1,0,0,0,0.473115," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{3} \arccos\left(c x\right) + a x^{3}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^3*arccos(c*x) + a*x^3)/(c^2*d*x^2 - d), x)","F",0
2,0,0,0,0.484332," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{2} \arccos\left(c x\right) + a x^{2}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^2*arccos(c*x) + a*x^2)/(c^2*d*x^2 - d), x)","F",0
3,0,0,0,0.453923," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x \arccos\left(c x\right) + a x}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x*arccos(c*x) + a*x)/(c^2*d*x^2 - d), x)","F",0
4,0,0,0,0.490832," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arccos\left(c x\right) + a}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*arccos(c*x) + a)/(c^2*d*x^2 - d), x)","F",0
5,0,0,0,0.480507," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arccos\left(c x\right) + a}{c^{2} d x^{3} - d x}, x\right)"," ",0,"integral(-(b*arccos(c*x) + a)/(c^2*d*x^3 - d*x), x)","F",0
6,0,0,0,0.464537," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arccos\left(c x\right) + a}{c^{2} d x^{4} - d x^{2}}, x\right)"," ",0,"integral(-(b*arccos(c*x) + a)/(c^2*d*x^4 - d*x^2), x)","F",0
7,0,0,0,0.517277," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arccos\left(c x\right) + a}{c^{2} d x^{5} - d x^{3}}, x\right)"," ",0,"integral(-(b*arccos(c*x) + a)/(c^2*d*x^5 - d*x^3), x)","F",0
8,0,0,0,0.507943," ","integrate(x^4*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \arccos\left(c x\right) + a x^{4}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^4*arccos(c*x) + a*x^4)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
9,0,0,0,0.478185," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arccos\left(c x\right) + a x^{3}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^3*arccos(c*x) + a*x^3)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
10,0,0,0,0.515414," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arccos\left(c x\right) + a x^{2}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arccos(c*x) + a*x^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
11,1,54,0,0.505521," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","-\frac{a c^{2} x^{2} + \sqrt{-c^{2} x^{2} + 1} b c x + b \arccos\left(c x\right)}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"-1/2*(a*c^2*x^2 + sqrt(-c^2*x^2 + 1)*b*c*x + b*arccos(c*x))/(c^4*d^2*x^2 - c^2*d^2)","A",0
12,0,0,0,0.442670," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arccos\left(c x\right) + a}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arccos(c*x) + a)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
13,0,0,0,0.527121," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arccos\left(c x\right) + a}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}, x\right)"," ",0,"integral((b*arccos(c*x) + a)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
14,0,0,0,0.503372," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arccos\left(c x\right) + a}{c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arccos(c*x) + a)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
15,0,0,0,0.470567," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arccos\left(c x\right) + a}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral((b*arccos(c*x) + a)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
