1,1,8169,0,9.041476," ","integrate(sin(x)^4/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(16 \, a^{7} b c^{4} + 4 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} - 8 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} + 2 \, {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) + 4 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) - {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} + 2 \, {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \sin\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(16 \, a^{7} b c^{4} + 4 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} - 8 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - 2 \, {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) + 4 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) + {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} + 2 \, {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \sin\left(x\right)\right) + \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(-16 \, a^{7} b c^{4} - 4 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} + 8 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} + 2 \, {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) - 4 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) + {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c - {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} - 2 \, {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \sin\left(x\right)\right) - \sqrt{2} c^{3} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} \log\left(-16 \, a^{7} b c^{4} - 4 \, {\left(3 \, a^{8} b - 10 \, a^{6} b^{3}\right)} c^{3} + 8 \, {\left(2 \, a^{7} b^{3} - 3 \, a^{5} b^{5}\right)} c^{2} - 2 \, {\left(4 \, a^{5} c^{9} + {\left(8 \, a^{6} - a^{4} b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2}\right)} c^{7} - {\left(a^{6} b^{2} - a^{4} b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \sin\left(x\right) - 4 \, {\left(a^{6} b^{5} - a^{4} b^{7}\right)} c - \sqrt{2} {\left({\left(8 \, a^{3} c^{12} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} c^{11} + 2 \, {\left(12 \, a^{5} - 25 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{10} + {\left(8 \, a^{6} - 38 \, a^{4} b^{2} + 35 \, a^{2} b^{4} - b^{6}\right)} c^{9} - 2 \, {\left(3 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 5 \, a b^{6}\right)} c^{8} + {\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} c^{7}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}} \cos\left(x\right) - {\left(32 \, a^{5} b^{2} c^{6} + 8 \, {\left(5 \, a^{6} b^{2} - 13 \, a^{4} b^{4}\right)} c^{5} + 2 \, {\left(6 \, a^{7} b^{2} - 47 \, a^{5} b^{4} + 56 \, a^{3} b^{6}\right)} c^{4} - {\left(19 \, a^{6} b^{4} - 69 \, a^{4} b^{6} + 54 \, a^{2} b^{8}\right)} c^{3} + 4 \, {\left(2 \, a^{5} b^{6} - 5 \, a^{3} b^{8} + 3 \, a b^{10}\right)} c^{2} - {\left(a^{4} b^{8} - 2 \, a^{2} b^{10} + b^{12}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{6} - b^{8} - 2 \, a^{4} c^{4} - 2 \, {\left(a^{5} - 8 \, a^{3} b^{2}\right)} c^{3} + {\left(9 \, a^{4} b^{2} - 20 \, a^{2} b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{4} - 4 \, a b^{6}\right)} c + {\left(4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}\right)} \sqrt{-\frac{a^{4} b^{10} - 2 \, a^{2} b^{12} + b^{14} + 16 \, a^{6} b^{2} c^{6} + 8 \, {\left(3 \, a^{7} b^{2} - 10 \, a^{5} b^{4}\right)} c^{5} + {\left(9 \, a^{8} b^{2} - 92 \, a^{6} b^{4} + 148 \, a^{4} b^{6}\right)} c^{4} - 4 \, {\left(6 \, a^{7} b^{4} - 31 \, a^{5} b^{6} + 32 \, a^{3} b^{8}\right)} c^{3} + 2 \, {\left(11 \, a^{6} b^{6} - 37 \, a^{4} b^{8} + 28 \, a^{2} b^{10}\right)} c^{2} - 4 \, {\left(2 \, a^{5} b^{8} - 5 \, a^{3} b^{10} + 3 \, a b^{12}\right)} c}{4 \, a c^{17} + {\left(16 \, a^{2} - b^{2}\right)} c^{16} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{15} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{14} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{13} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{12}}}}{4 \, a c^{9} + {\left(8 \, a^{2} - b^{2}\right)} c^{8} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{7} - {\left(a^{2} b^{2} - b^{4}\right)} c^{6}}} - 2 \, {\left(a^{6} b^{6} - a^{4} b^{8} + 4 \, a^{7} b^{2} c^{3} + {\left(3 \, a^{8} b^{2} - 10 \, a^{6} b^{4}\right)} c^{2} - 2 \, {\left(2 \, a^{7} b^{4} - 3 \, a^{5} b^{6}\right)} c\right)} \sin\left(x\right)\right) + 2 \, c^{2} \cos\left(x\right) \sin\left(x\right) - 4 \, b c \cos\left(x\right) - 2 \, {\left(2 \, b^{2} - 2 \, a c + c^{2}\right)} x}{4 \, c^{3}}"," ",0,"-1/4*(sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(16*a^7*b*c^4 + 4*(3*a^8*b - 10*a^6*b^3)*c^3 - 8*(2*a^7*b^3 - 3*a^5*b^5)*c^2 + 2*(4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) + 4*(a^6*b^5 - a^4*b^7)*c - sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) - (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*cos(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) + 2*(a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*sin(x)) - sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(16*a^7*b*c^4 + 4*(3*a^8*b - 10*a^6*b^3)*c^3 - 8*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - 2*(4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) + 4*(a^6*b^5 - a^4*b^7)*c - sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) + (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*cos(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) + 2*(a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*sin(x)) + sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(-16*a^7*b*c^4 - 4*(3*a^8*b - 10*a^6*b^3)*c^3 + 8*(2*a^7*b^3 - 3*a^5*b^5)*c^2 + 2*(4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) - 4*(a^6*b^5 - a^4*b^7)*c - sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) + (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*cos(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c - (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) - 2*(a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*sin(x)) - sqrt(2)*c^3*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6))*log(-16*a^7*b*c^4 - 4*(3*a^8*b - 10*a^6*b^3)*c^3 + 8*(2*a^7*b^3 - 3*a^5*b^5)*c^2 - 2*(4*a^5*c^9 + (8*a^6 - a^4*b^2)*c^8 + 2*(2*a^7 - 3*a^5*b^2)*c^7 - (a^6*b^2 - a^4*b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*sin(x) - 4*(a^6*b^5 - a^4*b^7)*c - sqrt(2)*((8*a^3*c^12 + 6*(4*a^4 - 3*a^2*b^2)*c^11 + 2*(12*a^5 - 25*a^3*b^2 + 4*a*b^4)*c^10 + (8*a^6 - 38*a^4*b^2 + 35*a^2*b^4 - b^6)*c^9 - 2*(3*a^5*b^2 - 8*a^3*b^4 + 5*a*b^6)*c^8 + (a^4*b^4 - 2*a^2*b^6 + b^8)*c^7)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12))*cos(x) - (32*a^5*b^2*c^6 + 8*(5*a^6*b^2 - 13*a^4*b^4)*c^5 + 2*(6*a^7*b^2 - 47*a^5*b^4 + 56*a^3*b^6)*c^4 - (19*a^6*b^4 - 69*a^4*b^6 + 54*a^2*b^8)*c^3 + 4*(2*a^5*b^6 - 5*a^3*b^8 + 3*a*b^10)*c^2 - (a^4*b^8 - 2*a^2*b^10 + b^12)*c)*cos(x))*sqrt((a^2*b^6 - b^8 - 2*a^4*c^4 - 2*(a^5 - 8*a^3*b^2)*c^3 + (9*a^4*b^2 - 20*a^2*b^4)*c^2 - 2*(3*a^3*b^4 - 4*a*b^6)*c + (4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)*sqrt(-(a^4*b^10 - 2*a^2*b^12 + b^14 + 16*a^6*b^2*c^6 + 8*(3*a^7*b^2 - 10*a^5*b^4)*c^5 + (9*a^8*b^2 - 92*a^6*b^4 + 148*a^4*b^6)*c^4 - 4*(6*a^7*b^4 - 31*a^5*b^6 + 32*a^3*b^8)*c^3 + 2*(11*a^6*b^6 - 37*a^4*b^8 + 28*a^2*b^10)*c^2 - 4*(2*a^5*b^8 - 5*a^3*b^10 + 3*a*b^12)*c)/(4*a*c^17 + (16*a^2 - b^2)*c^16 + 12*(2*a^3 - a*b^2)*c^15 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^14 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^13 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^12)))/(4*a*c^9 + (8*a^2 - b^2)*c^8 + 2*(2*a^3 - 3*a*b^2)*c^7 - (a^2*b^2 - b^4)*c^6)) - 2*(a^6*b^6 - a^4*b^8 + 4*a^7*b^2*c^3 + (3*a^8*b^2 - 10*a^6*b^4)*c^2 - 2*(2*a^7*b^4 - 3*a^5*b^6)*c)*sin(x)) + 2*c^2*cos(x)*sin(x) - 4*b*c*cos(x) - 2*(2*b^2 - 2*a*c + c^2)*x)/c^3","B",0
2,1,6531,0,4.717958," ","integrate(sin(x)^3/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(12 \, a^{5} b c^{3} + 8 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} + 2 \, {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) - 4 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) + {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} - 2 \, {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \sin\left(x\right)\right) - \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(12 \, a^{5} b c^{3} + 8 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) - 4 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) - {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} - 2 \, {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \sin\left(x\right)\right) + \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(-12 \, a^{5} b c^{3} - 8 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} + 2 \, {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) + 