integral of (x+9)/(x^2+4)

Lösung

\int \frac{x + 9}{x ^{2} + 4} d x

\frac{1}{2} ln x^{2} + 4 + \frac{9}{2} arctan (\frac{x}{2}) + C

Schritte zur Lösung

\int \frac{x + 9}{x ^{2} + 4} d x

Multipliziere aus

\frac{x + 9}{x ^{2} + 4} : \frac{x}{x ^{2} + 4} + \frac{9}{x ^{2} + 4}

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} + 4} d x + \int \frac{9}{x ^{2} + 4} d x

\int \frac{x}{x ^{2} + 4} d x = \frac{1}{2} ln x^{2} + 4

\int \frac{9}{x ^{2} + 4} d x = \frac{9}{2} arctan (\frac{x}{2})

= \frac{1}{2} ln x^{2} + 4 + \frac{9}{2} arctan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 4 + \frac{9}{2} arctan (\frac{x}{2}) + C

x \to \infty lim ((x!)^{2})

a re a x^{2} - 12, 4 x

n or ma l y = (x + 3)^{3}, at x = - \frac{1}{75}

\frac{d}{d x} (\frac{2}{( 2 - x ) ^{2}})

\frac{d}{d x} (\frac{2}{3} (x^{2} - 1)^{\frac{3}{2}})