16,1,125,0,0.552302," ","integrate(x^3*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""fricas"")","\frac{48 \, a c^{6} e x^{6} + 72 \, a c^{6} d x^{4} + 3 \, {\left(16 \, b c^{6} e x^{6} + 24 \, b c^{6} d x^{4} - 9 \, b c^{2} d - 5 \, b e\right)} \arccos\left(c x\right) - {\left(8 \, b c^{5} e x^{5} + 2 \, {\left(9 \, b c^{5} d + 5 \, b c^{3} e\right)} x^{3} + 3 \, {\left(9 \, b c^{3} d + 5 \, b c e\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{288 \, c^{6}}"," ",0,"1/288*(48*a*c^6*e*x^6 + 72*a*c^6*d*x^4 + 3*(16*b*c^6*e*x^6 + 24*b*c^6*d*x^4 - 9*b*c^2*d - 5*b*e)*arccos(c*x) - (8*b*c^5*e*x^5 + 2*(9*b*c^5*d + 5*b*c^3*e)*x^3 + 3*(9*b*c^3*d + 5*b*c*e)*x)*sqrt(-c^2*x^2 + 1))/c^6","A",0
17,1,108,0,0.474298," ","integrate(x^2*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""fricas"")","\frac{45 \, a c^{5} e x^{5} + 75 \, a c^{5} d x^{3} + 15 \, {\left(3 \, b c^{5} e x^{5} + 5 \, b c^{5} d x^{3}\right)} \arccos\left(c x\right) - {\left(9 \, b c^{4} e x^{4} + 50 \, b c^{2} d + {\left(25 \, b c^{4} d + 12 \, b c^{2} e\right)} x^{2} + 24 \, b e\right)} \sqrt{-c^{2} x^{2} + 1}}{225 \, c^{5}}"," ",0,"1/225*(45*a*c^5*e*x^5 + 75*a*c^5*d*x^3 + 15*(3*b*c^5*e*x^5 + 5*b*c^5*d*x^3)*arccos(c*x) - (9*b*c^4*e*x^4 + 50*b*c^2*d + (25*b*c^4*d + 12*b*c^2*e)*x^2 + 24*b*e)*sqrt(-c^2*x^2 + 1))/c^5","A",0
18,1,103,0,0.450357," ","integrate(x*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""fricas"")","\frac{8 \, a c^{4} e x^{4} + 16 \, a c^{4} d x^{2} + {\left(8 \, b c^{4} e x^{4} + 16 \, b c^{4} d x^{2} - 8 \, b c^{2} d - 3 \, b e\right)} \arccos\left(c x\right) - {\left(2 \, b c^{3} e x^{3} + {\left(8 \, b c^{3} d + 3 \, b c e\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{32 \, c^{4}}"," ",0,"1/32*(8*a*c^4*e*x^4 + 16*a*c^4*d*x^2 + (8*b*c^4*e*x^4 + 16*b*c^4*d*x^2 - 8*b*c^2*d - 3*b*e)*arccos(c*x) - (2*b*c^3*e*x^3 + (8*b*c^3*d + 3*b*c*e)*x)*sqrt(-c^2*x^2 + 1))/c^4","A",0
19,1,83,0,0.443913," ","integrate((e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{3} e x^{3} + 9 \, a c^{3} d x + 3 \, {\left(b c^{3} e x^{3} + 3 \, b c^{3} d x\right)} \arccos\left(c x\right) - {\left(b c^{2} e x^{2} + 9 \, b c^{2} d + 2 \, b e\right)} \sqrt{-c^{2} x^{2} + 1}}{9 \, c^{3}}"," ",0,"1/9*(3*a*c^3*e*x^3 + 9*a*c^3*d*x + 3*(b*c^3*e*x^3 + 3*b*c^3*d*x)*arccos(c*x) - (b*c^2*e*x^2 + 9*b*c^2*d + 2*b*e)*sqrt(-c^2*x^2 + 1))/c^3","A",0
20,0,0,0,0.441327," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arccos\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arccos(c*x))/x, x)","F",0
21,1,155,0,0.482296," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^2,x, algorithm=""fricas"")","\frac{b c^{2} d x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - b c^{2} d x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 2 \, a c e x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b e x - 2 \, a c d - 2 \, {\left(b c d - b c e\right)} x \arctan\left(\frac{\sqrt{-c^{2} x^{2} + 1} c x}{c^{2} x^{2} - 1}\right) + 2 \, {\left(b c e x^{2} - b c d + {\left(b c d - b c e\right)} x\right)} \arccos\left(c x\right)}{2 \, c x}"," ",0,"1/2*(b*c^2*d*x*log(sqrt(-c^2*x^2 + 1) + 1) - b*c^2*d*x*log(sqrt(-c^2*x^2 + 1) - 1) + 2*a*c*e*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*e*x - 2*a*c*d - 2*(b*c*d - b*c*e)*x*arctan(sqrt(-c^2*x^2 + 1)*c*x/(c^2*x^2 - 1)) + 2*(b*c*e*x^2 - b*c*d + (b*c*d - b*c*e)*x)*arccos(c*x))/(c*x)","B",0