4 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) - {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c + {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} + 2 \, {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \sin\left(x\right)\right) - \sqrt{2} c^{2} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} \log\left(-12 \, a^{5} b c^{3} - 8 \, {\left(a^{6} b - 2 \, a^{4} b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{4} c^{7} + {\left(8 \, a^{5} - a^{3} b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2}\right)} c^{5} - {\left(a^{5} b^{2} - a^{3} b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \sin\left(x\right) + 4 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} c - \sqrt{2} {\left({\left(12 \, a^{2} b c^{9} + 7 \, {\left(4 \, a^{3} b - a b^{3}\right)} c^{8} + {\left(20 \, a^{4} b - 27 \, a^{2} b^{3} + b^{5}\right)} c^{7} + {\left(4 \, a^{5} b - 13 \, a^{3} b^{3} + 9 \, a b^{5}\right)} c^{6} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} c^{5}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}} \cos\left(x\right) + {\left(12 \, a^{4} b c^{5} + {\left(20 \, a^{5} b - 31 \, a^{3} b^{3}\right)} c^{4} + {\left(8 \, a^{6} b - 33 \, a^{4} b^{3} + 27 \, a^{2} b^{5}\right)} c^{3} - 3 \, {\left(2 \, a^{5} b^{3} - 5 \, a^{3} b^{5} + 3 \, a b^{7}\right)} c^{2} + {\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{4} - b^{6} + 2 \, a^{3} c^{3} + {\left(2 \, a^{4} - 9 \, a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c - {\left(4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}\right)} \sqrt{-\frac{a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10} + 9 \, a^{4} b^{2} c^{4} + 12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4}\right)} c^{3} + 2 \, {\left(2 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 11 \, a^{2} b^{6}\right)} c^{2} - 4 \, {\left(a^{5} b^{4} - 3 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c}{4 \, a c^{13} + {\left(16 \, a^{2} - b^{2}\right)} c^{12} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{11} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{10} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{9} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{8}}}}{4 \, a c^{7} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{5} - {\left(a^{2} b^{2} - b^{4}\right)} c^{4}}} + 2 \, {\left(a^{5} b^{4} - a^{3} b^{6} - 3 \, a^{5} b^{2} c^{2} - 2 \, {\left(a^{6} b^{2} - 2 \, a^{4} b^{4}\right)} c\right)} \sin\left(x\right)\right) + 4 \, b x + 4 \, c \cos\left(x\right)}{4 \, c^{2}}"," ",0,"-1/4*(sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(12*a^5*b*c^3 + 8*(a^6*b - 2*a^4*b^3)*c^2 + 2*(4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) - 4*(a^5*b^3 - a^3*b^5)*c - sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) + (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*cos(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) - 2*(a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*sin(x)) - sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(12*a^5*b*c^3 + 8*(a^6*b - 2*a^4*b^3)*c^2 - 2*(4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) - 4*(a^5*b^3 - a^3*b^5)*c - sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) - (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*cos(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) - 2*(a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*sin(x)) + sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(-12*a^5*b*c^3 - 8*(a^6*b - 2*a^4*b^3)*c^2 + 2*(4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) + 4*(a^5*b^3 - a^3*b^5)*c - sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) - (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*cos(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c + (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) + 2*(a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*sin(x)) - sqrt(2)*c^2*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4))*log(-12*a^5*b*c^3 - 8*(a^6*b - 2*a^4*b^3)*c^2 - 2*(4*a^4*c^7 + (8*a^5 - a^3*b^2)*c^6 + 2*(2*a^6 - 3*a^4*b^2)*c^5 - (a^5*b^2 - a^3*b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*sin(x) + 4*(a^5*b^3 - a^3*b^5)*c - sqrt(2)*((12*a^2*b*c^9 + 7*(4*a^3*b - a*b^3)*c^8 + (20*a^4*b - 27*a^2*b^3 + b^5)*c^7 + (4*a^5*b - 13*a^3*b^3 + 9*a*b^5)*c^6 - (a^4*b^3 - 2*a^2*b^5 + b^7)*c^5)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8))*cos(x) + (12*a^4*b*c^5 + (20*a^5*b - 31*a^3*b^3)*c^4 + (8*a^6*b - 33*a^4*b^3 + 27*a^2*b^5)*c^3 - 3*(2*a^5*b^3 - 5*a^3*b^5 + 3*a*b^7)*c^2 + (a^4*b^5 - 2*a^2*b^7 + b^9)*c)*cos(x))*sqrt((a^2*b^4 - b^6 + 2*a^3*c^3 + (2*a^4 - 9*a^2*b^2)*c^2 - 2*(2*a^3*b^2 - 3*a*b^4)*c - (4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)*sqrt(-(a^4*b^6 - 2*a^2*b^8 + b^10 + 9*a^4*b^2*c^4 + 12*(a^5*b^2 - 2*a^3*b^4)*c^3 + 2*(2*a^6*b^2 - 11*a^4*b^4 + 11*a^2*b^6)*c^2 - 4*(a^5*b^4 - 3*a^3*b^6 + 2*a*b^8)*c)/(4*a*c^13 + (16*a^2 - b^2)*c^12 + 12*(2*a^3 - a*b^2)*c^11 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^10 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^9 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^8)))/(4*a*c^7 + (8*a^2 - b^2)*c^6 + 2*(2*a^3 - 3*a*b^2)*c^5 - (a^2*b^2 - b^4)*c^4)) + 2*(a^5*b^4 - a^3*b^6 - 3*a^5*b^2*c^2 - 2*(a^6*b^2 - 2*a^4*b^4)*c)*sin(x)) + 4*b*x + 4*c*cos(x))/c^2","B",0
3,1,4985,0,2.336706," ","integrate(sin(x)^2/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(8 \, a^{3} b c^{2} + 2 \, {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) + 4 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) - {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \sin\left(x\right)\right) - \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(8 \, a^{3} b c^{2} - 2 \, {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) + 4 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) + {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} + 2 \, {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \sin\left(x\right)\right) + \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(-8 \, a^{3} b c^{2} + 2 \, {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) - 4 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) + {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c - {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \sin\left(x\right)\right) - \sqrt{2} c \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} \log\left(-8 \, a^{3} b c^{2} - 2 \, {\left(4 \, a^{3} c^{5} + {\left(8 \, a^{4} - a^{2} b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2}\right)} c^{3} - {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \sin\left(x\right) - 4 \, {\left(a^{4} b - a^{2} b^{3}\right)} c - \sqrt{2} {\left({\left(8 \, a^{2} c^{7} + 6 \, {\left(4 \, a^{3} - a b^{2}\right)} c^{6} + {\left(24 \, a^{4} - 22 \, a^{2} b^{2} + b^{4}\right)} c^{5} + 2 \, {\left(4 \, a^{5} - 9 \, a^{3} b^{2} + 4 \, a b^{4}\right)} c^{4} - {\left(2 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6}\right)} c^{3}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}} \cos\left(x\right) - {\left(8 \, a^{2} b^{2} c^{3} + 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} c^{2} - {\left(a^{2} b^{4} - b^{6}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{\frac{a^{2} b^{2} - b^{4} - 2 \, a^{2} c^{2} - 2 \, {\left(a^{3} - 2 \, a b^{2}\right)} c + {\left(4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}\right)} \sqrt{-\frac{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} + 4 \, a^{2} b^{2} c^{2} + 4 \, {\left(a^{3} b^{2} - a b^{4}\right)} c}{4 \, a c^{9} + {\left(16 \, a^{2} - b^{2}\right)} c^{8} + 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{7} + 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c^{5} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} c^{4}}}}{4 \, a c^{5} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{3} - {\left(a^{2} b^{2} - b^{4}\right)} c^{2}}} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4} + 2 \, a^{3} b^{2} c\right)} \sin\left(x\right)\right) + 4 \, x}{4 \, c}"," ",0,"1/4*(sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(8*a^3*b*c^2 + 2*(4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) + 4*(a^4*b - a^2*b^3)*c - sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) - (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*cos(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) + 2*(a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*sin(x)) - sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(8*a^3*b*c^2 - 2*(4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) + 4*(a^4*b - a^2*b^3)*c - sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) + (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*cos(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) + 