1,0,0,0,0.000000," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{{\left(b \arccos\left(c x\right) + a\right)} x^{3}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)*x^3/(c^2*d*x^2 - d), x)","F",0
2,0,0,0,0.000000," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{{\left(b \arccos\left(c x\right) + a\right)} x^{2}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)*x^2/(c^2*d*x^2 - d), x)","F",0
3,0,0,0,0.000000," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{{\left(b \arccos\left(c x\right) + a\right)} x}{c^{2} d x^{2} - d}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)*x/(c^2*d*x^2 - d), x)","F",0
4,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{b \arccos\left(c x\right) + a}{c^{2} d x^{2} - d}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)/(c^2*d*x^2 - d), x)","F",0
5,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)} x}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)/((c^2*d*x^2 - d)*x), x)","F",0
6,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)} x^{2}}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)/((c^2*d*x^2 - d)*x^2), x)","F",0
7,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""giac"")","\int -\frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)} x^{3}}\,{d x}"," ",0,"integrate(-(b*arccos(c*x) + a)/((c^2*d*x^2 - d)*x^3), x)","F",0
8,0,0,0,0.000000," ","integrate(x^4*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \arccos\left(c x\right) + a\right)} x^{4}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)*x^4/(c^2*d*x^2 - d)^2, x)","F",0
9,0,0,0,0.000000," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \arccos\left(c x\right) + a\right)} x^{3}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)*x^3/(c^2*d*x^2 - d)^2, x)","F",0
10,0,0,0,0.000000," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \arccos\left(c x\right) + a\right)} x^{2}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)*x^2/(c^2*d*x^2 - d)^2, x)","F",0
11,1,100,0,0.232209," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","-\frac{b x^{2} \arccos\left(c x\right)}{2 \, {\left(c^{2} x^{2} - 1\right)} d^{2}} - \frac{a x^{2}}{2 \, {\left(c^{2} x^{2} - 1\right)} d^{2}} - \frac{\sqrt{-c^{2} x^{2} + 1} b x}{2 \, {\left(c^{2} x^{2} - 1\right)} c d^{2}} + \frac{b \arccos\left(c x\right)}{2 \, c^{2} d^{2}} + \frac{a}{2 \, c^{2} d^{2}}"," ",0,"-1/2*b*x^2*arccos(c*x)/((c^2*x^2 - 1)*d^2) - 1/2*a*x^2/((c^2*x^2 - 1)*d^2) - 1/2*sqrt(-c^2*x^2 + 1)*b*x/((c^2*x^2 - 1)*c*d^2) + 1/2*b*arccos(c*x)/(c^2*d^2) + 1/2*a/(c^2*d^2)","A",0
12,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)/(c^2*d*x^2 - d)^2, x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)}^{2} x}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)/((c^2*d*x^2 - d)^2*x), x)","F",0
14,-1,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""giac"")","\int \frac{b \arccos\left(c x\right) + a}{{\left(c^{2} d x^{2} - d\right)}^{2} x^{3}}\,{d x}"," ",0,"integrate((b*arccos(c*x) + a)/((c^2*d*x^2 - d)^2*x^3), x)","F",0
