integral of (2-x)/(sqrt(1-x^2))

Lösung

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

2 arcsin (x) + 1 - x^{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= 2 arcsin (x) - (- 1 - x^{2})

Vereinfache

= 2 arcsin (x) + 1 - x^{2}

Füge eine Konstante zur Lösung hinzu

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

\int e^{4 - 5 x} d x

\int \frac{ln ( x )}{x 1 + ln ^{2} ( x )} d x

\int \frac{x ^{2} - 4}{x ^{2} + 4} d x

\int \frac{4}{( x - 9 ) ( x - 5 )} d x

in t e g r a l \frac{5}{x}