2*(a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*sin(x)) + sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(-8*a^3*b*c^2 + 2*(4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) - 4*(a^4*b - a^2*b^3)*c - sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) + (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*cos(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c - (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) - 2*(a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*sin(x)) - sqrt(2)*c*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2))*log(-8*a^3*b*c^2 - 2*(4*a^3*c^5 + (8*a^4 - a^2*b^2)*c^4 + 2*(2*a^5 - 3*a^3*b^2)*c^3 - (a^4*b^2 - a^2*b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*sin(x) - 4*(a^4*b - a^2*b^3)*c - sqrt(2)*((8*a^2*c^7 + 6*(4*a^3 - a*b^2)*c^6 + (24*a^4 - 22*a^2*b^2 + b^4)*c^5 + 2*(4*a^5 - 9*a^3*b^2 + 4*a*b^4)*c^4 - (2*a^4*b^2 - 3*a^2*b^4 + b^6)*c^3)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4))*cos(x) - (8*a^2*b^2*c^3 + 2*(2*a^3*b^2 - 3*a*b^4)*c^2 - (a^2*b^4 - b^6)*c)*cos(x))*sqrt((a^2*b^2 - b^4 - 2*a^2*c^2 - 2*(a^3 - 2*a*b^2)*c + (4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)*sqrt(-(a^4*b^2 - 2*a^2*b^4 + b^6 + 4*a^2*b^2*c^2 + 4*(a^3*b^2 - a*b^4)*c)/(4*a*c^9 + (16*a^2 - b^2)*c^8 + 12*(2*a^3 - a*b^2)*c^7 + 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^6 + 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c^5 - (a^4*b^2 - 2*a^2*b^4 + b^6)*c^4)))/(4*a*c^5 + (8*a^2 - b^2)*c^4 + 2*(2*a^3 - 3*a*b^2)*c^3 - (a^2*b^2 - b^4)*c^2)) - 2*(a^4*b^2 - a^2*b^4 + 2*a^3*b^2*c)*sin(x)) + 4*x)/c","B",0
4,1,3519,0,1.586344," ","integrate(sin(x)/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, a b^{2} \sin\left(x\right) + 4 \, a b c + 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, a b^{2} \sin\left(x\right) + 4 \, a b c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, a b^{2} \sin\left(x\right) - 4 \, a b c + 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, a b^{2} \sin\left(x\right) - 4 \, a b c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{3} b^{3} - a b^{5} + 4 \, a b c^{4} + {\left(4 \, a^{2} b - b^{3}\right)} c^{3} - {\left(4 \, a^{3} b + 5 \, a b^{3}\right)} c^{2} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} - b^{5}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left(a b^{3} - 4 \, a b c^{2} - {\left(4 \, a^{2} b - b^{3}\right)} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{2 \, a^{2} - b^{2} + 2 \, a c - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right)"," ",0,"-1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*a*b^2*sin(x) + 4*a*b*c + 2*(a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*cos(x))*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*a*b^2*sin(x) + 4*a*b*c - 2*(a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*cos(x))*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) - 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*a*b^2*sin(x) - 4*a*b*c + 2*(a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*cos(x))*sqrt(-(2*a^2 - b^2 + 2*a*c + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*a*b^2*sin(x) - 4*a*b*c - 2*(a^3*b^2 - a*b^4 - 4*a^2*c^3 - (8*a^3 - a*b^2)*c^2 - 2*(2*a^4 - 3*a^2*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^3*b^3 - a*b^5 + 4*a*b*c^4 + (4*a^2*b - b^3)*c^3 - (4*a^3*b + 5*a*b^3)*c^2 - (4*a^4*b - 5*a^2*b^3 - b^5)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + (a*b^3 - 4*a*b*c^2 - (4*a^2*b - b^3)*c)*cos(x))*sqrt(-(2*a^2 - b^2 + 2*a*c - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)))","B",0
5,1,3495,0,1.493323," ","integrate(1/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, b^{2} c \sin\left(x\right) + 4 \, b c^{2} + 2 \, {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left(b^{4} - 4 \, a b^{2} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(2 \, b^{2} c \sin\left(x\right) + 4 \, b c^{2} - 2 \, {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left(b^{4} - 4 \, a b^{2} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, b^{2} c \sin\left(x\right) - 4 \, b c^{2} + 2 \, {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) + {\left(b^{4} - 4 \, a b^{2} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}} \log\left(-2 \, b^{2} c \sin\left(x\right) - 4 \, b c^{2} - 2 \, {\left(4 \, a