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Beliebt Rechnen >

integral of ((4-x))/(sqrt(2-x^2))

Lösung

\int \frac{( 4 - x )}{2 - x ^{2}} d x

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{4 - x}{2 - x ^{2}} : \frac{4}{2 - x ^{2}} - \frac{x}{2 - x ^{2}}

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

\int \frac{4}{2 - x ^{2}} d x = 4 arcsin (\frac{1}{2} x)

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

= 4 arcsin (\frac{1}{2} x) - (- 2 - x^{2})

Vereinfache

= 4 arcsin (\frac{1}{2} x) + 2 - x^{2}

Füge eine Konstante zur Lösung hinzu

= 4 arcsin (\frac{1}{2} x) + 2 - x^{2} + C

Graph

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\int 576 - 36 x^{2} d x

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\int cos^{6} (\frac{1}{2} x) sin (\frac{1}{2} x) d x