Prove that `int_0^1sqrt((1+x)(1+x^3))\ dx` cannot exceed `sqrt((15)/8)`.

Explanation

To prove that

\[ \int_0^1 \sqrt{(1+x)(1+x^3)} \, dx \leq \sqrt{\frac{15}{8}}, \]

we will first simplify the integrand and then evaluate the integral.

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