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Beliebt Rechnen >

integral of-6ln(x^2-1)

Lösung

\int - 6 ln (x^{2} - 1) d x

Lösung

- 6 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

Schritte zur Lösung

\int - 6 ln (x^{2} - 1) d x

Entferne die Konstante:

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

= - 6 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= - 6 (x ln (x^{2} - 1) - \int \frac{2 x ^{2}}{x ^{2} - 1} d x)

\int \frac{2 x ^{2}}{x ^{2} - 1} d x = - ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x

= - 6 (x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x))

Vereinfache

= - 6 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x)

Füge eine Konstante zur Lösung hinzu

= - 6 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

Graph

Beliebte Beispiele

integral of (xcos(4x))

\int (x cos (4 x)) d x

derivative of (2x+2x^2/((1+2x)^2))

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

derivative of xe^{-x}-e^{-x}

\frac{d}{d x} (x e^{- x} - e^{- x})

limit as x approaches 0 of 1/(3x)

x \to 0 lim (\frac{1}{3 x})

x y^{^{'}} - y = x ln (x)