1,1,8644,0,1.753716," ","integrate(x^6*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{336} \, c {\left(\frac{48 \, b \arccos\left(\frac{1}{c x}\right)}{c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}} - \frac{15 \, b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}} + \frac{15 \, b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}} + \frac{48 \, a}{c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}} - \frac{336 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{105 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{105 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{66 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{336 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{1008 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{315 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{315 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{56 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{1008 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{1680 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{525 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{525 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{170 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{1680 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{1680 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{525 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{525 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{1680 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{1008 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{315 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{315 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{170 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{1008 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{336 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{105 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{105 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{56 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} + \frac{336 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{48 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{14}} - \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{14}} + \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{14}} + \frac{66 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{13}} - \frac{48 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(c^{8} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{35 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{21 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{7 \, c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{c^{8} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{7}}{{\left(\frac{1}{c x} + 1\right)}^{14}}\right)} {\left(\frac{1}{c x} + 1\right)}^{14}}\right)}"," ",0,"1/336*c*(48*b*arccos(1/(c*x))/(c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14) - 15*b*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14) + 15*b*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14) + 48*a/(c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14) - 336*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^2) - 105*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^2) + 105*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^2) - 66*b*sqrt(-1/(c^2*x^2) + 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)) - 336*a*(1/(c^2*x^2) - 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^2) + 1008*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^4) - 315*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^4) + 315*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^4) + 56*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^3) + 1008*a*(1/(c^2*x^2) - 1)^2/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^4) - 1680*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^6) - 525*b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^6) + 525*b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^6) - 170*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^5) - 1680*a*(1/(c^2*x^2) - 1)^3/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^6) + 1680*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^8) - 525*b*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^8) + 525*b*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^8) + 1680*a*(1/(c^2*x^2) - 1)^4/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^8) - 1008*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^10) - 315*b*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^10) + 315*b*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^10) + 170*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^9) - 1008*a*(1/(c^2*x^2) - 1)^5/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^10) + 336*b*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^12) - 105*b*(1/(c^2*x^2) - 1)^6*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^12) + 105*b*(1/(c^2*x^2) - 1)^6*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^12) + 56*b*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^11) + 336*a*(1/(c^2*x^2) - 1)^6/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^12) - 48*b*(1/(c^2*x^2) - 1)^7*arccos(1/(c*x))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^14) - 15*b*(1/(c^2*x^2) - 1)^7*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^14) + 15*b*(1/(c^2*x^2) - 1)^7*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^14) + 66*b*(1/(c^2*x^2) - 1)^6*sqrt(-1/(c^2*x^2) + 1)/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^13) - 48*a*(1/(c^2*x^2) - 1)^7/((c^8 + 7*c^8*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 21*c^8*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 35*c^8*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 35*c^8*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 21*c^8*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + 7*c^8*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12 + c^8*(1/(c^2*x^2) - 1)^7/(1/(c*x) + 1)^14)*(1/(c*x) + 1)^14))","B",0
2,1,3862,0,0.232784," ","integrate(x^5*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{90} \, c {\left(\frac{15 \, b \arccos\left(\frac{1}{c x}\right)}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{15 \, a}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{30 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{90 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{225 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{70 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{225 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{300 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{156 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{300 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{225 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{156 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{225 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{70 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{90 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} + \frac{15 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}}\right)}"," ",0,"1/90*c*(15*b*arccos(1/(c*x))/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 15*a/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 90*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 30*b*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) - 90*a*(1/(c^2*x^2) - 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) + 225*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) + 70*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) + 225*a*(1/(c^2*x^2) - 1)^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 300*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 156*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) - 300*a*(1/(c^2*x^2) - 1)^3/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) + 225*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 156*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 225*a*(1/(c^2*x^2) - 1)^4/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) - 70*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) - 90*a*(1/(c^2*x^2) - 1)^5/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 15*b*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 30*b*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) + 15*a*(1/(c^2*x^2) - 1)^6/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12))","B",0
3,1,4828,0,1.315783," ","integrate(x^4*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{40} \, c {\left(\frac{8 \, b \arccos\left(\frac{1}{c x}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{3 \, b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{3 \, b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{8 \, a}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{40 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{10 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{40 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{80 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{80 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{80 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{80 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{40 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{4 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{40 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{8 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{10 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{8 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}}\right)}"," ",0,"1/40*c*(8*b*arccos(1/(c*x))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 3*b*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 3*b*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 8*a/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 40*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 15*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) + 15*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 10*b*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)) - 40*a*(1/(c^2*x^2) - 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) + 80*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) - 30*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 30*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 4*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^3) + 80*a*(1/(c^2*x^2) - 1)^2/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) - 80*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) - 30*b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 30*b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) - 80*a*(1/(c^2*x^2) - 1)^3/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 40*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 15*b*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) + 15*b*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) + 4*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^7) + 40*a*(1/(c^2*x^2) - 1)^4/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 8*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) - 3*b*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 3*b*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 10*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^9) - 8*a*(1/(c^2*x^2) - 1)^5/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10))","B",0
4,1,1926,0,0.196696," ","integrate(x^3*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{12} \, c {\left(\frac{3 \, b \arccos\left(\frac{1}{c x}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{3 \, a}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{18 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{10 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{3 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)}"," ",0,"1/12*c*(3*b*arccos(1/(c*x))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 3*a/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 6*b*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) - 12*a*(1/(c^2*x^2) - 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 10*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 18*a*(1/(c^2*x^2) - 1)^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 10*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*a*(1/(c^2*x^2) - 1)^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 6*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 3*a*(1/(c^2*x^2) - 1)^4/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))","B",0
5,1,2101,0,0.824190," ","integrate(x^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{6} \, c {\left(\frac{2 \, b \arccos\left(\frac{1}{c x}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{b \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{2 \, a}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}}\right)}"," ",0,"1/6*c*(2*b*arccos(1/(c*x))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - b*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + b*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 2*a/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 3*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 3*b*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 2*b*sqrt(-1/(c^2*x^2) + 1)/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)) - 6*a*(1/(c^2*x^2) - 1)/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 6*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 3*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 3*b*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*a*(1/(c^2*x^2) - 1)^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 2*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + b*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 2*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^5) - 2*a*(1/(c^2*x^2) - 1)^3/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6))","B",0
6,1,634,0,0.177049," ","integrate(x*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{2} \, c {\left(\frac{b \arccos\left(\frac{1}{c x}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{a}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}}\right)}"," ",0,"1/2*c*(b*arccos(1/(c*x))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + a/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 2*b*sqrt(-1/(c^2*x^2) + 1)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)) - 2*a*(1/(c^2*x^2) - 1)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + 2*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^3) + a*(1/(c^2*x^2) - 1)^2/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4))","B",0
7,1,63,0,0.136091," ","integrate(a+b*arcsec(c*x),x, algorithm=""giac"")","\frac{1}{2} \, b c {\left(\frac{2 \, x \arccos\left(\frac{1}{c x}\right)}{c} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}}\right)} + a x"," ",0,"1/2*b*c*(2*x*arccos(1/(c*x))/c - (log(sqrt(-1/(c^2*x^2) + 1) + 1) - log(-sqrt(-1/(c^2*x^2) + 1) + 1))/c^2) + a*x","B",0
8,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
9,1,43,0,0.146762," ","integrate((a+b*arcsec(c*x))/x^2,x, algorithm=""giac"")","{\left(b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{b \arccos\left(\frac{1}{c x}\right)}{c x} - \frac{a}{c x}\right)} c"," ",0,"(b*sqrt(-1/(c^2*x^2) + 1) - b*arccos(1/(c*x))/(c*x) - a/(c*x))*c","A",0
