integral of (x+5)/(x^2+9)

Lösung

\int \frac{x + 5}{x ^{2} + 9} d x

\frac{1}{2} ln x^{2} + 9 + \frac{5}{3} arctan (\frac{x}{3}) + C

Schritte zur Lösung

\int \frac{x + 5}{x ^{2} + 9} d x

Multipliziere aus

\frac{x + 5}{x ^{2} + 9} : \frac{x}{x ^{2} + 9} + \frac{5}{x ^{2} + 9}

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{x}{x ^{2} + 9} d x + \int \frac{5}{x ^{2} + 9} d x

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

\int \frac{5}{x ^{2} + 9} d x = \frac{5}{3} arctan (\frac{x}{3})

= \frac{1}{2} ln x^{2} + 9 + \frac{5}{3} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 9 + \frac{5}{3} arctan (\frac{x}{3}) + C

d er i v a t i v e \frac{1}{x - 8}

\int \frac{6 x ^{3} + 2 x ^{2} - 45 x - 15}{x ^{2} - 9} d x

d er i v a t i v e 6 - x

n = 0 \sum \infty \frac{n ^{2}}{2 ^{n}}

\frac{d}{d x} (x sin (\frac{6}{x}))