Let \( I=\int \frac{\left(\sqrt{1+x+x^{2}}-1\right)^{2}}{x^{2} \sqr...
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Let \( I=\int \frac{\left(\sqrt{1+x+x^{2}}-1\right)^{2}}{x^{2} \sqrt{1+x+x^{2}}} d x \), then
(a) \( \frac{2}{x}\left(1-\sqrt{1+x+x^{2}}\right)+C \)
(b) \( \frac{2}{x}\left(1-\sqrt{1+x+x^{2}}\right) \)
\[
+\ln \left(x+\frac{1}{2}+\sqrt{x^{2}+x+1}\right)+C
\]
(c) \( \frac{-2(1+x)}{\sqrt{1+x+x^{2}+1}}+\ln \left(x+\sqrt{x^{2}+x+1}\right)+C \)
(d) \( -\frac{1}{x}\left(1+\frac{1}{\sqrt{1+x+x^{2}}}\right)+\ln \left(x+\sqrt{x^{2}+x+1}\right)+C \)
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