Simple Definite Integral #1

Calculus Level 5

01x3(x+1)3+6ex+3x+5dx\large{\int_0^1 \dfrac{x^3}{(x+1)^3 + 6e^x + 3x+5}\, dx }

If the value of the integral above can be expressed as ln(AeBe+C)\ln\left( \frac {Ae}{Be+C} \right) for positive integers A,BA,B and CC, find the minimum value of A+B+CA+B+C.

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