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.
2026-03-29 23:59:56.1774828796
Solve $\int\frac{\sqrt{(x-5)(x+3)}}{(x-1)(x^2-25)}\ dx$
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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 $x-1=4\sec\theta$