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Beliebt Rechnen >

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

Lösung

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

Lösung

2 arctan (x) - \frac{x ^{3}}{3} + C

Schritte zur Lösung

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

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

\int x^{2} d x = \frac{x ^{3}}{3}

= 2 arctan (x) - \frac{x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 2 arctan (x) - \frac{x ^{3}}{3} + C

Graph

Beliebte Beispiele

derivative f(2)=-x^2+6x-3

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n = 1 \sum \infty (\frac{2}{3})^{n - 1}

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x \to o lim (f (x))

integral of 1/((x^2+7)^{3/2)}

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