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Beliebt Rechnen >

integral of 1/(x^3-8x^2+21x-18)

Lösung

\int \frac{1}{x ^{3} - 8 x ^{2} + 21 x - 18} d x

Lösung

\frac{x}{x ^{3} - 8 x ^{2} + 21 x - 18} - ln ∣ x - 3 ∣ + \frac{1}{x - 3} - \frac{3}{( x - 3 ) ^{2}} + ln ∣ x - 2 ∣ - \frac{2}{x - 2} + C

Schritte zur Lösung

\int \frac{1}{x ^{3} - 8 x ^{2} + 21 x - 18} d x

Wende die partielle Integration an

= \frac{x}{x ^{3} - 8 x ^{2} + 21 x - 18} - \int - \frac{x ( 3 x - 7 )}{( x - 3 ) ^{3} ( x - 2 ) ^{2}} d x

\int - \frac{x ( 3 x - 7 )}{( x - 3 ) ^{3} ( x - 2 ) ^{2}} d x = ln ∣ x - 3 ∣ - \frac{1}{x - 3} + \frac{3}{( x - 3 ) ^{2}} - ln ∣ x - 2 ∣ + \frac{2}{x - 2}

= \frac{x}{x ^{3} - 8 x ^{2} + 21 x - 18} - (ln ∣ x - 3 ∣ - \frac{1}{x - 3} + \frac{3}{( x - 3 ) ^{2}} - ln ∣ x - 2 ∣ + \frac{2}{x - 2})

Vereinfache

= \frac{x}{x ^{3} - 8 x ^{2} + 21 x - 18} - ln ∣ x - 3 ∣ + \frac{1}{x - 3} - \frac{3}{( x - 3 ) ^{2}} + ln ∣ x - 2 ∣ - \frac{2}{x - 2}

Füge eine Konstante zur Lösung hinzu

= \frac{x}{x ^{3} - 8 x ^{2} + 21 x - 18} - ln ∣ x - 3 ∣ + \frac{1}{x - 3} - \frac{3}{( x - 3 ) ^{2}} + ln ∣ x - 2 ∣ - \frac{2}{x - 2} + C

Graph

Beliebte Beispiele

integral of (2x^2+2x-9)/(x^2-4)

\int \frac{2 x ^{2} + 2 x - 9}{x ^{2} - 4} d x

integral of (6x^{-2}+10)

\int (6 x^{- 2} + 10) d x

integral of 6tan(x)

\int 6 tan (x) d x

integral of (sin(3t))/(cos(3t)-1)

\int \frac{sin ( 3 t )}{cos ( 3 t ) - 1} d t

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

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