10,1,58,0,0.136655," ","integrate((a+b*arcsec(c*x))/x^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(b c \arccos\left(\frac{1}{c x}\right) + \frac{b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{2 \, b \arccos\left(\frac{1}{c x}\right)}{c x^{2}} - \frac{2 \, a}{c x^{2}}\right)} c"," ",0,"1/4*(b*c*arccos(1/(c*x)) + b*sqrt(-1/(c^2*x^2) + 1)/x - 2*b*arccos(1/(c*x))/(c*x^2) - 2*a/(c*x^2))*c","A",0
11,1,65,0,0.148162," ","integrate((a+b*arcsec(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{9} \, {\left(2 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} - \frac{3 \, b \arccos\left(\frac{1}{c x}\right)}{c x^{3}} - \frac{3 \, a}{c x^{3}}\right)} c"," ",0,"1/9*(2*b*c^2*sqrt(-1/(c^2*x^2) + 1) + b*sqrt(-1/(c^2*x^2) + 1)/x^2 - 3*b*arccos(1/(c*x))/(c*x^3) - 3*a/(c*x^3))*c","A",0
12,1,83,0,0.151177," ","integrate((a+b*arcsec(c*x))/x^5,x, algorithm=""giac"")","\frac{1}{32} \, {\left(3 \, b c^{3} \arccos\left(\frac{1}{c x}\right) + \frac{3 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{3}} - \frac{8 \, b \arccos\left(\frac{1}{c x}\right)}{c x^{4}} - \frac{8 \, a}{c x^{4}}\right)} c"," ",0,"1/32*(3*b*c^3*arccos(1/(c*x)) + 3*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 2*b*sqrt(-1/(c^2*x^2) + 1)/x^3 - 8*b*arccos(1/(c*x))/(c*x^4) - 8*a/(c*x^4))*c","A",0
13,1,87,0,0.132824," ","integrate((a+b*arcsec(c*x))/x^6,x, algorithm=""giac"")","\frac{1}{75} \, {\left(8 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{4 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} + \frac{3 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{4}} - \frac{15 \, b \arccos\left(\frac{1}{c x}\right)}{c x^{5}} - \frac{15 \, a}{c x^{5}}\right)} c"," ",0,"1/75*(8*b*c^4*sqrt(-1/(c^2*x^2) + 1) + 4*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x^2 + 3*b*sqrt(-1/(c^2*x^2) + 1)/x^4 - 15*b*arccos(1/(c*x))/(c*x^5) - 15*a/(c*x^5))*c","A",0
14,1,104,0,0.138151," ","integrate((a+b*arcsec(c*x))/x^7,x, algorithm=""giac"")","\frac{1}{288} \, {\left(15 \, b c^{5} \arccos\left(\frac{1}{c x}\right) + \frac{15 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{10 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{3}} + \frac{8 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{5}} - \frac{48 \, b \arccos\left(\frac{1}{c x}\right)}{c x^{6}} - \frac{48 \, a}{c x^{6}}\right)} c"," ",0,"1/288*(15*b*c^5*arccos(1/(c*x)) + 15*b*c^4*sqrt(-1/(c^2*x^2) + 1)/x + 10*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x^3 + 8*b*sqrt(-1/(c^2*x^2) + 1)/x^5 - 48*b*arccos(1/(c*x))/(c*x^6) - 48*a/(c*x^6))*c","A",0
15,1,6625,0,0.808077," ","integrate(x^3*(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\frac{1}{12} \, {\left(\frac{3 \, b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{6 \, a b \arccos\left(\frac{1}{c x}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{4 \, b^{2} \log\left(2\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{4 \, b^{2} \log\left(\frac{2}{c x} + 2\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{4 \, b^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{4 \, b^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{3 \, a^{2}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{b^{2}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{24 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left(2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{20 \, b^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{12 \, a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{36 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{24 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left(2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{24 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{24 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{24 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, a b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{20 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} + \frac{18 \, a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{24 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left(2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{16 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{20 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} - \frac{12 \, a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left(2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{12 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{3 \, a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)} c"," ",0,"1/12*(3*b^2*arccos(1/(c*x))^2/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 6*a*b*arccos(1/(c*x))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 4*b^2*log(2)/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 4*b^2*log(2/(c*x) + 2)/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 4*b^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 4*b^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 3*a^2/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + b^2/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 24*a*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 16*b^2*(1/(c^2*x^2) - 1)*log(2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 16*b^2*(1/(c^2*x^2) - 1)*log(2/(c*x) + 2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 16*b^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 16*b^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*a*b*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 20*b^2*(-1/(c^2*x^2) + 1)^(3/2)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 12*a^2*(1/(c^2*x^2) - 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 36*a*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 24*b^2*(1/(c^2*x^2) - 1)^2*log(2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 24*b^2*(1/(c^2*x^2) - 1)^2*log(2/(c*x) + 2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 24*b^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 24*b^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 20*a*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 20*b^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) + 18*a^2*(1/(c^2*x^2) - 1)^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 2*b^2*(1/(c^2*x^2) - 1)^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 24*a*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 3*b^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 16*b^2*(1/(c^2*x^2) - 1)^3*log(2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 16*b^2*(1/(c^2*x^2) - 1)^3*log(2/(c*x) + 2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 16*b^2*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 16*b^2*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 20*a*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*b^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) - 12*a^2*(1/(c^2*x^2) - 1)^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 6*a*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 4*b^2*(1/(c^2*x^2) - 1)^4*log(2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 4*b^2*(1/(c^2*x^2) - 1)^4*log(2/(c*x) + 2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 4*b^2*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 4*b^2*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 12*a*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 3*a^2*(1/(c^2*x^2) - 1)^4/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + b^2*(1/(c^2*x^2) - 1)^4/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))*c","B",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^2*x^2, x)","F",0
17,1,2181,0,0.480918," ","integrate(x*(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, a b \arccos\left(\frac{1}{c x}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b^{2} \log\left(2\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, b^{2} \log\left(\frac{2}{c x} + 2\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{4 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{a^{2}}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{4 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left(2\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{4 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{4 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{4 \, b^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{2 \, a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, a b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left(2\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left(\frac{2}{c x} + 2\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, a b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{a^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}}\right)} c"," ",0,"1/2*(b^2*arccos(1/(c*x))^2/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*a*b*arccos(1/(c*x))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))^2/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 2*b^2*log(2)/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*b^2*log(2/(c*x) + 2)/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 4*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)) + a^2/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 4*a*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + b^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))^2/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 4*b^2*(1/(c^2*x^2) - 1)*log(2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + 4*b^2*(1/(c^2*x^2) - 1)*log(2/(c*x) + 2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 4*b^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 4*b^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 4*a*b*sqrt(-1/(c^2*x^2) + 1)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)) + 4*b^2*(-1/(c^2*x^2) + 1)^(3/2)*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^3) - 2*a^2*(1/(c^2*x^2) - 1)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + 2*a*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 2*b^2*(1/(c^2*x^2) - 1)^2*log(2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + 2*b^2*(1/(c^2*x^2) - 1)^2*log(2/(c*x) + 2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 2*b^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 2*b^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + 4*a*b*(-1/(c^2*x^2) + 1)^(3/2)/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^3) + a^2*(1/(c^2*x^2) - 1)^2/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4))*c","B",0
18,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^2, x)","F",0
19,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Evaluation time: 0.52ln of unsigned or minus infinity Error: Bad Argument Value","F(-2)",0
20,1,105,0,0.168020," ","integrate((a+b*arcsec(c*x))^2/x^2,x, algorithm=""giac"")","{\left(2 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right) + 2 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x} - \frac{2 \, a b \arccos\left(\frac{1}{c x}\right)}{c x} - \frac{a^{2}}{c x} + \frac{2 \, b^{2}}{c x}\right)} c"," ",0,"(2*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x)) + 2*a*b*sqrt(-1/(c^2*x^2) + 1) - b^2*arccos(1/(c*x))^2/(c*x) - 2*a*b*arccos(1/(c*x))/(c*x) - a^2/(c*x) + 2*b^2/(c*x))*c","B",0
21,1,147,0,0.164397," ","integrate((a+b*arcsec(c*x))^2/x^3,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b^{2} c \arccos\left(\frac{1}{c x}\right)^{2} + 4 \, a b c \arccos\left(\frac{1}{c x}\right) - b^{2} c + \frac{4 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x} + \frac{4 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{4 \, b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{2}} - \frac{8 \, a b \arccos\left(\frac{1}{c x}\right)}{c x^{2}} - \frac{4 \, a^{2}}{c x^{2}} + \frac{2 \, b^{2}}{c x^{2}}\right)} c"," ",0,"1/8*(2*b^2*c*arccos(1/(c*x))^2 + 4*a*b*c*arccos(1/(c*x)) - b^2*c + 4*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x + 4*a*b*sqrt(-1/(c^2*x^2) + 1)/x - 4*b^2*arccos(1/(c*x))^2/(c*x^2) - 8*a*b*arccos(1/(c*x))/(c*x^2) - 4*a^2/(c*x^2) + 2*b^2/(c*x^2))*c","A",0
22,1,168,0,0.156248," ","integrate((a+b*arcsec(c*x))^2/x^4,x, algorithm=""giac"")","\frac{1}{27} \, {\left(12 \, b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right) + 12 \, a b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{12 \, b^{2} c}{x} + \frac{6 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x^{2}} + \frac{6 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} - \frac{9 \, b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{3}} - \frac{18 \, a b \arccos\left(\frac{1}{c x}\right)}{c x^{3}} - \frac{9 \, a^{2}}{c x^{3}} + \frac{2 \, b^{2}}{c x^{3}}\right)} c"," ",0,"1/27*(12*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x)) + 12*a*b*c^2*sqrt(-1/(c^2*x^2) + 1) + 12*b^2*c/x + 6*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x^2 + 6*a*b*sqrt(-1/(c^2*x^2) + 1)/x^2 - 9*b^2*arccos(1/(c*x))^2/(c*x^3) - 18*a*b*arccos(1/(c*x))/(c*x^3) - 9*a^2/(c*x^3) + 2*b^2/(c*x^3))*c","A",0
23,1,215,0,0.149129," ","integrate((a+b*arcsec(c*x))^2/x^5,x, algorithm=""giac"")","\frac{1}{256} \, {\left(24 \, b^{2} c^{3} \arccos\left(\frac{1}{c x}\right)^{2} + 48 \, a b c^{3} \arccos\left(\frac{1}{c x}\right) - 15 \, b^{2} c^{3} + \frac{48 \, b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x} + \frac{48 \, a b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{24 \, b^{2} c}{x^{2}} + \frac{32 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x^{3}} + \frac{32 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{3}} - \frac{64 \, b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{4}} - \frac{128 \, a b \arccos\left(\frac{1}{c x}\right)}{c x^{4}} - \frac{64 \, a^{2}}{c x^{4}} + \frac{8 \, b^{2}}{c x^{4}}\right)} c"," ",0,"1/256*(24*b^2*c^3*arccos(1/(c*x))^2 + 48*a*b*c^3*arccos(1/(c*x)) - 15*b^2*c^3 + 48*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x + 48*a*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 24*b^2*c/x^2 + 32*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x^3 + 32*a*b*sqrt(-1/(c^2*x^2) + 1)/x^3 - 64*b^2*arccos(1/(c*x))^2/(c*x^4) - 128*a*b*arccos(1/(c*x))/(c*x^4) - 64*a^2/(c*x^4) + 8*b^2/(c*x^4))*c","A",0
24,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3*x^3, x)","F",0
25,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3*x^2, x)","F",0
26,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3*x, x)","F",0
27,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3, x)","F",0
28,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3/x, x)","F",0
29,1,196,0,0.185018," ","integrate((a+b*arcsec(c*x))^3/x^2,x, algorithm=""giac"")","{\left(3 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2} + 6 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right) - \frac{b^{3} \arccos\left(\frac{1}{c x}\right)^{3}}{c x} + 3 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 6 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{3 \, a b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x} - \frac{3 \, a^{2} b \arccos\left(\frac{1}{c x}\right)}{c x} + \frac{6 \, b^{3} \arccos\left(\frac{1}{c x}\right)}{c x} - \frac{a^{3}}{c x} + \frac{6 \, a b^{2}}{c x}\right)} c"," ",0,"(3*b^3*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2 + 6*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x)) - b^3*arccos(1/(c*x))^3/(c*x) + 3*a^2*b*sqrt(-1/(c^2*x^2) + 1) - 6*b^3*sqrt(-1/(c^2*x^2) + 1) - 3*a*b^2*arccos(1/(c*x))^2/(c*x) - 3*a^2*b*arccos(1/(c*x))/(c*x) + 6*b^3*arccos(1/(c*x))/(c*x) - a^3/(c*x) + 6*a*b^2/(c*x))*c","B",0
