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Prove that int0^1sqrt((1+x)(1+x^3))\ dx ...

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

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`int_(0)^(1)sqrt((1+x)(1+x^(3)))dx le sqrt((int_(0)^(1)(1+x)dx)(int_(0)^(1)(1+x^(3))dx))`
`=sqrt((x+(x^(2))/2)_(0)^(1)(x+(x^(4))/4)_(0)^(1))`
`=sqrt((3/2)(5/4))`
`=sqrt(15/8)`
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