Question-125426

Question Number 125426 by joki last updated on 11/Dec/20

Answered by bramlexs22 last updated on 11/Dec/20

x^{2} - 1 = u

\frac{1}{2} \int \frac{d u}{u^{2} (u + 2)} = \frac{1}{2} \int [\frac{A}{u} + \frac{B}{u^{2}} + \frac{C}{u + 2}] d u

= \frac{1}{2} (- \frac{1}{4} \ln ∣ u ∣ - \frac{1}{2 u} + \frac{1}{4} \ln ∣ u + 2 ∣) + c

= - \frac{1}{8} \ln ∣ u ∣ - \frac{1}{4 u} + \frac{1}{8} \ln ∣ u + 2 ∣ + c

= \frac{1}{8} \ln ∣ \frac{x^{2} + 1}{x^{2} - 1} ∣ - \frac{1}{4 (x^{2} - 1)} + c

Commented by joki last updated on 11/Dec/20

l d o n t u n d e s t a n d s i r, p l e a s e h e l p m e e x p l a i n

w i t h d e t a i l . t h a n k s s i r

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