22,0,0,0,0.457312," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arccos\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arccos(c*x))/x^3, x)","F",0
23,1,168,0,0.549558," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(b d + 3 \, b e\right)} x^{3} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + 1} c x}{c^{2} x^{2} - 1}\right) - {\left(b c^{3} d + 6 \, b c e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + {\left(b c^{3} d + 6 \, b c e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) - 2 \, \sqrt{-c^{2} x^{2} + 1} b c d x + 12 \, a e x^{2} + 4 \, a d + 4 \, {\left(3 \, b e x^{2} - {\left(b d + 3 \, b e\right)} x^{3} + b d\right)} \arccos\left(c x\right)}{12 \, x^{3}}"," ",0,"-1/12*(4*(b*d + 3*b*e)*x^3*arctan(sqrt(-c^2*x^2 + 1)*c*x/(c^2*x^2 - 1)) - (b*c^3*d + 6*b*c*e)*x^3*log(sqrt(-c^2*x^2 + 1) + 1) + (b*c^3*d + 6*b*c*e)*x^3*log(sqrt(-c^2*x^2 + 1) - 1) - 2*sqrt(-c^2*x^2 + 1)*b*c*d*x + 12*a*e*x^2 + 4*a*d + 4*(3*b*e*x^2 - (b*d + 3*b*e)*x^3 + b*d)*arccos(c*x))/x^3","B",0
24,1,110,0,0.477707," ","integrate((d*x^2+c)^2*arccos(a*x),x, algorithm=""fricas"")","\frac{15 \, {\left(3 \, a^{5} d^{2} x^{5} + 10 \, a^{5} c d x^{3} + 15 \, a^{5} c^{2} x\right)} \arccos\left(a x\right) - {\left(9 \, a^{4} d^{2} x^{4} + 225 \, a^{4} c^{2} + 100 \, a^{2} c d + 2 \, {\left(25 \, a^{4} c d + 6 \, a^{2} d^{2}\right)} x^{2} + 24 \, d^{2}\right)} \sqrt{-a^{2} x^{2} + 1}}{225 \, a^{5}}"," ",0,"1/225*(15*(3*a^5*d^2*x^5 + 10*a^5*c*d*x^3 + 15*a^5*c^2*x)*arccos(a*x) - (9*a^4*d^2*x^4 + 225*a^4*c^2 + 100*a^2*c*d + 2*(25*a^4*c*d + 6*a^2*d^2)*x^2 + 24*d^2)*sqrt(-a^2*x^2 + 1))/a^5","A",0
25,1,168,0,0.458537," ","integrate((d*x^2+c)^3*arccos(a*x),x, algorithm=""fricas"")","\frac{105 \, {\left(5 \, a^{7} d^{3} x^{7} + 21 \, a^{7} c d^{2} x^{5} + 35 \, a^{7} c^{2} d x^{3} + 35 \, a^{7} c^{3} x\right)} \arccos\left(a x\right) - {\left(75 \, a^{6} d^{3} x^{6} + 3675 \, a^{6} c^{3} + 2450 \, a^{4} c^{2} d + 1176 \, a^{2} c d^{2} + 9 \, {\left(49 \, a^{6} c d^{2} + 10 \, a^{4} d^{3}\right)} x^{4} + 240 \, d^{3} + {\left(1225 \, a^{6} c^{2} d + 588 \, a^{4} c d^{2} + 120 \, a^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} x^{2} + 1}}{3675 \, a^{7}}"," ",0,"1/3675*(105*(5*a^7*d^3*x^7 + 21*a^7*c*d^2*x^5 + 35*a^7*c^2*d*x^3 + 35*a^7*c^3*x)*arccos(a*x) - (75*a^6*d^3*x^6 + 3675*a^6*c^3 + 2450*a^4*c^2*d + 1176*a^2*c*d^2 + 9*(49*a^6*c*d^2 + 10*a^4*d^3)*x^4 + 240*d^3 + (1225*a^6*c^2*d + 588*a^4*c*d^2 + 120*a^2*d^3)*x^2)*sqrt(-a^2*x^2 + 1))/a^7","A",0
26,1,239,0,0.511683," ","integrate((d*x^2+c)^4*arccos(a*x),x, algorithm=""fricas"")","\frac{315 \, {\left(35 \, a^{9} d^{4} x^{9} + 180 \, a^{9} c d^{3} x^{7} + 378 \, a^{9} c^{2} d^{2} x^{5} + 420 \, a^{9} c^{3} d x^{3} + 315 \, a^{9} c^{4} x\right)} \arccos\left(a x\right) - {\left(1225 \, a^{8} d^{4} x^{8} + 99225 \, a^{8} c^{4} + 88200 \, a^{6} c^{3} d + 63504 \, a^{4} c^{2} d^{2} + 100 \, {\left(81 \, a^{8} c d^{3} + 14 \, a^{6} d^{4}\right)} x^{6} + 25920 \, a^{2} c d^{3} + 6 \, {\left(3969 \, a^{8} c^{2} d^{2} + 1620 \, a^{6} c d^{3} + 280 \, a^{4} d^{4}\right)} x^{4} + 4480 \, d^{4} + 4 \, {\left(11025 \, a^{8} c^{3} d + 7938 \, a^{6} c^{2} d^{2} + 3240 \, a^{4} c d^{3} + 560 \, a^{2} d^{4}\right)} x^{2}\right)} \sqrt{-a^{2} x^{2} + 1}}{99225 \, a^{9}}"," ",0,"1/99225*(315*(35*a^9*d^4*x^9 + 180*a^9*c*d^3*x^7 + 378*a^9*c^2*d^2*x^5 + 420*a^9*c^3*d*x^3 + 315*a^9*c^4*x)*arccos(a*x) - (1225*a^8*d^4*x^8 + 99225*a^8*c^4 + 88200*a^6*c^3*d + 63504*a^4*c^2*d^2 + 100*(81*a^8*c*d^3 + 14*a^6*d^4)*x^6 + 25920*a^2*c*d^3 + 6*(3969*a^8*c^2*d^2 + 1620*a^6*c*d^3 + 280*a^4*d^4)*x^4 + 4480*d^4 + 4*(11025*a^8*c^3*d + 7938*a^6*c^2*d^2 + 3240*a^4*c*d^3 + 560*a^2*d^4)*x^2)*sqrt(-a^2*x^2 + 1))/a^9","A",0
27,0,0,0,0.496870," ","integrate(arccos(a*x)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arccos\left(a x\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arccos(a*x)/(d*x^2 + c), x)","F",0
28,0,0,0,0.454569," ","integrate(arccos(a*x)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arccos\left(a x\right)}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral(arccos(a*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
29,0,0,0,0.440571," ","integrate((d*x^2+c)^(1/2)*arccos(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x^{2} + c} \arccos\left(a x\right), x\right)"," ",0,"integral(sqrt(d*x^2 + c)*arccos(a*x), x)","F",0
30,0,0,0,0.483379," ","integrate(arccos(a*x)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arccos\left(a x\right)}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(arccos(a*x)/sqrt(d*x^2 + c), x)","F",0
31,1,276,0,0.523539," ","integrate(arccos(a*x)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{d x^{2} + c} d x \arccos\left(a x\right) - {\left(d x^{2} + c\right)} \sqrt{-d} \log\left(8 \, a^{4} d^{2} x^{4} + a^{4} c^{2} - 6 \, a^{2} c d + 8 \, {\left(a^{4} c d - a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{3} d x^{2} + a^{3} c - a d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{-d} + d^{2}\right)}{4 \, {\left(c d^{2} x^{2} + c^{2} d\right)}}, \frac{2 \, \sqrt{d x^{2} + c} d x \arccos\left(a x\right) - {\left(d x^{2} + c\right)} \sqrt{d} \arctan\left(\frac{{\left(2 \, a^{2} d x^{2} + a^{2} c - d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{d}}{2 \, {\left(a^{3} d^{2} x^{4} - a c d + {\left(a^{3} c d - a d^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(c d^{2} x^{2} + c^{2} d\right)}}\right]"," ",0,"[1/4*(4*sqrt(d*x^2 + c)*d*x*arccos(a*x) - (d*x^2 + c)*sqrt(-d)*log(8*a^4*d^2*x^4 + a^4*c^2 - 6*a^2*c*d + 8*(a^4*c*d - a^2*d^2)*x^2 - 4*(2*a^3*d*x^2 + a^3*c - a*d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(-d) + d^2))/(c*d^2*x^2 + c^2*d), 1/2*(2*sqrt(d*x^2 + c)*d*x*arccos(a*x) - (d*x^2 + c)*sqrt(d)*arctan(1/2*(2*a^2*d*x^2 + a^2*c - d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(d)/(a^3*d^2*x^4 - a*c*d + (a^3*c*d - a*d^2)*x^2)))/(c*d^2*x^2 + c^2*d)]","B",0
