calculate-1-dx-x-2-1-x-2-3-

Question Number 98179 by abdomathmax last updated on 12/Jun/20

calculate \int_{1}^{+ \infty} \frac{dx}{x^{2} {(1 - x^{2})}^{3}}

Answered by MJS last updated on 12/Jun/20

I love {Ostrogradski}^{'} s Method \dots

it leads to

- \frac{15 x^{4} - 25 x^{2} + 8}{8 x {(x^{2} - 1)}^{2}} - \frac{15}{8} \int \frac{d x}{x^{2} - 1} =

= - \frac{15 x^{4} - 25 x^{2} + 8}{8 x {(x^{2} - 1)}^{2}} + \frac{15}{16} \ln ∣ \frac{x + 1}{x - 1} ∣ + C

\underset{2}{\int^{+ \infty}} \frac{d x}{x^{2} {(1 - x^{2})}^{3}} = \frac{37}{36} - \frac{15}{16} \ln 3

Commented by mathmax by abdo last updated on 12/Jun/20

thanks sir mjs

Answered by mathmax by abdo last updated on 12/Jun/20

sorry the Q is calculate \int_{2}^{+ \infty} \frac{dx}{x^{2} {(1 - x^{2})}^{3}}