1,1,101,0,0.446383," ","integrate(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{525 \, a c^{7} d x^{7} - 735 \, a c^{5} d x^{5} + 105 \, {\left(5 \, b c^{7} d x^{7} - 7 \, b c^{5} d x^{5}\right)} \arcsin\left(c x\right) + {\left(75 \, b c^{6} d x^{6} - 57 \, b c^{4} d x^{4} - 76 \, b c^{2} d x^{2} - 152 \, b d\right)} \sqrt{-c^{2} x^{2} + 1}}{3675 \, c^{5}}"," ",0,"-1/3675*(525*a*c^7*d*x^7 - 735*a*c^5*d*x^5 + 105*(5*b*c^7*d*x^7 - 7*b*c^5*d*x^5)*arcsin(c*x) + (75*b*c^6*d*x^6 - 57*b*c^4*d*x^4 - 76*b*c^2*d*x^2 - 152*b*d)*sqrt(-c^2*x^2 + 1))/c^5","A",0
2,1,96,0,0.547493," ","integrate(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{12 \, a c^{6} d x^{6} - 18 \, a c^{4} d x^{4} + 3 \, {\left(4 \, b c^{6} d x^{6} - 6 \, b c^{4} d x^{4} + b d\right)} \arcsin\left(c x\right) + {\left(2 \, b c^{5} d x^{5} - 2 \, b c^{3} d x^{3} - 3 \, b c d x\right)} \sqrt{-c^{2} x^{2} + 1}}{72 \, c^{4}}"," ",0,"-1/72*(12*a*c^6*d*x^6 - 18*a*c^4*d*x^4 + 3*(4*b*c^6*d*x^6 - 6*b*c^4*d*x^4 + b*d)*arcsin(c*x) + (2*b*c^5*d*x^5 - 2*b*c^3*d*x^3 - 3*b*c*d*x)*sqrt(-c^2*x^2 + 1))/c^4","A",0
3,1,91,0,0.424535," ","integrate(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{45 \, a c^{5} d x^{5} - 75 \, a c^{3} d x^{3} + 15 \, {\left(3 \, b c^{5} d x^{5} - 5 \, b c^{3} d x^{3}\right)} \arcsin\left(c x\right) + {\left(9 \, b c^{4} d x^{4} - 13 \, b c^{2} d x^{2} - 26 \, b d\right)} \sqrt{-c^{2} x^{2} + 1}}{225 \, c^{3}}"," ",0,"-1/225*(45*a*c^5*d*x^5 - 75*a*c^3*d*x^3 + 15*(3*b*c^5*d*x^5 - 5*b*c^3*d*x^3)*arcsin(c*x) + (9*b*c^4*d*x^4 - 13*b*c^2*d*x^2 - 26*b*d)*sqrt(-c^2*x^2 + 1))/c^3","A",0
4,1,86,0,0.495526," ","integrate(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{8 \, a c^{4} d x^{4} - 16 \, a c^{2} d x^{2} + {\left(8 \, b c^{4} d x^{4} - 16 \, b c^{2} d x^{2} + 5 \, b d\right)} \arcsin\left(c x\right) + {\left(2 \, b c^{3} d x^{3} - 5 \, b c d x\right)} \sqrt{-c^{2} x^{2} + 1}}{32 \, c^{2}}"," ",0,"-1/32*(8*a*c^4*d*x^4 - 16*a*c^2*d*x^2 + (8*b*c^4*d*x^4 - 16*b*c^2*d*x^2 + 5*b*d)*arcsin(c*x) + (2*b*c^3*d*x^3 - 5*b*c*d*x)*sqrt(-c^2*x^2 + 1))/c^2","A",0
5,1,71,0,0.407286," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{3 \, a c^{3} d x^{3} - 9 \, a c d x + 3 \, {\left(b c^{3} d x^{3} - 3 \, b c d x\right)} \arcsin\left(c x\right) + {\left(b c^{2} d x^{2} - 7 \, b d\right)} \sqrt{-c^{2} x^{2} + 1}}{9 \, c}"," ",0,"-1/9*(3*a*c^3*d*x^3 - 9*a*c*d*x + 3*(b*c^3*d*x^3 - 3*b*c*d*x)*arcsin(c*x) + (b*c^2*d*x^2 - 7*b*d)*sqrt(-c^2*x^2 + 1))/c","A",0
6,0,0,0,0.641614," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))/x, x)","F",0
7,1,98,0,0.527855," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} d x^{2} + b c d x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - b c d x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 2 \, \sqrt{-c^{2} x^{2} + 1} b c d x + 2 \, a d + 2 \, {\left(b c^{2} d x^{2} + b d\right)} \arcsin\left(c x\right)}{2 \, x}"," ",0,"-1/2*(2*a*c^2*d*x^2 + b*c*d*x*log(sqrt(-c^2*x^2 + 1) + 1) - b*c*d*x*log(sqrt(-c^2*x^2 + 1) - 1) + 2*sqrt(-c^2*x^2 + 1)*b*c*d*x + 2*a*d + 2*(b*c^2*d*x^2 + b*d)*arcsin(c*x))/x","A",0
8,0,0,0,0.513842," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))/x^3, x)","F",0
9,1,109,0,1.022441," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","\frac{5 \, b c^{3} d x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - 5 \, b c^{3} d x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 12 \, a c^{2} d x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b c d x - 4 \, a d + 4 \, {\left(3 \, b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)}{12 \, x^{3}}"," ",0,"1/12*(5*b*c^3*d*x^3*log(sqrt(-c^2*x^2 + 1) + 1) - 5*b*c^3*d*x^3*log(sqrt(-c^2*x^2 + 1) - 1) + 12*a*c^2*d*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*c*d*x - 4*a*d + 4*(3*b*c^2*d*x^2 - b*d)*arcsin(c*x))/x^3","A",0
10,1,153,0,0.531513," ","integrate(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{11025 \, a c^{9} d^{2} x^{9} - 28350 \, a c^{7} d^{2} x^{7} + 19845 \, a c^{5} d^{2} x^{5} + 315 \, {\left(35 \, b c^{9} d^{2} x^{9} - 90 \, b c^{7} d^{2} x^{7} + 63 \, b c^{5} d^{2} x^{5}\right)} \arcsin\left(c x\right) + {\left(1225 \, b c^{8} d^{2} x^{8} - 2650 \, b c^{6} d^{2} x^{6} + 789 \, b c^{4} d^{2} x^{4} + 1052 \, b c^{2} d^{2} x^{2} + 2104 \, b d^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{99225 \, c^{5}}"," ",0,"1/99225*(11025*a*c^9*d^2*x^9 - 28350*a*c^7*d^2*x^7 + 19845*a*c^5*d^2*x^5 + 315*(35*b*c^9*d^2*x^9 - 90*b*c^7*d^2*x^7 + 63*b*c^5*d^2*x^5)*arcsin(c*x) + (1225*b*c^8*d^2*x^8 - 2650*b*c^6*d^2*x^6 + 789*b*c^4*d^2*x^4 + 1052*b*c^2*d^2*x^2 + 2104*b*d^2)*sqrt(-c^2*x^2 + 1))/c^5","A",0
11,1,149,0,0.956492," ","integrate(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{1152 \, a c^{8} d^{2} x^{8} - 3072 \, a c^{6} d^{2} x^{6} + 2304 \, a c^{4} d^{2} x^{4} + 3 \, {\left(384 \, b c^{8} d^{2} x^{8} - 1024 \, b c^{6} d^{2} x^{6} + 768 \, b c^{4} d^{2} x^{4} - 73 \, b d^{2}\right)} \arcsin\left(c x\right) + {\left(144 \, b c^{7} d^{2} x^{7} - 344 \, b c^{5} d^{2} x^{5} + 146 \, b c^{3} d^{2} x^{3} + 219 \, b c d^{2} x\right)} \sqrt{-c^{2} x^{2} + 1}}{9216 \, c^{4}}"," ",0,"1/9216*(1152*a*c^8*d^2*x^8 - 3072*a*c^6*d^2*x^6 + 2304*a*c^4*d^2*x^4 + 3*(384*b*c^8*d^2*x^8 - 1024*b*c^6*d^2*x^6 + 768*b*c^4*d^2*x^4 - 73*b*d^2)*arcsin(c*x) + (144*b*c^7*d^2*x^7 - 344*b*c^5*d^2*x^5 + 146*b*c^3*d^2*x^3 + 219*b*c*d^2*x)*sqrt(-c^2*x^2 + 1))/c^4","A",0
12,1,141,0,0.498155," ","integrate(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{1575 \, a c^{7} d^{2} x^{7} - 4410 \, a c^{5} d^{2} x^{5} + 3675 \, a c^{3} d^{2} x^{3} + 105 \, {\left(15 \, b c^{7} d^{2} x^{7} - 42 \, b c^{5} d^{2} x^{5} + 35 \, b c^{3} d^{2} x^{3}\right)} \arcsin\left(c x\right) + {\left(225 \, b c^{6} d^{2} x^{6} - 612 \, b c^{4} d^{2} x^{4} + 409 \, b c^{2} d^{2} x^{2} + 818 \, b d^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{11025 \, c^{3}}"," ",0,"1/11025*(1575*a*c^7*d^2*x^7 - 4410*a*c^5*d^2*x^5 + 3675*a*c^3*d^2*x^3 + 105*(15*b*c^7*d^2*x^7 - 42*b*c^5*d^2*x^5 + 35*b*c^3*d^2*x^3)*arcsin(c*x) + (225*b*c^6*d^2*x^6 - 612*b*c^4*d^2*x^4 + 409*b*c^2*d^2*x^2 + 818*b*d^2)*sqrt(-c^2*x^2 + 1))/c^3","A",0
13,1,137,0,1.150698," ","integrate(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{48 \, a c^{6} d^{2} x^{6} - 144 \, a c^{4} d^{2} x^{4} + 144 \, a c^{2} d^{2} x^{2} + 3 \, {\left(16 \, b c^{6} d^{2} x^{6} - 48 \, b c^{4} d^{2} x^{4} + 48 \, b c^{2} d^{2} x^{2} - 11 \, b d^{2}\right)} \arcsin\left(c x\right) + {\left(8 \, b c^{5} d^{2} x^{5} - 26 \, b c^{3} d^{2} x^{3} + 33 \, b c d^{2} x\right)} \sqrt{-c^{2} x^{2} + 1}}{288 \, c^{2}}"," ",0,"1/288*(48*a*c^6*d^2*x^6 - 144*a*c^4*d^2*x^4 + 144*a*c^2*d^2*x^2 + 3*(16*b*c^6*d^2*x^6 - 48*b*c^4*d^2*x^4 + 48*b*c^2*d^2*x^2 - 11*b*d^2)*arcsin(c*x) + (8*b*c^5*d^2*x^5 - 26*b*c^3*d^2*x^3 + 33*b*c*d^2*x)*sqrt(-c^2*x^2 + 1))/c^2","A",0
14,1,121,0,0.684745," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{45 \, a c^{5} d^{2} x^{5} - 150 \, a c^{3} d^{2} x^{3} + 225 \, a c d^{2} x + 15 \, {\left(3 \, b c^{5} d^{2} x^{5} - 10 \, b c^{3} d^{2} x^{3} + 15 \, b c d^{2} x\right)} \arcsin\left(c x\right) + {\left(9 \, b c^{4} d^{2} x^{4} - 38 \, b c^{2} d^{2} x^{2} + 149 \, b d^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{225 \, c}"," ",0,"1/225*(45*a*c^5*d^2*x^5 - 150*a*c^3*d^2*x^3 + 225*a*c*d^2*x + 15*(3*b*c^5*d^2*x^5 - 10*b*c^3*d^2*x^3 + 15*b*c*d^2*x)*arcsin(c*x) + (9*b*c^4*d^2*x^4 - 38*b*c^2*d^2*x^2 + 149*b*d^2)*sqrt(-c^2*x^2 + 1))/c","A",0
15,0,0,0,0.470723," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))/x, x)","F",0
16,1,152,0,0.627383," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","\frac{6 \, a c^{4} d^{2} x^{4} - 36 \, a c^{2} d^{2} x^{2} - 9 \, b c d^{2} x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + 9 \, b c d^{2} x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) - 18 \, a d^{2} + 6 \, {\left(b c^{4} d^{2} x^{4} - 6 \, b c^{2} d^{2} x^{2} - 3 \, b d^{2}\right)} \arcsin\left(c x\right) + 2 \, {\left(b c^{3} d^{2} x^{3} - 16 \, b c d^{2} x\right)} \sqrt{-c^{2} x^{2} + 1}}{18 \, x}"," ",0,"1/18*(6*a*c^4*d^2*x^4 - 36*a*c^2*d^2*x^2 - 9*b*c*d^2*x*log(sqrt(-c^2*x^2 + 1) + 1) + 9*b*c*d^2*x*log(sqrt(-c^2*x^2 + 1) - 1) - 18*a*d^2 + 6*(b*c^4*d^2*x^4 - 6*b*c^2*d^2*x^2 - 3*b*d^2)*arcsin(c*x) + 2*(b*c^3*d^2*x^3 - 16*b*c*d^2*x)*sqrt(-c^2*x^2 + 1))/x","A",0
17,0,0,0,0.473645," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))/x^3, x)","F",0
18,1,162,0,0.565906," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","\frac{12 \, a c^{4} d^{2} x^{4} + 11 \, b c^{3} d^{2} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - 11 \, b c^{3} d^{2} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 24 \, a c^{2} d^{2} x^{2} - 4 \, a d^{2} + 4 \, {\left(3 \, b c^{4} d^{2} x^{4} + 6 \, b c^{2} d^{2} x^{2} - b d^{2}\right)} \arcsin\left(c x\right) + 2 \, {\left(6 \, b c^{3} d^{2} x^{3} - b c d^{2} x\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, x^{3}}"," ",0,"1/12*(12*a*c^4*d^2*x^4 + 11*b*c^3*d^2*x^3*log(sqrt(-c^2*x^2 + 1) + 1) - 11*b*c^3*d^2*x^3*log(sqrt(-c^2*x^2 + 1) - 1) + 24*a*c^2*d^2*x^2 - 4*a*d^2 + 4*(3*b*c^4*d^2*x^4 + 6*b*c^2*d^2*x^2 - b*d^2)*arcsin(c*x) + 2*(6*b*c^3*d^2*x^3 - b*c*d^2*x)*sqrt(-c^2*x^2 + 1))/x^3","A",0
19,1,189,0,0.512667," ","integrate(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{363825 \, a c^{11} d^{3} x^{11} - 1334025 \, a c^{9} d^{3} x^{9} + 1715175 \, a c^{7} d^{3} x^{7} - 800415 \, a c^{5} d^{3} x^{5} + 3465 \, {\left(105 \, b c^{11} d^{3} x^{11} - 385 \, b c^{9} d^{3} x^{9} + 495 \, b c^{7} d^{3} x^{7} - 231 \, b c^{5} d^{3} x^{5}\right)} \arcsin\left(c x\right) + {\left(33075 \, b c^{10} d^{3} x^{10} - 111475 \, b c^{8} d^{3} x^{8} + 117625 \, b c^{6} d^{3} x^{6} - 18933 \, b c^{4} d^{3} x^{4} - 25244 \, b c^{2} d^{3} x^{2} - 50488 \, b d^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{4002075 \, c^{5}}"," ",0,"-1/4002075*(363825*a*c^11*d^3*x^11 - 1334025*a*c^9*d^3*x^9 + 1715175*a*c^7*d^3*x^7 - 800415*a*c^5*d^3*x^5 + 3465*(105*b*c^11*d^3*x^11 - 385*b*c^9*d^3*x^9 + 495*b*c^7*d^3*x^7 - 231*b*c^5*d^3*x^5)*arcsin(c*x) + (33075*b*c^10*d^3*x^10 - 111475*b*c^8*d^3*x^8 + 117625*b*c^6*d^3*x^6 - 18933*b*c^4*d^3*x^4 - 25244*b*c^2*d^3*x^2 - 50488*b*d^3)*sqrt(-c^2*x^2 + 1))/c^5","A",0
20,1,185,0,0.520435," ","integrate(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{7680 \, a c^{10} d^{3} x^{10} - 28800 \, a c^{8} d^{3} x^{8} + 38400 \, a c^{6} d^{3} x^{6} - 19200 \, a c^{4} d^{3} x^{4} + 15 \, {\left(512 \, b c^{10} d^{3} x^{10} - 1920 \, b c^{8} d^{3} x^{8} + 2560 \, b c^{6} d^{3} x^{6} - 1280 \, b c^{4} d^{3} x^{4} + 79 \, b d^{3}\right)} \arcsin\left(c x\right) + {\left(768 \, b c^{9} d^{3} x^{9} - 2736 \, b c^{7} d^{3} x^{7} + 3208 \, b c^{5} d^{3} x^{5} - 790 \, b c^{3} d^{3} x^{3} - 1185 \, b c d^{3} x\right)} \sqrt{-c^{2} x^{2} + 1}}{76800 \, c^{4}}"," ",0,"-1/76800*(7680*a*c^10*d^3*x^10 - 28800*a*c^8*d^3*x^8 + 38400*a*c^6*d^3*x^6 - 19200*a*c^4*d^3*x^4 + 15*(512*b*c^10*d^3*x^10 - 1920*b*c^8*d^3*x^8 + 2560*b*c^6*d^3*x^6 - 1280*b*c^4*d^3*x^4 + 79*b*d^3)*arcsin(c*x) + (768*b*c^9*d^3*x^9 - 2736*b*c^7*d^3*x^7 + 3208*b*c^5*d^3*x^5 - 790*b*c^3*d^3*x^3 - 1185*b*c*d^3*x)*sqrt(-c^2*x^2 + 1))/c^4","A",0
21,1,177,0,0.498074," ","integrate(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{11025 \, a c^{9} d^{3} x^{9} - 42525 \, a c^{7} d^{3} x^{7} + 59535 \, a c^{5} d^{3} x^{5} - 33075 \, a c^{3} d^{3} x^{3} + 315 \, {\left(35 \, b c^{9} d^{3} x^{9} - 135 \, b c^{7} d^{3} x^{7} + 189 \, b c^{5} d^{3} x^{5} - 105 \, b c^{3} d^{3} x^{3}\right)} \arcsin\left(c x\right) + {\left(1225 \, b c^{8} d^{3} x^{8} - 4675 \, b c^{6} d^{3} x^{6} + 6297 \, b c^{4} d^{3} x^{4} - 2629 \, b c^{2} d^{3} x^{2} - 5258 \, b d^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{99225 \, c^{3}}"," ",0,"-1/99225*(11025*a*c^9*d^3*x^9 - 42525*a*c^7*d^3*x^7 + 59535*a*c^5*d^3*x^5 - 33075*a*c^3*d^3*x^3 + 315*(35*b*c^9*d^3*x^9 - 135*b*c^7*d^3*x^7 + 189*b*c^5*d^3*x^5 - 105*b*c^3*d^3*x^3)*arcsin(c*x) + (1225*b*c^8*d^3*x^8 - 4675*b*c^6*d^3*x^6 + 6297*b*c^4*d^3*x^4 - 2629*b*c^2*d^3*x^2 - 5258*b*d^3)*sqrt(-c^2*x^2 + 1))/c^3","A",0
