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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of f(x)=x^2+8x+7

\frac{d}{d x} f (x) = x^{2} + 8 x + 7

limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x)

x \to 0 lim (\frac{7 x ^{5} + 5 x ^{2} + 12 x}{3 x ^{5} + 4 x})

tangent x^2-3xy=10

t an g e n t x^{2} - 3 x y = 10

y^'=(sec(y))/((x-3)^2)

y^{^{'}} = \frac{sec ( y )}{( x - 3 ) ^{2}}

sum from n=0 to infinity of 2/1

n = 0 \sum \infty \frac{2}{1}