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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x-2)/(sqrt(x^2-6x))

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