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

Lösung

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

\frac{1}{2} ln x^{2} - 1 - ln ∣ x + 1 ∣ + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e cos (2 θ)

x \to 0 lim (\frac{8}{\frac{2 + e ^{1}}{x}})

t an g e n t f (x) = 14 x sin (x), at x = \frac{π}{2}

\int \frac{11 x ^{2}}{( 25 + x ^{2} ) ^{2}} d x

\int 30 (x + 2) (x + 3)^{4} d x