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Beliebt Rechnen >

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

Lösung

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

Lösung

5 ln ∣ x - 2 ∣ - 5 ln ∣ x - 3 ∣ - \frac{7}{x - 3} + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{2 x + 1}{( x - 2 ) ( x - 3 ) ^{2}} : \frac{5}{x - 2} - \frac{5}{x - 3} + \frac{7}{( x - 3 ) ^{2}}

= \int \frac{5}{x - 2} - \frac{5}{x - 3} + \frac{7}{( x - 3 ) ^{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{5}{x - 2} d x - \int \frac{5}{x - 3} d x + \int \frac{7}{( x - 3 ) ^{2}} d x

\int \frac{5}{x - 2} d x = 5 ln ∣ x - 2 ∣

\int \frac{5}{x - 3} d x = 5 ln ∣ x - 3 ∣

\int \frac{7}{( x - 3 ) ^{2}} d x = - \frac{7}{x - 3}

= 5 ln ∣ x - 2 ∣ - 5 ln ∣ x - 3 ∣ - \frac{7}{x - 3}

Füge eine Konstante zur Lösung hinzu

= 5 ln ∣ x - 2 ∣ - 5 ln ∣ x - 3 ∣ - \frac{7}{x - 3} + C

Graph

Beliebte Beispiele

derivative of x^5-3x^3+x-1

\frac{d}{d x} (x^{5} - 3 x^{3} + x - 1)

integral of 1/(x(x^4+1))

\int \frac{1}{x ( x ^{4} + 1 )} d x

steigung y=(3x^3+2x)^{1/2}

s l o p e y = (3 x^{3} + 2 x)^{\frac{1}{2}}

derivative f(x)=e^{-9}

d er i v a t i v e f (x) = e^{- 9}

integral from 0 to 0.08 of 2000x

\int_{0}^{0.08} 2000 x d x