integral of (1-sqrt(x))/(1+sqrt(x))

Lösung

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

4 (1 + x - ln 1 + x) - x + C

Schritte zur Lösung

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

\frac{1 - x}{1 + x} = \frac{2}{1 + x} - 1

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

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

\int 1 d x = x

= 4 (1 + x - ln 1 + x) - x

Füge eine Konstante zur Lösung hinzu

= 4 (1 + x - ln 1 + x) - x + C

d er i v a t i v e \frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{8 x ^{3} - 6 x ^{2}}{x ^{2} + 3 x - 2})

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

x \to 2 lim (2 x - 2)

\int \frac{sec ( x )}{x} d x