22,1,173,0,0.455640," ","integrate(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{384 \, a c^{8} d^{3} x^{8} - 1536 \, a c^{6} d^{3} x^{6} + 2304 \, a c^{4} d^{3} x^{4} - 1536 \, a c^{2} d^{3} x^{2} + 3 \, {\left(128 \, b c^{8} d^{3} x^{8} - 512 \, b c^{6} d^{3} x^{6} + 768 \, b c^{4} d^{3} x^{4} - 512 \, b c^{2} d^{3} x^{2} + 93 \, b d^{3}\right)} \arcsin\left(c x\right) + {\left(48 \, b c^{7} d^{3} x^{7} - 200 \, b c^{5} d^{3} x^{5} + 326 \, b c^{3} d^{3} x^{3} - 279 \, b c d^{3} x\right)} \sqrt{-c^{2} x^{2} + 1}}{3072 \, c^{2}}"," ",0,"-1/3072*(384*a*c^8*d^3*x^8 - 1536*a*c^6*d^3*x^6 + 2304*a*c^4*d^3*x^4 - 1536*a*c^2*d^3*x^2 + 3*(128*b*c^8*d^3*x^8 - 512*b*c^6*d^3*x^6 + 768*b*c^4*d^3*x^4 - 512*b*c^2*d^3*x^2 + 93*b*d^3)*arcsin(c*x) + (48*b*c^7*d^3*x^7 - 200*b*c^5*d^3*x^5 + 326*b*c^3*d^3*x^3 - 279*b*c*d^3*x)*sqrt(-c^2*x^2 + 1))/c^2","A",0
23,1,157,0,0.547749," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{525 \, a c^{7} d^{3} x^{7} - 2205 \, a c^{5} d^{3} x^{5} + 3675 \, a c^{3} d^{3} x^{3} - 3675 \, a c d^{3} x + 105 \, {\left(5 \, b c^{7} d^{3} x^{7} - 21 \, b c^{5} d^{3} x^{5} + 35 \, b c^{3} d^{3} x^{3} - 35 \, b c d^{3} x\right)} \arcsin\left(c x\right) + {\left(75 \, b c^{6} d^{3} x^{6} - 351 \, b c^{4} d^{3} x^{4} + 757 \, b c^{2} d^{3} x^{2} - 2161 \, b d^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{3675 \, c}"," ",0,"-1/3675*(525*a*c^7*d^3*x^7 - 2205*a*c^5*d^3*x^5 + 3675*a*c^3*d^3*x^3 - 3675*a*c*d^3*x + 105*(5*b*c^7*d^3*x^7 - 21*b*c^5*d^3*x^5 + 35*b*c^3*d^3*x^3 - 35*b*c*d^3*x)*arcsin(c*x) + (75*b*c^6*d^3*x^6 - 351*b*c^4*d^3*x^4 + 757*b*c^2*d^3*x^2 - 2161*b*d^3)*sqrt(-c^2*x^2 + 1))/c","A",0
24,0,0,0,0.486196," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a c^{6} d^{3} x^{6} - 3 \, a c^{4} d^{3} x^{4} + 3 \, a c^{2} d^{3} x^{2} - a d^{3} + {\left(b c^{6} d^{3} x^{6} - 3 \, b c^{4} d^{3} x^{4} + 3 \, b c^{2} d^{3} x^{2} - b d^{3}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral(-(a*c^6*d^3*x^6 - 3*a*c^4*d^3*x^4 + 3*a*c^2*d^3*x^2 - a*d^3 + (b*c^6*d^3*x^6 - 3*b*c^4*d^3*x^4 + 3*b*c^2*d^3*x^2 - b*d^3)*arcsin(c*x))/x, x)","F",0
25,1,188,0,0.574344," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","-\frac{10 \, a c^{6} d^{3} x^{6} - 50 \, a c^{4} d^{3} x^{4} + 150 \, a c^{2} d^{3} x^{2} + 25 \, b c d^{3} x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) - 25 \, b c d^{3} x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 50 \, a d^{3} + 10 \, {\left(b c^{6} d^{3} x^{6} - 5 \, b c^{4} d^{3} x^{4} + 15 \, b c^{2} d^{3} x^{2} + 5 \, b d^{3}\right)} \arcsin\left(c x\right) + 2 \, {\left(b c^{5} d^{3} x^{5} - 7 \, b c^{3} d^{3} x^{3} + 61 \, b c d^{3} x\right)} \sqrt{-c^{2} x^{2} + 1}}{50 \, x}"," ",0,"-1/50*(10*a*c^6*d^3*x^6 - 50*a*c^4*d^3*x^4 + 150*a*c^2*d^3*x^2 + 25*b*c*d^3*x*log(sqrt(-c^2*x^2 + 1) + 1) - 25*b*c*d^3*x*log(sqrt(-c^2*x^2 + 1) - 1) + 50*a*d^3 + 10*(b*c^6*d^3*x^6 - 5*b*c^4*d^3*x^4 + 15*b*c^2*d^3*x^2 + 5*b*d^3)*arcsin(c*x) + 2*(b*c^5*d^3*x^5 - 7*b*c^3*d^3*x^3 + 61*b*c*d^3*x)*sqrt(-c^2*x^2 + 1))/x","A",0
26,0,0,0,0.473225," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a c^{6} d^{3} x^{6} - 3 \, a c^{4} d^{3} x^{4} + 3 \, a c^{2} d^{3} x^{2} - a d^{3} + {\left(b c^{6} d^{3} x^{6} - 3 \, b c^{4} d^{3} x^{4} + 3 \, b c^{2} d^{3} x^{2} - b d^{3}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a*c^6*d^3*x^6 - 3*a*c^4*d^3*x^4 + 3*a*c^2*d^3*x^2 - a*d^3 + (b*c^6*d^3*x^6 - 3*b*c^4*d^3*x^4 + 3*b*c^2*d^3*x^2 - b*d^3)*arcsin(c*x))/x^3, x)","F",0
27,1,196,0,0.550022," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","-\frac{12 \, a c^{6} d^{3} x^{6} - 108 \, a c^{4} d^{3} x^{4} - 51 \, b c^{3} d^{3} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + 51 \, b c^{3} d^{3} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) - 108 \, a c^{2} d^{3} x^{2} + 12 \, a d^{3} + 12 \, {\left(b c^{6} d^{3} x^{6} - 9 \, b c^{4} d^{3} x^{4} - 9 \, b c^{2} d^{3} x^{2} + b d^{3}\right)} \arcsin\left(c x\right) + 2 \, {\left(2 \, b c^{5} d^{3} x^{5} - 50 \, b c^{3} d^{3} x^{3} + 3 \, b c d^{3} x\right)} \sqrt{-c^{2} x^{2} + 1}}{36 \, x^{3}}"," ",0,"-1/36*(12*a*c^6*d^3*x^6 - 108*a*c^4*d^3*x^4 - 51*b*c^3*d^3*x^3*log(sqrt(-c^2*x^2 + 1) + 1) + 51*b*c^3*d^3*x^3*log(sqrt(-c^2*x^2 + 1) - 1) - 108*a*c^2*d^3*x^2 + 12*a*d^3 + 12*(b*c^6*d^3*x^6 - 9*b*c^4*d^3*x^4 - 9*b*c^2*d^3*x^2 + b*d^3)*arcsin(c*x) + 2*(2*b*c^5*d^3*x^5 - 50*b*c^3*d^3*x^3 + 3*b*c*d^3*x)*sqrt(-c^2*x^2 + 1))/x^3","A",0
28,0,0,0,0.517652," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{4} \arcsin\left(c x\right) + a x^{4}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^4*arcsin(c*x) + a*x^4)/(c^2*d*x^2 - d), x)","F",0
29,0,0,0,0.533109," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{3} \arcsin\left(c x\right) + a x^{3}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^3*arcsin(c*x) + a*x^3)/(c^2*d*x^2 - d), x)","F",0
30,0,0,0,0.468642," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{2} \arcsin\left(c x\right) + a x^{2}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^2*arcsin(c*x) + a*x^2)/(c^2*d*x^2 - d), x)","F",0
31,0,0,0,0.518533," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x \arcsin\left(c x\right) + a x}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x*arcsin(c*x) + a*x)/(c^2*d*x^2 - d), x)","F",0
32,0,0,0,0.505171," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^2*d*x^2 - d), x)","F",0
33,0,0,0,0.572001," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{2} d x^{3} - d x}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^2*d*x^3 - d*x), x)","F",0
34,0,0,0,0.690679," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{2} d x^{4} - d x^{2}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^2*d*x^4 - d*x^2), x)","F",0
35,0,0,0,0.544407," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{2} d x^{5} - d x^{3}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^2*d*x^5 - d*x^3), x)","F",0
36,0,0,0,0.606120," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{2} d x^{6} - d x^{4}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^2*d*x^6 - d*x^4), x)","F",0
37,0,0,0,0.511227," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \arcsin\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*arcsin(c*x) + a*x^4)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
38,0,0,0,0.583745," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arcsin\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*arcsin(c*x) + a*x^3)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
39,0,0,0,0.544632," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arcsin\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*arcsin(c*x) + a*x^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
40,1,55,0,0.478841," ","integrate(x*(a+b*arcsin(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 \arcsin\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*arcsin(c*x))/(c^4*d^2*x^2 - c^2*d^2)","A",0
41,0,0,0,0.511233," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\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*arcsin(c*x) + a)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
42,0,0,0,0.562049," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\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*arcsin(c*x) + a)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
43,0,0,0,0.478549," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\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*arcsin(c*x) + a)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
44,0,0,0,0.480094," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\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*arcsin(c*x) + a)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
45,0,0,0,0.602837," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
46,0,0,0,0.810483," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{4} \arcsin\left(c x\right) + a x^{4}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*x^4*arcsin(c*x) + a*x^4)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
47,1,91,0,0.534190," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","\frac{3 \, a c^{4} x^{4} + 3 \, {\left(2 \, b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - {\left(4 \, b c^{3} x^{3} - 3 \, b c x\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"1/12*(3*a*c^4*x^4 + 3*(2*b*c^2*x^2 - b)*arcsin(c*x) - (4*b*c^3*x^3 - 3*b*c*x)*sqrt(-c^2*x^2 + 1))/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)","A",0
48,0,0,0,0.449098," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{2} \arcsin\left(c x\right) + a x^{2}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*x^2*arcsin(c*x) + a*x^2)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
49,1,88,0,0.620551," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","-\frac{3 \, a c^{4} x^{4} - 6 \, a c^{2} x^{2} - 3 \, b \arcsin\left(c x\right) - {\left(2 \, b c^{3} x^{3} - 3 \, b c x\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"-1/12*(3*a*c^4*x^4 - 6*a*c^2*x^2 - 3*b*arcsin(c*x) - (2*b*c^3*x^3 - 3*b*c*x)*sqrt(-c^2*x^2 + 1))/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)","A",0
50,0,0,0,0.473259," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
51,0,0,0,0.470854," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x)","F",0
52,0,0,0,0.416819," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x)","F",0
53,0,0,0,0.547076," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3), x)","F",0
54,0,0,0,0.566400," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arcsin\left(c x\right) + a}{c^{6} d^{3} x^{10} - 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} - d^{3} x^{4}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)/(c^6*d^3*x^10 - 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 - d^3*x^4), x)","F",0
55,0,0,0,0.430985," ","integrate(x^4*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} \arcsin\left(c x\right) + a x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((b*x^4*arcsin(c*x) + a*x^4)*sqrt(-c^2*d*x^2 + d), x)","F",0
56,0,0,0,0.477077," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b x^{2} \arcsin\left(c x\right) + a x^{2}\right)}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*x^2*arcsin(c*x) + a*x^2), x)","F",0
57,0,0,0,0.405785," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a), x)","F",0
58,0,0,0,0.548299," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/x^2, x)","F",0
59,1,414,0,0.892703," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","\left[\frac{{\left(b c^{5} x^{5} - b c^{3} x^{3}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - \sqrt{-c^{2} d x^{2} + d} {\left(b c x^{3} - b c x\right)} \sqrt{-c^{2} x^{2} + 1} + 2 \, {\left(a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{-c^{2} d x^{2} + d}}{6 \, {\left(c^{2} x^{5} - x^{3}\right)}}, -\frac{2 \, {\left(b c^{5} x^{5} - b c^{3} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + \sqrt{-c^{2} d x^{2} + d} {\left(b c x^{3} - b c x\right)} \sqrt{-c^{2} x^{2} + 1} - 2 \, {\left(a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{-c^{2} d x^{2} + d}}{6 \, {\left(c^{2} x^{5} - x^{3}\right)}}\right]"," ",0,"[1/6*((b*c^5*x^5 - b*c^3*x^3)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - sqrt(-c^2*d*x^2 + d)*(b*c*x^3 - b*c*x)*sqrt(-c^2*x^2 + 1) + 2*(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^5 - x^3), -1/6*(2*(b*c^5*x^5 - b*c^3*x^3)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + sqrt(-c^2*d*x^2 + d)*(b*c*x^3 - b*c*x)*sqrt(-c^2*x^2 + 1) - 2*(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^5 - x^3)]","B",0
