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How do I solve $x\sin(x)=b$ for $x$?

This came up while I was trying to solve something else. It seems simple but I can't figure it out right now.

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No closed-form solution. Furthermore, infinitely many solutions if there is no bound on $x.$ – Will Jagy Nov 15 '12 at 23:02

I suspect you can only do it numerically via Newton's method or the like, but not algebraically. Newton's method is very efficient.

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