de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 7/(x^4-1)

Lösung

\int \frac{7}{x ^{4} - 1} d x

Lösung

7 (- \frac{1}{2} arctan (x) - \frac{1}{4} ln ∣ x + 1 ∣ + \frac{1}{4} ln ∣ x - 1 ∣) + C

Schritte zur Lösung

\int \frac{7}{x ^{4} - 1} d x

Entferne die Konstante:

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

= 7 \cdot \int \frac{1}{x ^{4} - 1} d x

Ermittle den Partialbruch von

\frac{1}{x ^{4} - 1} : - \frac{1}{2 ( x ^{2} + 1 )} - \frac{1}{4 ( x + 1 )} + \frac{1}{4 ( x - 1 )}

= 7 \cdot \int - \frac{1}{2 ( x ^{2} + 1 )} - \frac{1}{4 ( x + 1 )} + \frac{1}{4 ( x - 1 )} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 7 (- \int \frac{1}{2 ( x ^{2} + 1 )} d x - \int \frac{1}{4 ( x + 1 )} d x + \int \frac{1}{4 ( x - 1 )} d x)

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

\int \frac{1}{4 ( x + 1 )} d x = \frac{1}{4} ln ∣ x + 1 ∣

\int \frac{1}{4 ( x - 1 )} d x = \frac{1}{4} ln ∣ x - 1 ∣

= 7 (- \frac{1}{2} arctan (x) - \frac{1}{4} ln ∣ x + 1 ∣ + \frac{1}{4} ln ∣ x - 1 ∣)

Füge eine Konstante zur Lösung hinzu

= 7 (- \frac{1}{2} arctan (x) - \frac{1}{4} ln ∣ x + 1 ∣ + \frac{1}{4} ln ∣ x - 1 ∣) + C

Graph

Beliebte Beispiele

integral of-3/2 x^2cos(2x)

\int - \frac{3}{2} x^{2} cos (2 x) d x

integral of x/(sqrt(1-4x))

\int \frac{x}{1 - 4 x} d x

integral of-(sin(3x))/(cos^3(3x))

\int - \frac{sin ( 3 x )}{cos ^{3} ( 3 x )} d x

integral of (x^2-5)/((1+x)^3)

\int \frac{x ^{2} - 5}{( 1 + x ) ^{3}} d x

integral 1/(4x)

in t e g r a l \frac{1}{4 x}