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Beliebt Rechnen >

integral of (x-3)/(sqrt(4-9x^2))

Lösung

\int \frac{x - 3}{4 - 9 x ^{2}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x - 3}{4 - 9 x ^{2}} d x

Multipliziere aus

\frac{x - 3}{4 - 9 x ^{2}} : \frac{x}{4 - 9 x ^{2}} - \frac{3}{4 - 9 x ^{2}}

= \int \frac{x}{4 - 9 x ^{2}} - \frac{3}{4 - 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{x}{4 - 9 x ^{2}} d x - \int \frac{3}{4 - 9 x ^{2}} d x

\int \frac{x}{4 - 9 x ^{2}} d x = - \frac{1}{9} 4 - 9 x^{2}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x^2-3)/(x^3+5x)

\int \frac{x ^{2} - 3}{x ^{3} + 5 x} d x

integral of y^3e^{-2y}

\int y^{3} e^{- 2 y} d y

integral of (6x^3+5x)^{12}

\int (6 x^{3} + 5 x)^{12} d x

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\int cos^{2} (2 θ) sin^{3} (2 θ) d θ

integral of (1-x)/((x-3)(x-2)^2)

\int \frac{1 - x}{( x - 3 ) ( x - 2 ) ^{2}} d x