Fourier Series based on 2 limits for x

[mullzer]

i have an exam in these kind of questions in a few days so i was pracitsing a a few problems but I can't do them!
Any help would be appreciated.

Calculate the Fourier series for f(x) when f(x) = 0, on -pi <= x <= 0, and f(x) = coshx, on 0 <= x <= pi.
and show that SUM (from n=1 to infinity) 1/(1+n^2)= (1/2)((pi/tanhx) - 1)

So far i have that A0 = sinhx. When i try to integrate An, i get stuck at the integral of coshx cosx dx. i tried changing coshx into exponential form but i still end up in an endless circle of integration by parts.

 

[tiny-tim]

welcome to pf!

hi mullzer! welcome to pf!

(have a pi: π and an infinity: ∞ and try using the X² and X₂ icons just above the Reply box )

When i try to integrate An, i get stuck at the integral of coshx cosx dx. i tried changing coshx into exponential form but i still end up in an endless circle of integration by parts.

you should get something like ∫ e^xcosx dx = something - ∫ e^xcosx dx …

now just put the second integral over on the LHS ​

 

[mullzer]

Thanks very much for the help. The substitution of the integral worked.. and my the test went well in the end!