32,1,580,0,0.510283," ","integrate(arccos(a*x)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} c^{3} + {\left(a^{2} c d^{2} + d^{3}\right)} x^{4} + c^{2} d + 2 \, {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)} \sqrt{-d} \log\left(8 \, a^{4} d^{2} x^{4} + a^{4} c^{2} - 6 \, a^{2} c d + 8 \, {\left(a^{4} c d - a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{3} d x^{2} + a^{3} c - a d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{-d} + d^{2}\right) - 2 \, \sqrt{d x^{2} + c} {\left({\left(2 \, {\left(a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{2} c^{2} d + c d^{2}\right)} x\right)} \arccos\left(a x\right) - {\left(a c d^{2} x^{2} + a c^{2} d\right)} \sqrt{-a^{2} x^{2} + 1}\right)}}{6 \, {\left(a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}, -\frac{{\left(a^{2} c^{3} + {\left(a^{2} c d^{2} + d^{3}\right)} x^{4} + c^{2} d + 2 \, {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)} \sqrt{d} \arctan\left(\frac{{\left(2 \, a^{2} d x^{2} + a^{2} c - d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{d}}{2 \, {\left(a^{3} d^{2} x^{4} - a c d + {\left(a^{3} c d - a d^{2}\right)} x^{2}\right)}}\right) - \sqrt{d x^{2} + c} {\left({\left(2 \, {\left(a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{2} c^{2} d + c d^{2}\right)} x\right)} \arccos\left(a x\right) - {\left(a c d^{2} x^{2} + a c^{2} d\right)} \sqrt{-a^{2} x^{2} + 1}\right)}}{3 \, {\left(a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/6*((a^2*c^3 + (a^2*c*d^2 + d^3)*x^4 + c^2*d + 2*(a^2*c^2*d + c*d^2)*x^2)*sqrt(-d)*log(8*a^4*d^2*x^4 + a^4*c^2 - 6*a^2*c*d + 8*(a^4*c*d - a^2*d^2)*x^2 - 4*(2*a^3*d*x^2 + a^3*c - a*d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(-d) + d^2) - 2*sqrt(d*x^2 + c)*((2*(a^2*c*d^2 + d^3)*x^3 + 3*(a^2*c^2*d + c*d^2)*x)*arccos(a*x) - (a*c*d^2*x^2 + a*c^2*d)*sqrt(-a^2*x^2 + 1)))/(a^2*c^5*d + c^4*d^2 + (a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^2*c^4*d^2 + c^3*d^3)*x^2), -1/3*((a^2*c^3 + (a^2*c*d^2 + d^3)*x^4 + c^2*d + 2*(a^2*c^2*d + c*d^2)*x^2)*sqrt(d)*arctan(1/2*(2*a^2*d*x^2 + a^2*c - d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(d)/(a^3*d^2*x^4 - a*c*d + (a^3*c*d - a*d^2)*x^2)) - sqrt(d*x^2 + c)*((2*(a^2*c*d^2 + d^3)*x^3 + 3*(a^2*c^2*d + c*d^2)*x)*arccos(a*x) - (a*c*d^2*x^2 + a*c^2*d)*sqrt(-a^2*x^2 + 1)))/(a^2*c^5*d + c^4*d^2 + (a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^2*c^4*d^2 + c^3*d^3)*x^2)]","B",0
33,1,1066,0,0.609668," ","integrate(arccos(a*x)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{4} c^{5} + 2 \, a^{2} c^{4} d + {\left(a^{4} c^{2} d^{3} + 2 \, a^{2} c d^{4} + d^{5}\right)} x^{6} + c^{3} d^{2} + 3 \, {\left(a^{4} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{4} + 3 \, {\left(a^{4} c^{4} d + 2 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-d} \log\left(8 \, a^{4} d^{2} x^{4} + a^{4} c^{2} - 6 \, a^{2} c d + 8 \, {\left(a^{4} c d - a^{2} d^{2}\right)} x^{2} - 4 \, {\left(2 \, a^{3} d x^{2} + a^{3} c - a d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{-d} + d^{2}\right) - \sqrt{d x^{2} + c} {\left({\left(8 \, {\left(a^{4} c^{2} d^{3} + 2 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{4} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{4} c^{4} d + 2 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \arccos\left(a x\right) - {\left(7 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + 2 \, {\left(3 \, a^{3} c^{2} d^{3} + 2 \, a c d^{4}\right)} x^{4} + {\left(13 \, a^{3} c^{3} d^{2} + 9 \, a c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} x^{2} + 1}\right)}}{15 \, {\left(a^{4} c^{8} d + 2 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{4} c^{5} d^{4} + 2 