integral of (3x-1)/(xsqrt(x^2-25))

Lösung

\int \frac{3 x - 1}{x x ^{2} - 25} d x

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

Schritte zur Lösung

\int \frac{3 x - 1}{x x ^{2} - 25} d x

Multipliziere aus

\frac{3 x - 1}{x x ^{2} - 25} : \frac{3}{x ^{2} - 25} - \frac{1}{x x ^{2} - 25}

= \int \frac{3}{x ^{2} - 25} - \frac{1}{x x ^{2} - 25} 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} - 25} d x - \int \frac{1}{x x ^{2} - 25} d x

\int \frac{3}{x ^{2} - 25} d x = 3 ln (\frac{1}{5} x^{2} - 25 + x)

\int \frac{1}{x x ^{2} - 25} d x = \frac{1}{5} arcsec (\frac{1}{5} x)

= 3 ln (\frac{1}{5} x^{2} - 25 + x) - \frac{1}{5} arcsec (\frac{1}{5} x)

Füge eine Konstante zur Lösung hinzu

= 3 ln (\frac{1}{5} x^{2} - 25 + x) - \frac{1}{5} arcsec (\frac{1}{5} x) + C

\frac{d}{d x} (ln (3 x - 2))

\frac{d}{d x} (\frac{2}{x ^{3} ln ( 10 )})

\frac{\partial}{\partial y} (y - x)

a re a x = y, y^{2} - 2 y = x

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