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

Lösung

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

arctan (9 x^{2} - 1) + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= arctan (u)

Setze in

u = 9 x^{2} - 1

ein

= arctan (9 x^{2} - 1)

Füge eine Konstante zur Lösung hinzu

= arctan (9 x^{2} - 1) + C

x^{^{'}} = \frac{1}{1 + t ^{2}}

t an g e n t f (x) = 4 - 2 x^{2}, at x = 5

d er i v a t i v e (\frac{- 2 x - 1}{- 4 x + 2})^{5}

\frac{\partial}{\partial y} (x^{2} + x y^{4})

\int_{1}^{x} \frac{1}{t} d t