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I have some problems with the task. How to evaluate $$\int\frac{\sqrt{(x-5)(x+3)}}{(x-1)(x^2-25)}\ \mathrm{d}x$$ I have absolutely no idea. Help me please. Thank you.

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  • $\begingroup$ Can you please confirm the correctness of the edit $\endgroup$ – lab bhattacharjee May 22 '14 at 14:57
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For $x\ge3,$

$$\sqrt{x+3}\sqrt{x-5}=\sqrt{(x+3)(x-5)}=\sqrt{x^2-2x-15}=\sqrt{(x-1)^2-4^2}$$

Using this, start with $x-1=4\sec\theta$

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  • $\begingroup$ and how it can help me?! $\endgroup$ – uley May 22 '14 at 14:50
  • $\begingroup$ change of variable $\endgroup$ – PA6OTA May 22 '14 at 14:51
  • $\begingroup$ @user151833, Simplify and find where you have reached $\endgroup$ – lab bhattacharjee May 22 '14 at 14:51
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    $\begingroup$ I did not understand :( $\endgroup$ – uley May 22 '14 at 15:01
  • $\begingroup$ @user151833, Why don't you simplify? $\endgroup$ – lab bhattacharjee May 22 '14 at 15:04

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