Evaluate the integral.

Integral from negative StartFraction pi Over $4$ EndFraction to negative StartFraction pi Over $6$ EndFraction left parenthesis $5$ secant squared t plus StartFraction $7$ pi Over t squared EndFraction right parenthesis dt$$$4$$65$sec$2$t$+7$t$2$dt

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Part $1$

Integral from negative StartFraction pi Over $4$ EndFraction to negative StartFraction pi Over $6$ EndFraction left parenthesis $5$ secant squared t plus StartFraction $7$ pi Over t squared EndFraction right parenthesis dt$$$4$$65$sec$2$t$+7$t$2$dtequals$=$enter your response here

$($Type an exact$$ answer, using radicals as$$ needed.$)$