text: While not conceptually difficult, this is computationally problematic. The problem is that you have to factor x^7 +1. Essentially, we are finding the 7th roots of -1, so the roots are\n-1,\ncos(pi/7)+-i sin(pi/7)\ncos(3pi/7)+-i sin(3pi/7)\ncos(5pi/7)+-i sin(5pi/7).\nThe corresponding factors of x^7 +1 are\nx+1\nx^2 - 2cos(pi/7) x +1\nx^2 -2cos(3pi/7) x +1\nx^2 -2cos(5pi/7) x +1.\nEach of these can be written in the form\n(x-cos(kpi/7) )^2 +sin^2 (kpi/7).\n\nThe next step is to find the partial fraction decomposition of 1/(x^7 +1) using these factors. I would recommend a form looking like\nA/(x+1) for the first term and\n[B(x-cos(kpi/7))+C]/\n[(x-cos(kpi/7)^2 +sin^2(kpi/7)]\nfor the other terms. This will allow easier integration once the\ncoefficients are found.