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With is the integral of (9(sinx+cosx))/sin(2x)

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9(sinx + cosx)/sin2x
= 9( sinx/(2sinxcosx) + cosx/(2sinxcosx)
= (9/2)(1/cosx + 1/sinx)
= (9/2) (secx + cscs)

can you take it from there?
(the integrals of secx and cscx should be part of your repertoire of basic integrals)

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