integral of ((x^2+31))/(x^2+36)

Lösung

\int \frac{( x ^{2} + 31 )}{x ^{2} + 36} d x

- \frac{5}{6} arctan (\frac{x}{6}) + x + C

Schritte zur Lösung

\int \frac{x ^{2} + 31}{x ^{2} + 36} d x

\frac{x ^{2} + 31}{x ^{2} + 36} = - \frac{5}{x ^{2} + 36} + 1

= \int - \frac{5}{x ^{2} + 36} + 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{5}{x ^{2} + 36} d x + \int 1 d x

\int \frac{5}{x ^{2} + 36} d x = \frac{5}{6} arctan (\frac{x}{6})

\int 1 d x = x

= - \frac{5}{6} arctan (\frac{x}{6}) + x

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{6} arctan (\frac{x}{6}) + x + C

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