16,1,171,0,0.186873," ","integrate(x^3*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""giac"")","\frac{1}{6} \, b x^{6} \arccos\left(c x\right) e + \frac{1}{6} \, a x^{6} e + \frac{1}{4} \, b d x^{4} \arccos\left(c x\right) - \frac{\sqrt{-c^{2} x^{2} + 1} b x^{5} e}{36 \, c} + \frac{1}{4} \, a d x^{4} - \frac{\sqrt{-c^{2} x^{2} + 1} b d x^{3}}{16 \, c} - \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b x^{3} e}{144 \, c^{3}} - \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b d x}{32 \, c^{3}} - \frac{3 \, b d \arccos\left(c x\right)}{32 \, c^{4}} - \frac{5 \, \sqrt{-c^{2} x^{2} + 1} b x e}{96 \, c^{5}} - \frac{5 \, b \arccos\left(c x\right) e}{96 \, c^{6}}"," ",0,"1/6*b*x^6*arccos(c*x)*e + 1/6*a*x^6*e + 1/4*b*d*x^4*arccos(c*x) - 1/36*sqrt(-c^2*x^2 + 1)*b*x^5*e/c + 1/4*a*d*x^4 - 1/16*sqrt(-c^2*x^2 + 1)*b*d*x^3/c - 5/144*sqrt(-c^2*x^2 + 1)*b*x^3*e/c^3 - 3/32*sqrt(-c^2*x^2 + 1)*b*d*x/c^3 - 3/32*b*d*arccos(c*x)/c^4 - 5/96*sqrt(-c^2*x^2 + 1)*b*x*e/c^5 - 5/96*b*arccos(c*x)*e/c^6","A",0
17,1,146,0,0.203749," ","integrate(x^2*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""giac"")","\frac{1}{5} \, b x^{5} \arccos\left(c x\right) e + \frac{1}{5} \, a x^{5} e + \frac{1}{3} \, b d x^{3} \arccos\left(c x\right) - \frac{\sqrt{-c^{2} x^{2} + 1} b x^{4} e}{25 \, c} + \frac{1}{3} \, a d x^{3} - \frac{\sqrt{-c^{2} x^{2} + 1} b d x^{2}}{9 \, c} - \frac{4 \, \sqrt{-c^{2} x^{2} + 1} b x^{2} e}{75 \, c^{3}} - \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b d}{9 \, c^{3}} - \frac{8 \, \sqrt{-c^{2} x^{2} + 1} b e}{75 \, c^{5}}"," ",0,"1/5*b*x^5*arccos(c*x)*e + 1/5*a*x^5*e + 1/3*b*d*x^3*arccos(c*x) - 1/25*sqrt(-c^2*x^2 + 1)*b*x^4*e/c + 1/3*a*d*x^3 - 1/9*sqrt(-c^2*x^2 + 1)*b*d*x^2/c - 4/75*sqrt(-c^2*x^2 + 1)*b*x^2*e/c^3 - 2/9*sqrt(-c^2*x^2 + 1)*b*d/c^3 - 8/75*sqrt(-c^2*x^2 + 1)*b*e/c^5","A",0
18,1,126,0,0.181310," ","integrate(x*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""giac"")","\frac{1}{4} \, b x^{4} \arccos\left(c x\right) e + \frac{1}{4} \, a x^{4} e + \frac{1}{2} \, b d x^{2} \arccos\left(c x\right) - \frac{\sqrt{-c^{2} x^{2} + 1} b x^{3} e}{16 \, c} + \frac{1}{2} \, a d x^{2} - \frac{\sqrt{-c^{2} x^{2} + 1} b d x}{4 \, c} - \frac{b d \arccos\left(c x\right)}{4 \, c^{2}} - \frac{3 \, \sqrt{-c^{2} x^{2} + 1} b x e}{32 \, c^{3}} - \frac{3 \, b \arccos\left(c x\right) e}{32 \, c^{4}}"," ",0,"1/4*b*x^4*arccos(c*x)*e + 1/4*a*x^4*e + 1/2*b*d*x^2*arccos(c*x) - 1/16*sqrt(-c^2*x^2 + 1)*b*x^3*e/c + 1/2*a*d*x^2 - 1/4*sqrt(-c^2*x^2 + 1)*b*d*x/c - 1/4*b*d*arccos(c*x)/c^2 - 3/32*sqrt(-c^2*x^2 + 1)*b*x*e/c^3 - 3/32*b*arccos(c*x)*e/c^4","A",0
19,1,95,0,0.786276," ","integrate((e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, b x^{3} \arccos\left(c x\right) e + \frac{1}{3} \, a x^{3} e + b d x \arccos\left(c x\right) - \frac{\sqrt{-c^{2} x^{2} + 1} b x^{2} e}{9 \, c} + a d x - \frac{\sqrt{-c^{2} x^{2} + 1} b d}{c} - \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b e}{9 \, c^{3}}"," ",0,"1/3*b*x^3*arccos(c*x)*e + 1/3*a*x^3*e + b*d*x*arccos(c*x) - 1/9*sqrt(-c^2*x^2 + 1)*b*x^2*e/c + a*d*x - sqrt(-c^2*x^2 + 1)*b*d/c - 2/9*sqrt(-c^2*x^2 + 1)*b*e/c^3","A",0
20,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} {\left(b \arccos\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arccos(c*x) + a)/x, x)","F",0
21,1,867,0,0.618000," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^2,x, algorithm=""giac"")","-\frac{b c^{2} d \arccos\left(c x\right)}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} + \frac{b c^{2} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} - \frac{b c^{2} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} - \frac{a c^{2} d}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b c^{2} d \arccos\left(c x\right)}{{\left(c x + 1\right)}^{2} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a c^{2} d}{{\left(c x + 1\right)}^{2} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{2} d \arccos\left(c x\right)}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{b \arccos\left(c x\right) e}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{2} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{2} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a c^{2} d}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{a e}{c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} b \arccos\left(c x\right) e}{{\left(c x + 1\right)}^{2} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} - \frac{2 \, \sqrt{-c^{2} x^{2} + 1} b e}{{\left(c x + 1\right)} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{2 \, {\left(c^{2} x^{2} - 1\right)} a e}{{\left(c x + 1\right)}^{2} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b \arccos\left(c x\right) e}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{2 \, {\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} b e}{{\left(c x + 1\right)}^{3} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a e}{{\left(c x + 1\right)}^{4} {\left(c - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} c}{{\left(c x + 1\right)}^{4}}\right)}}"," ",0,"-b*c^2*d*arccos(c*x)/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) + b*c^2*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) - b*c^2*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) - a*c^2*d/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) + 2*(c^2*x^2 - 1)*b*c^2*d*arccos(c*x)/((c*x + 1)^2*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + 2*(c^2*x^2 - 1)*a*c^2*d/((c*x + 1)^2*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) - (c^2*x^2 - 1)^2*b*c^2*d*arccos(c*x)/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + b*arccos(c*x)*e/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) - (c^2*x^2 - 1)^2*b*c^2*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + (c^2*x^2 - 1)^2*b*c^2*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) - (c^2*x^2 - 1)^2*a*c^2*d/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + a*e/(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4) + 2*(c^2*x^2 - 1)*b*arccos(c*x)*e/((c*x + 1)^2*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) - 2*sqrt(-c^2*x^2 + 1)*b*e/((c*x + 1)*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + 2*(c^2*x^2 - 1)*a*e/((c*x + 1)^2*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + (c^2*x^2 - 1)^2*b*arccos(c*x)*e/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + 2*(-c^2*x^2 + 1)^(3/2)*b*e/((c*x + 1)^3*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4)) + (c^2*x^2 - 1)^2*a*e/((c*x + 1)^4*(c - (c^2*x^2 - 1)^2*c/(c*x + 1)^4))","B",0
22,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} {\left(b \arccos\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arccos(c*x) + a)/x^3, x)","F",0
23,1,3098,0,4.375350," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^4,x, algorithm=""giac"")","-\frac{b c^{3} d \arccos\left(c x\right)}{3 \, {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{b c^{3} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{6 \, {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{b c^{3} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{6 \, {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{a c^{3} d}{3 \, {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)} b c^{3} d \arccos\left(c x\right)}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)} b c^{3} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{2 \, {\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)} b c^{3} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{2 \, {\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{\sqrt{-c^{2} x^{2} + 1} b c^{3} d}{3 \, {\left(c x + 1\right)} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)} a c^{3} d}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{3} d \arccos\left(c x\right)}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{b c \arccos\left(c x\right) e}{\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{3} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{2 \, {\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{b c e \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c^{3} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{2 \, {\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{b c e \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a c^{3} d}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c^{3} d \arccos\left(c x\right)}{3 \, {\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{a c e}{\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1} - \frac{{\left(c^{2} x^{2} - 1\right)} b c \arccos\left(c x\right) e}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c^{3} d \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{6 \, {\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b c e \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c^{3} d \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{6 \, {\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)} b c e \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{2} \sqrt{-c^{2} x^{2} + 1} b c^{3} d}{3 \, {\left(c x + 1\right)}^{5} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} a c^{3} d}{3 \, {\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)} a c e}{{\left(c x + 1\right)}^{2} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} b c \arccos\left(c x\right) e}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b c e \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2} b c e \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{2} a c e}{{\left(c x + 1\right)}^{4} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c \arccos\left(c x\right) e}{{\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c e \log\left({\left| c x + \sqrt{-c^{2} x^{2} + 1} + 1 \right|}\right)}{{\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} - \frac{{\left(c^{2} x^{2} - 1\right)}^{3} b c e \log\left({\left| -c x + \sqrt{-c^{2} x^{2} + 1} - 1 \right|}\right)}{{\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3} a c e}{{\left(c x + 1\right)}^{6} {\left(\frac{3 \, {\left(c^{2} x^{2} - 1\right)}}{{\left(c x + 1\right)}^{2}} + \frac{3 \, {\left(c^{2} x^{2} - 1\right)}^{2}}{{\left(c x + 1\right)}^{4}} + \frac{{\left(c^{2} x^{2} - 1\right)}^{3}}{{\left(c x + 1\right)}^{6}} + 1\right)}}"," ",0,"-1/3*b*c^3*d*arccos(c*x)/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) + 1/6*b*c^3*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) - 1/6*b*c^3*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) - 1/3*a*c^3*d/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) + (c^2*x^2 - 1)*b*c^3*d*arccos(c*x)/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 1/2*(c^2*x^2 - 1)*b*c^3*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - 1/2*(c^2*x^2 - 1)*b*c^3*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 1/3*sqrt(-c^2*x^2 + 1)*b*c^3*d/((c*x + 