de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (8x+9)/((x^2+9)(8-x))

Lösung

\int \frac{8 x + 9}{( x ^{2} + 9 ) ( 8 - x )} d x

Lösung

\frac{1}{2} ln x^{2} + 9 - ln ∣ x - 8 ∣ + C

Schritte zur Lösung

\int \frac{8 x + 9}{( x ^{2} + 9 ) ( 8 - x )} d x

Ermittle den Partialbruch von

\frac{8 x + 9}{( x ^{2} + 9 ) ( 8 - x )} : \frac{x}{x ^{2} + 9} - \frac{1}{x - 8}

= \int \frac{x}{x ^{2} + 9} - \frac{1}{x - 8} 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{x}{x ^{2} + 9} d x - \int \frac{1}{x - 8} d x

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

\int \frac{1}{x - 8} d x = ln ∣ x - 8 ∣

= \frac{1}{2} ln x^{2} + 9 - ln ∣ x - 8 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 9 - ln ∣ x - 8 ∣ + C

Graph

Beliebte Beispiele

integral of 1/(6y)

\int \frac{1}{6 y} d y

integral of 1/(sqrt(49+t^2))

\int \frac{1}{49 + t ^{2}} d t

tangent y=sin(x),\at x=(7pi)/6

t an g e n t y = sin (x), at x = \frac{7 π}{6}

limit as x approaches 0.9 of 2x^2-5x+1

x \to 0.9 lim (2 x^{2} - 5 x + 1)

integral of-x/(x+1)

\int - \frac{x}{x + 1} d x