30,1,278,0,0.176787," ","integrate((a+b*arcsec(c*x))^3/x^3,x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b^{3} c \arccos\left(\frac{1}{c x}\right)^{3} + 6 \, a b^{2} c \arccos\left(\frac{1}{c x}\right)^{2} + 6 \, a^{2} b c \arccos\left(\frac{1}{c x}\right) - 3 \, b^{3} c \arccos\left(\frac{1}{c x}\right) + \frac{6 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2}}{x} - 3 \, a b^{2} c + \frac{12 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x} - \frac{4 \, b^{3} \arccos\left(\frac{1}{c x}\right)^{3}}{c x^{2}} + \frac{6 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{3 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{12 \, a b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{2}} - \frac{12 \, a^{2} b \arccos\left(\frac{1}{c x}\right)}{c x^{2}} + \frac{6 \, b^{3} \arccos\left(\frac{1}{c x}\right)}{c x^{2}} - \frac{4 \, a^{3}}{c x^{2}} + \frac{6 \, a b^{2}}{c x^{2}}\right)} c"," ",0,"1/8*(2*b^3*c*arccos(1/(c*x))^3 + 6*a*b^2*c*arccos(1/(c*x))^2 + 6*a^2*b*c*arccos(1/(c*x)) - 3*b^3*c*arccos(1/(c*x)) + 6*b^3*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2/x - 3*a*b^2*c + 12*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x - 4*b^3*arccos(1/(c*x))^3/(c*x^2) + 6*a^2*b*sqrt(-1/(c^2*x^2) + 1)/x - 3*b^3*sqrt(-1/(c^2*x^2) + 1)/x - 12*a*b^2*arccos(1/(c*x))^2/(c*x^2) - 12*a^2*b*arccos(1/(c*x))/(c*x^2) + 6*b^3*arccos(1/(c*x))/(c*x^2) - 4*a^3/(c*x^2) + 6*a*b^2/(c*x^2))*c","B",0
31,1,336,0,0.189657," ","integrate((a+b*arcsec(c*x))^3/x^4,x, algorithm=""giac"")","\frac{1}{27} \, {\left(18 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2} + 36 \, a b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right) + 18 \, a^{2} b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 40 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{36 \, b^{3} c \arccos\left(\frac{1}{c x}\right)}{x} + \frac{9 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2}}{x^{2}} + \frac{36 \, a b^{2} c}{x} + \frac{18 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x^{2}} - \frac{9 \, b^{3} \arccos\left(\frac{1}{c x}\right)^{3}}{c x^{3}} + \frac{9 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} - \frac{2 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} - \frac{27 \, a b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{3}} - \frac{27 \, a^{2} b \arccos\left(\frac{1}{c x}\right)}{c x^{3}} + \frac{6 \, b^{3} \arccos\left(\frac{1}{c x}\right)}{c x^{3}} - \frac{9 \, a^{3}}{c x^{3}} + \frac{6 \, a b^{2}}{c x^{3}}\right)} c"," ",0,"1/27*(18*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2 + 36*a*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x)) + 18*a^2*b*c^2*sqrt(-1/(c^2*x^2) + 1) - 40*b^3*c^2*sqrt(-1/(c^2*x^2) + 1) + 36*b^3*c*arccos(1/(c*x))/x + 9*b^3*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2/x^2 + 36*a*b^2*c/x + 18*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x^2 - 9*b^3*arccos(1/(c*x))^3/(c*x^3) + 9*a^2*b*sqrt(-1/(c^2*x^2) + 1)/x^2 - 2*b^3*sqrt(-1/(c^2*x^2) + 1)/x^2 - 27*a*b^2*arccos(1/(c*x))^2/(c*x^3) - 27*a^2*b*arccos(1/(c*x))/(c*x^3) + 6*b^3*arccos(1/(c*x))/(c*x^3) - 9*a^3/(c*x^3) + 6*a*b^2/(c*x^3))*c","B",0
32,1,427,0,0.192461," ","integrate((a+b*arcsec(c*x))^3/x^5,x, algorithm=""giac"")","\frac{1}{256} \, {\left(24 \, b^{3} c^{3} \arccos\left(\frac{1}{c x}\right)^{3} + 72 \, a b^{2} c^{3} \arccos\left(\frac{1}{c x}\right)^{2} + 72 \, a^{2} b c^{3} \arccos\left(\frac{1}{c x}\right) - 45 \, b^{3} c^{3} \arccos\left(\frac{1}{c x}\right) + \frac{72 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2}}{x} - 45 \, a b^{2} c^{3} + \frac{144 \, a b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x} + \frac{72 \, a^{2} b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{45 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{72 \, b^{3} c \arccos\left(\frac{1}{c x}\right)}{x^{2}} + \frac{48 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)^{2}}{x^{3}} + \frac{72 \, a b^{2} c}{x^{2}} + \frac{96 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arccos\left(\frac{1}{c x}\right)}{x^{3}} - \frac{64 \, b^{3} \arccos\left(\frac{1}{c x}\right)^{3}}{c x^{4}} + \frac{48 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{3}} - \frac{6 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{3}} - \frac{192 \, a b^{2} \arccos\left(\frac{1}{c x}\right)^{2}}{c x^{4}} - \frac{192 \, a^{2} b \arccos\left(\frac{1}{c x}\right)}{c x^{4}} + \frac{24 \, b^{3} \arccos\left(\frac{1}{c x}\right)}{c x^{4}} - \frac{64 \, a^{3}}{c x^{4}} + \frac{24 \, a b^{2}}{c x^{4}}\right)} c"," ",0,"1/256*(24*b^3*c^3*arccos(1/(c*x))^3 + 72*a*b^2*c^3*arccos(1/(c*x))^2 + 72*a^2*b*c^3*arccos(1/(c*x)) - 45*b^3*c^3*arccos(1/(c*x)) + 72*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2/x - 45*a*b^2*c^3 + 144*a*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x + 72*a^2*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x - 45*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 72*b^3*c*arccos(1/(c*x))/x^2 + 48*b^3*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))^2/x^3 + 72*a*b^2*c/x^2 + 96*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arccos(1/(c*x))/x^3 - 64*b^3*arccos(1/(c*x))^3/(c*x^4) + 48*a^2*b*sqrt(-1/(c^2*x^2) + 1)/x^3 - 6*b^3*sqrt(-1/(c^2*x^2) + 1)/x^3 - 192*a*b^2*arccos(1/(c*x))^2/(c*x^4) - 192*a^2*b*arccos(1/(c*x))/(c*x^4) + 24*b^3*arccos(1/(c*x))/(c*x^4) - 64*a^3/(c*x^4) + 24*a*b^2/(c*x^4))*c","B",0
33,0,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \frac{x}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate(x/(b*arcsec(c*x) + a), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \frac{1}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsec(c*x) + a), x)","F",0
35,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)*x), x)","F",0
36,1,55,0,0.148721," ","integrate(1/x^2/(a+b*arcsec(c*x)),x, algorithm=""giac"")","-c {\left(\frac{\operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} - \frac{\cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b}\right)}"," ",0,"-c*(cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/b - cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/b)","A",0
37,1,95,0,0.129739," ","integrate(1/x^3/(a+b*arcsec(c*x)),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, c \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} - \frac{2 \, c \cos\left(\frac{a}{b}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b} + \frac{c \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b}\right)} c"," ",0,"-1/2*(2*c*cos(a/b)*cos_integral(2*a/b + 2*arccos(1/(c*x)))*sin(a/b)/b - 2*c*cos(a/b)^2*sin_integral(2*a/b + 2*arccos(1/(c*x)))/b + c*sin_integral(2*a/b + 2*arccos(1/(c*x)))/b)*c","A",0
38,1,199,0,0.141413," ","integrate(1/x^4/(a+b*arcsec(c*x)),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{4 \, c^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} - \frac{4 \, c^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b} - \frac{c^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} + \frac{c^{2} \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} + \frac{3 \, c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b} - \frac{c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b}\right)} c"," ",0,"-1/4*(4*c^2*cos(a/b)^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/b - 4*c^2*cos(a/b)^3*sin_integral(3*a/b + 3*arccos(1/(c*x)))/b - c^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/b + c^2*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/b + 3*c^2*cos(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/b - c^2*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/b)*c","A",0
39,0,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int \frac{x}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(x/(b*arcsec(c*x) + a)^2, x)","F",0
40,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^(-2), x)","F",0
41,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2} x}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)^2*x), x)","F",0
42,1,226,0,0.128945," ","integrate(1/x^2/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","{\left(\frac{b \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{b \arccos\left(\frac{1}{c x}\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{a \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{a \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}}\right)} c"," ",0,"(b*arccos(1/(c*x))*cos(a/b)*cos_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + b*arccos(1/(c*x))*sin(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + a*cos(a/b)*cos_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + a*sin(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - b*sqrt(-1/(c^2*x^2) + 1)/(b^3*arccos(1/(c*x)) + a*b^2))*c","B",0
43,1,357,0,0.155304," ","integrate(1/x^3/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","{\left(\frac{2 \, b c \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{2 \, b c \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{2 \, a c \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{2 \, a c \cos\left(\frac{a}{b}\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{b c \arccos\left(\frac{1}{c x}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{a c \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}\right)} x}\right)} c"," ",0,"(2*b*c*arccos(1/(c*x))*cos(a/b)^2*cos_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 2*b*c*arccos(1/(c*x))*cos(a/b)*sin(a/b)*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 2*a*c*cos(a/b)^2*cos_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 2*a*c*cos(a/b)*sin(a/b)*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - b*c*arccos(1/(c*x))*cos_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - a*c*cos_integral(2*a/b + 2*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - b*sqrt(-1/(c^2*x^2) + 1)/((b^3*arccos(1/(c*x)) + a*b^2)*x))*c","B",0
44,1,694,0,0.218670," ","integrate(1/x^4/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{12 \, b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{12 \, b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{12 \, a c^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{12 \, a c^{2} \cos\left(\frac{a}{b}\right)^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{9 \, b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{3 \, b c^{2} \arccos\left(\frac{1}{c x}\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{b c^{2} \arccos\left(\frac{1}{c x}\right) \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{9 \, a c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{a c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{3 \, a c^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} + \frac{a c^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}} - \frac{4 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(b^{3} \arccos\left(\frac{1}{c x}\right) + a b^{2}\right)} x^{2}}\right)} c"," ",0,"1/4*(12*b*c^2*arccos(1/(c*x))*cos(a/b)^3*cos_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 12*b*c^2*arccos(1/(c*x))*cos(a/b)^2*sin(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 12*a*c^2*cos(a/b)^3*cos_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + 12*a*c^2*cos(a/b)^2*sin(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - 9*b*c^2*arccos(1/(c*x))*cos(a/b)*cos_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + b*c^2*arccos(1/(c*x))*cos(a/b)*cos_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - 3*b*c^2*arccos(1/(c*x))*sin(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + b*c^2*arccos(1/(c*x))*sin(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - 9*a*c^2*cos(a/b)*cos_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + a*c^2*cos(a/b)*cos_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - 3*a*c^2*sin(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) + a*c^2*sin(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^3*arccos(1/(c*x)) + a*b^2) - 4*b*sqrt(-1/(c^2*x^2) + 1)/((b^3*arccos(1/(c*x)) + a*b^2)*x^2))*c","B",0
45,-1,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^(-3), x)","F",0
47,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3} x}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)^3*x), x)","F",0
48,1,580,0,0.141489," ","integrate(1/x^2/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{b^{2} \arccos\left(\frac{1}{c x}\right)^{2} \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{b^{2} \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{2 \, a b \arccos\left(\frac{1}{c x}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{2 \, a b \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{a^{2} \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{a^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{b^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x} - \frac{a b}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x}\right)} c"," ",0,"1/2*(b^2*arccos(1/(c*x))^2*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - b^2*arccos(1/(c*x))^2*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 2*a*b*arccos(1/(c*x))*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 2*a*b*arccos(1/(c*x))*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + a^2*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - a^2*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - b^2*sqrt(-1/(c^2*x^2) + 1)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - b^2*arccos(1/(c*x))/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x) - a*b/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x))*c","B",0
49,1,929,0,0.143799," ","integrate(1/x^3/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{4 \, b^{2} c \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{4 \, b^{2} c \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{8 \, a b c \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{8 \, a b c \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{4 \, a^{2} c \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{2 \, b^{2} c \arccos\left(\frac{1}{c x}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{4 \, a^{2} c \cos\left(\frac{a}{b}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{4 \, a b c \arccos\left(\frac{1}{c x}\right) \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{b^{2} c \arccos\left(\frac{1}{c x}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{2 \, a^{2} c \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{a b c}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} x} - \frac{2 \, b^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x^{2}} - \frac{2 \, a b}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x^{2}}\right)} c"," ",0,"1/2*(4*b^2*c*arccos(1/(c*x))^2*cos(a/b)*cos_integral(2*a/b + 2*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 4*b^2*c*arccos(1/(c*x))^2*cos(a/b)^2*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 8*a*b*c*arccos(1/(c*x))*cos(a/b)*cos_integral(2*a/b + 2*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 8*a*b*c*arccos(1/(c*x))*cos(a/b)^2*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 4*a^2*c*cos(a/b)*cos_integral(2*a/b + 2*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 2*b^2*c*arccos(1/(c*x))^2*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 4*a^2*c*cos(a/b)^2*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 4*a*b*c*arccos(1/(c*x))*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + b^2*c*arccos(1/(c*x))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 2*a^2*c*sin_integral(2*a/b + 2*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + a*b*c/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - b^2*sqrt(-1/(c^2*x^2) + 1)/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*x) - 2*b^2*arccos(1/(c*x))/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x^2) - 2*a*b/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x^2))*c","B",0
