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Beliebt Rechnen >

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

Lösung

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

Lösung

- ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + x + C

Schritte zur Lösung

\int \frac{x ^{2} + 1}{x ^{2} - 1} d x

\frac{x ^{2} + 1}{x ^{2} - 1} = \frac{2}{x ^{2} - 1} + 1

= \int \frac{2}{x ^{2} - 1} + 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

= \int \frac{2}{x ^{2} - 1} d x + \int 1 d x

\int \frac{2}{x ^{2} - 1} d x = - ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣

\int 1 d x = x

= - ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + x

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + x + C

Graph

Beliebte Beispiele

integral of cos^4(y)

\int cos^{4} (y) d y

integral of 5/(4x+3)

\int \frac{5}{4 x + 3} d x

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

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

integral of (4x^2)/(sqrt(1-12x^3))

\int \frac{4 x ^{2}}{1 - 12 x ^{3}} d x

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

\int \frac{1}{y ^{2} + x ^{2}} d x