Integration [ 1/(c+cos(x)) ] by dx

[desmal]

Hi all

Can you solve the following integration: -

Integration [ cos(x)/(c+cos(x)) ] by dx
where c is a constant

or that one: -

Integration [ 1/(c+cos(x)) ] by dx

if one is solved I will be able to make the other

 

[nikkor180]

Greetings:

If you let u = tan(x/2), then dx = 2*du /(u^2+1), sin(x) = 2u/(u^2+1), cos(x) = (1-u^2)/(1+u^2). If you substitute these values appropriately, each integral should return an inverse trig function.

Regards,

Rich B.

 

[desmal]

Wow really really amazing

Unfortunately, there is something puzzling me which is:-
How did you get the idea of substituting u=tan(x/2)

 

[HallsofIvy]

Actually, "u= tan(x/2)" is a common substitution method. Check this:
http://en.wikipedia.org/wiki/Tangent_half-angle_formula

 

[Cyosis]

Wow really really amazing

Unfortunately, there is something puzzling me which is:-
How did you get the idea of substituting u=tan(x/2)

There is no clear cut method to finding primitives. It's much like puzzling, try something out and remember what works.