de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 9ln(x^2-1)

Lösung

\int 9 ln (x^{2} - 1) d x

Lösung

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

Schritte zur Lösung

\int 9 ln (x^{2} - 1) d x

Entferne die Konstante:

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

= 9 \cdot \int ln (x^{2} - 1) d x

Wende die partielle Integration an

= 9 (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

= 9 (x ln (x^{2} - 1) - (- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + 2 x))

Vereinfache

= 9 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x)

Füge eine Konstante zur Lösung hinzu

= 9 (x ln (x^{2} - 1) + ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣ - 2 x) + C

Graph

Beliebte Beispiele

y^'+y/x =(y^2)/x

y^{^{'}} + \frac{y}{x} = \frac{y ^{2}}{x}

derivative of x^4-5x^2+4

\frac{d}{d x} (x^{4} - 5 x^{2} + 4)

derivative y= 4/((4-x^4)^{3/2)}

d er i v a t i v e y = \frac{4}{( 4 - x ^{4} ) ^{\frac{3}{2}}}

integral from 0 to pi/2 of 9(cos(x))^2

\int_{0}^{\frac{π}{2}} 9 (cos (x))^{2} d x

derivative of x^3+3x^2-24x

\frac{d}{d x} (x^{3} + 3 x^{2} - 24 x)