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∫01x3(x+1)3+6ex+3x+5 dx\large{\int_0^1 \dfrac{x^3}{(x+1)^3 + 6e^x + 3x+5}\, dx }∫01(x+1)3+6ex+3x+5x3dx
If the value of the integral above can be expressed as ln(AeBe+C)\ln\left( \frac {Ae}{Be+C} \right) ln(Be+CAe) for positive integers A,BA,BA,B and CCC, find the minimum value of A+B+CA+B+CA+B+C.
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