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

l a pl a ce t r an s f or m 1 - 1 e^{(- t - 2)}

a re a x = 2 - y^{2}, x = y

x \to 0 lim (sin (x^{x}))

\int \frac{1}{x ^{2} + 6 x + 58} d x

d er i v a t i v e f (t) = sin^{2} (e^{s i n^{2} (t)})