 3} d y