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Beliebt Rechnen >

integral ((1-x^2))/((1+x^2))

Lösung

integral

\frac{( 1 - x ^{2} )}{( 1 + x ^{2} )}

Lösung

2 arctan (x) - x + C

Schritte zur Lösung

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

\frac{1 - x ^{2}}{1 + x ^{2}} = \frac{2}{1 + x ^{2}} - 1

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

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

\int 1 d x = x

= 2 arctan (x) - x

Füge eine Konstante zur Lösung hinzu

= 2 arctan (x) - x + C

Graph

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