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Beliebt Rechnen >

integral of-7ln(x^2-1)

Lösung

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

Lösung

- 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

Graph

Beliebte Beispiele

sum from n=2 to infinity of 1/(n(n-1))

n = 2 \sum \infty \frac{1}{n ( n - 1 )}

implicit (dy)/(dx),4y^2-5y+8=2x^2-3x

im pl i c i t \frac{d y}{d x}, 4 y^{2} - 5 y + 8 = 2 x^{2} - 3 x

integral of 2x(1+x^2)^2

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

y^{''}-4y^'+4y=2e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 e^{2 x}

derivative of 5e^{-x}+e^{3x}

\frac{d}{d x} (5 e^{- x} + e^{3 x})