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I'd like to graph these expressions

  1. enter image description here

    \frac1{2\pi}\int_{-\pi}^\pi{f(x)}dx+\sum_{n=1}^2\left[\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\cos(nx)dx\right)\cos(nx)+\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\sin(nx)dx\right)\sin(nx)\right]
    
  2. enter image description here

    \frac1{2\pi}\int_{-\pi}^\pi{f(x)}dx+\sum_{n=1}^5\left[\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\cos(nx)dx\right)\cos(nx)+\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\sin(nx)dx\right)\sin(nx)\right]
    
  3. enter image description here

    \frac1{2\pi}\int_{-\pi}^\pi{f(x)}dx+\sum_{n=1}^{10}\left[\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\cos(nx)dx\right)\cos(nx)+\left(\frac1\pi\int_{-\pi}^\pi{f(x)}\sin(nx)dx\right)\sin(nx)\right]
    

Is it possible to graph them without having to tediously convert them all into pgfplots-maths by hand?

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