A casino offers a game in which a random number \(x\) in the range \([0,1]\) is chosen, and the player receives \(\dfrac{1}{x^3+1}\) dollars. What, in dollars, is the maximum you should be willing to pay to play this game?

Details:

• Assume that it is possible to win a fraction of a cent.

• The value of each cent is the same, regardless of whether the person is rich or poor.

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