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

Lösung

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

\frac{1}{2} ln x^{2} + 9 + \frac{7}{3} arctan (\frac{x}{3}) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{7}{x ^{2} + 9} d x = \frac{7}{3} arctan (\frac{x}{3})

= \frac{1}{2} ln x^{2} + 9 + \frac{7}{3} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 9 + \frac{7}{3} arctan (\frac{x}{3}) + C

n = 1 \sum \infty \frac{x ^{n}}{n}

\frac{d y}{d x} + 2 y = x^{2} + 2 x

\int \frac{13 x ^{2}}{x ^{2} - 4} d x

f (x) = \frac{3}{2 x ^{2}}

\frac{d}{d x} (\frac{1}{x ^{2} - 9})