integral of 4ln(x^2-1)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= 4 (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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int 2 x^{2} - 4 x - 6 d x

\frac{d}{d x} (x^{\frac{9}{x}})

\frac{d y}{d t} = 2100 - 300 (\frac{y}{17000})

\int \frac{5}{x ^{6}} d x

\frac{d}{d x} (ln ((x + 3)^{- 1}))