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Beliebt Rechnen >

integral of 8ln(x^2-1)

Lösung

\int 8 ln (x^{2} - 1) d x

Lösung

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

Schritte zur Lösung

\int 8 ln (x^{2} - 1) d x

Entferne die Konstante:

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

= 8 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= 8 (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

= 8 (x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x))

Vereinfache

= 8 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x)

Füge eine Konstante zur Lösung hinzu

= 8 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

Graph

Beliebte Beispiele

f(x)= 1/(xln(x))

f (x) = \frac{1}{x ln ( x )}

integral from 0 to 1 of sqrt(64t^2+9t^4)

\int_{0}^{1} 64 t^{2} + 9 t^{4} d t

derivative tan(sqrt(3t))

d er i v a t i v e tan (3 t)

integral of 2tsqrt(2t-3)

\int 2 t 2 t - 3 d t

x^'(t)=(1/3 x)(1-x/3),x(0)=6

x^{^{'}} (t) = (\frac{1}{3} x) (1 - \frac{x}{3}), x (0) = 6