60,1,501,0,1.099624," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b c^{7} x^{7} - b c^{5} x^{5}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - {\left(2 \, b c^{3} x^{3} - {\left(2 \, b c^{3} - 3 \, b c\right)} x^{5} - 3 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 4 \, {\left(2 \, a c^{6} x^{6} - a c^{4} x^{4} - 4 \, a c^{2} x^{2} + {\left(2 \, b c^{6} x^{6} - b c^{4} x^{4} - 4 \, b c^{2} x^{2} + 3 \, b\right)} \arcsin\left(c x\right) + 3 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{60 \, {\left(c^{2} x^{7} - x^{5}\right)}}, -\frac{8 \, {\left(b c^{7} x^{7} - b c^{5} x^{5}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(2 \, b c^{3} x^{3} - {\left(2 \, b c^{3} - 3 \, b c\right)} x^{5} - 3 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 4 \, {\left(2 \, a c^{6} x^{6} - a c^{4} x^{4} - 4 \, a c^{2} x^{2} + {\left(2 \, b c^{6} x^{6} - b c^{4} x^{4} - 4 \, b c^{2} x^{2} + 3 \, b\right)} \arcsin\left(c x\right) + 3 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{60 \, {\left(c^{2} x^{7} - x^{5}\right)}}\right]"," ",0,"[1/60*(4*(b*c^7*x^7 - b*c^5*x^5)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - (2*b*c^3*x^3 - (2*b*c^3 - 3*b*c)*x^5 - 3*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 4*(2*a*c^6*x^6 - a*c^4*x^4 - 4*a*c^2*x^2 + (2*b*c^6*x^6 - b*c^4*x^4 - 4*b*c^2*x^2 + 3*b)*arcsin(c*x) + 3*a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^7 - x^5), -1/60*(8*(b*c^7*x^7 - b*c^5*x^5)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (2*b*c^3*x^3 - (2*b*c^3 - 3*b*c)*x^5 - 3*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 4*(2*a*c^6*x^6 - a*c^4*x^4 - 4*a*c^2*x^2 + (2*b*c^6*x^6 - b*c^4*x^4 - 4*b*c^2*x^2 + 3*b)*arcsin(c*x) + 3*a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^7 - x^5)]","A",0
61,1,567,0,1.075647," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(b c^{9} x^{9} - b c^{7} x^{7}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - {\left(8 \, b c^{5} x^{5} - {\left(8 \, b c^{5} + 3 \, b c^{3} - 10 \, b c\right)} x^{7} + 3 \, b c^{3} x^{3} - 10 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 4 \, {\left(8 \, a c^{8} x^{8} - 4 \, a c^{6} x^{6} - a c^{4} x^{4} - 18 \, a c^{2} x^{2} + {\left(8 \, b c^{8} x^{8} - 4 \, b c^{6} x^{6} - b c^{4} x^{4} - 18 \, b c^{2} x^{2} + 15 \, b\right)} \arcsin\left(c x\right) + 15 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{420 \, {\left(c^{2} x^{9} - x^{7}\right)}}, -\frac{32 \, {\left(b c^{9} x^{9} - b c^{7} x^{7}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(8 \, b c^{5} x^{5} - {\left(8 \, b c^{5} + 3 \, b c^{3} - 10 \, b c\right)} x^{7} + 3 \, b c^{3} x^{3} - 10 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 4 \, {\left(8 \, a c^{8} x^{8} - 4 \, a c^{6} x^{6} - a c^{4} x^{4} - 18 \, a c^{2} x^{2} + {\left(8 \, b c^{8} x^{8} - 4 \, b c^{6} x^{6} - b c^{4} x^{4} - 18 \, b c^{2} x^{2} + 15 \, b\right)} \arcsin\left(c x\right) + 15 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{420 \, {\left(c^{2} x^{9} - x^{7}\right)}}\right]"," ",0,"[1/420*(16*(b*c^9*x^9 - b*c^7*x^7)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - (8*b*c^5*x^5 - (8*b*c^5 + 3*b*c^3 - 10*b*c)*x^7 + 3*b*c^3*x^3 - 10*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 4*(8*a*c^8*x^8 - 4*a*c^6*x^6 - a*c^4*x^4 - 18*a*c^2*x^2 + (8*b*c^8*x^8 - 4*b*c^6*x^6 - b*c^4*x^4 - 18*b*c^2*x^2 + 15*b)*arcsin(c*x) + 15*a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7), -1/420*(32*(b*c^9*x^9 - b*c^7*x^7)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (8*b*c^5*x^5 - (8*b*c^5 + 3*b*c^3 - 10*b*c)*x^7 + 3*b*c^3*x^3 - 10*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 4*(8*a*c^8*x^8 - 4*a*c^6*x^6 - a*c^4*x^4 - 18*a*c^2*x^2 + (8*b*c^8*x^8 - 4*b*c^6*x^6 - b*c^4*x^4 - 18*b*c^2*x^2 + 15*b)*arcsin(c*x) + 15*a)*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7)]","A",0
62,1,177,0,0.592929," ","integrate(x^5*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(225 \, b c^{7} x^{7} - 63 \, b c^{5} x^{5} - 140 \, b c^{3} x^{3} - 840 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 105 \, {\left(15 \, a c^{8} x^{8} - 18 \, a c^{6} x^{6} - a c^{4} x^{4} - 4 \, a c^{2} x^{2} + {\left(15 \, b c^{8} x^{8} - 18 \, b c^{6} x^{6} - b c^{4} x^{4} - 4 \, b c^{2} x^{2} + 8 \, b\right)} \arcsin\left(c x\right) + 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{11025 \, {\left(c^{8} x^{2} - c^{6}\right)}}"," ",0,"1/11025*((225*b*c^7*x^7 - 63*b*c^5*x^5 - 140*b*c^3*x^3 - 840*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 105*(15*a*c^8*x^8 - 18*a*c^6*x^6 - a*c^4*x^4 - 4*a*c^2*x^2 + (15*b*c^8*x^8 - 18*b*c^6*x^6 - b*c^4*x^4 - 4*b*c^2*x^2 + 8*b)*arcsin(c*x) + 8*a)*sqrt(-c^2*d*x^2 + d))/(c^8*x^2 - c^6)","A",0
63,1,150,0,0.574761," ","integrate(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(9 \, b c^{5} x^{5} - 5 \, b c^{3} x^{3} - 30 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 15 \, {\left(3 \, a c^{6} x^{6} - 4 \, a c^{4} x^{4} - a c^{2} x^{2} + {\left(3 \, b c^{6} x^{6} - 4 \, b c^{4} x^{4} - b c^{2} x^{2} + 2 \, b\right)} \arcsin\left(c x\right) + 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{225 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"1/225*((9*b*c^5*x^5 - 5*b*c^3*x^3 - 30*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 15*(3*a*c^6*x^6 - 4*a*c^4*x^4 - a*c^2*x^2 + (3*b*c^6*x^6 - 4*b*c^4*x^4 - b*c^2*x^2 + 2*b)*arcsin(c*x) + 2*a)*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
64,1,116,0,0.546308," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(b c^{3} x^{3} - 3 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 3 \, {\left(a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{-c^{2} d x^{2} + d}}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"1/9*((b*c^3*x^3 - 3*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 3*(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a)*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
65,0,0,0,0.440591," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{x}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/x, x)","F",0
66,0,0,0,0.855474," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/x^3, x)","F",0
67,0,0,0,0.513931," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{x^{5}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/x^5, x)","F",0
68,0,0,0,0.559530," ","integrate(x^4*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d x^{6} - a d x^{4} + {\left(b c^{2} d x^{6} - b d x^{4}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral(-(a*c^2*d*x^6 - a*d*x^4 + (b*c^2*d*x^6 - b*d*x^4)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
69,0,0,0,0.460197," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d x^{4} - a d x^{2} + {\left(b c^{2} d x^{4} - b d x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral(-(a*c^2*d*x^4 - a*d*x^2 + (b*c^2*d*x^4 - b*d*x^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
70,0,0,0,0.535875," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
71,0,0,0,0.519208," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^2, x)","F",0
72,0,0,0,0.542274," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^4, x)","F",0
73,1,525,0,0.768373," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c^{7} d x^{7} - b c^{5} d x^{5}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - {\left(4 \, b c^{3} d x^{3} - {\left(4 \, b c^{3} - b c\right)} d x^{5} - b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 4 \, {\left(a c^{6} d x^{6} - 3 \, a c^{4} d x^{4} + 3 \, a c^{2} d x^{2} - a d + {\left(b c^{6} d x^{6} - 3 \, b c^{4} d x^{4} + 3 \, b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{20 \, {\left(c^{2} x^{7} - x^{5}\right)}}, \frac{4 \, {\left(b c^{7} d x^{7} - b c^{5} d x^{5}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) - {\left(4 \, b c^{3} d x^{3} - {\left(4 \, b c^{3} - b c\right)} d x^{5} - b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 4 \, {\left(a c^{6} d x^{6} - 3 \, a c^{4} d x^{4} + 3 \, a c^{2} d x^{2} - a d + {\left(b c^{6} d x^{6} - 3 \, b c^{4} d x^{4} + 3 \, b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{20 \, {\left(c^{2} x^{7} - x^{5}\right)}}\right]"," ",0,"[1/20*(2*(b*c^7*d*x^7 - b*c^5*d*x^5)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - (4*b*c^3*d*x^3 - (4*b*c^3 - b*c)*d*x^5 - b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 4*(a*c^6*d*x^6 - 3*a*c^4*d*x^4 + 3*a*c^2*d*x^2 - a*d + (b*c^6*d*x^6 - 3*b*c^4*d*x^4 + 3*b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^7 - x^5), 1/20*(4*(b*c^7*d*x^7 - b*c^5*d*x^5)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) - (4*b*c^3*d*x^3 - (4*b*c^3 - b*c)*d*x^5 - b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 4*(a*c^6*d*x^6 - 3*a*c^4*d*x^4 + 3*a*c^2*d*x^2 - a*d + (b*c^6*d*x^6 - 3*b*c^4*d*x^4 + 3*b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^7 - x^5)]","A",0
74,1,599,0,1.232794," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b c^{9} d x^{9} - b c^{7} d x^{7}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) + {\left(3 \, b c^{5} d x^{5} - {\left(3 \, b c^{5} - 12 \, b c^{3} + 5 \, b c\right)} d x^{7} - 12 \, b c^{3} d x^{3} + 5 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 6 \, {\left(2 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 9 \, a c^{4} d x^{4} + 13 \, a c^{2} d x^{2} - 5 \, a d + {\left(2 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 9 \, b c^{4} d x^{4} + 13 \, b c^{2} d x^{2} - 5 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{210 \, {\left(c^{2} x^{9} - x^{7}\right)}}, \frac{12 \, {\left(b c^{9} d x^{9} - b c^{7} d x^{7}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(3 \, b c^{5} d x^{5} - {\left(3 \, b c^{5} - 12 \, b c^{3} + 5 \, b c\right)} d x^{7} - 12 \, b c^{3} d x^{3} + 5 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 6 \, {\left(2 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 9 \, a c^{4} d x^{4} + 13 \, a c^{2} d x^{2} - 5 \, a d + {\left(2 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 9 \, b c^{4} d x^{4} + 13 \, b c^{2} d x^{2} - 5 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{210 \, {\left(c^{2} x^{9} - x^{7}\right)}}\right]"," ",0,"[1/210*(6*(b*c^9*d*x^9 - b*c^7*d*x^7)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) + (3*b*c^5*d*x^5 - (3*b*c^5 - 12*b*c^3 + 5*b*c)*d*x^7 - 12*b*c^3*d*x^3 + 5*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 6*(2*a*c^8*d*x^8 - a*c^6*d*x^6 - 9*a*c^4*d*x^4 + 13*a*c^2*d*x^2 - 5*a*d + (2*b*c^8*d*x^8 - b*c^6*d*x^6 - 9*b*c^4*d*x^4 + 13*b*c^2*d*x^2 - 5*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7), 1/210*(12*(b*c^9*d*x^9 - b*c^7*d*x^7)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (3*b*c^5*d*x^5 - (3*b*c^5 - 12*b*c^3 + 5*b*c)*d*x^7 - 12*b*c^3*d*x^3 + 5*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 6*(2*a*c^8*d*x^8 - a*c^6*d*x^6 - 9*a*c^4*d*x^4 + 13*a*c^2*d*x^2 - 5*a*d + (2*b*c^8*d*x^8 - b*c^6*d*x^6 - 9*b*c^4*d*x^4 + 13*b*c^2*d*x^2 - 5*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7)]","A",0
