Suggest Ideas to integrate the following:?

Question

Intregrate (cos5x+cos4x)/(1-2cos3x) dx

& tanx tan2x tan3x dx

Answer 1

For the first one, I'd break down the cos 5x, cos 4x, and cos 3x with repeated use of the trig identities
cos (a + b) = cos a cos b - sin a sin b,
and cos 2a = 2 cos^2 a - 1 = 1 - 2 sin^2 a
where a = 2x and b = 3x
then at some point I'd use the fact that integral du/u = ln u + C

For the second one I'd write it as
(sin x sin 2x sin 3x ) / (cos x cos 2x cos 3x)
use the product identities
sin a sin b = (1/2)(cos (a-b) - cos(a+b) and
cos a cos b = (1/2)(cos(a-b) + cos(a+b))
Again you'd probalby wind up using the ln integral.

Answer 2

Look up some trig identities, I am sure you will find something there