50,1,1640,0,0.159825," ","integrate(1/x^4/(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{36 \, b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{36 \, b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{72 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{72 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right)^{3} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{9 \, b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{36 \, a^{2} c^{2} \cos\left(\frac{a}{b}\right)^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{27 \, b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{36 \, a^{2} c^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{b^{2} c^{2} \arccos\left(\frac{1}{c x}\right)^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{18 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{2 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{54 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{2 \, a b c^{2} \arccos\left(\frac{1}{c x}\right) \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{9 \, a^{2} c^{2} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{a^{2} c^{2} \operatorname{Ci}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{27 \, a^{2} c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} - \frac{a^{2} c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arccos\left(\frac{1}{c x}\right)\right)}{b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}} + \frac{8 \, b^{2} c \arccos\left(\frac{1}{c x}\right)}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} x} + \frac{8 \, a b c}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} x} - \frac{4 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} x^{2}} - \frac{12 \, b^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x^{3}} - \frac{12 \, a b}{{\left(b^{5} \arccos\left(\frac{1}{c x}\right)^{2} + 2 \, a b^{4} \arccos\left(\frac{1}{c x}\right) + a^{2} b^{3}\right)} c x^{3}}\right)} c"," ",0,"1/8*(36*b^2*c^2*arccos(1/(c*x))^2*cos(a/b)^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 36*b^2*c^2*arccos(1/(c*x))^2*cos(a/b)^3*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 72*a*b*c^2*arccos(1/(c*x))*cos(a/b)^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 72*a*b*c^2*arccos(1/(c*x))*cos(a/b)^3*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 9*b^2*c^2*arccos(1/(c*x))^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 36*a^2*c^2*cos(a/b)^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + b^2*c^2*arccos(1/(c*x))^2*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 27*b^2*c^2*arccos(1/(c*x))^2*cos(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 36*a^2*c^2*cos(a/b)^3*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - b^2*c^2*arccos(1/(c*x))^2*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 18*a*b*c^2*arccos(1/(c*x))*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 2*a*b*c^2*arccos(1/(c*x))*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 54*a*b*c^2*arccos(1/(c*x))*cos(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 2*a*b*c^2*arccos(1/(c*x))*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - 9*a^2*c^2*cos_integral(3*a/b + 3*arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + a^2*c^2*cos_integral(a/b + arccos(1/(c*x)))*sin(a/b)/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 27*a^2*c^2*cos(a/b)*sin_integral(3*a/b + 3*arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) - a^2*c^2*cos(a/b)*sin_integral(a/b + arccos(1/(c*x)))/(b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3) + 8*b^2*c*arccos(1/(c*x))/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*x) + 8*a*b*c/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*x) - 4*b^2*sqrt(-1/(c^2*x^2) + 1)/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*x^2) - 12*b^2*arccos(1/(c*x))/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x^3) - 12*a*b/((b^5*arccos(1/(c*x))^2 + 2*a*b^4*arccos(1/(c*x)) + a^2*b^3)*c*x^3))*c","B",0
51,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^3*(d*x)^m, x)","F",0
52,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)^2*(d*x)^m, x)","F",0
53,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(d*x)^m, x)","F",0
54,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arcsec(c*x) + a), x)","F",0
55,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsec(c*x))^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arcsec(c*x) + a)^2, x)","F",0
56,1,9404,0,2.941394," ","integrate((e*x+d)^3*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{12} \, {\left(\frac{12 \, b c^{3} d^{3} \arccos\left(\frac{1}{c x}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b c^{3} d^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{12 \, b c^{3} d^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{12 \, a c^{3} d^{3}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{24 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d^{2} \arccos\left(\frac{1}{c x}\right) e}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{48 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{48 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{24 \, a c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, a c^{2} d^{2} e}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{72 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{72 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{36 \, b c^{2} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{24 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{12 \, b c d \arccos\left(\frac{1}{c x}\right) e^{2}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{36 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{48 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{6 \, b c d e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{48 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, b c d e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{108 \, b c^{2} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{24 \, a c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{12 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{12 \, a c d e^{2}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{36 \, a c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{12 \, b c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, b c d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{108 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, a c^{3} d^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{3 \, b \arccos\left(\frac{1}{c x}\right) e^{3}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{24 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{36 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{36 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{12 \, b c d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{36 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{3 \, a e^{3}}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{18 \, a c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{24 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{6 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{12 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{24 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{12 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{6 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{10 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{12 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{18 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{12 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{10 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{3 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{3}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)} c"," ",0,"1/12*(12*b*c^3*d^3*arccos(1/(c*x))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*c^3*d^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 12*b*c^3*d^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 12*a*c^3*d^3/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 24*b*c^3*d^3*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*c^2*d^2*arccos(1/(c*x))*e/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 48*b*c^3*d^3*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 48*b*c^3*d^3*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 24*a*c^3*d^3*(1/(c^2*x^2) - 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*a*c^2*d^2*e/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 72*b*c^3*d^3*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 72*b*c^3*d^3*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 36*b*c^2*d^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) - 24*b*c^3*d^3*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 12*b*c*d*arccos(1/(c*x))*e^2/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 36*b*c^2*d^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 48*b*c^3*d^3*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 6*b*c*d*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 48*b*c^3*d^3*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 6*b*c*d*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 108*b*c^2*d^2*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 24*a*c^3*d^3*(1/(c^2*x^2) - 1)^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 12*b*c^3*d^3*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 12*a*c*d*e^2/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 24*b*c*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 36*a*c^2*d^2*(1/(c^2*x^2) - 1)^2*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*c^3*d^3*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 24*b*c*d*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 12*b*c^3*d^3*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 24*b*c*d*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*b*c*d*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) - 108*b*c^2*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*a*c^3*d^3*(1/(c^2*x^2) - 1)^4/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 3*b*arccos(1/(c*x))*e^3/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 24*a*c*d*(1/(c^2*x^2) - 1)*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*c^2*d^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 36*b*c*d*(1/(c^2*x^2) - 1)^2*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 36*b*c*d*(1/(c^2*x^2) - 1)^2*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 12*b*c*d*(-1/(c^2*x^2) + 1)^(3/2)*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 36*b*c^2*d^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 3*a*e^3/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 24*b*c*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 18*a*c^2*d^2*(1/(c^2*x^2) - 1)^4*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 24*b*c*d*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 24*b*c*d*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 6*b*sqrt(-1/(c^2*x^2) + 1)*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 12*b*c*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*a*(1/(c^2*x^2) - 1)*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 24*a*c*d*(1/(c^2*x^2) - 1)^3*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 12*b*c*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 6*b*c*d*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 6*b*c*d*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 10*b*(-1/(c^2*x^2) + 1)^(3/2)*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 12*b*c*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 18*a*(1/(c^2*x^2) - 1)^2*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 12*a*c*d*(1/(c^2*x^2) - 1)^4*e^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 10*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*a*(1/(c^2*x^2) - 1)^3*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 6*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 3*a*(1/(c^2*x^2) - 1)^4*e^3/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))*c","B",0
57,1,6418,0,4.956037," ","integrate((e*x+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{6 \, b c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, a c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{18 \, b c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, a c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{18 \, a c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, b c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, b c^{2} d x \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b c^{2} d^{2} \arccos\left(\frac{1}{c x}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, a c^{3} d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, b c^{2} d^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b c^{2} d^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{18 \, b c^{2} d x {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, a c^{2} d^{2}}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b c d \arccos\left(\frac{1}{c x}\right) e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{18 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{18 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d x {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, a c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, a c d e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{18 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{18 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, b c^{2} d x {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, a c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{18 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{18 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, a c^{2} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, a e^{2}}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{18 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} + \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}}\right)} c"," ",0,"-1/6*(6*b*c^3*d*x^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*a*c^3*d*x^2*(1/(c^2*x^2) - 1)*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 18*b*c^3*d*x^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 18*a*c^3*d*x^2*(1/(c^2*x^2) - 1)^2*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 18*b*c^3*d*x^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 