# 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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