Evaluate the definite integral.

Integral from $0$ to $2$ StartFraction e Superscript $2$ t Over left parenthesis $3$ plus e Superscript $2$ t right parenthesis squared EndFraction dt

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Part $1$

Integral from $0$ to $2$ StartFraction e Superscript $2$ t Over left parenthesis $3$ plus e Superscript $2$ t right parenthesis squared EndFraction dtequalsenter your response here

$($Type an exact answer in terms of

e$.)$