Posted by Em on Thursday, March 7, 2013 at 12:22am.
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)