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Beliebt Rechnen >

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

Lösung

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

Lösung

x - arctan (x) + C

Schritte zur Lösung

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

\int 1 d x = x

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

= x - arctan (x)

Füge eine Konstante zur Lösung hinzu

= x - arctan (x) + C

Graph

Beliebte Beispiele

in t e g r a l 5

integral of x^2ln(ax)

\int x^{2} ln (a x) d x

integral of sqrt(1/4-x^2)

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

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\int 4 ln (2 x) d x

integral of (xe^x)/(1+x)

\int \frac{x e ^{x}}{1 + x} d x