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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of ((cos^3(x)))/(sin(x))

\int \frac{( cos ^{3} ( x ) )}{sin ( x )} d x

integral of 10y

\int 10 y d y

integral of (x+5)(4x-11)

\int (x + 5) (4 x - 11) d x

integral of (13)/(sqrt(36-36x^2))

\int \frac{13}{36 - 36 x ^{2}} d x

derivative of cos(12x)

\frac{d}{d x} (cos (12 x))