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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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