75,1,671,0,0.896113," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^10,x, algorithm=""fricas"")","\left[\frac{96 \, {\left(b c^{11} d x^{11} - b c^{9} d x^{9}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) + {\left(48 \, b c^{7} d x^{7} + 18 \, b c^{5} d x^{5} - {\left(48 \, b c^{7} + 18 \, b c^{5} - 200 \, b c^{3} + 105 \, b c\right)} d x^{9} - 200 \, b c^{3} d x^{3} + 105 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 24 \, {\left(8 \, a c^{10} d x^{10} - 4 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 53 \, a c^{4} d x^{4} + 85 \, a c^{2} d x^{2} - 35 \, a d + {\left(8 \, b c^{10} d x^{10} - 4 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 53 \, b c^{4} d x^{4} + 85 \, b c^{2} d x^{2} - 35 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{7560 \, {\left(c^{2} x^{11} - x^{9}\right)}}, \frac{192 \, {\left(b c^{11} d x^{11} - b c^{9} d x^{9}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(48 \, b c^{7} d x^{7} + 18 \, b c^{5} d x^{5} - {\left(48 \, b c^{7} + 18 \, b c^{5} - 200 \, b c^{3} + 105 \, b c\right)} d x^{9} - 200 \, b c^{3} d x^{3} + 105 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 24 \, {\left(8 \, a c^{10} d x^{10} - 4 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 53 \, a c^{4} d x^{4} + 85 \, a c^{2} d x^{2} - 35 \, a d + {\left(8 \, b c^{10} d x^{10} - 4 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 53 \, b c^{4} d x^{4} + 85 \, b c^{2} d x^{2} - 35 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{7560 \, {\left(c^{2} x^{11} - x^{9}\right)}}\right]"," ",0,"[1/7560*(96*(b*c^11*d*x^11 - b*c^9*d*x^9)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) + (48*b*c^7*d*x^7 + 18*b*c^5*d*x^5 - (48*b*c^7 + 18*b*c^5 - 200*b*c^3 + 105*b*c)*d*x^9 - 200*b*c^3*d*x^3 + 105*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 24*(8*a*c^10*d*x^10 - 4*a*c^8*d*x^8 - a*c^6*d*x^6 - 53*a*c^4*d*x^4 + 85*a*c^2*d*x^2 - 35*a*d + (8*b*c^10*d*x^10 - 4*b*c^8*d*x^8 - b*c^6*d*x^6 - 53*b*c^4*d*x^4 + 85*b*c^2*d*x^2 - 35*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^11 - x^9), 1/7560*(192*(b*c^11*d*x^11 - b*c^9*d*x^9)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (48*b*c^7*d*x^7 + 18*b*c^5*d*x^5 - (48*b*c^7 + 18*b*c^5 - 200*b*c^3 + 105*b*c)*d*x^9 - 200*b*c^3*d*x^3 + 105*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 24*(8*a*c^10*d*x^10 - 4*a*c^8*d*x^8 - a*c^6*d*x^6 - 53*a*c^4*d*x^4 + 85*a*c^2*d*x^2 - 35*a*d + (8*b*c^10*d*x^10 - 4*b*c^8*d*x^8 - b*c^6*d*x^6 - 53*b*c^4*d*x^4 + 85*b*c^2*d*x^2 - 35*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^11 - x^9)]","A",0
76,1,743,0,0.806552," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^12,x, algorithm=""fricas"")","\left[\frac{48 \, {\left(b c^{13} d x^{13} - b c^{11} d x^{11}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) + {\left(24 \, b c^{9} d x^{9} + 9 \, b c^{7} d x^{7} - {\left(24 \, b c^{9} + 9 \, b c^{7} + 5 \, b c^{5} - 105 \, b c^{3} + 63 \, b c\right)} d x^{11} + 5 \, b c^{5} d x^{5} - 105 \, b c^{3} d x^{3} + 63 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 6 \, {\left(16 \, a c^{12} d x^{12} - 8 \, a c^{10} d x^{10} - 2 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 145 \, a c^{4} d x^{4} + 245 \, a c^{2} d x^{2} - 105 \, a d + {\left(16 \, b c^{12} d x^{12} - 8 \, b c^{10} d x^{10} - 2 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 145 \, b c^{4} d x^{4} + 245 \, b c^{2} d x^{2} - 105 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{6930 \, {\left(c^{2} x^{13} - x^{11}\right)}}, \frac{96 \, {\left(b c^{13} d x^{13} - b c^{11} d x^{11}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(24 \, b c^{9} d x^{9} + 9 \, b c^{7} d x^{7} - {\left(24 \, b c^{9} + 9 \, b c^{7} + 5 \, b c^{5} - 105 \, b c^{3} + 63 \, b c\right)} d x^{11} + 5 \, b c^{5} d x^{5} - 105 \, b c^{3} d x^{3} + 63 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 6 \, {\left(16 \, a c^{12} d x^{12} - 8 \, a c^{10} d x^{10} - 2 \, a c^{8} d x^{8} - a c^{6} d x^{6} - 145 \, a c^{4} d x^{4} + 245 \, a c^{2} d x^{2} - 105 \, a d + {\left(16 \, b c^{12} d x^{12} - 8 \, b c^{10} d x^{10} - 2 \, b c^{8} d x^{8} - b c^{6} d x^{6} - 145 \, b c^{4} d x^{4} + 245 \, b c^{2} d x^{2} - 105 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{6930 \, {\left(c^{2} x^{13} - x^{11}\right)}}\right]"," ",0,"[1/6930*(48*(b*c^13*d*x^13 - b*c^11*d*x^11)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) + (24*b*c^9*d*x^9 + 9*b*c^7*d*x^7 - (24*b*c^9 + 9*b*c^7 + 5*b*c^5 - 105*b*c^3 + 63*b*c)*d*x^11 + 5*b*c^5*d*x^5 - 105*b*c^3*d*x^3 + 63*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 6*(16*a*c^12*d*x^12 - 8*a*c^10*d*x^10 - 2*a*c^8*d*x^8 - a*c^6*d*x^6 - 145*a*c^4*d*x^4 + 245*a*c^2*d*x^2 - 105*a*d + (16*b*c^12*d*x^12 - 8*b*c^10*d*x^10 - 2*b*c^8*d*x^8 - b*c^6*d*x^6 - 145*b*c^4*d*x^4 + 245*b*c^2*d*x^2 - 105*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^13 - x^11), 1/6930*(96*(b*c^13*d*x^13 - b*c^11*d*x^11)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (24*b*c^9*d*x^9 + 9*b*c^7*d*x^7 - (24*b*c^9 + 9*b*c^7 + 5*b*c^5 - 105*b*c^3 + 63*b*c)*d*x^11 + 5*b*c^5*d*x^5 - 105*b*c^3*d*x^3 + 63*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 6*(16*a*c^12*d*x^12 - 8*a*c^10*d*x^10 - 2*a*c^8*d*x^8 - a*c^6*d*x^6 - 145*a*c^4*d*x^4 + 245*a*c^2*d*x^2 - 105*a*d + (16*b*c^12*d*x^12 - 8*b*c^10*d*x^10 - 2*b*c^8*d*x^8 - b*c^6*d*x^6 - 145*b*c^4*d*x^4 + 245*b*c^2*d*x^2 - 105*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^13 - x^11)]","A",0
77,1,249,0,1.014210," ","integrate(x^7*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{{\left(33075 \, b c^{11} d x^{11} - 53900 \, b c^{9} d x^{9} + 2475 \, b c^{7} d x^{7} + 4158 \, b c^{5} d x^{5} + 9240 \, b c^{3} d x^{3} + 55440 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 3465 \, {\left(105 \, a c^{12} d x^{12} - 245 \, a c^{10} d x^{10} + 145 \, a c^{8} d x^{8} + a c^{6} d x^{6} + 2 \, a c^{4} d x^{4} + 8 \, a c^{2} d x^{2} - 16 \, a d + {\left(105 \, b c^{12} d x^{12} - 245 \, b c^{10} d x^{10} + 145 \, b c^{8} d x^{8} + b c^{6} d x^{6} + 2 \, b c^{4} d x^{4} + 8 \, b c^{2} d x^{2} - 16 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{4002075 \, {\left(c^{10} x^{2} - c^{8}\right)}}"," ",0,"-1/4002075*((33075*b*c^11*d*x^11 - 53900*b*c^9*d*x^9 + 2475*b*c^7*d*x^7 + 4158*b*c^5*d*x^5 + 9240*b*c^3*d*x^3 + 55440*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 3465*(105*a*c^12*d*x^12 - 245*a*c^10*d*x^10 + 145*a*c^8*d*x^8 + a*c^6*d*x^6 + 2*a*c^4*d*x^4 + 8*a*c^2*d*x^2 - 16*a*d + (105*b*c^12*d*x^12 - 245*b*c^10*d*x^10 + 145*b*c^8*d*x^8 + b*c^6*d*x^6 + 2*b*c^4*d*x^4 + 8*b*c^2*d*x^2 - 16*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^10*x^2 - c^8)","A",0
78,1,219,0,2.061280," ","integrate(x^5*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{{\left(1225 \, b c^{9} d x^{9} - 2250 \, b c^{7} d x^{7} + 189 \, b c^{5} d x^{5} + 420 \, b c^{3} d x^{3} + 2520 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 315 \, {\left(35 \, a c^{10} d x^{10} - 85 \, a c^{8} d x^{8} + 53 \, a c^{6} d x^{6} + a c^{4} d x^{4} + 4 \, a c^{2} d x^{2} - 8 \, a d + {\left(35 \, b c^{10} d x^{10} - 85 \, b c^{8} d x^{8} + 53 \, b c^{6} d x^{6} + b c^{4} d x^{4} + 4 \, b c^{2} d x^{2} - 8 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{99225 \, {\left(c^{8} x^{2} - c^{6}\right)}}"," ",0,"-1/99225*((1225*b*c^9*d*x^9 - 2250*b*c^7*d*x^7 + 189*b*c^5*d*x^5 + 420*b*c^3*d*x^3 + 2520*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 315*(35*a*c^10*d*x^10 - 85*a*c^8*d*x^8 + 53*a*c^6*d*x^6 + a*c^4*d*x^4 + 4*a*c^2*d*x^2 - 8*a*d + (35*b*c^10*d*x^10 - 85*b*c^8*d*x^8 + 53*b*c^6*d*x^6 + b*c^4*d*x^4 + 4*b*c^2*d*x^2 - 8*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^8*x^2 - c^6)","A",0
79,1,189,0,0.546604," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{{\left(75 \, b c^{7} d x^{7} - 168 \, b c^{5} d x^{5} + 35 \, b c^{3} d x^{3} + 210 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 105 \, {\left(5 \, a c^{8} d x^{8} - 13 \, a c^{6} d x^{6} + 9 \, a c^{4} d x^{4} + a c^{2} d x^{2} - 2 \, a d + {\left(5 \, b c^{8} d x^{8} - 13 \, b c^{6} d x^{6} + 9 \, b c^{4} d x^{4} + b c^{2} d x^{2} - 2 \, b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{3675 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"-1/3675*((75*b*c^7*d*x^7 - 168*b*c^5*d*x^5 + 35*b*c^3*d*x^3 + 210*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 105*(5*a*c^8*d*x^8 - 13*a*c^6*d*x^6 + 9*a*c^4*d*x^4 + a*c^2*d*x^2 - 2*a*d + (5*b*c^8*d*x^8 - 13*b*c^6*d*x^6 + 9*b*c^4*d*x^4 + b*c^2*d*x^2 - 2*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
80,1,159,0,0.628279," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","-\frac{{\left(3 \, b c^{5} d x^{5} - 10 \, b c^{3} d x^{3} + 15 \, b c d x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 15 \, {\left(a c^{6} d x^{6} - 3 \, a c^{4} d x^{4} + 3 \, a c^{2} d x^{2} - a d + {\left(b c^{6} d x^{6} - 3 \, b c^{4} d x^{4} + 3 \, b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{75 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"-1/75*((3*b*c^5*d*x^5 - 10*b*c^3*d*x^3 + 15*b*c*d*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 15*(a*c^6*d*x^6 - 3*a*c^4*d*x^4 + 3*a*c^2*d*x^2 - a*d + (b*c^6*d*x^6 - 3*b*c^4*d*x^4 + 3*b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
81,0,0,0,0.679314," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x, x)","F",0
82,0,0,0,0.679544," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^3, x)","F",0
83,0,0,0,0.655455," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{5}}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^5, x)","F",0
84,0,0,0,1.382442," ","integrate(x^4*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} x^{8} - 2 \, a c^{2} d^{2} x^{6} + a d^{2} x^{4} + {\left(b c^{4} d^{2} x^{8} - 2 \, b c^{2} d^{2} x^{6} + b d^{2} x^{4}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((a*c^4*d^2*x^8 - 2*a*c^2*d^2*x^6 + a*d^2*x^4 + (b*c^4*d^2*x^8 - 2*b*c^2*d^2*x^6 + b*d^2*x^4)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
85,0,0,0,1.472697," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} x^{6} - 2 \, a c^{2} d^{2} x^{4} + a d^{2} x^{2} + {\left(b c^{4} d^{2} x^{6} - 2 \, b c^{2} d^{2} x^{4} + b d^{2} x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((a*c^4*d^2*x^6 - 2*a*c^2*d^2*x^4 + a*d^2*x^2 + (b*c^4*d^2*x^6 - 2*b*c^2*d^2*x^4 + b*d^2*x^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
86,0,0,0,0.690957," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
87,0,0,0,0.611571," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^2, x)","F",0
88,0,0,0,3.441947," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^4, x)","F",0
89,0,0,0,0.777378," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{6}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^6, x)","F",0
90,1,655,0,0.767567," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(b c^{9} d^{2} x^{9} - b c^{7} d^{2} x^{7}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) + {\left(18 \, b c^{5} d^{2} x^{5} - {\left(18 \, b c^{5} - 9 \, b c^{3} + 2 \, b c\right)} d^{2} x^{7} - 9 \, b c^{3} d^{2} x^{3} + 2 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 12 \, {\left(a c^{8} d^{2} x^{8} - 4 \, a c^{6} d^{2} x^{6} + 6 \, a c^{4} d^{2} x^{4} - 4 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{8} d^{2} x^{8} - 4 \, b c^{6} d^{2} x^{6} + 6 \, b c^{4} d^{2} x^{4} - 4 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{84 \, {\left(c^{2} x^{9} - x^{7}\right)}}, -\frac{12 \, {\left(b c^{9} d^{2} x^{9} - b c^{7} d^{2} x^{7}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) - {\left(18 \, b c^{5} d^{2} x^{5} - {\left(18 \, b c^{5} - 9 \, b c^{3} + 2 \, b c\right)} d^{2} x^{7} - 9 \, b c^{3} d^{2} x^{3} + 2 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 12 \, {\left(a c^{8} d^{2} x^{8} - 4 \, a c^{6} d^{2} x^{6} + 6 \, a c^{4} d^{2} x^{4} - 4 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{8} d^{2} x^{8} - 4 \, b c^{6} d^{2} x^{6} + 6 \, b c^{4} d^{2} x^{4} - 4 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{84 \, {\left(c^{2} x^{9} - x^{7}\right)}}\right]"," ",0,"[1/84*(6*(b*c^9*d^2*x^9 - b*c^7*d^2*x^7)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) + (18*b*c^5*d^2*x^5 - (18*b*c^5 - 9*b*c^3 + 2*b*c)*d^2*x^7 - 9*b*c^3*d^2*x^3 + 2*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 12*(a*c^8*d^2*x^8 - 4*a*c^6*d^2*x^6 + 6*a*c^4*d^2*x^4 - 4*a*c^2*d^2*x^2 + a*d^2 + (b*c^8*d^2*x^8 - 4*b*c^6*d^2*x^6 + 6*b*c^4*d^2*x^4 - 4*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7), -1/84*(12*(b*c^9*d^2*x^9 - b*c^7*d^2*x^7)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) - (18*b*c^5*d^2*x^5 - (18*b*c^5 - 9*b*c^3 + 2*b*c)*d^2*x^7 - 9*b*c^3*d^2*x^3 + 2*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 12*(a*c^8*d^2*x^8 - 4*a*c^6*d^2*x^6 + 6*a*c^4*d^2*x^4 - 4*a*c^2*d^2*x^2 + a*d^2 + (b*c^8*d^2*x^8 - 4*b*c^6*d^2*x^6 + 6*b*c^4*d^2*x^4 - 4*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^9 - x^7)]","A",0
