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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{x ^{3}}{3} - 2 x - \frac{1}{x} d x = \frac{x ^{4}}{12} - x^{2} - ln ∣ x ∣

= \frac{x ^{4}}{3} - 2 x^{2} - 1 - (\frac{x ^{4}}{12} - x^{2} - ln ∣ x ∣)

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of e^{cosh(8x})

\frac{d}{d x} (e^{c o s h (8 x)})

\frac{d}{d y} (4 y)

limit as x approaches 0 of 5/(x+1)+4x

x \to 0 lim (\frac{5}{x + 1} + 4 x)

integral of (x^2+4x+8)/(x-2)

\int \frac{x ^{2} + 4 x + 8}{x - 2} d x

derivative of-ln(x^2)

\frac{d}{d x} (- ln (x^{2}))