de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/((x-2)(x-3))

Lösung

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

Lösung

- ln ∣ x - 2 ∣ + ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x - 2} d x = ln ∣ x - 2 ∣

\int \frac{1}{x - 3} d x = ln ∣ x - 3 ∣

= - ln ∣ x - 2 ∣ + ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x - 2 ∣ + ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral from-3 to 3 of (18)/(x^2-6x-72)

\int_{- 3}^{3} \frac{18}{x ^{2} - 6 x - 72} d x

(\partial)/(\partial y)((2x)/((2x+3y)^2))

\frac{\partial}{\partial y} (\frac{2 x}{( 2 x + 3 y ) ^{2}})

derivative f(x)=e^t

d er i v a t i v e f (x) = e^{t}

tangent y=sqrt(2x+1),(4,3)

t an g e n t y = 2 x + 1, (4, 3)

integral of (x^2)/(e^{x/3)}

\int \frac{x ^{2}}{e ^{\frac{x}{3}}} d x