18*a*c^3*d*x^2*(1/(c^2*x^2) - 1)^3*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*b*c^3*d*x^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 6*b*c^2*d*x*sqrt(-1/(c^2*x^2) + 1)*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*c^2*d^2*arccos(1/(c*x))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*a*c^3*d*x^2*(1/(c^2*x^2) - 1)^4*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 6*b*c^2*d^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*c^2*d^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 18*b*c^2*d*x*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 6*a*c^2*d^2/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*c^2*d^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 6*b*c*d*arccos(1/(c*x))*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 18*b*c^2*d^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 18*b*c^2*d^2*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 18*b*c^2*d*x*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*a*c^2*d^2*(1/(c^2*x^2) - 1)/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 6*b*c^2*d^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*a*c*d*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 18*b*c*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 18*b*c^2*d^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 18*b*c^2*d^2*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*b*c^2*d*x*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 6*a*c^2*d^2*(1/(c^2*x^2) - 1)^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*b*c^2*d^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - 2*b*arccos(1/(c*x))*e^2/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 18*a*c*d*(1/(c^2*x^2) - 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 18*b*c*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*b*c^2*d^2*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*c^2*d^2*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*a*c^2*d^2*(1/(c^2*x^2) - 1)^3/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - 2*a*e^2/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 18*a*c*d*(1/(c^2*x^2) - 1)^2*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*b*c*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 3*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 2*b*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)) + 6*a*(1/(c^2*x^2) - 1)*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 6*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*a*c*d*(1/(c^2*x^2) - 1)^3*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)^2*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 3*b*(1/(c^2*x^2) - 1)^2*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*a*(1/(c^2*x^2) - 1)^2*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 2*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - 2*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^5) + 2*a*(1/(c^2*x^2) - 1)^3*e^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6))*c","B",0
58,1,1555,0,0.677002," ","integrate((e*x+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, b c d \arccos\left(\frac{1}{c x}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b c d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, b c d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, a c d}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{b \arccos\left(\frac{1}{c x}\right) e}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{4 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{4 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{a e}{c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{2 \, a c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{3} + \frac{2 \, c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}}\right)} c"," ",0,"1/2*(2*b*c*d*arccos(1/(c*x))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b*c*d*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*b*c*d*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*a*c*d/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + b*arccos(1/(c*x))*e/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 4*b*c*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + 4*b*c*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 2*b*c*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + a*e/(c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - 2*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 2*b*c*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + 2*b*c*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 2*b*sqrt(-1/(c^2*x^2) + 1)*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)) - 2*a*c*d*(1/(c^2*x^2) - 1)^2/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - 2*a*(1/(c^2*x^2) - 1)*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + 2*b*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^3) + a*(1/(c^2*x^2) - 1)^2*e/((c^3 + 2*c^3*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + c^3*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4))*c","B",0
59,1,63,0,0.149989," ","integrate(a+b*arcsec(c*x),x, algorithm=""giac"")","\frac{1}{2} \, b c {\left(\frac{2 \, x \arccos\left(\frac{1}{c x}\right)}{c} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}}\right)} + a x"," ",0,"1/2*b*c*(2*x*arccos(1/(c*x))/c - (log(sqrt(-1/(c^2*x^2) + 1) + 1) - log(-sqrt(-1/(c^2*x^2) + 1) + 1))/c^2) + a*x","B",0
60,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
61,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
62,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
63,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)*(b*arcsec(c*x) + a), x)","F",0
64,0,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arcsec(c*x) + a), x)","F",0
65,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/sqrt(e*x + d), x)","F",0
66,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(e*x + d)^(3/2), x)","F",0
67,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(e*x + d)^(5/2), x)","F",0
68,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(e*x + d)^(7/2), x)","F",0
69,-1,0,0,0.000000," ","integrate(x^4*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,1,9820,0,3.034948," ","integrate(x^2*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{120} \, {\left(\frac{40 \, b c^{2} d \arccos\left(\frac{1}{c x}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{20 \, b c^{2} d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{20 \, b c^{2} d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{40 \, a c^{2} d}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{40 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{100 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{100 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{40 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{40 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{80 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{24 \, b \arccos\left(\frac{1}{c x}\right) e}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{200 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{9 \, b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{200 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{9 \, b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} + \frac{80 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{80 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{80 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{24 \, a e}{c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}} - \frac{120 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{200 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{45 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{200 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{45 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{30 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{80 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{40 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{120 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{240 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{100 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{100 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{80 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{12 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{40 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{40 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{240 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{240 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{20 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{20 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{40 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{40 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{240 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{120 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{45 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{45 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{120 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{24 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{9 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{9 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{24 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e}{{\left(c^{6} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{10 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{5 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}}\right)} c"," ",0,"1/120*(40*b*c^2*d*arccos(1/(c*x))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 20*b*c^2*d*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 20*b*c^2*d*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 40*a*c^2*d/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 40*b*c^2*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 100*b*c^2*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) + 100*b*c^2*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 40*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)) - 40*a*c^2*d*(1/(c^2*x^2) - 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 80*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 24*b*arccos(1/(c*x))*e/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 200*b*c^2*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) - 9*b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 200*b*c^2*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 9*b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) + 80*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^3) - 80*a*c^2*d*(1/(c^2*x^2) - 1)^2/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 80*b*c^2*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 24*a*e/(c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10) - 120*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 200*b*c^2*d*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) - 45*b*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) + 200*b*c^2*d*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 45*b*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) - 30*b*sqrt(-1/(c^2*x^2) + 1)*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)) + 80*a*c^2*d*(1/(c^2*x^2) - 1)^3/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 40*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 120*a*(1/(c^2*x^2) - 1)*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^2) + 240*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) - 100*b*c^2*d*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 90*b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 100*b*c^2*d*(1/(c^2*x^2) - 1)^4*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) + 90*b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) + 80*b*c^2*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^7) + 12*b*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^3) + 40*a*c^2*d*(1/(c^2*x^2) - 1)^4/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 40*b*c^2*d*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 240*a*(1/(c^2*x^2) - 1)^2*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^4) - 240*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) - 20*b*c^2*d*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) - 90*b*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 20*b*c^2*d*(1/(c^2*x^2) - 1)^5*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 90*b*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 40*b*c^2*d*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^9) - 40*a*c^2*d*(1/(c^2*x^2) - 1)^5/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) - 240*a*(1/(c^2*x^2) - 1)^3*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^6) + 120*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 45*b*(1/(c^2*x^2) - 1)^4*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) + 45*b*(1/(c^2*x^2) - 1)^4*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) + 12*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^7) + 120*a*(1/(c^2*x^2) - 1)^4*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^8) - 24*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) - 9*b*(1/(c^2*x^2) - 1)^5*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 9*b*(1/(c^2*x^2) - 1)^5*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10) + 30*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^9) - 24*a*(1/(c^2*x^2) - 1)^5*e/((c^6 + 5*c^6*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 10*c^6*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 10*c^6*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 5*c^6*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + c^6*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10)*(1/(c*x) + 1)^10))*c","B",0