91,1,747,0,0.857500," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^10,x, algorithm=""fricas"")","\left[\frac{24 \, {\left(b c^{11} d^{2} x^{11} - b c^{9} d^{2} x^{9}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - {\left(12 \, b c^{7} d^{2} x^{7} - 90 \, b c^{5} d^{2} x^{5} - {\left(12 \, b c^{7} - 90 \, b c^{5} + 76 \, b c^{3} - 21 \, b c\right)} d^{2} x^{9} + 76 \, b c^{3} d^{2} x^{3} - 21 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 24 \, {\left(2 \, a c^{10} d^{2} x^{10} - a c^{8} d^{2} x^{8} - 16 \, a c^{6} d^{2} x^{6} + 34 \, a c^{4} d^{2} x^{4} - 26 \, a c^{2} d^{2} x^{2} + 7 \, a d^{2} + {\left(2 \, b c^{10} d^{2} x^{10} - b c^{8} d^{2} x^{8} - 16 \, b c^{6} d^{2} x^{6} + 34 \, b c^{4} d^{2} x^{4} - 26 \, b c^{2} d^{2} x^{2} + 7 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{1512 \, {\left(c^{2} x^{11} - x^{9}\right)}}, -\frac{48 \, {\left(b c^{11} d^{2} x^{11} - b c^{9} d^{2} x^{9}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(12 \, b c^{7} d^{2} x^{7} - 90 \, b c^{5} d^{2} x^{5} - {\left(12 \, b c^{7} - 90 \, b c^{5} + 76 \, b c^{3} - 21 \, b c\right)} d^{2} x^{9} + 76 \, b c^{3} d^{2} x^{3} - 21 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 24 \, {\left(2 \, a c^{10} d^{2} x^{10} - a c^{8} d^{2} x^{8} - 16 \, a c^{6} d^{2} x^{6} + 34 \, a c^{4} d^{2} x^{4} - 26 \, a c^{2} d^{2} x^{2} + 7 \, a d^{2} + {\left(2 \, b c^{10} d^{2} x^{10} - b c^{8} d^{2} x^{8} - 16 \, b c^{6} d^{2} x^{6} + 34 \, b c^{4} d^{2} x^{4} - 26 \, b c^{2} d^{2} x^{2} + 7 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{1512 \, {\left(c^{2} x^{11} - x^{9}\right)}}\right]"," ",0,"[1/1512*(24*(b*c^11*d^2*x^11 - b*c^9*d^2*x^9)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - (12*b*c^7*d^2*x^7 - 90*b*c^5*d^2*x^5 - (12*b*c^7 - 90*b*c^5 + 76*b*c^3 - 21*b*c)*d^2*x^9 + 76*b*c^3*d^2*x^3 - 21*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 24*(2*a*c^10*d^2*x^10 - a*c^8*d^2*x^8 - 16*a*c^6*d^2*x^6 + 34*a*c^4*d^2*x^4 - 26*a*c^2*d^2*x^2 + 7*a*d^2 + (2*b*c^10*d^2*x^10 - b*c^8*d^2*x^8 - 16*b*c^6*d^2*x^6 + 34*b*c^4*d^2*x^4 - 26*b*c^2*d^2*x^2 + 7*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^11 - x^9), -1/1512*(48*(b*c^11*d^2*x^11 - b*c^9*d^2*x^9)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (12*b*c^7*d^2*x^7 - 90*b*c^5*d^2*x^5 - (12*b*c^7 - 90*b*c^5 + 76*b*c^3 - 21*b*c)*d^2*x^9 + 76*b*c^3*d^2*x^3 - 21*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 24*(2*a*c^10*d^2*x^10 - a*c^8*d^2*x^8 - 16*a*c^6*d^2*x^6 + 34*a*c^4*d^2*x^4 - 26*a*c^2*d^2*x^2 + 7*a*d^2 + (2*b*c^10*d^2*x^10 - b*c^8*d^2*x^8 - 16*b*c^6*d^2*x^6 + 34*b*c^4*d^2*x^4 - 26*b*c^2*d^2*x^2 + 7*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^11 - x^9)]","A",0
92,1,831,0,0.958453," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^12,x, algorithm=""fricas"")","\left[\frac{480 \, {\left(b c^{13} d^{2} x^{13} - b c^{11} d^{2} x^{11}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} + \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - {\left(240 \, b c^{9} d^{2} x^{9} + 90 \, b c^{7} d^{2} x^{7} - {\left(240 \, b c^{9} + 90 \, b c^{7} - 2260 \, b c^{5} + 2415 \, b c^{3} - 756 \, b c\right)} d^{2} x^{11} - 2260 \, b c^{5} d^{2} x^{5} + 2415 \, b c^{3} d^{2} x^{3} - 756 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 120 \, {\left(8 \, a c^{12} d^{2} x^{12} - 4 \, a c^{10} d^{2} x^{10} - a c^{8} d^{2} x^{8} - 116 \, a c^{6} d^{2} x^{6} + 274 \, a c^{4} d^{2} x^{4} - 224 \, a c^{2} d^{2} x^{2} + 63 \, a d^{2} + {\left(8 \, b c^{12} d^{2} x^{12} - 4 \, b c^{10} d^{2} x^{10} - b c^{8} d^{2} x^{8} - 116 \, b c^{6} d^{2} x^{6} + 274 \, b c^{4} d^{2} x^{4} - 224 \, b c^{2} d^{2} x^{2} + 63 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{83160 \, {\left(c^{2} x^{13} - x^{11}\right)}}, -\frac{960 \, {\left(b c^{13} d^{2} x^{13} - b c^{11} d^{2} x^{11}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) + {\left(240 \, b c^{9} d^{2} x^{9} + 90 \, b c^{7} d^{2} x^{7} - {\left(240 \, b c^{9} + 90 \, b c^{7} - 2260 \, b c^{5} + 2415 \, b c^{3} - 756 \, b c\right)} d^{2} x^{11} - 2260 \, b c^{5} d^{2} x^{5} + 2415 \, b c^{3} d^{2} x^{3} - 756 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 120 \, {\left(8 \, a c^{12} d^{2} x^{12} - 4 \, a c^{10} d^{2} x^{10} - a c^{8} d^{2} x^{8} - 116 \, a c^{6} d^{2} x^{6} + 274 \, a c^{4} d^{2} x^{4} - 224 \, a c^{2} d^{2} x^{2} + 63 \, a d^{2} + {\left(8 \, b c^{12} d^{2} x^{12} - 4 \, b c^{10} d^{2} x^{10} - b c^{8} d^{2} x^{8} - 116 \, b c^{6} d^{2} x^{6} + 274 \, b c^{4} d^{2} x^{4} - 224 \, b c^{2} d^{2} x^{2} + 63 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{83160 \, {\left(c^{2} x^{13} - x^{11}\right)}}\right]"," ",0,"[1/83160*(480*(b*c^13*d^2*x^13 - b*c^11*d^2*x^11)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 + sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - (240*b*c^9*d^2*x^9 + 90*b*c^7*d^2*x^7 - (240*b*c^9 + 90*b*c^7 - 2260*b*c^5 + 2415*b*c^3 - 756*b*c)*d^2*x^11 - 2260*b*c^5*d^2*x^5 + 2415*b*c^3*d^2*x^3 - 756*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 120*(8*a*c^12*d^2*x^12 - 4*a*c^10*d^2*x^10 - a*c^8*d^2*x^8 - 116*a*c^6*d^2*x^6 + 274*a*c^4*d^2*x^4 - 224*a*c^2*d^2*x^2 + 63*a*d^2 + (8*b*c^12*d^2*x^12 - 4*b*c^10*d^2*x^10 - b*c^8*d^2*x^8 - 116*b*c^6*d^2*x^6 + 274*b*c^4*d^2*x^4 - 224*b*c^2*d^2*x^2 + 63*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^13 - x^11), -1/83160*(960*(b*c^13*d^2*x^13 - b*c^11*d^2*x^11)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) + (240*b*c^9*d^2*x^9 + 90*b*c^7*d^2*x^7 - (240*b*c^9 + 90*b*c^7 - 2260*b*c^5 + 2415*b*c^3 - 756*b*c)*d^2*x^11 - 2260*b*c^5*d^2*x^5 + 2415*b*c^3*d^2*x^3 - 756*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 120*(8*a*c^12*d^2*x^12 - 4*a*c^10*d^2*x^10 - a*c^8*d^2*x^8 - 116*a*c^6*d^2*x^6 + 274*a*c^4*d^2*x^4 - 224*a*c^2*d^2*x^2 + 63*a*d^2 + (8*b*c^12*d^2*x^12 - 4*b*c^10*d^2*x^10 - b*c^8*d^2*x^8 - 116*b*c^6*d^2*x^6 + 274*b*c^4*d^2*x^4 - 224*b*c^2*d^2*x^2 + 63*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^2*x^13 - x^11)]","A",0
93,1,291,0,1.221071," ","integrate(x^5*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(19845 \, b c^{11} d^{2} x^{11} - 61985 \, b c^{9} d^{2} x^{9} + 55935 \, b c^{7} d^{2} x^{7} - 2079 \, b c^{5} d^{2} x^{5} - 4620 \, b c^{3} d^{2} x^{3} - 27720 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 3465 \, {\left(63 \, a c^{12} d^{2} x^{12} - 224 \, a c^{10} d^{2} x^{10} + 274 \, a c^{8} d^{2} x^{8} - 116 \, a c^{6} d^{2} x^{6} - a c^{4} d^{2} x^{4} - 4 \, a c^{2} d^{2} x^{2} + 8 \, a d^{2} + {\left(63 \, b c^{12} d^{2} x^{12} - 224 \, b c^{10} d^{2} x^{10} + 274 \, b c^{8} d^{2} x^{8} - 116 \, b c^{6} d^{2} x^{6} - b c^{4} d^{2} x^{4} - 4 \, b c^{2} d^{2} x^{2} + 8 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{2401245 \, {\left(c^{8} x^{2} - c^{6}\right)}}"," ",0,"1/2401245*((19845*b*c^11*d^2*x^11 - 61985*b*c^9*d^2*x^9 + 55935*b*c^7*d^2*x^7 - 2079*b*c^5*d^2*x^5 - 4620*b*c^3*d^2*x^3 - 27720*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 3465*(63*a*c^12*d^2*x^12 - 224*a*c^10*d^2*x^10 + 274*a*c^8*d^2*x^8 - 116*a*c^6*d^2*x^6 - a*c^4*d^2*x^4 - 4*a*c^2*d^2*x^2 + 8*a*d^2 + (63*b*c^12*d^2*x^12 - 224*b*c^10*d^2*x^10 + 274*b*c^8*d^2*x^8 - 116*b*c^6*d^2*x^6 - b*c^4*d^2*x^4 - 4*b*c^2*d^2*x^2 + 8*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^8*x^2 - c^6)","A",0
94,1,255,0,0.532871," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(49 \, b c^{9} d^{2} x^{9} - 171 \, b c^{7} d^{2} x^{7} + 189 \, b c^{5} d^{2} x^{5} - 21 \, b c^{3} d^{2} x^{3} - 126 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 63 \, {\left(7 \, a c^{10} d^{2} x^{10} - 26 \, a c^{8} d^{2} x^{8} + 34 \, a c^{6} d^{2} x^{6} - 16 \, a c^{4} d^{2} x^{4} - a c^{2} d^{2} x^{2} + 2 \, a d^{2} + {\left(7 \, b c^{10} d^{2} x^{10} - 26 \, b c^{8} d^{2} x^{8} + 34 \, b c^{6} d^{2} x^{6} - 16 \, b c^{4} d^{2} x^{4} - b c^{2} d^{2} x^{2} + 2 \, b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{3969 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"1/3969*((49*b*c^9*d^2*x^9 - 171*b*c^7*d^2*x^7 + 189*b*c^5*d^2*x^5 - 21*b*c^3*d^2*x^3 - 126*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 63*(7*a*c^10*d^2*x^10 - 26*a*c^8*d^2*x^8 + 34*a*c^6*d^2*x^6 - 16*a*c^4*d^2*x^4 - a*c^2*d^2*x^2 + 2*a*d^2 + (7*b*c^10*d^2*x^10 - 26*b*c^8*d^2*x^8 + 34*b*c^6*d^2*x^6 - 16*b*c^4*d^2*x^4 - b*c^2*d^2*x^2 + 2*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
95,1,215,0,0.713219," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{{\left(5 \, b c^{7} d^{2} x^{7} - 21 \, b c^{5} d^{2} x^{5} + 35 \, b c^{3} d^{2} x^{3} - 35 \, b c d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 35 \, {\left(a c^{8} d^{2} x^{8} - 4 \, a c^{6} d^{2} x^{6} + 6 \, a c^{4} d^{2} x^{4} - 4 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{8} d^{2} x^{8} - 4 \, b c^{6} d^{2} x^{6} + 6 \, b c^{4} d^{2} x^{4} - 4 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{245 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"1/245*((5*b*c^7*d^2*x^7 - 21*b*c^5*d^2*x^5 + 35*b*c^3*d^2*x^3 - 35*b*c*d^2*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 35*(a*c^8*d^2*x^8 - 4*a*c^6*d^2*x^6 + 6*a*c^4*d^2*x^4 - 4*a*c^2*d^2*x^2 + a*d^2 + (b*c^8*d^2*x^8 - 4*b*c^6*d^2*x^6 + 6*b*c^4*d^2*x^4 - 4*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
96,0,0,0,1.570930," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x, x)","F",0
97,0,0,0,0.686081," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^3, x)","F",0
98,0,0,0,0.748288," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{5}}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^5, x)","F",0
99,1,26,0,1.948248," ","integrate(arcsin(x)*(-x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{-x^{2} + 1} x \arcsin\left(x\right) - \frac{1}{4} \, x^{2} + \frac{1}{4} \, \arcsin\left(x\right)^{2}"," ",0,"1/2*sqrt(-x^2 + 1)*x*arcsin(x) - 1/4*x^2 + 1/4*arcsin(x)^2","A",0
100,0,0,0,0.830887," ","integrate((a+b*arcsin(c*x))*(-pi*c^2*x^2+pi)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\pi - \pi c^{2} x^{2}} {\left(b \arcsin\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(pi - pi*c^2*x^2)*(b*arcsin(c*x) + a), x)","F",0
101,1,60,0,3.429559," ","integrate(x^4*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a^{4} x^{4} + 3 \, a^{2} x^{2} - 2 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right) + 3 \, \arcsin\left(a x\right)^{2}}{16 \, a^{5}}"," ",0,"1/16*(a^4*x^4 + 3*a^2*x^2 - 2*(2*a^3*x^3 + 3*a*x)*sqrt(-a^2*x^2 + 1)*arcsin(a*x) + 3*arcsin(a*x)^2)/a^5","A",0
102,1,44,0,0.497415," ","integrate(x^3*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 3 \, {\left(a^{2} x^{2} + 2\right)} \sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right) + 6 \, a x}{9 \, a^{4}}"," ",0,"1/9*(a^3*x^3 - 3*(a^2*x^2 + 2)*sqrt(-a^2*x^2 + 1)*arcsin(a*x) + 6*a*x)/a^4","A",0
103,1,39,0,2.427477," ","integrate(x^2*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a^{2} x^{2} - 2 \, \sqrt{-a^{2} x^{2} + 1} a x \arcsin\left(a x\right) + \arcsin\left(a x\right)^{2}}{4 \, a^{3}}"," ",0,"1/4*(a^2*x^2 - 2*sqrt(-a^2*x^2 + 1)*a*x*arcsin(a*x) + arcsin(a*x)^2)/a^3","A",0
