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

Lösung

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

- arctan (x) + x + C

Schritte zur Lösung

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

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

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

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

\int 1 d x = x

= - arctan (x) + x

Füge eine Konstante zur Lösung hinzu

= - arctan (x) + x + C

\frac{d}{d x} (5 - 2 (x - 2)^{2})

\frac{d}{d y} (y x)

\frac{\partial}{\partial t} (cos (t) - sin (t))

\frac{\partial}{\partial x} (\frac{x + y}{1 + x ^{2}})

\frac{d ^{4}}{d x ^{4}} (\frac{1}{1 - x})