Untitled

sage: integral(1/(x**10+1),x,0,1)
-3125*(2*(sqrt(11*sqrt(5) + 25)*(2^(3/4)*sqrt(5) - 3*2^(3/4))*arctan(1/2*sqrt(4*sqrt(2)*sqrt(5) + 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)) - 8*2^(1/4)*arctan(1/2*sqrt(4*sqrt(2)*sqrt(5) + 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)))*sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(4*sqrt(2)*sqrt(5) - 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2)) - (2*(sqrt(11*sqrt(5) + 25)*(2^(3/4)*sqrt(5) - 3*2^(3/4))*arctan(1/2*sqrt(4*sqrt(2)*sqrt(5) - 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)) + 8*2^(1/4)*arctan(1/2*sqrt(4*sqrt(2)*sqrt(5) - 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)))*sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2)) + (2*(sqrt(-11*sqrt(5) + 25)*(2^(3/4)*sqrt(5) + 3*2^(3/4))*arctan(1/2*sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)) + 8*2^(1/4)*arctan(1/2*sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)))*sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2)) - sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*(2*sqrt(-11*sqrt(5) + 25)*(2^(3/4)*sqrt(5) + 3*2^(3/4))*arctan(1/2*sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4)) - sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*(4*pi + sqrt(-11*sqrt(5) + 25)*((sqrt(2)*sqrt(5) + 3*sqrt(2))*log(-1/2*(sqrt(2)*sqrt(5) - sqrt(-11*sqrt(5) + 25) - 3*sqrt(2))*sqrt(2)) - (sqrt(2)*sqrt(5) + 3*sqrt(2))*log(-1/2*(sqrt(2)*sqrt(5) + sqrt(-11*sqrt(5) + 25) - 3*sqrt(2))*sqrt(2))) + sqrt(11*sqrt(5) + 25)*((sqrt(2)*sqrt(5) - 3*sqrt(2))*log(1/2*(sqrt(2)*sqrt(5) - sqrt(11*sqrt(5) + 25) + 3*sqrt(2))*sqrt(2)) - (sqrt(2)*sqrt(5) - 3*sqrt(2))*log(1/2*(sqrt(2)*sqrt(5) + sqrt(11*sqrt(5) + 25) + 3*sqrt(2))*sqrt(2)))) - 16*2^(1/4)*arctan(1/2*sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*2^(3/4))))*sqrt(4*sqrt(2)*sqrt(5) - 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2)))*sqrt(4*sqrt(2)*sqrt(5) + 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2)))/(sqrt(-4*sqrt(2)*sqrt(5) - 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(-4*sqrt(2)*sqrt(5) + 4*sqrt(-11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(4*sqrt(2)*sqrt(5) - 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*sqrt(4*sqrt(2)*sqrt(5) + 4*sqrt(11*sqrt(5) + 25) + 11*sqrt(2))*((11*sqrt(5) + 20)*sqrt(11*sqrt(5) + 25) - 50*sqrt(2)*sqrt(5) - 110*sqrt(2))^2*((11*sqrt(5) + 20)*sqrt(11*sqrt(5) + 25) + 50*sqrt(2)*sqrt(5) + 110*sqrt(2))^2*(sqrt(-11*sqrt(5) + 25)*(11*sqrt(5) - 20) - 50*sqrt(2)*sqrt(5) + 110*sqrt(2))^2*(sqrt(-11*sqrt(5) + 25)*(11*sqrt(5) - 20) + 50*sqrt(2)*sqrt(5) - 110*sqrt(2))^2)