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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

Mossaab Sama
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    Whatever you use, you will end up "calculating that integral". Directly or not. – metamorphy Oct 20 '19 at 18:47
  • but you could use this method for evaluating An and Bn of exp(x) without really calculating them just try it with this equation y'+y=0 y= sum Ancos(nx)+Bnsin(nx) y(0)=1 you could find An and Bn without any calculation whatsoever – Mossaab Sama Oct 20 '19 at 18:52

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