integral of 1/(sqrt(x^2+11))

Lösung

\int \frac{1}{x ^{2} + 11} d x

ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2}) + C

Schritte zur Lösung

\int \frac{1}{x ^{2} + 11} 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 = arctan (\frac{1}{11} x)

ein

= ln tan (arctan (\frac{1}{11} x)) + sec (arctan (\frac{1}{11} x))

Vereinfache

ln tan (arctan (\frac{1}{11} x)) + sec (arctan (\frac{1}{11} x)) : ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2})

= ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2})

Füge eine Konstante zur Lösung hinzu

= ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2}) + C

\frac{d P}{d t} = (\frac{P}{5}) (lo g_{e} (\frac{3000}{P}))

\frac{\partial}{\partial x} (6 y^{5} sin (3 x))

d er i v a t i v e y = (x^{2} + 5 x + 2)^{3}

x \to \frac{c}{2 ^{-}} lim ([2 x - 4])

(y^{2} + x y^{2}) y^{^{'}} = 1