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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{x ^{4}}{x - 1} + 4 (\frac{1}{3} (x - 1)^{3} + \frac{3}{2} (x - 1)^{2} + 3 (x - 1) + ln ∣ x - 1 ∣) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

- \frac{x ^{4}}{x - 1} - (- 4 (\frac{( x - 1 ) ^{3}}{3} + \frac{3 ( x - 1 ) ^{2}}{2} + 3 (x - 1) + ln ∣ x - 1 ∣)) : - \frac{x ^{4}}{x - 1} + 4 (\frac{1}{3} (x - 1)^{3} + \frac{3}{2} (x - 1)^{2} + 3 (x - 1) + ln ∣ x - 1 ∣)

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

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{4}}{x - 1} + 4 (\frac{1}{3} (x - 1)^{3} + \frac{3}{2} (x - 1)^{2} + 3 (x - 1) + ln ∣ x - 1 ∣) + C

Graph

Beliebte Beispiele

integral of 1/((5x^2+3)^2)

\int \frac{1}{( 5 x ^{2} + 3 ) ^{2}} d x

integral of (s^2-4s-6)/(s^4)

\int \frac{s ^{2} - 4 s - 6}{s ^{4}} d s

integral of 1/2 xe^{x/4}

\int \frac{1}{2} x e^{\frac{x}{4}} d x

integral of (7^x+1sin(10x)+3sec^2(x))

\int (7^{x} + 1 sin (10 x) + 3 sec^{2} (x)) d x

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

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