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{4} c^{6} d^{3} + 2 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{4} c^{7} d^{2} + 2 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}, -\frac{4 \, {\left(a^{4} c^{5} + 2 \, a^{2} c^{4} d + {\left(a^{4} c^{2} d^{3} + 2 \, a^{2} c d^{4} + d^{5}\right)} x^{6} + c^{3} d^{2} + 3 \, {\left(a^{4} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{4} + 3 \, {\left(a^{4} c^{4} d + 2 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x^{2}\right)} \sqrt{d} \arctan\left(\frac{{\left(2 \, a^{2} d x^{2} + a^{2} c - d\right)} \sqrt{-a^{2} x^{2} + 1} \sqrt{d x^{2} + c} \sqrt{d}}{2 \, {\left(a^{3} d^{2} x^{4} - a c d + {\left(a^{3} c d - a d^{2}\right)} x^{2}\right)}}\right) - \sqrt{d x^{2} + c} {\left({\left(8 \, {\left(a^{4} c^{2} d^{3} + 2 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{4} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{4} c^{4} d + 2 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \arccos\left(a x\right) - {\left(7 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + 2 \, {\left(3 \, a^{3} c^{2} d^{3} + 2 \, a c d^{4}\right)} x^{4} + {\left(13 \, a^{3} c^{3} d^{2} + 9 \, a c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} x^{2} + 1}\right)}}{15 \, {\left(a^{4} c^{8} d + 2 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{4} c^{5} d^{4} + 2 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{4} c^{6} d^{3} + 2 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{4} c^{7} d^{2} + 2 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/15*(2*(a^4*c^5 + 2*a^2*c^4*d + (a^4*c^2*d^3 + 2*a^2*c*d^4 + d^5)*x^6 + c^3*d^2 + 3*(a^4*c^3*d^2 + 2*a^2*c^2*d^3 + c*d^4)*x^4 + 3*(a^4*c^4*d + 2*a^2*c^3*d^2 + c^2*d^3)*x^2)*sqrt(-d)*log(8*a^4*d^2*x^4 + a^4*c^2 - 6*a^2*c*d + 8*(a^4*c*d - a^2*d^2)*x^2 - 4*(2*a^3*d*x^2 + a^3*c - a*d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(-d) + d^2) - sqrt(d*x^2 + c)*((8*(a^4*c^2*d^3 + 2*a^2*c*d^4 + d^5)*x^5 + 20*(a^4*c^3*d^2 + 2*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^4*c^4*d + 2*a^2*c^3*d^2 + c^2*d^3)*x)*arccos(a*x) - (7*a^3*c^4*d + 5*a*c^3*d^2 + 2*(3*a^3*c^2*d^3 + 2*a*c*d^4)*x^4 + (13*a^3*c^3*d^2 + 9*a*c^2*d^3)*x^2)*sqrt(-a^2*x^2 + 1)))/(a^4*c^8*d + 2*a^2*c^7*d^2 + c^6*d^3 + (a^4*c^5*d^4 + 2*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^4*c^6*d^3 + 2*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^4*c^7*d^2 + 2*a^2*c^6*d^3 + c^5*d^4)*x^2), -1/15*(4*(a^4*c^5 + 2*a^2*c^4*d + (a^4*c^2*d^3 + 2*a^2*c*d^4 + d^5)*x^6 + c^3*d^2 + 3*(a^4*c^3*d^2 + 2*a^2*c^2*d^3 + c*d^4)*x^4 + 3*(a^4*c^4*d + 2*a^2*c^3*d^2 + c^2*d^3)*x^2)*sqrt(d)*arctan(1/2*(2*a^2*d*x^2 + a^2*c - d)*sqrt(-a^2*x^2 + 1)*sqrt(d*x^2 + c)*sqrt(d)/(a^3*d^2*x^4 - a*c*d + (a^3*c*d - a*d^2)*x^2)) - sqrt(d*x^2 + c)*((8*(a^4*c^2*d^3 + 2*a^2*c*d^4 + d^5)*x^5 + 20*(a^4*c^3*d^2 + 2*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^4*c^4*d + 2*a^2*c^3*d^2 + c^2*d^3)*x)*arccos(a*x) - (7*a^3*c^4*d + 5*a*c^3*d^2 + 2*(3*a^3*c^2*d^3 + 2*a*c*d^4)*x^4 + (13*a^3*c^3*d^2 + 9*a*c^2*d^3)*x^2)*sqrt(-a^2*x^2 + 1)))/(a^4*c^8*d + 2*a^2*c^7*d^2 + c^6*d^3 + (a^4*c^5*d^4 + 2*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^4*c^6*d^3 + 2*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^4*c^7*d^2 + 2*a^2*c^6*d^3 + c^5*d^4)*x^2)]","B",0
