E and pi?

Calculus Level 5

0x1ex21dx=1A(BeCeDπ)\large \int _{ 0 }^{ \infty }{ \dfrac { x-1 }{ { e }^{ x^{ 2 }-1 } } \, dx } =\dfrac { 1 }{ A } (Be-Ce\sqrt { D\pi } )

If the equation above holds true for positive integers A,B,CA,B,C and DD, find A+B+C+DA+B+C+D.

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