104,1,26,0,0.654001," ","integrate(x*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a x - \sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{a^{2}}"," ",0,"(a*x - sqrt(-a^2*x^2 + 1)*arcsin(a*x))/a^2","A",0
105,1,11,0,0.554142," ","integrate(arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\arcsin\left(a x\right)^{2}}{2 \, a}"," ",0,"1/2*arcsin(a*x)^2/a","A",0
106,0,0,0,2.026036," ","integrate(arcsin(a*x)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)/(a^2*x^3 - x), x)","F",0
107,1,28,0,0.965513," ","integrate(arcsin(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{a x \log\left(x\right) - \sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{x}"," ",0,"(a*x*log(x) - sqrt(-a^2*x^2 + 1)*arcsin(a*x))/x","A",0
108,0,0,0,1.369309," ","integrate(arcsin(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)/(a^2*x^5 - x^3), x)","F",0
109,1,150,0,0.743197," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(9 \, b c^{5} x^{5} + 20 \, b c^{3} x^{3} + 120 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 15 \, {\left(3 \, a c^{6} x^{6} + a c^{4} x^{4} + 4 \, a c^{2} x^{2} + {\left(3 \, b c^{6} x^{6} + b c^{4} x^{4} + 4 \, b c^{2} x^{2} - 8 \, b\right)} \arcsin\left(c x\right) - 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{225 \, {\left(c^{8} d x^{2} - c^{6} d\right)}}"," ",0,"-1/225*((9*b*c^5*x^5 + 20*b*c^3*x^3 + 120*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 15*(3*a*c^6*x^6 + a*c^4*x^4 + 4*a*c^2*x^2 + (3*b*c^6*x^6 + b*c^4*x^4 + 4*b*c^2*x^2 - 8*b)*arcsin(c*x) - 8*a)*sqrt(-c^2*d*x^2 + d))/(c^8*d*x^2 - c^6*d)","A",0
110,0,0,0,1.559832," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} \arcsin\left(c x\right) + a x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*x^4*arcsin(c*x) + a*x^4)*sqrt(-c^2*d*x^2 + d)/(c^2*d*x^2 - d), x)","F",0
111,1,120,0,0.580123," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(b c^{3} x^{3} + 6 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 3 \, {\left(a c^{4} x^{4} + a c^{2} x^{2} + {\left(b c^{4} x^{4} + b c^{2} x^{2} - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{9 \, {\left(c^{6} d x^{2} - c^{4} d\right)}}"," ",0,"-1/9*((b*c^3*x^3 + 6*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 3*(a*c^4*x^4 + a*c^2*x^2 + (b*c^4*x^4 + b*c^2*x^2 - 2*b)*arcsin(c*x) - 2*a)*sqrt(-c^2*d*x^2 + d))/(c^6*d*x^2 - c^4*d)","A",0
112,0,0,0,1.044799," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b x^{2} \arcsin\left(c x\right) + a x^{2}\right)}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*x^2*arcsin(c*x) + a*x^2)/(c^2*d*x^2 - d), x)","F",0
113,1,92,0,1.368188," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x + {\left(a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d x^{2} - c^{2} d}"," ",0,"-(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x + (a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a)*sqrt(-c^2*d*x^2 + d))/(c^4*d*x^2 - c^2*d)","A",0
114,0,0,0,1.075500," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^2*d*x^2 - d), x)","F",0
115,0,0,0,1.084087," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d x^{3} - d x}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^2*d*x^3 - d*x), x)","F",0
116,1,218,0,0.910283," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{b c \sqrt{d} x \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - 2 \, \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{2 \, d x}, \frac{b c \sqrt{-d} x \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) - \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{d x}\right]"," ",0,"[1/2*(b*c*sqrt(d)*x*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - 2*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(d*x), (b*c*sqrt(-d)*x*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) - sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(d*x)]","A",0
117,0,0,0,1.871924," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d x^{5} - d x^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^2*d*x^5 - d*x^3), x)","F",0
118,1,433,0,1.517265," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b c^{5} x^{5} - b c^{3} x^{3}\right)} \sqrt{d} \log\left(\frac{c^{2} d x^{6} + c^{2} d x^{2} - d x^{4} - \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{4} - 1\right)} \sqrt{d} - d}{c^{2} x^{4} - x^{2}}\right) - \sqrt{-c^{2} d x^{2} + d} {\left(b c x^{3} - b c x\right)} \sqrt{-c^{2} x^{2} + 1} - 2 \, {\left(2 \, a c^{4} x^{4} - a c^{2} x^{2} + {\left(2 \, b c^{4} x^{4} - b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a\right)} \sqrt{-c^{2} d x^{2} + d}}{6 \, {\left(c^{2} d x^{5} - d x^{3}\right)}}, \frac{4 \, {\left(b c^{5} x^{5} - b c^{3} x^{3}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} {\left(x^{2} + 1\right)} \sqrt{-d}}{c^{2} d x^{4} - {\left(c^{2} + 1\right)} d x^{2} + d}\right) - \sqrt{-c^{2} d x^{2} + d} {\left(b c x^{3} - b c x\right)} \sqrt{-c^{2} x^{2} + 1} - 2 \, {\left(2 \, a c^{4} x^{4} - a c^{2} x^{2} + {\left(2 \, b c^{4} x^{4} - b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a\right)} \sqrt{-c^{2} d x^{2} + d}}{6 \, {\left(c^{2} d x^{5} - d x^{3}\right)}}\right]"," ",0,"[1/6*(2*(b*c^5*x^5 - b*c^3*x^3)*sqrt(d)*log((c^2*d*x^6 + c^2*d*x^2 - d*x^4 - sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^4 - 1)*sqrt(d) - d)/(c^2*x^4 - x^2)) - sqrt(-c^2*d*x^2 + d)*(b*c*x^3 - b*c*x)*sqrt(-c^2*x^2 + 1) - 2*(2*a*c^4*x^4 - a*c^2*x^2 + (2*b*c^4*x^4 - b*c^2*x^2 - b)*arcsin(c*x) - a)*sqrt(-c^2*d*x^2 + d))/(c^2*d*x^5 - d*x^3), 1/6*(4*(b*c^5*x^5 - b*c^3*x^3)*sqrt(-d)*arctan(sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*(x^2 + 1)*sqrt(-d)/(c^2*d*x^4 - (c^2 + 1)*d*x^2 + d)) - sqrt(-c^2*d*x^2 + d)*(b*c*x^3 - b*c*x)*sqrt(-c^2*x^2 + 1) - 2*(2*a*c^4*x^4 - a*c^2*x^2 + (2*b*c^4*x^4 - b*c^2*x^2 - b)*arcsin(c*x) - a)*sqrt(-c^2*d*x^2 + d))/(c^2*d*x^5 - d*x^3)]","A",0
119,1,441,0,1.007333," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{9 \, {\left(b c^{2} x^{2} - b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} + 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) + 4 \, {\left(b c^{3} x^{3} + 15 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + 12 \, {\left(a c^{4} x^{4} + 4 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} + 4 \, b c^{2} x^{2} - 8 \, b\right)} \arcsin\left(c x\right) - 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{36 \, {\left(c^{8} d^{2} x^{2} - c^{6} d^{2}\right)}}, -\frac{9 \, {\left(b c^{2} x^{2} - b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) - 2 \, {\left(b c^{3} x^{3} + 15 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 6 \, {\left(a c^{4} x^{4} + 4 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} + 4 \, b c^{2} x^{2} - 8 \, b\right)} \arcsin\left(c x\right) - 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{18 \, {\left(c^{8} d^{2} x^{2} - c^{6} d^{2}\right)}}\right]"," ",0,"[1/36*(9*(b*c^2*x^2 - b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 + 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) + 4*(b*c^3*x^3 + 15*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + 12*(a*c^4*x^4 + 4*a*c^2*x^2 + (b*c^4*x^4 + 4*b*c^2*x^2 - 8*b)*arcsin(c*x) - 8*a)*sqrt(-c^2*d*x^2 + d))/(c^8*d^2*x^2 - c^6*d^2), -1/18*(9*(b*c^2*x^2 - b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) - 2*(b*c^3*x^3 + 15*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 6*(a*c^4*x^4 + 4*a*c^2*x^2 + (b*c^4*x^4 + 4*b*c^2*x^2 - 8*b)*arcsin(c*x) - 8*a)*sqrt(-c^2*d*x^2 + d))/(c^8*d^2*x^2 - c^6*d^2)]","A",0
120,0,0,0,0.416957," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \arcsin\left(c x\right) + a x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^4*arcsin(c*x) + a*x^4)*sqrt(-c^2*d*x^2 + d)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
121,1,382,0,0.719066," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x + {\left(b c^{2} x^{2} - b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} + 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) + 4 \, {\left(a c^{2} x^{2} + {\left(b c^{2} x^{2} - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{4 \, {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)}}, \frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x - {\left(b c^{2} x^{2} - b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) + 2 \, {\left(a c^{2} x^{2} + {\left(b c^{2} x^{2} - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{2 \, {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)}}\right]"," ",0,"[1/4*(4*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x + (b*c^2*x^2 - b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 + 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) + 4*(a*c^2*x^2 + (b*c^2*x^2 - 2*b)*arcsin(c*x) - 2*a)*sqrt(-c^2*d*x^2 + d))/(c^6*d^2*x^2 - c^4*d^2), 1/2*(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x - (b*c^2*x^2 - b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) + 2*(a*c^2*x^2 + (b*c^2*x^2 - 2*b)*arcsin(c*x) - 2*a)*sqrt(-c^2*d*x^2 + d))/(c^6*d^2*x^2 - c^4*d^2)]","A",0
122,0,0,0,0.606143," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b x^{2} \arcsin\left(c x\right) + a x^{2}\right)}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*x^2*arcsin(c*x) + a*x^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
123,1,279,0,0.699164," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{2} x^{2} - b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} + 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) - 4 \, \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{4 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}, -\frac{{\left(b c^{2} x^{2} - b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) + 2 \, \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}\right]"," ",0,"[1/4*((b*c^2*x^2 - b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 + 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) - 4*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(c^4*d^2*x^2 - c^2*d^2), -1/2*((b*c^2*x^2 - b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) + 2*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(c^4*d^2*x^2 - c^2*d^2)]","A",0
124,0,0,0,0.653043," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
125,0,0,0,0.618037," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
126,0,0,0,15.029532," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
127,0,0,0,0.535657," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
128,0,0,0,19.557784," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
129,0,0,0,0.723454," ","integrate(x^6*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{6} \arcsin\left(c x\right) + a x^{6}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*x^6*arcsin(c*x) + a*x^6)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
130,1,481,0,1.138932," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{11 \, {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} - 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) - 4 \, {\left(6 \, b c^{3} x^{3} - 5 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 8 \, {\left(3 \, a c^{4} x^{4} - 12 \, a c^{2} x^{2} + {\left(3 \, b c^{4} x^{4} - 12 \, b c^{2} x^{2} + 8 \, b\right)} \arcsin\left(c x\right) + 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{24 \, {\left(c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)}}, \frac{11 \, {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) - 2 \, {\left(6 \, b c^{3} x^{3} - 5 \, b c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} - 4 \, {\left(3 \, a c^{4} x^{4} - 12 \, a c^{2} x^{2} + {\left(3 \, b c^{4} x^{4} - 12 \, b c^{2} x^{2} + 8 \, b\right)} \arcsin\left(c x\right) + 8 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{12 \, {\left(c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)}}\right]"," ",0,"[1/24*(11*(b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 - 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) - 4*(6*b*c^3*x^3 - 5*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 8*(3*a*c^4*x^4 - 12*a*c^2*x^2 + (3*b*c^4*x^4 - 12*b*c^2*x^2 + 8*b)*arcsin(c*x) + 8*a)*sqrt(-c^2*d*x^2 + d))/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3), 1/12*(11*(b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) - 2*(6*b*c^3*x^3 - 5*b*c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) - 4*(3*a*c^4*x^4 - 12*a*c^2*x^2 + (3*b*c^4*x^4 - 12*b*c^2*x^2 + 8*b)*arcsin(c*x) + 8*a)*sqrt(-c^2*d*x^2 + d))/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3)]","A",0
