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I asked a questiona question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here:

Is it possible to express the following indefinite integral in elementary functions? $${\large\int}\sqrt{x+\sqrt{x+\sqrt{x+1}}}\ dx$$

I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here:

Is it possible to express the following indefinite integral in elementary functions? $${\large\int}\sqrt{x+\sqrt{x+\sqrt{x+1}}}\ dx$$

I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here:

Is it possible to express the following indefinite integral in elementary functions? $${\large\int}\sqrt{x+\sqrt{x+\sqrt{x+1}}}\ dx$$

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Vladimir Reshetnikov
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Is it possible to express $\int\sqrt{x+\sqrt{x+\sqrt{x+1}}}dx$ in elementary functions?

I asked a question at Math.SE last year and later offered a bounty for it, but it remains unsolved even in the simplest case. So I finally decided to repost this case here:

Is it possible to express the following indefinite integral in elementary functions? $${\large\int}\sqrt{x+\sqrt{x+\sqrt{x+1}}}\ dx$$