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Beliebt Rechnen >

integral of (4-x)/(sqrt(16-x^2))

Lösung

\int \frac{4 - x}{16 - x ^{2}} d x

Lösung

4 arcsin (\frac{1}{4} x) + 16 - x^{2} + C

Schritte zur Lösung

\int \frac{4 - x}{16 - x ^{2}} d x

Multipliziere aus

\frac{4 - x}{16 - x ^{2}} : \frac{4}{16 - x ^{2}} - \frac{x}{16 - x ^{2}}

= \int \frac{4}{16 - x ^{2}} - \frac{x}{16 - 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}{16 - x ^{2}} d x - \int \frac{x}{16 - x ^{2}} d x

\int \frac{4}{16 - x ^{2}} d x = 4 arcsin (\frac{1}{4} x)

\int \frac{x}{16 - x ^{2}} d x = - 16 - x^{2}

= 4 arcsin (\frac{1}{4} x) - (- 16 - x^{2})

Vereinfache

= 4 arcsin (\frac{1}{4} x) + 16 - x^{2}

Füge eine Konstante zur Lösung hinzu

= 4 arcsin (\frac{1}{4} x) + 16 - x^{2} + C

Graph

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