71,1,4069,0,2.053753," ","integrate((e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{6 \, b c^{2} d \arccos\left(\frac{1}{c x}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b c^{2} d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, b c^{2} d \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, a c^{2} d}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{18 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{2 \, b \arccos\left(\frac{1}{c x}\right) e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{18 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} + \frac{18 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{2 \, a e}{c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{6 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{6 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{4} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{3 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}}\right)} c"," ",0,"1/6*(6*b*c^2*d*arccos(1/(c*x))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*c^2*d*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*b*c^2*d*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*a*c^2*d/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 6*b*c^2*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 18*b*c^2*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 18*b*c^2*d*(1/(c^2*x^2) - 1)*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 6*a*c^2*d*(1/(c^2*x^2) - 1)/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 6*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 2*b*arccos(1/(c*x))*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 18*b*c^2*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) + 18*b*c^2*d*(1/(c^2*x^2) - 1)^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*a*c^2*d*(1/(c^2*x^2) - 1)^2/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 6*b*c^2*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 2*a*e/(c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6) - 6*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 6*b*c^2*d*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - 3*b*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 6*b*c^2*d*(1/(c^2*x^2) - 1)^3*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) - 2*b*sqrt(-1/(c^2*x^2) + 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)) - 6*a*c^2*d*(1/(c^2*x^2) - 1)^3/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - 6*a*(1/(c^2*x^2) - 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^2) + 6*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 3*b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 3*b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) + 6*a*(1/(c^2*x^2) - 1)^2*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^4) - 2*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) - b*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + b*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6) + 2*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^5) - 2*a*(1/(c^2*x^2) - 1)^3*e/((c^4 + 3*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 3*c^4*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6)*(1/(c*x) + 1)^6))*c","B",0
72,1,1098,0,0.619196," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^2,x, algorithm=""giac"")","-{\left(\frac{b c^{2} d \arccos\left(\frac{1}{c x}\right)}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{a c^{2} d}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{2 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{b \arccos\left(\frac{1}{c x}\right) e}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} - \frac{b e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{a e}{c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{2} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}}\right)} c"," ",0,"-(b*c^2*d*arccos(1/(c*x))/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + a*c^2*d/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*b*c^2*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - 2*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)) + 2*a*c^2*d*(1/(c^2*x^2) - 1)/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - b*arccos(1/(c*x))*e/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) - b*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^3) + a*c^2*d*(1/(c^2*x^2) - 1)^2/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - a*e/(c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4) + 2*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) + 2*a*(1/(c^2*x^2) - 1)*e/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^2) - b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) + b*(1/(c^2*x^2) - 1)^2*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4) - a*(1/(c^2*x^2) - 1)^2*e/((c^2 - c^2*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4)*(1/(c*x) + 1)^4))*c","B",0
73,1,116,0,0.163012," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{9} \, {\left(2 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 9 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e - \frac{9 \, b \arccos\left(\frac{1}{c x}\right) e}{c x} + \frac{b d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} - \frac{9 \, a e}{c x} - \frac{3 \, b d \arccos\left(\frac{1}{c x}\right)}{c x^{3}} - \frac{3 \, a d}{c x^{3}}\right)} c"," ",0,"1/9*(2*b*c^2*d*sqrt(-1/(c^2*x^2) + 1) + 9*b*sqrt(-1/(c^2*x^2) + 1)*e - 9*b*arccos(1/(c*x))*e/(c*x) + b*d*sqrt(-1/(c^2*x^2) + 1)/x^2 - 9*a*e/(c*x) - 3*b*d*arccos(1/(c*x))/(c*x^3) - 3*a*d/(c*x^3))*c","A",0
74,1,162,0,0.160614," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^6,x, algorithm=""giac"")","\frac{1}{225} \, {\left(24 \, b c^{4} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 50 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{12 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} + \frac{25 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{2}} - \frac{75 \, b \arccos\left(\frac{1}{c x}\right) e}{c x^{3}} + \frac{9 \, b d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{4}} - \frac{75 \, a e}{c x^{3}} - \frac{45 \, b d \arccos\left(\frac{1}{c x}\right)}{c x^{5}} - \frac{45 \, a d}{c x^{5}}\right)} c"," ",0,"1/225*(24*b*c^4*d*sqrt(-1/(c^2*x^2) + 1) + 50*b*c^2*sqrt(-1/(c^2*x^2) + 1)*e + 12*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/x^2 + 25*b*sqrt(-1/(c^2*x^2) + 1)*e/x^2 - 75*b*arccos(1/(c*x))*e/(c*x^3) + 9*b*d*sqrt(-1/(c^2*x^2) + 1)/x^4 - 75*a*e/(c*x^3) - 45*b*d*arccos(1/(c*x))/(c*x^5) - 45*a*d/(c*x^5))*c","A",0
75,1,207,0,0.159644," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^8,x, algorithm=""giac"")","\frac{1}{3675} \, {\left(240 \, b c^{6} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 392 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{120 \, b c^{4} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} + \frac{196 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{2}} + \frac{90 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{4}} + \frac{147 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{4}} - \frac{735 \, b \arccos\left(\frac{1}{c x}\right) e}{c x^{5}} + \frac{75 \, b d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{6}} - \frac{735 \, a e}{c x^{5}} - \frac{525 \, b d \arccos\left(\frac{1}{c x}\right)}{c x^{7}} - \frac{525 \, a d}{c x^{7}}\right)} c"," ",0,"1/3675*(240*b*c^6*d*sqrt(-1/(c^2*x^2) + 1) + 392*b*c^4*sqrt(-1/(c^2*x^2) + 1)*e + 120*b*c^4*d*sqrt(-1/(c^2*x^2) + 1)/x^2 + 196*b*c^2*sqrt(-1/(c^2*x^2) + 1)*e/x^2 + 90*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/x^4 + 147*b*sqrt(-1/(c^2*x^2) + 1)*e/x^4 - 735*b*arccos(1/(c*x))*e/(c*x^5) + 75*b*d*sqrt(-1/(c^2*x^2) + 1)/x^6 - 735*a*e/(c*x^5) - 525*b*d*arccos(1/(c*x))/(c*x^7) - 525*a*d/(c*x^7))*c","A",0
76,-1,0,0,0.000000," ","integrate(x^5*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,1,7840,0,0.309619," ","integrate(x^3*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{180} \, {\left(\frac{45 \, b c^{2} d \arccos\left(\frac{1}{c x}\right)}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{45 \, a c^{2} d}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{90 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{90 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{30 \, b \arccos\left(\frac{1}{c x}\right) e}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{330 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{180 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{30 \, a e}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{180 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{540 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{60 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{180 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{180 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{450 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{540 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{140 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{450 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{600 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{330 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{312 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{90 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{600 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{450 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} - \frac{312 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{450 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{180 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{140 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{180 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{60 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} + \frac{30 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}}\right)} c"," ",0,"1/180*(45*b*c^2*d*arccos(1/(c*x))/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 45*a*c^2*d/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 90*b*c^2*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 90*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) - 90*a*c^2*d*(1/(c^2*x^2) - 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 45*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) + 30*b*arccos(1/(c*x))*e/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 330*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) - 45*a*c^2*d*(1/(c^2*x^2) - 1)^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) + 180*b*c^2*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) + 30*a*e/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 180*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 540*b*c^2*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) - 60*b*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) + 180*a*c^2*d*(1/(c^2*x^2) - 1)^3/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 45*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 180*a*(1/(c^2*x^2) - 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) + 450*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 540*b*c^2*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 140*b*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) - 45*a*c^2*d*(1/(c^2*x^2) - 1)^4/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*c^2*d*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 450*a*(1/(c^2*x^2) - 1)^2*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 600*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 330*b*c^2*d*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) - 312*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) - 90*a*c^2*d*(1/(c^2*x^2) - 1)^5/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 45*b*c^2*d*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 600*a*(1/(c^2*x^2) - 1)^3*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) + 450*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*c^2*d*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) - 312*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 45*a*c^2*d*(1/(c^2*x^2) - 1)^6/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) + 450*a*(1/(c^2*x^2) - 1)^4*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 180*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) - 140*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) - 180*a*(1/(c^2*x^2) - 1)^5*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 30*b*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 60*b*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) + 30*a*(1/(c^2*x^2) - 1)^6*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12))*c","B",0
78,1,3360,0,0.228125," ","integrate(x*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{12} \, {\left(\frac{6 \, b c^{2} d \arccos\left(\frac{1}{c x}\right)}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{6 \, a c^{2} d}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{12 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{3 \, b \arccos\left(\frac{1}{c x}\right) e}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{36 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{12 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{3 \, a e}{c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{36 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{6 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{6 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{10 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{6 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{18 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{10 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{6 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{3 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{5} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{6 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{4 \, c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)} c"," ",0,"1/12*(6*b*c^2*d*arccos(1/(c*x))/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 6*a*c^2*d/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) - 12*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 3*b*arccos(1/(c*x))*e/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 36*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 12*a*c^2*d*(1/(c^2*x^2) - 1)^2/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 3*a*e/(c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 36*b*c^2*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 6*b*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 6*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 12*a*(1/(c^2*x^2) - 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*c^2*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 10*b*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 6*a*c^2*d*(1/(c^2*x^2) - 1)^4/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 18*a*(1/(c^2*x^2) - 1)^2*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 10*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 12*a*(1/(c^2*x^2) - 1)^3*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 3*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 6*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 3*a*(1/(c^2*x^2) - 1)^4*e/((c^5 + 4*c^5*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 6*c^5*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 4*c^5*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + c^5*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))*c","B",0
79,-2,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
80,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arcsec(c*x) + a)/x^3, x)","F",0
