de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^2+3)/(x^2(x^2+9))

Lösung

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

Lösung

- \frac{1}{3 x} + \frac{2}{9} arctan (\frac{x}{3}) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{2} + 3}{x ^{2} ( x ^{2} + 9 )} : \frac{1}{3 x ^{2}} + \frac{2}{3 ( x ^{2} + 9 )}

= \int \frac{1}{3 x ^{2}} + \frac{2}{3 ( x ^{2} + 9 )} 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{1}{3 x ^{2}} d x + \int \frac{2}{3 ( x ^{2} + 9 )} d x

\int \frac{1}{3 x ^{2}} d x = - \frac{1}{3 x}

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

= - \frac{1}{3 x} + \frac{2}{9} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3 x} + \frac{2}{9} arctan (\frac{x}{3}) + C

Graph

Beliebte Beispiele

integral of x^2-4x+10

\int x^{2} - 4 x + 10 d x

integral of (3x^2+14x-12+3/(x^2))

\int (3 x^{2} + 14 x - 12 + \frac{3}{x ^{2}}) d x

integral of 4/((x-6)(x-2))

\int \frac{4}{( x - 6 ) ( x - 2 )} d x

integral of (x^3)/(1-x)

\int \frac{x ^{3}}{1 - x} d x

integral of xe^{x^2}sin(x^2+4)

\int x e^{x^{2}} sin (x^{2} + 4) d x