Integrate ∫ cos(10x) / [cos(5x)+sin(5x)] dx

Any help and steps or explanations would be deeply appreciated. Thank you!

∫ cos(10x) dx / [cos(5x) + sin(5x)]
= ∫ [cos^2(5x) - sin^2(5x)] dx / [cos(5x) + sin(5x)], via double angle identity
= ∫ [cos(5x) + sin(5x)] * [cos(5x) - sin(5x)] dx / [cos(5x) + sin(5x)]
= ∫ [cos(5x) - sin(5x)] dx
= (1/5) sin(5x) + (1/5) cos(5x) + C.

I hope this helps!