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Beliebt Rechnen >

integral of 1/(sqrt(x^2-25))

Lösung

\int \frac{1}{x ^{2} - 25} d x

Lösung

ln (\frac{1}{5} x^{2} - 25 + x) + C

Schritte zur Lösung

\int \frac{1}{x ^{2} - 25} d x

Trigonometrische Substitution anwenden

= \int sec (u) d u

Nutze das gemeinsame Integral :

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= ln ∣ tan (u) + sec (u) ∣

Setze in

u = arcsec (\frac{1}{5} x)

ein

= ln tan (arcsec (\frac{1}{5} x)) + sec (arcsec (\frac{1}{5} x))

Vereinfache

ln tan (arcsec (\frac{1}{5} x)) + sec (arcsec (\frac{1}{5} x)) : ln (\frac{1}{5} x^{2} - 25 + x)

= ln (\frac{1}{5} x^{2} - 25 + x)

Füge eine Konstante zur Lösung hinzu

= ln (\frac{1}{5} x^{2} - 25 + x) + C

Graph

Beliebte Beispiele

integral of (3/(x^2))

\int (\frac{3}{x ^{2}}) d x

integral of 2/3 x^2ln(x)

\int \frac{2}{3} x^{2} ln (x) d x

limit as x approaches 1 of ((x^2-5))/x

x \to 1 lim (\frac{( x ^{2} - 5 )}{x})

limit as x approaches 5 of sqrt(8x+5)

x \to 5 lim (8 x + 5)

derivative of e^{x^2y}-2x-2y

\frac{d}{d x} (e^{x^{2} y} - 2 x - 2 y)