131,0,0,0,2.929525," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} \arcsin\left(c x\right) + a x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*x^4*arcsin(c*x) + a*x^4)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
132,1,421,0,2.885141," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x - 5 \, {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} - 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) - 8 \, {\left(3 \, a c^{2} x^{2} + {\left(3 \, b c^{2} x^{2} - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{24 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}, -\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x - 5 \, {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) - 4 \, {\left(3 \, a c^{2} x^{2} + {\left(3 \, b c^{2} x^{2} - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{-c^{2} d x^{2} + d}}{12 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}\right]"," ",0,"[-1/24*(4*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x - 5*(b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 - 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) - 8*(3*a*c^2*x^2 + (3*b*c^2*x^2 - 2*b)*arcsin(c*x) - 2*a)*sqrt(-c^2*d*x^2 + d))/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3), -1/12*(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x - 5*(b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) - 4*(3*a*c^2*x^2 + (3*b*c^2*x^2 - 2*b)*arcsin(c*x) - 2*a)*sqrt(-c^2*d*x^2 + d))/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)]","A",0
133,0,0,0,0.877287," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b x^{2} \arcsin\left(c x\right) + a x^{2}\right)}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*x^2*arcsin(c*x) + a*x^2)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
134,1,374,0,1.219090," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x - {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{d} \log\left(-\frac{c^{6} d x^{6} + 5 \, c^{4} d x^{4} - 5 \, c^{2} d x^{2} + 4 \, {\left(c^{3} x^{3} + c x\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} \sqrt{d} - d}{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1}\right) - 8 \, \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{24 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}, -\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} b c x + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \sqrt{-d} \arctan\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} c \sqrt{-d} x}{c^{4} d x^{4} - d}\right) - 4 \, \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{12 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}\right]"," ",0,"[-1/24*(4*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x - (b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(d)*log(-(c^6*d*x^6 + 5*c^4*d*x^4 - 5*c^2*d*x^2 + 4*(c^3*x^3 + c*x)*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*sqrt(d) - d)/(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)) - 8*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3), -1/12*(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*b*c*x + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*sqrt(-d)*arctan(2*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1)*c*sqrt(-d)*x/(c^4*d*x^4 - d)) - 4*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a))/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)]","A",0
135,0,0,0,0.740253," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
136,0,0,0,0.851227," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x)","F",0
137,0,0,0,13.036266," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x)","F",0
138,0,0,0,1.266067," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3), x)","F",0
139,0,0,0,1.188216," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} x^{10} - 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} - d^{3} x^{4}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)/(c^6*d^3*x^10 - 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 - d^3*x^4), x)","F",0
140,0,0,0,1.940636," ","integrate(arcsin(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)}{a^{8} c^{4} x^{8} - 4 \, a^{6} c^{4} x^{6} + 6 \, a^{4} c^{4} x^{4} - 4 \, a^{2} c^{4} x^{2} + c^{4}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)/(a^8*c^4*x^8 - 4*a^6*c^4*x^6 + 6*a^4*c^4*x^4 - 4*a^2*c^4*x^2 + c^4), x)","F",0
141,0,0,0,0.880947," ","integrate((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} {\left(b f x \arcsin\left(c x\right) + a f x\right)} \sqrt{f x}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*(b*f*x*arcsin(c*x) + a*f*x)*sqrt(f*x)/(c^2*x^2 - 1), x)","F",0
142,0,0,0,0.548396," ","integrate((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b f x \arcsin\left(c x\right) + a f x\right)} \sqrt{f x}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*f*x*arcsin(c*x) + a*f*x)*sqrt(f*x)/(c^2*d*x^2 - d), x)","F",0
143,0,0,0,0.690896," ","integrate(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{6} d^{3} x^{6} - 3 \, a c^{4} d^{3} x^{4} + 3 \, a c^{2} d^{3} x^{2} - a d^{3} + {\left(b c^{6} d^{3} x^{6} - 3 \, b c^{4} d^{3} x^{4} + 3 \, b c^{2} d^{3} x^{2} - b d^{3}\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral(-(a*c^6*d^3*x^6 - 3*a*c^4*d^3*x^4 + 3*a*c^2*d^3*x^2 - a*d^3 + (b*c^6*d^3*x^6 - 3*b*c^4*d^3*x^4 + 3*b*c^2*d^3*x^2 - b*d^3)*arcsin(c*x))*x^m, x)","F",0
144,0,0,0,1.646857," ","integrate(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*x^m, x)","F",0
145,0,0,0,0.726654," ","integrate(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*x^m, x)","F",0
146,0,0,0,0.726847," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)*x^m/(c^2*d*x^2 - d), x)","F",0
147,0,0,0,0.808326," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)*x^m/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
148,0,0,0,0.761544," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b*arcsin(c*x) + a)*x^m/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
149,0,0,0,0.709124," ","integrate(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} x^{4} - 2 \, a c^{2} d^{2} x^{2} + a d^{2} + {\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} x^{m}, x\right)"," ",0,"integral((a*c^4*d^2*x^4 - 2*a*c^2*d^2*x^2 + a*d^2 + (b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*x^m, x)","F",0
150,0,0,0,1.426863," ","integrate(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d x^{2} - a d + {\left(b c^{2} d x^{2} - b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} x^{m}, x\right)"," ",0,"integral(-(a*c^2*d*x^2 - a*d + (b*c^2*d*x^2 - b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*x^m, x)","F",0
151,0,0,0,1.953375," ","integrate(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)*x^m, x)","F",0
152,0,0,0,0.513567," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)*x^m/(c^2*d*x^2 - d), x)","F",0
153,0,0,0,0.581438," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)*x^m/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
154,0,0,0,1.971041," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)*x^m/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
155,0,0,0,0.688444," ","integrate(x^m*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \arcsin\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)/(a^2*x^2 - 1), x)","F",0
156,1,229,0,0.559403," ","integrate(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{1125 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{7} d x^{7} - 63 \, {\left(1225 \, a^{2} - 38 \, b^{2}\right)} c^{5} d x^{5} + 5320 \, b^{2} c^{3} d x^{3} + 31920 \, b^{2} c d x + 11025 \, {\left(5 \, b^{2} c^{7} d x^{7} - 7 \, b^{2} c^{5} d x^{5}\right)} \arcsin\left(c x\right)^{2} + 22050 \, {\left(5 \, a b c^{7} d x^{7} - 7 \, a b c^{5} d x^{5}\right)} \arcsin\left(c x\right) + 210 \, {\left(75 \, a b c^{6} d x^{6} - 57 \, a b c^{4} d x^{4} - 76 \, a b c^{2} d x^{2} - 152 \, a b d + {\left(75 \, b^{2} c^{6} d x^{6} - 57 \, b^{2} c^{4} d x^{4} - 76 \, b^{2} c^{2} d x^{2} - 152 \, b^{2} d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{385875 \, c^{5}}"," ",0,"-1/385875*(1125*(49*a^2 - 2*b^2)*c^7*d*x^7 - 63*(1225*a^2 - 38*b^2)*c^5*d*x^5 + 5320*b^2*c^3*d*x^3 + 31920*b^2*c*d*x + 11025*(5*b^2*c^7*d*x^7 - 7*b^2*c^5*d*x^5)*arcsin(c*x)^2 + 22050*(5*a*b*c^7*d*x^7 - 7*a*b*c^5*d*x^5)*arcsin(c*x) + 210*(75*a*b*c^6*d*x^6 - 57*a*b*c^4*d*x^4 - 76*a*b*c^2*d*x^2 - 152*a*b*d + (75*b^2*c^6*d*x^6 - 57*b^2*c^4*d*x^4 - 76*b^2*c^2*d*x^2 - 152*b^2*d)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^5","A",0
157,1,211,0,0.701045," ","integrate(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(18 \, a^{2} - b^{2}\right)} c^{6} d x^{6} - 3 \, {\left(18 \, a^{2} - b^{2}\right)} c^{4} d x^{4} + 9 \, b^{2} c^{2} d x^{2} + 9 \, {\left(4 \, b^{2} c^{6} d x^{6} - 6 \, b^{2} c^{4} d x^{4} + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 18 \, {\left(4 \, a b c^{6} d x^{6} - 6 \, a b c^{4} d x^{4} + a b d\right)} \arcsin\left(c x\right) + 6 \, {\left(2 \, a b c^{5} d x^{5} - 2 \, a b c^{3} d x^{3} - 3 \, a b c d x + {\left(2 \, b^{2} c^{5} d x^{5} - 2 \, b^{2} c^{3} d x^{3} - 3 \, b^{2} c d x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{216 \, c^{4}}"," ",0,"-1/216*(2*(18*a^2 - b^2)*c^6*d*x^6 - 3*(18*a^2 - b^2)*c^4*d*x^4 + 9*b^2*c^2*d*x^2 + 9*(4*b^2*c^6*d*x^6 - 6*b^2*c^4*d*x^4 + b^2*d)*arcsin(c*x)^2 + 18*(4*a*b*c^6*d*x^6 - 6*a*b*c^4*d*x^4 + a*b*d)*arcsin(c*x) + 6*(2*a*b*c^5*d*x^5 - 2*a*b*c^3*d*x^3 - 3*a*b*c*d*x + (2*b^2*c^5*d*x^5 - 2*b^2*c^3*d*x^3 - 3*b^2*c*d*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^4","A",0
158,1,194,0,0.661274," ","integrate(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{27 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{5} d x^{5} - 5 \, {\left(225 \, a^{2} - 26 \, b^{2}\right)} c^{3} d x^{3} + 780 \, b^{2} c d x + 225 \, {\left(3 \, b^{2} c^{5} d x^{5} - 5 \, b^{2} c^{3} d x^{3}\right)} \arcsin\left(c x\right)^{2} + 450 \, {\left(3 \, a b c^{5} d x^{5} - 5 \, a b c^{3} d x^{3}\right)} \arcsin\left(c x\right) + 30 \, {\left(9 \, a b c^{4} d x^{4} - 13 \, a b c^{2} d x^{2} - 26 \, a b d + {\left(9 \, b^{2} c^{4} d x^{4} - 13 \, b^{2} c^{2} d x^{2} - 26 \, b^{2} d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{3375 \, c^{3}}"," ",0,"-1/3375*(27*(25*a^2 - 2*b^2)*c^5*d*x^5 - 5*(225*a^2 - 26*b^2)*c^3*d*x^3 + 780*b^2*c*d*x + 225*(3*b^2*c^5*d*x^5 - 5*b^2*c^3*d*x^3)*arcsin(c*x)^2 + 450*(3*a*b*c^5*d*x^5 - 5*a*b*c^3*d*x^3)*arcsin(c*x) + 30*(9*a*b*c^4*d*x^4 - 13*a*b*c^2*d*x^2 - 26*a*b*d + (9*b^2*c^4*d*x^4 - 13*b^2*c^2*d*x^2 - 26*b^2*d)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^3","A",0
