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Beliebt Rechnen >

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

Lösung

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

Lösung

- arctan (x) + x + C

Schritte zur Lösung

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

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

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

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

\int 1 d x = x

= - arctan (x) + x

Füge eine Konstante zur Lösung hinzu

= - arctan (x) + x + C

Graph

Beliebte Beispiele

integral of x^2-9x+8

\int x^{2} - 9 x + 8 d x

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\int \frac{18}{x ^{4}} d x

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

integral of 1/(x^2-15)

\int \frac{1}{x ^{2} - 15} d x

integral of (5e^{5x})

\int (5 e^{5 x}) d x