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∫03x+x+x+… dx=1a(b+cd)\large \int_0^3 \sqrt{x+\sqrt{x+\sqrt{x+\dots}}}\ dx = \frac1a\left(b+c\sqrt{d}\right) ∫03x+x+x+… dx=a1(b+cd)
If the equation above holds true for some positive integers aaa, bbb, ccc, and ddd such that gcd(a,b,c)=1\gcd{(a,b,c)}=1gcd(a,b,c)=1 and ddd is square-free, then find the value of a+b+c+da+b+c+da+b+c+d.
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