Maximum value of integral \( \int_{0}^{1} \sqrt{(1+x)\left(1+x^{3}\...

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Maximum value of integral \( \int_{0}^{1} \sqrt{(1+x)\left(1+x^{3}\right)} d x \) is
\( \mathrm{P}^{20.5} \)
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(1) \( \sqrt{\frac{15}{8}} \)
(2) \( \sqrt{\frac{8}{15}} \)
(3) \( \sqrt{\frac{1}{8}} \)
(4) \( \sqrt{\frac{13}{8}} \)
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