Evaluate the following integral.

Integral from one third to $1$ StartFraction tangent Superscript negative $1$ Baseline left parenthesis StartRoot $3$ x EndRoot right parenthesis Over left parenthesis $3$ x right parenthesis Superscript one half Baseline plus left parenthesis $3$ x right parenthesis Superscript three halves EndFraction dx$131$tan$13$x$(3$x$)12+(3$x$)32$dx

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Part $1$

Integral from one third to $1$ StartFraction tangent Superscript negative $1$ Baseline left parenthesis StartRoot $3$ x EndRoot right parenthesis Over left parenthesis $3$ x right parenthesis Superscript one half Baseline plus left parenthesis $3$ x right parenthesis Superscript three halves EndFraction dx$131$tan$13$x$(3$x$)12+(3$x$)32$dxequals$=$enter your response here

$($Type an exact answer. Use parentheses to clearly denote the argument of each$$ function.$)$