c^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \sin\left(x\right) - \sqrt{2} {\left({\left(a^{2} b^{4} - b^{6} + 8 \, a c^{5} + 2 \, {\left(12 \, a^{2} - b^{2}\right)} c^{4} + 6 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} c^{3} + {\left(8 \, a^{4} - 22 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}} \cos\left(x\right) - {\left(b^{4} - 4 \, a b^{2} c\right)} \cos\left(x\right)\right)} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)} \sqrt{\frac{b^{2}}{a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c}}}{a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c}}\right)"," ",0,"-1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*b^2*c*sin(x) + 4*b*c^2 + 2*(4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - (b^4 - 4*a*b^2*c)*cos(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(2*b^2*c*sin(x) + 4*b*c^2 - 2*(4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + (b^4 - 4*a*b^2*c)*cos(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) - 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*b^2*c*sin(x) - 4*b*c^2 + 2*(4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) + (b^4 - 4*a*b^2*c)*cos(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))) + 1/4*sqrt(2)*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c))*log(-2*b^2*c*sin(x) - 4*b*c^2 - 2*(4*a*c^4 + (8*a^2 - b^2)*c^3 + 2*(2*a^3 - 3*a*b^2)*c^2 - (a^2*b^2 - b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*sin(x) - sqrt(2)*((a^2*b^4 - b^6 + 8*a*c^5 + 2*(12*a^2 - b^2)*c^4 + 6*(4*a^3 - 3*a*b^2)*c^3 + (8*a^4 - 22*a^2*b^2 + 3*b^4)*c^2 - 2*(3*a^3*b^2 - 4*a*b^4)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c))*cos(x) - (b^4 - 4*a*b^2*c)*cos(x))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)*sqrt(b^2/(a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)))","B",0
6,-1,0,0,0.000000," ","integrate(csc(x)/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate(csc(x)^2/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate(csc(x)^3/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,276,0,1.771711," ","integrate(cos(x)^3/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} - 2 \, b c \sin\left(x\right) - b^{2} + 2 \, a c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} - b \sin\left(x\right) - a - c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sin\left(x\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(b^{3} - 4 \, a b c\right)} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} \sin\left(x\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c - 2*c^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 - 2*b*c*sin(x) - b^2 + 2*a*c - 2*c^2 + sqrt(b^2 - 4*a*c)*(2*c*sin(x) + b))/(c*cos(x)^2 - b*sin(x) - a - c)) - (b^3 - 4*a*b*c)*log(-c*cos(x)^2 + b*sin(x) + a + c) + 2*(b^2*c - 4*a*c^2)*sin(x))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(b^2 - 2*a*c - 2*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*sin(x) + b)/(b^2 - 4*a*c)) + (b^3 - 4*a*b*c)*log(-c*cos(x)^2 + b*sin(x) + a + c) - 2*(b^2*c - 4*a*c^2)*sin(x))/(b^2*c^2 - 4*a*c^3)]","A",0
10,1,971,0,1.356939," ","integrate(cos(x)^2/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \cos\left(x\right) + b^{2} \sin\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sin\left(x\right) + 2 \, b c\right) - \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \cos\left(x\right) - b^{2} \sin\left(x\right) - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sin\left(x\right) - 2 \, b c\right) - \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \cos\left(x\right) + b^{2} \sin\left(x\right) - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sin\left(x\right) + 2 \, b c\right) + \sqrt{2} c \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \log\left(\sqrt{2} {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sqrt{-\frac{b^{2} - 2 \, a c - 2 \, c^{2} - {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}}}{b^{2} c^{2} - 4 \, a c^{3}}} \cos\left(x\right) - b^{2} \sin\left(x\right) + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} \sqrt{\frac{b^{2}}{b^{2} c^{4} - 4 \, a c^{5}}} \sin\left(x\right) - 2 \, b c\right) - 4 \, x}{4 \, c}"," ",0,"1/4*(sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*cos(x) + b^2*sin(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sin(x) + 2*b*c) - sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*cos(x) - b^2*sin(x) - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sin(x) - 2*b*c) - sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*cos(x) + b^2*sin(x) - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sin(x) + 2*b*c) + sqrt(2)*c*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*log(sqrt(2)*(b^2*c^3 - 4*a*c^4)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sqrt(-(b^2 - 2*a*c - 2*c^2 - (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5)))/(b^2*c^2 - 4*a*c^3))*cos(x) - b^2*sin(x) + (b^2*c^2 - 4*a*c^3)*sqrt(b^2/(b^2*c^4 - 4*a*c^5))*sin(x) - 2*b*c) - 4*x)/c","B",0
