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Beliebt Rechnen >

integral of (x+1)/(sqrt(16-x^2))

Lösung

\int \frac{x + 1}{16 - x ^{2}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x + 1}{16 - x ^{2}} d x

Multipliziere aus

\frac{x + 1}{16 - x ^{2}} : \frac{x}{16 - x ^{2}} + \frac{1}{16 - x ^{2}}

= \int \frac{x}{16 - x ^{2}} + \frac{1}{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{x}{16 - x ^{2}} d x + \int \frac{1}{16 - x ^{2}} d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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