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Beliebt Rechnen >

integral of (1-2x)/(sqrt(16-9x^2))

Lösung

\int \frac{1 - 2 x}{16 - 9 x ^{2}} d x

Lösung

\frac{1}{3} arcsin (\frac{3}{4} x) + \frac{2}{9} 16 - 9 x^{2} + C

Schritte zur Lösung

\int \frac{1 - 2 x}{16 - 9 x ^{2}} d x

Multipliziere aus

\frac{1 - 2 x}{16 - 9 x ^{2}} : \frac{1}{16 - 9 x ^{2}} - \frac{2 x}{16 - 9 x ^{2}}

= \int \frac{1}{16 - 9 x ^{2}} - \frac{2 x}{16 - 9 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}{16 - 9 x ^{2}} d x - \int \frac{2 x}{16 - 9 x ^{2}} d x

\int \frac{1}{16 - 9 x ^{2}} d x = \frac{1}{3} arcsin (\frac{3}{4} x)

\int \frac{2 x}{16 - 9 x ^{2}} d x = - \frac{2}{9} 16 - 9 x^{2}

= \frac{1}{3} arcsin (\frac{3}{4} x) - (- \frac{2}{9} 16 - 9 x^{2})

Vereinfache

= \frac{1}{3} arcsin (\frac{3}{4} x) + \frac{2}{9} 16 - 9 x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} arcsin (\frac{3}{4} x) + \frac{2}{9} 16 - 9 x^{2} + C

Graph

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