i wanna find the fourier series for the function f(x)= 1/(x+1) defined from [0,pi] which is definied as an even function so Bn=0 now i have to find An but i don't think it is gonna be simple to calculate that integral so i tried to use differential equation method y+(1+x)y'=0 which is satisfied for f(x) and making f(x)= $$\sum_{n=1}^{\infty} an cos(nx)$$
sinse it a even periodique function , but i couldn't really precede from here ,can anyone help me what to do next