I think you want to break the integral into two parts by the sum. Then make the u substitution u=1/2cos(x). That will get you the sin(x)dx you need. so you will have a
May need to break this integral up again to deal with that absolute value.
Then I think just do the integration by parts twice trick and you will get back something familar and solve that way. I assume you know what you are doing if you were assigned this kind of problem, so I left out a lot of steps. Let me know if you need me to fill in details.
ooh, i just started working it out a bit and I got the first one to reduce to
But this is an odd function, with symmetric limits of integration so it should be 0.
For the second one
I get which is an even function, so this is going to be
which yeah should be able to just do the integration by parts twice to solve.
Be advised I did these on the back of an envelope really quicky, but hope that helps.