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Beliebt Rechnen >

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

Lösung

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

Lösung

3 arctan (x) - 2 arcsin (x) + C

Schritte zur Lösung

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

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x)

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

= 3 arctan (x) - 2 arcsin (x)

Füge eine Konstante zur Lösung hinzu

= 3 arctan (x) - 2 arcsin (x) + C

Graph

Beliebte Beispiele

integral of (-8)/(x(ln(x))^2)

\int \frac{- 8}{x ( ln ( x ) ) ^{2}} d x

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

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