81,-1,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,1,6010,0,2.945970," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^2,x, algorithm=""giac"")","-\frac{1}{6} \, {\left(\frac{6 \, b c^{4} d^{2} \arccos\left(\frac{1}{c x}\right)}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{6 \, a c^{4} d^{2}}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{24 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{24 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{36 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b c^{2} d \arccos\left(\frac{1}{c x}\right) e}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{12 \, b c^{2} d e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{12 \, b c^{2} d e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{36 \, b c^{4} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{36 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{24 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{12 \, a c^{2} d e}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{24 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{24 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{36 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} + \frac{24 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{6 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{24 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{6 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{2 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{24 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{24 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{24 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, a e^{2}}{c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{8 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{12 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{2 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{8 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{12 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{12 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{2 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{12 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{8 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} + \frac{8 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{2 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} - \frac{2 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2}}{{\left(c^{4} + \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)} c"," ",0,"-1/6*(6*b*c^4*d^2*arccos(1/(c*x))/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 6*a*c^4*d^2/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 24*b*c^4*d^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1)/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 24*a*c^4*d^2*(1/(c^2*x^2) - 1)/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 36*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*c^2*d*arccos(1/(c*x))*e/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 12*b*c^2*d*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 12*b*c^2*d*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 36*b*c^4*d^2*(-1/(c^2*x^2) + 1)^(3/2)/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 36*a*c^4*d^2*(1/(c^2*x^2) - 1)^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 24*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 12*a*c^2*d*e/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 24*b*c^2*d*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 24*b*c^2*d*(1/(c^2*x^2) - 1)*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 36*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) + 24*a*c^4*d^2*(1/(c^2*x^2) - 1)^3/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 6*b*c^4*d^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 24*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 6*a*c^4*d^2*(1/(c^2*x^2) - 1)^4/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 2*b*arccos(1/(c*x))*e^2/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 24*a*c^2*d*(1/(c^2*x^2) - 1)^2*e/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 24*b*c^2*d*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 24*b*c^2*d*(1/(c^2*x^2) - 1)^3*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 2*a*e^2/(c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 8*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 2*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*b*c^2*d*(1/(c^2*x^2) - 1)^4*e*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 2*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 12*b*c^2*d*(1/(c^2*x^2) - 1)^4*e*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 2*b*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 8*a*(1/(c^2*x^2) - 1)*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 12*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 12*a*c^2*d*(1/(c^2*x^2) - 1)^4*e/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 2*b*(-1/(c^2*x^2) + 1)^(3/2)*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) - 12*a*(1/(c^2*x^2) - 1)^2*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 8*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 2*b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 2*b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 2*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) + 8*a*(1/(c^2*x^2) - 1)^3*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 2*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - b*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + b*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 2*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) - 2*a*(1/(c^2*x^2) - 1)^4*e^2/((c^4 + 2*c^4*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 - 2*c^4*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^4*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))*c","B",0
84,1,4960,0,14.579356," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^4,x, algorithm=""giac"")","-\frac{1}{9} \, {\left(\frac{3 \, b c^{4} d^{2} \arccos\left(\frac{1}{c x}\right)}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{3 \, a c^{4} d^{2}}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{12 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{6 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{12 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{18 \, b c^{2} d \arccos\left(\frac{1}{c x}\right) e}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{2 \, b c^{4} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{18 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{12 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{18 \, a c^{2} d e}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{2 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{36 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{12 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{3 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{36 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{6 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} - \frac{36 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} + \frac{3 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{9 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{36 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{9 \, b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} - \frac{9 \, b e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{36 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{9 \, a e^{2}}{c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}} + \frac{36 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{36 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{36 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{54 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{18 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{54 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{36 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{18 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{36 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{9 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{9 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x} + 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{9 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2} \log\left({\left| \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{1}{c x} - 1 \right|}\right)}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{9 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2}}{{\left(c^{2} - \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{2 \, c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}}\right)} c"," ",0,"-1/9*(3*b*c^4*d^2*arccos(1/(c*x))/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 3*a*c^4*d^2/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 12*b*c^4*d^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 6*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1)/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 12*a*c^4*d^2*(1/(c^2*x^2) - 1)/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 18*b*c^2*d*arccos(1/(c*x))*e/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 2*b*c^4*d^2*(-1/(c^2*x^2) + 1)^(3/2)/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 18*a*c^4*d^2*(1/(c^2*x^2) - 1)^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 12*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 18*a*c^2*d*e/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 2*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 36*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)) + 12*a*c^4*d^2*(1/(c^2*x^2) - 1)^3/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 3*b*c^4*d^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 36*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) - 6*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) - 36*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^3) + 3*a*c^4*d^2*(1/(c^2*x^2) - 1)^4/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 9*b*arccos(1/(c*x))*e^2/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 36*a*c^2*d*(1/(c^2*x^2) - 1)^2*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 9*b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) - 9*b*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 36*b*c^2*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^5) - 9*a*e^2/(c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8) + 36*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 18*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) + 18*b*(1/(c^2*x^2) - 1)*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 36*b*c^2*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^7) + 36*a*(1/(c^2*x^2) - 1)*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^2) - 54*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 18*a*c^2*d*(1/(c^2*x^2) - 1)^4*e/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 54*a*(1/(c^2*x^2) - 1)^2*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^4) + 36*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 18*b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 18*b*(1/(c^2*x^2) - 1)^3*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) + 36*a*(1/(c^2*x^2) - 1)^3*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^6) - 9*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 9*b*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) + 1/(c*x) + 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) + 9*b*(1/(c^2*x^2) - 1)^4*e^2*log(abs(sqrt(-1/(c^2*x^2) + 1) - 1/(c*x) - 1))/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8) - 9*a*(1/(c^2*x^2) - 1)^4*e^2/((c^2 - 2*c^2*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 2*c^2*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 - c^2*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8)*(1/(c*x) + 1)^8))*c","B",0
85,1,223,0,0.153533," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^6,x, algorithm=""giac"")","\frac{1}{225} \, {\left(24 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 100 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{12 \, b c^{2} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} + 225 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2} + \frac{50 \, b d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{2}} - \frac{225 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c x} - \frac{225 \, a e^{2}}{c x} - \frac{150 \, b d \arccos\left(\frac{1}{c x}\right) e}{c x^{3}} + \frac{9 \, b d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{4}} - \frac{150 \, a d e}{c x^{3}} - \frac{45 \, b d^{2} \arccos\left(\frac{1}{c x}\right)}{c x^{5}} - \frac{45 \, a d^{2}}{c x^{5}}\right)} c"," ",0,"1/225*(24*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1) + 100*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)*e + 12*b*c^2*d^2*sqrt(-1/(c^2*x^2) + 1)/x^2 + 225*b*sqrt(-1/(c^2*x^2) + 1)*e^2 + 50*b*d*sqrt(-1/(c^2*x^2) + 1)*e/x^2 - 225*b*arccos(1/(c*x))*e^2/(c*x) - 225*a*e^2/(c*x) - 150*b*d*arccos(1/(c*x))*e/(c*x^3) + 9*b*d^2*sqrt(-1/(c^2*x^2) + 1)/x^4 - 150*a*d*e/(c*x^3) - 45*b*d^2*arccos(1/(c*x))/(c*x^5) - 45*a*d^2/(c*x^5))*c","A",0
86,1,294,0,0.158435," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^8,x, algorithm=""giac"")","\frac{1}{11025} \, {\left(720 \, b c^{6} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 2352 \, b c^{4} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{360 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{2}} + 2450 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2} + \frac{1176 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{2}} + \frac{270 \, b c^{2} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{4}} + \frac{1225 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{x^{2}} + \frac{882 \, b d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{x^{4}} - \frac{3675 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c x^{3}} - \frac{3675 \, a e^{2}}{c x^{3}} - \frac{4410 \, b d \arccos\left(\frac{1}{c x}\right) e}{c x^{5}} + \frac{225 \, b d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x^{6}} - \frac{4410 \, a d e}{c x^{5}} - \frac{1575 \, b d^{2} \arccos\left(\frac{1}{c x}\right)}{c x^{7}} - \frac{1575 \, a d^{2}}{c x^{7}}\right)} c"," ",0,"1/11025*(720*b*c^6*d^2*sqrt(-1/(c^2*x^2) + 1) + 2352*b*c^4*d*sqrt(-1/(c^2*x^2) + 1)*e + 360*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1)/x^2 + 2450*b*c^2*sqrt(-1/(c^2*x^2) + 1)*e^2 + 1176*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)*e/x^2 + 270*b*c^2*d^2*sqrt(-1/(c^2*x^2) + 1)/x^4 + 1225*b*sqrt(-1/(c^2*x^2) + 1)*e^2/x^2 + 882*b*d*sqrt(-1/(c^2*x^2) + 1)*e/x^4 - 3675*b*arccos(1/(c*x))*e^2/(c*x^3) - 3675*a*e^2/(c*x^3) - 4410*b*d*arccos(1/(c*x))*e/(c*x^5) + 225*b*d^2*sqrt(-1/(c^2*x^2) + 1)/x^6 - 4410*a*d*e/(c*x^5) - 1575*b*d^2*arccos(1/(c*x))/(c*x^7) - 1575*a*d^2/(c*x^7))*c","A",0
