\( \int \frac{d x}{\sqrt[4]{1+x^{4}}} \) is (1) \( \frac{1}{4} \log _{e}\left|\frac{\left(1+x^{4....

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\( \int \frac{d x}{\sqrt[4]{1+x^{4}}} \) is
\( \mathrm{P} \)
(1) \( \frac{1}{4} \log _{e}\left|\frac{\left(1+x^{4}\right)^{1 / 4}-x}{\left(1+x^{4}\right)^{1 / 4}+x}\right|+\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{\left(1+x^{4}\right)^{1 / 4}}{x}\right)+c \)
(2) \( \frac{1}{4} \log _{e}\left|\frac{(1+x)^{1 / 4}-x}{(1+x)^{1 / 4}+x}\right|-\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{(1+x)^{1 / 4}}{x}\right)+c \)
(3) \( \frac{-1}{4} \log _{e}\left|\frac{\left(1+x^{4}\right)^{1 / 4}-x}{\left(1+x^{4}\right)^{1 / 4}+x}\right|-\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{\left(1+x^{4}\right)^{1 / 4}}{x}\right)+c \)
(4) \( \frac{-1}{4} \log \left|\frac{\left(1+x^{4}\right)^{1 / 4}-x}{\left(1+x^{4}\right)^{1 / 4}+x}\right|+\frac{1}{2} \operatorname{Tan}^{-1}\left(\frac{\left(1+x^{4}\right)^{1 / 4}}{x}\right)+c \)
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