Arc length

Calculus Level pending

Define \(\gamma (t)=({ e }^{ t }\cos { t } ,{ e }^{ t }\sin { t } )\),then if the arc-length starting at \(\gamma (0)=(1,0)\) and ending at \(t=1\) is in the form \(\sqrt { A } (Be-C)\) where \(A,B,C\) are positive integers,find \(A+B+C\).

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