integral of (x^2+7)/(x^2+9)

Lösung

\int \frac{x ^{2} + 7}{x ^{2} + 9} d x

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

Schritte zur Lösung

\int \frac{x ^{2} + 7}{x ^{2} + 9} d x

\frac{x ^{2} + 7}{x ^{2} + 9} = - \frac{2}{x ^{2} + 9} + 1

= \int - \frac{2}{x ^{2} + 9} + 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{2}{x ^{2} + 9} d x + \int 1 d x

\int \frac{2}{x ^{2} + 9} d x = \frac{2}{3} arctan (\frac{x}{3})

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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