1)*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)*a*c^3*d/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - (c^2*x^2 - 1)^2*b*c^3*d*arccos(c*x)/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - b*c*arccos(c*x)*e/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) + 1/2*(c^2*x^2 - 1)^2*b*c^3*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + b*c*e*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) - 1/2*(c^2*x^2 - 1)^2*b*c^3*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - b*c*e*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) - (c^2*x^2 - 1)^2*a*c^3*d/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 1/3*(c^2*x^2 - 1)^3*b*c^3*d*arccos(c*x)/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - a*c*e/(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1) - (c^2*x^2 - 1)*b*c*arccos(c*x)*e/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 1/6*(c^2*x^2 - 1)^3*b*c^3*d*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 3*(c^2*x^2 - 1)*b*c*e*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - 1/6*(c^2*x^2 - 1)^3*b*c^3*d*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - 3*(c^2*x^2 - 1)*b*c*e*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - 1/3*(c^2*x^2 - 1)^2*sqrt(-c^2*x^2 + 1)*b*c^3*d/((c*x + 1)^5*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 1/3*(c^2*x^2 - 1)^3*a*c^3*d/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - (c^2*x^2 - 1)*a*c*e/((c*x + 1)^2*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)^2*b*c*arccos(c*x)*e/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + 3*(c^2*x^2 - 1)^2*b*c*e*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - 3*(c^2*x^2 - 1)^2*b*c*e*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)^2*a*c*e/((c*x + 1)^4*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)^3*b*c*arccos(c*x)*e/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)^3*b*c*e*log(abs(c*x + sqrt(-c^2*x^2 + 1) + 1))/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) - (c^2*x^2 - 1)^3*b*c*e*log(abs(-c*x + sqrt(-c^2*x^2 + 1) - 1))/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1)) + (c^2*x^2 - 1)^3*a*c*e/((c*x + 1)^6*(3*(c^2*x^2 - 1)/(c*x + 1)^2 + 3*(c^2*x^2 - 1)^2/(c*x + 1)^4 + (c^2*x^2 - 1)^3/(c*x + 1)^6 + 1))","B",0
24,1,160,0,1.269703," ","integrate((d*x^2+c)^2*arccos(a*x),x, algorithm=""giac"")","\frac{1}{5} \, d^{2} x^{5} \arccos\left(a x\right) + \frac{2}{3} \, c d x^{3} \arccos\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} d^{2} x^{4}}{25 \, a} + c^{2} x \arccos\left(a x\right) - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c d x^{2}}{9 \, a} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2}}{a} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} d^{2} x^{2}}{75 \, a^{3}} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c d}{9 \, a^{3}} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} d^{2}}{75 \, a^{5}}"," ",0,"1/5*d^2*x^5*arccos(a*x) + 2/3*c*d*x^3*arccos(a*x) - 1/25*sqrt(-a^2*x^2 + 1)*d^2*x^4/a + c^2*x*arccos(a*x) - 2/9*sqrt(-a^2*x^2 + 1)*c*d*x^2/a - sqrt(-a^2*x^2 + 1)*c^2/a - 4/75*sqrt(-a^2*x^2 + 1)*d^2*x^2/a^3 - 4/9*sqrt(-a^2*x^2 + 1)*c*d/a^3 - 8/75*sqrt(-a^2*x^2 + 1)*d^2/a^5","A",0