11,1,139,0,0.979109," ","integrate(cos(x)/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} - 2 \, b c \sin\left(x\right) - b^{2} + 2 \, a c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} - b \sin\left(x\right) - a - c}\right)}{\sqrt{b^{2} - 4 \, a c}}, -\frac{2 \, \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right)}{b^{2} - 4 \, a c}\right]"," ",0,"[log(-(2*c^2*cos(x)^2 - 2*b*c*sin(x) - b^2 + 2*a*c - 2*c^2 + sqrt(b^2 - 4*a*c)*(2*c*sin(x) + b))/(c*cos(x)^2 - b*sin(x) - a - c))/sqrt(b^2 - 4*a*c), -2*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*sin(x) + b)/(b^2 - 4*a*c))/(b^2 - 4*a*c)]","A",0
12,1,482,0,2.220959," ","integrate(sec(x)/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} - 2 \, b c \sin\left(x\right) - b^{2} + 2 \, a c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} - b \sin\left(x\right) - a - c}\right) + {\left(b^{3} - 4 \, a b c\right)} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) - {\left(a b^{2} + b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c\right)} \log\left(\sin\left(x\right) + 1\right) + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)}}, \frac{2 \, {\left(b^{2} - 2 \, a c - 2 \, c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{3} - 4 \, a b c\right)} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) + {\left(a b^{2} + b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c\right)} \log\left(\sin\left(x\right) + 1\right) - {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a^{2} b^{2} - b^{4} - 4 \, a c^{3} - {\left(8 \, a^{2} - b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c\right)}}\right]"," ",0,"[-1/2*((b^2 - 2*a*c - 2*c^2)*sqrt(b^2 - 4*a*c)*log(-(2*c^2*cos(x)^2 - 2*b*c*sin(x) - b^2 + 2*a*c - 2*c^2 + sqrt(b^2 - 4*a*c)*(2*c*sin(x) + b))/(c*cos(x)^2 - b*sin(x) - a - c)) + (b^3 - 4*a*b*c)*log(-c*cos(x)^2 + b*sin(x) + a + c) - (a*b^2 + b^3 - 4*a*c^2 - (4*a^2 + 4*a*b - b^2)*c)*log(sin(x) + 1) + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*log(-sin(x) + 1))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c), 1/2*(2*(b^2 - 2*a*c - 2*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*sin(x) + b)/(b^2 - 4*a*c)) - (b^3 - 4*a*b*c)*log(-c*cos(x)^2 + b*sin(x) + a + c) + (a*b^2 + b^3 - 4*a*c^2 - (4*a^2 + 4*a*b - b^2)*c)*log(sin(x) + 1) - (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*log(-sin(x) + 1))/(a^2*b^2 - b^4 - 4*a*c^3 - (8*a^2 - b^2)*c^2 - 2*(2*a^3 - 3*a*b^2)*c)]","A",0
13,-1,0,0,0.000000," ","integrate(sec(x)^2/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,1,1244,0,12.661652," ","integrate(sec(x)^3/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a b c^{3} - 2 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \sqrt{b^{2} - 4 \, a c} \cos\left(x\right)^{2} \log\left(-\frac{2 \, c^{2} \cos\left(x\right)^{2} - 2 \, b c \sin\left(x\right) - b^{2} + 2 \, a c - 2 \, c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{c \cos\left(x\right)^{2} - b \sin\left(x\right) - a - c}\right) - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \cos\left(x\right)^{2} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) + {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a c^{4} - {\left(12 \, a^{2} - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 7 \, a b^{2}\right)} c^{2} - {\left(4 \, a^{4} - 7 \, a^{2} b^{2} + b^{4}\right)} c\right)} \sin\left(x\right)}{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)} \cos\left(x\right)^{2}}, -\frac{2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a b c^{3} + 4 \, {\left(b^{4} - 4 \, a b^{2} c + 4 \, a c^{3} + 2 \, c^{4} + 2 \, {\left(a^{2} - b^{2}\right)} c^{2}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c \sin\left(x\right) + b\right)}}{b^{2} - 4 \, a c}\right) \cos\left(x\right)^{2} - 2 \, {\left(b^{5} - 6 \, a b^{3} c + 8 \, a b