Evaluate the integral.$$$40($tan$5($x$))($sec$3($x$))$dx

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Give an exact answer.

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Provide your answer below:

$$\backslash$int$\_0^\{\backslash$frac$\{\backslash$pi$\}\{4\}\}\backslash$left$(\backslash$tan$^5\backslash$left$($x$\backslash$right$)\backslash$right$)\backslash$left$(-\backslash$sec$^3\backslash$left$($x$\backslash$right$)\backslash$right$)\backslash$ dx$=$$$$$40($tan$5($x$))($sec$3($x$))$ dx$=$