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Ok, we're supposed to use basic trig identities to get the integral down to something manageable where we can use u-substitution and/or integration by parts. I've worked out one but I'm having trouble on the other two...

1. the integral of (cos(x))^4 dx. [Hint: also (cos(x)^2)^2]

2. the integral of sec(v) dv. [Hint: multiply sec(v) by (sec(v)+tan(v))/(sec(v)+tan(v)).]

Some identities to use:

sin(2x)=2sin(x)cos(x)

cos(2x)=(cos(x))^2-(sin(x))^2

cos(2x)=2(cos(x))^2-1

cos(2x)=1-2(sin(x))^2

(sin(x))^2=(1/2)[1-COS(2X)]

I'm not looking for the answer, just a push in the right direction, thanks...