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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{( x + 2 ) ( x - 2 )} : - \frac{1}{4 ( x + 2 )} + \frac{1}{4 ( x - 2 )}

= \int - \frac{1}{4 ( x + 2 )} + \frac{1}{4 ( x - 2 )} 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}{4 ( x + 2 )} d x + \int \frac{1}{4 ( x - 2 )} d x

\int \frac{1}{4 ( x + 2 )} d x = \frac{1}{4} ln ∣ x + 2 ∣

\int \frac{1}{4 ( x - 2 )} d x = \frac{1}{4} ln ∣ x - 2 ∣

= - \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(sin(5pix+4y))

\frac{\partial}{\partial x} (sin (5 π x + 4 y))

derivative of (1/(e^x)^{100})

\frac{d}{d x} ((\frac{1}{e ^{x}})^{100})

integral of (e^x)/((e^x+1)ln(e^x+1))

\int \frac{e ^{x}}{( e ^{x} + 1 ) ln ( e ^{x} + 1 )} d x

tangent y=ln(x^2),\at x=3

t an g e n t y = ln (x^{2}), at x = 3

integral of sinh^2(x)

\int sinh^{2} (x) d x