First of all--Skeeter was right about the exponential integral. Sorry to doubt you skeeter...had the wrong function goin there for a minute.
As for your 4th power cos function, payme, use the reduction formula for cos to the n first, with n = 4, that leaves you with a mess in front of integral cos squared. Then use the reduction formula for integral cos squared on the last bit.
Try it one more time, then ill post my solution if you can't get there.
Sorry friend, I snoozed a bit, and am gonna snooze more in a sec. For simplicity, the attachment is the maple output for your problem. It's a bit...shall we say...longish, but it should work for you. Son't let the filename throw you, it's your exercise.