25,1,270,0,2.969881," ","integrate((d*x^2+c)^3*arccos(a*x),x, algorithm=""giac"")","\frac{1}{7} \, d^{3} x^{7} \arccos\left(a x\right) + \frac{3}{5} \, c d^{2} x^{5} \arccos\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} d^{3} x^{6}}{49 \, a} + c^{2} d x^{3} \arccos\left(a x\right) - \frac{3 \, \sqrt{-a^{2} x^{2} + 1} c d^{2} x^{4}}{25 \, a} + c^{3} x \arccos\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} c^{2} d x^{2}}{3 \, a} - \frac{6 \, \sqrt{-a^{2} x^{2} + 1} d^{3} x^{4}}{245 \, a^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{3}}{a} - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c d^{2} x^{2}}{25 \, a^{3}} - \frac{2 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d}{3 \, a^{3}} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} d^{3} x^{2}}{245 \, a^{5}} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} c d^{2}}{25 \, a^{5}} - \frac{16 \, \sqrt{-a^{2} x^{2} + 1} d^{3}}{245 \, a^{7}}"," ",0,"1/7*d^3*x^7*arccos(a*x) + 3/5*c*d^2*x^5*arccos(a*x) - 1/49*sqrt(-a^2*x^2 + 1)*d^3*x^6/a + c^2*d*x^3*arccos(a*x) - 3/25*sqrt(-a^2*x^2 + 1)*c*d^2*x^4/a + c^3*x*arccos(a*x) - 1/3*sqrt(-a^2*x^2 + 1)*c^2*d*x^2/a - 6/245*sqrt(-a^2*x^2 + 1)*d^3*x^4/a^3 - sqrt(-a^2*x^2 + 1)*c^3/a - 4/25*sqrt(-a^2*x^2 + 1)*c*d^2*x^2/a^3 - 2/3*sqrt(-a^2*x^2 + 1)*c^2*d/a^3 - 8/245*sqrt(-a^2*x^2 + 1)*d^3*x^2/a^5 - 8/25*sqrt(-a^2*x^2 + 1)*c*d^2/a^5 - 16/245*sqrt(-a^2*x^2 + 1)*d^3/a^7","A",0
26,1,408,0,0.210027," ","integrate((d*x^2+c)^4*arccos(a*x),x, algorithm=""giac"")","\frac{1}{9} \, d^{4} x^{9} \arccos\left(a x\right) + \frac{4}{7} \, c d^{3} x^{7} \arccos\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} d^{4} x^{8}}{81 \, a} + \frac{6}{5} \, c^{2} d^{2} x^{5} \arccos\left(a x\right) - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{6}}{49 \, a} + \frac{4}{3} \, c^{3} d x^{3} \arccos\left(a x\right) - \frac{6 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2} x^{4}}{25 \, a} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{6}}{567 \, a^{3}} + c^{4} x \arccos\left(a x\right) - \frac{4 \, \sqrt{-a^{2} x^{2} + 1} c^{3} d x^{2}}{9 \, a} - \frac{24 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{4}}{245 \, a^{3}} - \frac{\sqrt{-a^{2} x^{2} + 1} c^{4}}{a} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2} x^{2}}{25 \, a^{3}} - \frac{16 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{4}}{945 \, a^{5}} - \frac{8 \, \sqrt{-a^{2} x^{2} + 1} c^{3} d}{9 \, a^{3}} - \frac{32 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{2}}{245 \, a^{5}} - \frac{16 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2}}{25 \, a^{5}} - \frac{64 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{2}}{2835 \, a^{7}} - \frac{64 \, \sqrt{-a^{2} x^{2} + 1} c d^{3}}{245 \, a^{7}} - \frac{128 \, \sqrt{-a^{2} x^{2} + 1} d^{4}}{2835 \, a^{9}}"," ",0,"1/9*d^4*x^9*arccos(a*x) + 4/7*c*d^3*x^7*arccos(a*x) - 1/81*sqrt(-a^2*x^2 + 1)*d^4*x^8/a + 6/5*c^2*d^2*x^5*arccos(a*x) - 4/49*sqrt(-a^2*x^2 + 1)*c*d^3*x^6/a + 4/3*c^3*d*x^3*arccos(a*x) - 6/25*sqrt(-a^2*x^2 + 1)*c^2*d^2*x^4/a - 8/567*sqrt(-a^2*x^2 + 1)*d^4*x^6/a^3 + c^4*x*arccos(a*x) - 4/9*sqrt(-a^2*x^2 + 1)*c^3*d*x^2/a - 24/245*sqrt(-a^2*x^2 + 1)*c*d^3*x^4/a^3 - sqrt(-a^2*x^2 + 1)*c^4/a - 8/25*sqrt(-a^2*x^2 + 1)*c^2*d^2*x^2/a^3 - 16/945*sqrt(-a^2*x^2 + 1)*d^4*x^4/a^5 - 8/9*sqrt(-a^2*x^2 + 1)*c^3*d/a^3 - 32/245*sqrt(-a^2*x^2 + 1)*c*d^3*x^2/a^5 - 16/25*sqrt(-a^2*x^2 + 1)*c^2*d^2/a^5 - 64/2835*sqrt(-a^2*x^2 + 1)*d^4*x^2/a^7 - 64/245*sqrt(-a^2*x^2 + 1)*c*d^3/a^7 - 128/2835*sqrt(-a^2*x^2 + 1)*d^4/a^9","A",0
27,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{\arccos\left(a x\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(arccos(a*x)/(d*x^2 + c), x)","F",0
