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

Lösung

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

arctan (x) + x + C

Schritte zur Lösung

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

\frac{x ^{2} + 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

\int (x + \frac{1}{x} + π) d x

\int \frac{1}{x ^{12}} d x

d er i v a t i v e f (x) = x (3 x + x^{2})

\frac{d r}{d s} = e^{r - 7 s}

\int [3 sin (x) + (\frac{1}{2}) tan (x)] d x