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Beliebt Rechnen >

integral of ((5x-3))/(x^4+x^3-2x^2)

Lösung

\int \frac{( 5 x - 3 )}{x ^{4} + x ^{3} - 2 x ^{2}} d x

Lösung

- \frac{7}{4} ln ∣ x ∣ - \frac{3}{2 x} + \frac{2}{3} ln ∣ x - 1 ∣ + \frac{13}{12} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{5 x - 3}{x ^{4} + x ^{3} - 2 x ^{2}} d x

Ermittle den Partialbruch von

\frac{5 x - 3}{x ^{4} + x ^{3} - 2 x ^{2}} : - \frac{7}{4 x} + \frac{3}{2 x ^{2}} + \frac{2}{3 ( x - 1 )} + \frac{13}{12 ( x + 2 )}

= \int - \frac{7}{4 x} + \frac{3}{2 x ^{2}} + \frac{2}{3 ( x - 1 )} + \frac{13}{12 ( 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{7}{4 x} d x + \int \frac{3}{2 x ^{2}} d x + \int \frac{2}{3 ( x - 1 )} d x + \int \frac{13}{12 ( x + 2 )} d x

\int \frac{7}{4 x} d x = \frac{7}{4} ln ∣ x ∣

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

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

\int \frac{13}{12 ( x + 2 )} d x = \frac{13}{12} ln ∣ x + 2 ∣

= - \frac{7}{4} ln ∣ x ∣ - \frac{3}{2 x} + \frac{2}{3} ln ∣ x - 1 ∣ + \frac{13}{12} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{7}{4} ln ∣ x ∣ - \frac{3}{2 x} + \frac{2}{3} ln ∣ x - 1 ∣ + \frac{13}{12} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of (7x^2)/(sqrt(4x^3-5))

\int \frac{7 x ^{2}}{4 x ^{3} - 5} d x

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

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

integral of 8cos^3(5x)

\int 8 cos^{3} (5 x) d x

integral of cot(2x)(cot(2x)+3csc(2x))

\int cot (2 x) (cot (2 x) + 3 csc (2 x)) d x

integral of (1-x)^{(-1)/2}

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