integral from 4 to 7 of 1/(sqrt(x^2-16))

Lösung

\int_{4}^{7} \frac{1}{x ^{2} - 16} d x

ln (\frac{7}{4} + \frac{33}{4})

Dezimale

1.15881 \dots

Schritte zur Lösung

\int_{4}^{7} \frac{1}{x ^{2} - 16} d x

Trigonometrische Substitution anwenden

= \int_{0}^{arcsec (\frac{7}{4})} sec (u) d u

Nutze das gemeinsame Integral :

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

= [ln ∣ tan (u) + sec (u) ∣]_{0}^{arcsec (\frac{7}{4})}

Berechne die Grenzen:

ln (\frac{7}{4} + \frac{33}{4})

= ln (\frac{7}{4} + \frac{33}{4})

\frac{d}{d x} (2 x)

t an g e n t f (x) = x^{2} - 2 x - 6, at x = - 2

x \to 8 lim (\frac{4}{x - 8})

\frac{d}{d x} (\frac{- 2 ( - 3 x ^{2} + 1 )}{( 1 + x ^{2} ) ^{3}})

\int x^{4} (x^{5} + 1)^{18} d x