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Beliebt Rechnen >

integral of (2x^4)/((x-1)^3)

Lösung

\int \frac{2 x ^{4}}{( x - 1 ) ^{3}} d x

Lösung

- \frac{x ^{4}}{( x - 1 ) ^{2}} + 2 x^{2} + 8 x - \frac{4}{x - 1} + 12 ln ∣ x - 1 ∣ - 10 + C

Schritte zur Lösung

\int \frac{2 x ^{4}}{( x - 1 ) ^{3}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{x ^{4}}{( x - 1 ) ^{3}} d x

Wende die partielle Integration an

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

\int - \frac{2 x ^{3}}{( x - 1 ) ^{2}} d x = - x^{2} - 4 x + \frac{2}{x - 1} - 6 ln ∣ x - 1 ∣ + 5

= 2 (- \frac{x ^{4}}{2 ( x - 1 ) ^{2}} - (- x^{2} - 4 x + \frac{2}{x - 1} - 6 ln ∣ x - 1 ∣ + 5))

Vereinfache

2 (- \frac{x ^{4}}{2 ( x - 1 ) ^{2}} - (- x^{2} - 4 x + \frac{2}{x - 1} - 6 ln ∣ x - 1 ∣ + 5)) : - \frac{x ^{4}}{( x - 1 ) ^{2}} + 2 x^{2} + 8 x - \frac{4}{x - 1} + 12 ln ∣ x - 1 ∣ - 10

= - \frac{x ^{4}}{( x - 1 ) ^{2}} + 2 x^{2} + 8 x - \frac{4}{x - 1} + 12 ln ∣ x - 1 ∣ - 10

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{4}}{( x - 1 ) ^{2}} + 2 x^{2} + 8 x - \frac{4}{x - 1} + 12 ln ∣ x - 1 ∣ - 10 + C

Graph

Beliebte Beispiele

integral of cos(w)

\int cos (w) d w

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

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

integral of 8/(x^2-16)

\int \frac{8}{x ^{2} - 16} d x

integral of (sin^3(x))(cos^4(x))

\int (sin^{3} (x)) (cos^{4} (x)) d x

integral of 7(2x-9)^6

\int 7 (2 x - 9)^{6} d x