I'll do #1, you can show us where you get stuck on the others.
Let I = ∫e^2x cos4x dx
du = -4sin4x dx
dv = e^2x dx
v = 1/2 e^2x
I = uv - ∫v du
= 1/2 e^2x cos4x - ∫-2e^2x sin4x dx
Now do it again, letting u = sin4x
I = 1/2 e^2x cos4x + (e^2x sin4x - ∫4e^2x cos4x dx)
= 1/2 e^2x cos4x + e^2x sin4x - 4I
5I = 1/2 e^2x cos4x + e^2x sin4x
I = 1/10 e^2x (cos4x + 2sin4x)
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