c^{3} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} c^{2}\right)} \cos\left(x\right)^{2} \log\left(-c \cos\left(x\right)^{2} + b \sin\left(x\right) + a + c\right) - {\left(a^{3} b^{2} - 3 \, a b^{4} - 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} + 16 \, a^{2} b - 11 \, a b^{2} - 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} \log\left(\sin\left(x\right) + 1\right) + {\left(a^{3} b^{2} - 3 \, a b^{4} + 2 \, b^{5} - 12 \, a c^{4} - {\left(28 \, a^{2} - 16 \, a b - 3 \, b^{2}\right)} c^{3} - {\left(20 \, a^{3} - 16 \, a^{2} b - 11 \, a b^{2} + 4 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 17 \, a^{2} b^{2} + 12 \, a b^{3} + b^{4}\right)} c\right)} \cos\left(x\right)^{2} \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(8 \, a^{2} b - b^{3}\right)} c^{2} - 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} c - 2 \, {\left(a^{3} b^{2} - a b^{4} - 4 \, a c^{4} - {\left(12 \, a^{2} - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 7 \, a b^{2}\right)} c^{2} - {\left(4 \, a^{4} - 7 \, a^{2} b^{2} + b^{4}\right)} c\right)} \sin\left(x\right)}{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6} - 4 \, a c^{5} - {\left(16 \, a^{2} - b^{2}\right)} c^{4} - 12 \, {\left(2 \, a^{3} - a b^{2}\right)} c^{3} - 2 \, {\left(8 \, a^{4} - 11 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 4 \, {\left(a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} c\right)} \cos\left(x\right)^{2}}\right]"," ",0,"[-1/4*(2*a^2*b^3 - 2*b^5 - 8*a*b*c^3 - 2*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*sqrt(b^2 - 4*a*c)*cos(x)^2*log(-(2*c^2*cos(x)^2 - 2*b*c*sin(x) - b^2 + 2*a*c - 2*c^2 + sqrt(b^2 - 4*a*c)*(2*c*sin(x) + b))/(c*cos(x)^2 - b*sin(x) - a - c)) - 2*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*cos(x)^2*log(-c*cos(x)^2 + b*sin(x) + a + c) - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*cos(x)^2*log(sin(x) + 1) + (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*cos(x)^2*log(-sin(x) + 1) - 2*(8*a^2*b - b^3)*c^2 - 4*(2*a^3*b - 3*a*b^3)*c - 2*(a^3*b^2 - a*b^4 - 4*a*c^4 - (12*a^2 - b^2)*c^3 - (12*a^3 - 7*a*b^2)*c^2 - (4*a^4 - 7*a^2*b^2 + b^4)*c)*sin(x))/((a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)*cos(x)^2), -1/4*(2*a^2*b^3 - 2*b^5 - 8*a*b*c^3 + 4*(b^4 - 4*a*b^2*c + 4*a*c^3 + 2*c^4 + 2*(a^2 - b^2)*c^2)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*sin(x) + b)/(b^2 - 4*a*c))*cos(x)^2 - 2*(b^5 - 6*a*b^3*c + 8*a*b*c^3 + 2*(4*a^2*b - b^3)*c^2)*cos(x)^2*log(-c*cos(x)^2 + b*sin(x) + a + c) - (a^3*b^2 - 3*a*b^4 - 2*b^5 - 12*a*c^4 - (28*a^2 + 16*a*b - 3*b^2)*c^3 - (20*a^3 + 16*a^2*b - 11*a*b^2 - 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 - 12*a*b^3 + b^4)*c)*cos(x)^2*log(sin(x) + 1) + (a^3*b^2 - 3*a*b^4 + 2*b^5 - 12*a*c^4 - (28*a^2 - 16*a*b - 3*b^2)*c^3 - (20*a^3 - 16*a^2*b - 11*a*b^2 + 4*b^3)*c^2 - (4*a^4 - 17*a^2*b^2 + 12*a*b^3 + b^4)*c)*cos(x)^2*log(-sin(x) + 1) - 2*(8*a^2*b - b^3)*c^2 - 4*(2*a^3*b - 3*a*b^3)*c - 2*(a^3*b^2 - a*b^4 - 4*a*c^4 - (12*a^2 - b^2)*c^3 - (12*a^3 - 7*a*b^2)*c^2 - (4*a^4 - 7*a^2*b^2 + b^4)*c)*sin(x))/((a^4*b^2 - 2*a^2*b^4 + b^6 - 4*a*c^5 - (16*a^2 - b^2)*c^4 - 12*(2*a^3 - a*b^2)*c^3 - 2*(8*a^4 - 11*a^2*b^2 + b^4)*c^2 - 4*(a^5 - 3*a^3*b^2 + 2*a*b^4)*c)*cos(x)^2)]","B",0
15,1,17,0,0.556417," ","integrate(cos(x)/(-6+sin(x)+sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{5} \, \log\left(\sin\left(x\right) + 3\right) + \frac{1}{5} \, \log\left(-\frac{1}{2} \, \sin\left(x\right) + 1\right)"," ",0,"-1/5*log(sin(x) + 3) + 1/5*log(-1/2*sin(x) + 1)","A",0
16,1,17,0,0.675474," ","integrate(cos(x)/(2-3*sin(x)+sin(x)^2),x, algorithm=""fricas"")","\log\left(-\frac{1}{2} \, \sin\left(x\right) + 1\right) - \log\left(-\sin\left(x\right) + 1\right)"," ",0,"log(-1/2*sin(x) + 1) - log(-sin(x) + 1)","A",0
17,1,17,0,0.565438," ","integrate(cos(x)/(-5+4*sin(x)+sin(x)^2),x, algorithm=""fricas"")","-\frac{1}{6} \, \log\left(\sin\left(x\right) + 5\right) + \frac{1}{6} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1/6*log(sin(x) + 5) + 1/6*log(-sin(x) + 1)","A",0
18,1,5,0,0.550871," ","integrate(cos(x)/(10-6*sin(x)+sin(x)^2),x, algorithm=""fricas"")","\arctan\left(\sin\left(x\right) - 3\right)"," ",0,"arctan(sin(x) - 3)","A",0
19,1,5,0,0.555726," ","integrate(cos(x)/(2+2*sin(x)+sin(x)^2),x, algorithm=""fricas"")","\arctan\left(\sin\left(x\right) + 1\right)"," ",0,"arctan(sin(x) + 1)","A",0
