integral (cos x+cos^3x+cos^5x+.....) dx

cos x + (cos x)^3 + (cos x)^5 + ...
S~ = a/(1 - r)
S~ = cos x/(1 - cos² x)
S~ = cos x / sin² x
S~ = csc x cot x

∫(cos x + (cos x)^3 + (cos x)^5 + ... ) dx
= ∫csc x cot x dx
= - ∫dcsc x
= - csc x + c