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Integrals of the form \( \int R\left(x, \sqrt{\left.a x^{2}+b x+c\right)} d x\right. \) are calculated
\( \mathrm{P} \) with the aid of one of the following three Euler substitutions:

W
i. \( \sqrt{a x^{2}+b x+c}=t \pm x \sqrt{a} \) if \( a0 \)
ii. \( \sqrt{a x^{2}+b x+c}=t x \pm \sqrt{c} \) if \( c0 \)
iii. \( \sqrt{a x^{2}+b x+c}=(x-a) t \) if \( a x^{2}+b x+c=a(x-a)(x-b) \) i.e., if \( \alpha \) is a real root of \( a x^{2}+b x+c=0 \)

Which of the following functions does not appear in the primitive of \( \frac{1}{1+\sqrt{x^{2}+2 x+2}} \) if \( t \) is a function of \( x \) ?
(1) \( \log _{e}|t+1| \)
(2) \( \log _{e}|t+2| \)
(3) \( \frac{1}{t+2} \)
(4) None of these
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