integral of 7ln(x^2-1)

Lösung

\int 7 ln (x^{2} - 1) d x

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

Schritte zur Lösung

\int 7 ln (x^{2} - 1) d x

Entferne die Konstante:

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

= 7 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= 7 (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

= 7 (x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x))

Vereinfache

= 7 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x)

Füge eine Konstante zur Lösung hinzu

= 7 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

\frac{\partial}{\partial z} (x e^{y} + y e^{z} + z e^{x})

t an g e n t \frac{2}{4 - x}, at x = 1

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x \to \infty lim (9^{x})