28,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\arccos\left(a x\right)}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arccos(a*x)/(d*x^2 + c)^2, x)","F",0
29,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccos(a*x),x, algorithm=""giac"")","\int \sqrt{d x^{2} + c} \arccos\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arccos(a*x), x)","F",0
30,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\arccos\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arccos(a*x)/sqrt(d*x^2 + c), x)","F",0
31,1,75,0,1.360965," ","integrate(arccos(a*x)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{x \arccos\left(a x\right)}{\sqrt{d x^{2} + c} c} + \frac{a \log\left({\left| -\sqrt{-a^{2} x^{2} + 1} \sqrt{-d} + \sqrt{a^{2} c + {\left(a^{2} x^{2} - 1\right)} d + d} \right|}\right)}{c \sqrt{-d} {\left| a \right|}}"," ",0,"x*arccos(a*x)/(sqrt(d*x^2 + c)*c) + a*log(abs(-sqrt(-a^2*x^2 + 1)*sqrt(-d) + sqrt(a^2*c + (a^2*x^2 - 1)*d + d)))/(c*sqrt(-d)*abs(a))","A",0
32,1,185,0,0.436137," ","integrate(arccos(a*x)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{2 \, a^{2} {\left| d \right|}}{{\left(a^{2} c d - {\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2} + d^{2}\right)} c \sqrt{-d} {\left| a \right|}} - \frac{{\left| d \right|} \log\left({\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2}\right)}{c^{2} \sqrt{-d} d {\left| a \right|}}\right)} + \frac{x {\left(\frac{2 \, d x^{2}}{c^{2}} + \frac{3}{c}\right)} \arccos\left(a x\right)}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"1/3*a*(2*a^2*abs(d)/((a^2*c*d - (sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2 + d^2)*c*sqrt(-d)*abs(a)) - abs(d)*log((sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2)/(c^2*sqrt(-d)*d*abs(a))) + 1/3*x*(2*d*x^2/c^2 + 3/c)*arccos(a*x)/(d*x^2 + c)^(3/2)","A",0
33,1,398,0,2.422092," ","integrate(arccos(a*x)/(d*x^2+c)^(7/2),x, algorithm=""giac"")","-\frac{4}{15} \, a {\left(\frac{{\left| d \right|} \log\left({\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2}\right)}{c^{3} \sqrt{-d} d {\left| a \right|}} - \frac{3 \, a^{6} c^{2} d^{2} {\left| d \right|} - 7 \, {\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2} a^{4} c d {\left| d \right|} + 5 \, a^{4} c d^{3} {\left| d \right|} + 2 \, {\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{4} a^{2} {\left| d \right|} - 4 \, {\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2} a^{2} d^{2} {\left| d \right|} + 2 \, a^{2} d^{4} {\left| d \right|}}{{\left(a^{2} c d - {\left(\sqrt{-a^{2} d} \sqrt{d x^{2} + c} - \sqrt{-{\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}}\right)}^{2} + d^{2}\right)}^{3} c^{2} \sqrt{-d} {\left| a \right|}}\right)} + \frac{{\left(4 \, x^{2} {\left(\frac{2 \, d^{2} x^{2}}{c^{3}} + \frac{5 \, d}{c^{2}}\right)} + \frac{15}{c}\right)} x \arccos\left(a x\right)}{15 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}}}"," ",0,"-4/15*a*(abs(d)*log((sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2)/(c^3*sqrt(-d)*d*abs(a)) - (3*a^6*c^2*d^2*abs(d) - 7*(sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2*a^4*c*d*abs(d) + 5*a^4*c*d^3*abs(d) + 2*(sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^4*a^2*abs(d) - 4*(sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2*a^2*d^2*abs(d) + 2*a^2*d^4*abs(d))/((a^2*c*d - (sqrt(-a^2*d)*sqrt(d*x^2 + c) - sqrt(-(d*x^2 + c)*a^2*d + a^2*c*d + d^2))^2 + d^2)^3*c^2*sqrt(-d)*abs(a))) + 1/15*(4*x^2*(2*d^2*x^2/c^3 + 5*d/c^2) + 15/c)*x*arccos(a*x)/(d*x^2 + c)^(5/2)","B",0
