integral of 5ln(x^2-1)

Lösung

\int 5 ln (x^{2} - 1) d x

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

Schritte zur Lösung

\int 5 ln (x^{2} - 1) d x

Entferne die Konstante:

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

= 5 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= 5 (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

= 5 (x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x))

Vereinfache

= 5 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x)

Füge eine Konstante zur Lösung hinzu

= 5 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

\int (l - x)^{2} d x

x \to \infty lim ((3 x - 7)^{2 x - 1})

\int [(3 x^{5} - 4)^{2} \cdot 5 x^{4}] d x

\int_{0}^{1} π (3 x^{2} - 3 x^{6}) d x

\frac{\partial}{\partial x} (8 - x^{2} - y^{2})