integral of ((3x-1))/(xsqrt(x^2-4))

Lösung

\int \frac{( 3 x - 1 )}{x x ^{2} - 4} d x

3 ln (\frac{1}{2} x^{2} - 4 + x) - \frac{1}{2} arcsec (\frac{1}{2} x) + C

Schritte zur Lösung

\int \frac{3 x - 1}{x x ^{2} - 4} d x

Multipliziere aus

\frac{3 x - 1}{x x ^{2} - 4} : \frac{3}{x ^{2} - 4} - \frac{1}{x x ^{2} - 4}

= \int \frac{3}{x ^{2} - 4} - \frac{1}{x x ^{2} - 4} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{3}{x ^{2} - 4} d x - \int \frac{1}{x x ^{2} - 4} d x

\int \frac{3}{x ^{2} - 4} d x = 3 ln (\frac{1}{2} x^{2} - 4 + x)

\int \frac{1}{x x ^{2} - 4} d x = \frac{1}{2} arcsec (\frac{1}{2} x)

= 3 ln (\frac{1}{2} x^{2} - 4 + x) - \frac{1}{2} arcsec (\frac{1}{2} x)

Füge eine Konstante zur Lösung hinzu

= 3 ln (\frac{1}{2} x^{2} - 4 + x) - \frac{1}{2} arcsec (\frac{1}{2} x) + C

x \to 1 lim (7^{x^{4} - x^{2}})

\int_{0}^{1} ln (x + 1) d x

\frac{d}{d x} ((3 + 4 x - x^{2})^{\frac{1}{2}})

\frac{d}{d x} (lo g_{e} (tan (x)))

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