87,-1,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,1,11858,0,0.406078," ","integrate(x*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\frac{1}{90} \, {\left(\frac{45 \, b c^{4} d^{2} \arccos\left(\frac{1}{c x}\right)}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{45 \, a c^{4} d^{2}}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{90 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{90 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} + \frac{90 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{45 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{45 \, b c^{2} d \arccos\left(\frac{1}{c x}\right) e}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} + \frac{450 \, b c^{4} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{45 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{180 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{45 \, a c^{2} d e}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{900 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{90 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{180 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{45 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} - \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{900 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{330 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{45 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{90 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{15 \, b \arccos\left(\frac{1}{c x}\right) e^{2}}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{180 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{450 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{540 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} + \frac{90 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{45 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right)}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} + \frac{15 \, a e^{2}}{c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{180 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} - \frac{30 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}} - \frac{540 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{45 \, a c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{90 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{225 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{70 \, b {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{3}} - \frac{330 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} + \frac{225 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{4}} - \frac{300 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} - \frac{90 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{45 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right) e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{156 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{5}} - \frac{90 \, b c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} - \frac{300 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{225 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{45 \, a c^{2} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} e}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{156 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{7}} + \frac{225 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{8}} - \frac{90 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} - \frac{70 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{9}} - \frac{90 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{15 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} \arccos\left(\frac{1}{c x}\right) e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}} - \frac{30 \, b {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{11}} + \frac{15 \, a {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6} e^{2}}{{\left(c^{7} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{{\left(\frac{1}{c x} + 1\right)}^{2}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2}}{{\left(\frac{1}{c x} + 1\right)}^{4}} + \frac{20 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3}}{{\left(\frac{1}{c x} + 1\right)}^{6}} + \frac{15 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{4}}{{\left(\frac{1}{c x} + 1\right)}^{8}} + \frac{6 \, c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{5}}{{\left(\frac{1}{c x} + 1\right)}^{10}} + \frac{c^{7} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{6}}{{\left(\frac{1}{c x} + 1\right)}^{12}}\right)} {\left(\frac{1}{c x} + 1\right)}^{12}}\right)} c"," ",0,"1/90*(45*b*c^4*d^2*arccos(1/(c*x))/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 45*a*c^4*d^2/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 90*b*c^4*d^2*(1/(c^2*x^2) - 1)*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 90*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) + 90*a*c^4*d^2*(1/(c^2*x^2) - 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 45*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) + 45*b*c^2*d*arccos(1/(c*x))*e/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) + 450*b*c^4*d^2*(-1/(c^2*x^2) + 1)^(3/2)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) - 45*a*c^4*d^2*(1/(c^2*x^2) - 1)^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 180*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) + 45*a*c^2*d*e/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 90*b*c^2*d*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 900*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) - 90*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) - 180*a*c^4*d^2*(1/(c^2*x^2) - 1)^3/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 45*b*c^4*d^2*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*a*c^2*d*(1/(c^2*x^2) - 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) - 45*b*c^2*d*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 900*b*c^4*d^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 330*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) - 45*a*c^4*d^2*(1/(c^2*x^2) - 1)^4/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) + 90*b*c^4*d^2*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 15*b*arccos(1/(c*x))*e^2/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 45*a*c^2*d*(1/(c^2*x^2) - 1)^2*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) + 180*b*c^2*d*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 450*b*c^4*d^2*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) - 540*b*c^2*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) + 90*a*c^4*d^2*(1/(c^2*x^2) - 1)^5/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 45*b*c^4*d^2*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) + 15*a*e^2/(c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12) - 90*b*(1/(c^2*x^2) - 1)*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) + 180*a*c^2*d*(1/(c^2*x^2) - 1)^3*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 45*b*c^2*d*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*c^4*d^2*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) - 30*b*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)) - 540*b*c^2*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 45*a*c^4*d^2*(1/(c^2*x^2) - 1)^6/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 90*a*(1/(c^2*x^2) - 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^2) + 225*b*(1/(c^2*x^2) - 1)^2*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 45*a*c^2*d*(1/(c^2*x^2) - 1)^4*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*c^2*d*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 70*b*(-1/(c^2*x^2) + 1)^(3/2)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^3) - 330*b*c^2*d*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) + 225*a*(1/(c^2*x^2) - 1)^2*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^4) - 300*b*(1/(c^2*x^2) - 1)^3*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) - 90*a*c^2*d*(1/(c^2*x^2) - 1)^5*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 45*b*c^2*d*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 156*b*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^5) - 90*b*c^2*d*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) - 300*a*(1/(c^2*x^2) - 1)^3*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^6) + 225*b*(1/(c^2*x^2) - 1)^4*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) + 45*a*c^2*d*(1/(c^2*x^2) - 1)^6*e/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 156*b*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^7) + 225*a*(1/(c^2*x^2) - 1)^4*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^8) - 90*b*(1/(c^2*x^2) - 1)^5*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) - 70*b*(1/(c^2*x^2) - 1)^4*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^9) - 90*a*(1/(c^2*x^2) - 1)^5*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^10) + 15*b*(1/(c^2*x^2) - 1)^6*arccos(1/(c*x))*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12) - 30*b*(1/(c^2*x^2) - 1)^5*sqrt(-1/(c^2*x^2) + 1)*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^11) + 15*a*(1/(c^2*x^2) - 1)^6*e^2/((c^7 + 6*c^7*(1/(c^2*x^2) - 1)/(1/(c*x) + 1)^2 + 15*c^7*(1/(c^2*x^2) - 1)^2/(1/(c*x) + 1)^4 + 20*c^7*(1/(c^2*x^2) - 1)^3/(1/(c*x) + 1)^6 + 15*c^7*(1/(c^2*x^2) - 1)^4/(1/(c*x) + 1)^8 + 6*c^7*(1/(c^2*x^2) - 1)^5/(1/(c*x) + 1)^10 + c^7*(1/(c^2*x^2) - 1)^6/(1/(c*x) + 1)^12)*(1/(c*x) + 1)^12))*c","B",0
89,-2,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitEvaluation time: 0.95Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
90,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*(b*arcsec(c*x) + a)/x^3, x)","F",0
91,-1,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-2,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
93,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
94,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
95,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
96,-1,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-2,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
99,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
100,-1,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
102,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
103,-1,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-2,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
106,-2,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
107,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
108,-2,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
109,-2,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
110,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
111,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{5}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*x^5, x)","F",0
112,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*x^3, x)","F",0
113,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*x, x)","F",0
114,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x, x)","F",0
115,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^3, x)","F",0
116,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*x^2, x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^2, x)","F",0
119,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^4, x)","F",0
120,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^6, x)","F",0
121,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)*x^3, x)","F",0
122,0,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)*x, x)","F",0
123,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x, x)","F",0
124,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x^3, x)","F",0
125,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)*x^2, x)","F",0
126,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a), x)","F",0
127,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x^2, x)","F",0
128,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^4,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x^4, x)","F",0
129,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^6,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{6}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x^6, x)","F",0
130,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^8,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x^{8}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)/x^8, x)","F",0
131,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{5}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^5/sqrt(e*x^2 + d), x)","F",0
132,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^3/sqrt(e*x^2 + d), x)","F",0
133,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x/sqrt(e*x^2 + d), x)","F",0
134,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d} x}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(e*x^2 + d)*x), x)","F",0
135,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{3}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(e*x^2 + d)*x^3), x)","F",0
136,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^2/sqrt(e*x^2 + d), x)","F",0
137,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(e*x^2 + d)*x^2), x)","F",0
139,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{4}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(e*x^2 + d)*x^4), x)","F",0
140,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^6/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{6}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(e*x^2 + d)*x^6), x)","F",0
141,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{5}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^5/(e*x^2 + d)^(3/2), x)","F",0
142,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^3/(e*x^2 + d)^(3/2), x)","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x/(e*x^2 + d)^(3/2), x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(3/2)*x), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(3/2)*x^3), x)","F",0
146,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{4}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^4/(e*x^2 + d)^(3/2), x)","F",0
147,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^2/(e*x^2 + d)^(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(e*x^2 + d)^(3/2), x)","F",0
149,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(3/2)*x^2), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(3/2)*x^4), x)","F",0
151,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{5}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^5/(e*x^2 + d)^(5/2), x)","F",0
152,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^3/(e*x^2 + d)^(5/2), x)","F",0
153,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x/(e*x^2 + d)^(5/2), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(5/2)*x), x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(5/2)*x^3), x)","F",0
156,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{6}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^6/(e*x^2 + d)^(5/2), x)","F",0
157,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{4}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^4/(e*x^2 + d)^(5/2), x)","F",0
158,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^2/(e*x^2 + d)^(5/2), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(e*x^2 + d)^(5/2), x)","F",0
160,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/((e*x^2 + d)^(5/2)*x^2), x)","F",0
161,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{3} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^3*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
162,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
163,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
164,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
165,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
166,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
167,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
168,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
169,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d)^(3/2), x)","F",0
170,-2,0,0,0.000000," ","integrate(x^11*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
171,-2,0,0,0.000000," ","integrate(x^7*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
172,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}}{\sqrt{-c^{4} x^{4} + 1}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*x^3/sqrt(-c^4*x^4 + 1), x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{-c^{4} x^{4} + 1} x}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(-c^4*x^4 + 1)*x), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^5/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{-c^{4} x^{4} + 1} x^{5}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)/(sqrt(-c^4*x^4 + 1)*x^5), x)","F",0