159,1,176,0,0.654628," ","integrate(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{2} - b^{2}\right)} c^{4} d x^{4} - {\left(16 \, a^{2} - 5 \, b^{2}\right)} c^{2} d x^{2} + {\left(8 \, b^{2} c^{4} d x^{4} - 16 \, b^{2} c^{2} d x^{2} + 5 \, b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(8 \, a b c^{4} d x^{4} - 16 \, a b c^{2} d x^{2} + 5 \, a b d\right)} \arcsin\left(c x\right) + 2 \, {\left(2 \, a b c^{3} d x^{3} - 5 \, a b c d x + {\left(2 \, b^{2} c^{3} d x^{3} - 5 \, b^{2} c d x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{32 \, c^{2}}"," ",0,"-1/32*((8*a^2 - b^2)*c^4*d*x^4 - (16*a^2 - 5*b^2)*c^2*d*x^2 + (8*b^2*c^4*d*x^4 - 16*b^2*c^2*d*x^2 + 5*b^2*d)*arcsin(c*x)^2 + 2*(8*a*b*c^4*d*x^4 - 16*a*b*c^2*d*x^2 + 5*a*b*d)*arcsin(c*x) + 2*(2*a*b*c^3*d*x^3 - 5*a*b*c*d*x + (2*b^2*c^3*d*x^3 - 5*b^2*c*d*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^2","A",0
160,1,146,0,0.964242," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{3} d x^{3} - 3 \, {\left(9 \, a^{2} - 14 \, b^{2}\right)} c d x + 9 \, {\left(b^{2} c^{3} d x^{3} - 3 \, b^{2} c d x\right)} \arcsin\left(c x\right)^{2} + 18 \, {\left(a b c^{3} d x^{3} - 3 \, a b c d x\right)} \arcsin\left(c x\right) + 6 \, {\left(a b c^{2} d x^{2} - 7 \, a b d + {\left(b^{2} c^{2} d x^{2} - 7 \, b^{2} d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{27 \, c}"," ",0,"-1/27*((9*a^2 - 2*b^2)*c^3*d*x^3 - 3*(9*a^2 - 14*b^2)*c*d*x + 9*(b^2*c^3*d*x^3 - 3*b^2*c*d*x)*arcsin(c*x)^2 + 18*(a*b*c^3*d*x^3 - 3*a*b*c*d*x)*arcsin(c*x) + 6*(a*b*c^2*d*x^2 - 7*a*b*d + (b^2*c^2*d*x^2 - 7*b^2*d)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c","A",0
161,0,0,0,0.945923," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))/x, x)","F",0
162,0,0,0,0.758003," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))/x^2, x)","F",0
163,0,0,0,0.673646," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))/x^3, x)","F",0
164,0,0,0,2.214891," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))/x^4, x)","F",0
165,1,337,0,0.585802," ","integrate(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{42875 \, {\left(81 \, a^{2} - 2 \, b^{2}\right)} c^{9} d^{2} x^{9} - 2250 \, {\left(3969 \, a^{2} - 106 \, b^{2}\right)} c^{7} d^{2} x^{7} + 189 \, {\left(33075 \, a^{2} - 526 \, b^{2}\right)} c^{5} d^{2} x^{5} - 220920 \, b^{2} c^{3} d^{2} x^{3} - 1325520 \, b^{2} c d^{2} x + 99225 \, {\left(35 \, b^{2} c^{9} d^{2} x^{9} - 90 \, b^{2} c^{7} d^{2} x^{7} + 63 \, b^{2} c^{5} d^{2} x^{5}\right)} \arcsin\left(c x\right)^{2} + 198450 \, {\left(35 \, a b c^{9} d^{2} x^{9} - 90 \, a b c^{7} d^{2} x^{7} + 63 \, a b c^{5} d^{2} x^{5}\right)} \arcsin\left(c x\right) + 630 \, {\left(1225 \, a b c^{8} d^{2} x^{8} - 2650 \, a b c^{6} d^{2} x^{6} + 789 \, a b c^{4} d^{2} x^{4} + 1052 \, a b c^{2} d^{2} x^{2} + 2104 \, a b d^{2} + {\left(1225 \, b^{2} c^{8} d^{2} x^{8} - 2650 \, b^{2} c^{6} d^{2} x^{6} + 789 \, b^{2} c^{4} d^{2} x^{4} + 1052 \, b^{2} c^{2} d^{2} x^{2} + 2104 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{31255875 \, c^{5}}"," ",0,"1/31255875*(42875*(81*a^2 - 2*b^2)*c^9*d^2*x^9 - 2250*(3969*a^2 - 106*b^2)*c^7*d^2*x^7 + 189*(33075*a^2 - 526*b^2)*c^5*d^2*x^5 - 220920*b^2*c^3*d^2*x^3 - 1325520*b^2*c*d^2*x + 99225*(35*b^2*c^9*d^2*x^9 - 90*b^2*c^7*d^2*x^7 + 63*b^2*c^5*d^2*x^5)*arcsin(c*x)^2 + 198450*(35*a*b*c^9*d^2*x^9 - 90*a*b*c^7*d^2*x^7 + 63*a*b*c^5*d^2*x^5)*arcsin(c*x) + 630*(1225*a*b*c^8*d^2*x^8 - 2650*a*b*c^6*d^2*x^6 + 789*a*b*c^4*d^2*x^4 + 1052*a*b*c^2*d^2*x^2 + 2104*a*b*d^2 + (1225*b^2*c^8*d^2*x^8 - 2650*b^2*c^6*d^2*x^6 + 789*b^2*c^4*d^2*x^4 + 1052*b^2*c^2*d^2*x^2 + 2104*b^2*d^2)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^5","A",0
166,1,319,0,0.669173," ","integrate(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{108 \, {\left(32 \, a^{2} - b^{2}\right)} c^{8} d^{2} x^{8} - 8 \, {\left(1152 \, a^{2} - 43 \, b^{2}\right)} c^{6} d^{2} x^{6} + 3 \, {\left(2304 \, a^{2} - 73 \, b^{2}\right)} c^{4} d^{2} x^{4} - 657 \, b^{2} c^{2} d^{2} x^{2} + 9 \, {\left(384 \, b^{2} c^{8} d^{2} x^{8} - 1024 \, b^{2} c^{6} d^{2} x^{6} + 768 \, b^{2} c^{4} d^{2} x^{4} - 73 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 18 \, {\left(384 \, a b c^{8} d^{2} x^{8} - 1024 \, a b c^{6} d^{2} x^{6} + 768 \, a b c^{4} d^{2} x^{4} - 73 \, a b d^{2}\right)} \arcsin\left(c x\right) + 6 \, {\left(144 \, a b c^{7} d^{2} x^{7} - 344 \, a b c^{5} d^{2} x^{5} + 146 \, a b c^{3} d^{2} x^{3} + 219 \, a b c d^{2} x + {\left(144 \, b^{2} c^{7} d^{2} x^{7} - 344 \, b^{2} c^{5} d^{2} x^{5} + 146 \, b^{2} c^{3} d^{2} x^{3} + 219 \, b^{2} c d^{2} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{27648 \, c^{4}}"," ",0,"1/27648*(108*(32*a^2 - b^2)*c^8*d^2*x^8 - 8*(1152*a^2 - 43*b^2)*c^6*d^2*x^6 + 3*(2304*a^2 - 73*b^2)*c^4*d^2*x^4 - 657*b^2*c^2*d^2*x^2 + 9*(384*b^2*c^8*d^2*x^8 - 1024*b^2*c^6*d^2*x^6 + 768*b^2*c^4*d^2*x^4 - 73*b^2*d^2)*arcsin(c*x)^2 + 18*(384*a*b*c^8*d^2*x^8 - 1024*a*b*c^6*d^2*x^6 + 768*a*b*c^4*d^2*x^4 - 73*a*b*d^2)*arcsin(c*x) + 6*(144*a*b*c^7*d^2*x^7 - 344*a*b*c^5*d^2*x^5 + 146*a*b*c^3*d^2*x^3 + 219*a*b*c*d^2*x + (144*b^2*c^7*d^2*x^7 - 344*b^2*c^5*d^2*x^5 + 146*b^2*c^3*d^2*x^3 + 219*b^2*c*d^2*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^4","A",0
167,1,296,0,0.779415," ","integrate(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{3375 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{7} d^{2} x^{7} - 378 \, {\left(1225 \, a^{2} - 68 \, b^{2}\right)} c^{5} d^{2} x^{5} + 35 \, {\left(11025 \, a^{2} - 818 \, b^{2}\right)} c^{3} d^{2} x^{3} - 171780 \, b^{2} c d^{2} x + 11025 \, {\left(15 \, b^{2} c^{7} d^{2} x^{7} - 42 \, b^{2} c^{5} d^{2} x^{5} + 35 \, b^{2} c^{3} d^{2} x^{3}\right)} \arcsin\left(c x\right)^{2} + 22050 \, {\left(15 \, a b c^{7} d^{2} x^{7} - 42 \, a b c^{5} d^{2} x^{5} + 35 \, a b c^{3} d^{2} x^{3}\right)} \arcsin\left(c x\right) + 210 \, {\left(225 \, a b c^{6} d^{2} x^{6} - 612 \, a b c^{4} d^{2} x^{4} + 409 \, a b c^{2} d^{2} x^{2} + 818 \, a b d^{2} + {\left(225 \, b^{2} c^{6} d^{2} x^{6} - 612 \, b^{2} c^{4} d^{2} x^{4} + 409 \, b^{2} c^{2} d^{2} x^{2} + 818 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{1157625 \, c^{3}}"," ",0,"1/1157625*(3375*(49*a^2 - 2*b^2)*c^7*d^2*x^7 - 378*(1225*a^2 - 68*b^2)*c^5*d^2*x^5 + 35*(11025*a^2 - 818*b^2)*c^3*d^2*x^3 - 171780*b^2*c*d^2*x + 11025*(15*b^2*c^7*d^2*x^7 - 42*b^2*c^5*d^2*x^5 + 35*b^2*c^3*d^2*x^3)*arcsin(c*x)^2 + 22050*(15*a*b*c^7*d^2*x^7 - 42*a*b*c^5*d^2*x^5 + 35*a*b*c^3*d^2*x^3)*arcsin(c*x) + 210*(225*a*b*c^6*d^2*x^6 - 612*a*b*c^4*d^2*x^4 + 409*a*b*c^2*d^2*x^2 + 818*a*b*d^2 + (225*b^2*c^6*d^2*x^6 - 612*b^2*c^4*d^2*x^4 + 409*b^2*c^2*d^2*x^2 + 818*b^2*d^2)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^3","A",0
168,1,278,0,0.668483," ","integrate(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(18 \, a^{2} - b^{2}\right)} c^{6} d^{2} x^{6} - 3 \, {\left(144 \, a^{2} - 13 \, b^{2}\right)} c^{4} d^{2} x^{4} + 9 \, {\left(48 \, a^{2} - 11 \, b^{2}\right)} c^{2} d^{2} x^{2} + 9 \, {\left(16 \, b^{2} c^{6} d^{2} x^{6} - 48 \, b^{2} c^{4} d^{2} x^{4} + 48 \, b^{2} c^{2} d^{2} x^{2} - 11 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 18 \, {\left(16 \, a b c^{6} d^{2} x^{6} - 48 \, a b c^{4} d^{2} x^{4} + 48 \, a b c^{2} d^{2} x^{2} - 11 \, a b d^{2}\right)} \arcsin\left(c x\right) + 6 \, {\left(8 \, a b c^{5} d^{2} x^{5} - 26 \, a b c^{3} d^{2} x^{3} + 33 \, a b c d^{2} x + {\left(8 \, b^{2} c^{5} d^{2} x^{5} - 26 \, b^{2} c^{3} d^{2} x^{3} + 33 \, b^{2} c d^{2} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{864 \, c^{2}}"," ",0,"1/864*(8*(18*a^2 - b^2)*c^6*d^2*x^6 - 3*(144*a^2 - 13*b^2)*c^4*d^2*x^4 + 9*(48*a^2 - 11*b^2)*c^2*d^2*x^2 + 9*(16*b^2*c^6*d^2*x^6 - 48*b^2*c^4*d^2*x^4 + 48*b^2*c^2*d^2*x^2 - 11*b^2*d^2)*arcsin(c*x)^2 + 18*(16*a*b*c^6*d^2*x^6 - 48*a*b*c^4*d^2*x^4 + 48*a*b*c^2*d^2*x^2 - 11*a*b*d^2)*arcsin(c*x) + 6*(8*a*b*c^5*d^2*x^5 - 26*a*b*c^3*d^2*x^3 + 33*a*b*c*d^2*x + (8*b^2*c^5*d^2*x^5 - 26*b^2*c^3*d^2*x^3 + 33*b^2*c*d^2*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^2","A",0
169,1,247,0,0.758126," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{27 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{5} d^{2} x^{5} - 10 \, {\left(225 \, a^{2} - 38 \, b^{2}\right)} c^{3} d^{2} x^{3} + 15 \, {\left(225 \, a^{2} - 298 \, b^{2}\right)} c d^{2} x + 225 \, {\left(3 \, b^{2} c^{5} d^{2} x^{5} - 10 \, b^{2} c^{3} d^{2} x^{3} + 15 \, b^{2} c d^{2} x\right)} \arcsin\left(c x\right)^{2} + 450 \, {\left(3 \, a b c^{5} d^{2} x^{5} - 10 \, a b c^{3} d^{2} x^{3} + 15 \, a b c d^{2} x\right)} \arcsin\left(c x\right) + 30 \, {\left(9 \, a b c^{4} d^{2} x^{4} - 38 \, a b c^{2} d^{2} x^{2} + 149 \, a b d^{2} + {\left(9 \, b^{2} c^{4} d^{2} x^{4} - 38 \, b^{2} c^{2} d^{2} x^{2} + 149 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{3375 \, c}"," ",0,"1/3375*(27*(25*a^2 - 2*b^2)*c^5*d^2*x^5 - 10*(225*a^2 - 38*b^2)*c^3*d^2*x^3 + 15*(225*a^2 - 298*b^2)*c*d^2*x + 225*(3*b^2*c^5*d^2*x^5 - 10*b^2*c^3*d^2*x^3 + 15*b^2*c*d^2*x)*arcsin(c*x)^2 + 450*(3*a*b*c^5*d^2*x^5 - 10*a*b*c^3*d^2*x^3 + 15*a*b*c*d^2*x)*arcsin(c*x) + 30*(9*a*b*c^4*d^2*x^4 - 38*a*b*c^2*d^2*x^2 + 149*a*b*d^2 + (9*b^2*c^4*d^2*x^4 - 38*b^2*c^2*d^2*x^2 + 149*b^2*d^2)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c","A",0
170,0,0,0,2.017382," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))/x, x)","F",0
171,0,0,0,2.551560," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))/x^2, x)","F",0
172,0,0,0,0.861231," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))/x^3, x)","F",0
173,0,0,0,1.418154," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))/x^4, x)","F",0
174,1,413,0,1.945480," ","integrate(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{10418625 \, {\left(121 \, a^{2} - 2 \, b^{2}\right)} c^{11} d^{3} x^{11} - 471625 \, {\left(9801 \, a^{2} - 182 \, b^{2}\right)} c^{9} d^{3} x^{9} + 12375 \, {\left(480249 \, a^{2} - 9410 \, b^{2}\right)} c^{7} d^{3} x^{7} - 2079 \, {\left(1334025 \, a^{2} - 12622 \, b^{2}\right)} c^{5} d^{3} x^{5} + 58313640 \, b^{2} c^{3} d^{3} x^{3} + 349881840 \, b^{2} c d^{3} x + 12006225 \, {\left(105 \, b^{2} c^{11} d^{3} x^{11} - 385 \, b^{2} c^{9} d^{3} x^{9} + 495 \, b^{2} c^{7} d^{3} x^{7} - 231 \, b^{2} c^{5} d^{3} x^{5}\right)} \arcsin\left(c x\right)^{2} + 24012450 \, {\left(105 \, a b c^{11} d^{3} x^{11} - 385 \, a b c^{9} d^{3} x^{9} + 495 \, a b c^{7} d^{3} x^{7} - 231 \, a b c^{5} d^{3} x^{5}\right)} \arcsin\left(c x\right) + 6930 \, {\left(33075 \, a b c^{10} d^{3} x^{10} - 111475 \, a b c^{8} d^{3} x^{8} + 117625 \, a b c^{6} d^{3} x^{6} - 18933 \, a b c^{4} d^{3} x^{4} - 25244 \, a b c^{2} d^{3} x^{2} - 50488 \, a b d^{3} + {\left(33075 \, b^{2} c^{10} d^{3} x^{10} - 111475 \, b^{2} c^{8} d^{3} x^{8} + 117625 \, b^{2} c^{6} d^{3} x^{6} - 18933 \, b^{2} c^{4} d^{3} x^{4} - 25244 \, b^{2} c^{2} d^{3} x^{2} - 50488 \, b^{2} d^{3}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{13867189875 \, c^{5}}"," ",0,"-1/13867189875*(10418625*(121*a^2 - 2*b^2)*c^11*d^3*x^11 - 471625*(9801*a^2 - 182*b^2)*c^9*d^3*x^9 + 12375*(480249*a^2 - 9410*b^2)*c^7*d^3*x^7 - 2079*(1334025*a^2 - 12622*b^2)*c^5*d^3*x^5 + 58313640*b^2*c^3*d^3*x^3 + 349881840*b^2*c*d^3*x + 12006225*(105*b^2*c^11*d^3*x^11 - 385*b^2*c^9*d^3*x^9 + 495*b^2*c^7*d^3*x^7 - 231*b^2*c^5*d^3*x^5)*arcsin(c*x)^2 + 24012450*(105*a*b*c^11*d^3*x^11 - 385*a*b*c^9*d^3*x^9 + 495*a*b*c^7*d^3*x^7 - 231*a*b*c^5*d^3*x^5)*arcsin(c*x) + 6930*(33075*a*b*c^10*d^3*x^10 - 111475*a*b*c^8*d^3*x^8 + 117625*a*b*c^6*d^3*x^6 - 18933*a*b*c^4*d^3*x^4 - 25244*a*b*c^2*d^3*x^2 - 50488*a*b*d^3 + (33075*b^2*c^10*d^3*x^10 - 111475*b^2*c^8*d^3*x^8 + 117625*b^2*c^6*d^3*x^6 - 18933*b^2*c^4*d^3*x^4 - 25244*b^2*c^2*d^3*x^2 - 50488*b^2*d^3)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^5","A",0
175,1,395,0,0.741824," ","integrate(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{2304 \, {\left(50 \, a^{2} - b^{2}\right)} c^{10} d^{3} x^{10} - 540 \, {\left(800 \, a^{2} - 19 \, b^{2}\right)} c^{8} d^{3} x^{8} + 40 \, {\left(14400 \, a^{2} - 401 \, b^{2}\right)} c^{6} d^{3} x^{6} - 75 \, {\left(3840 \, a^{2} - 79 \, b^{2}\right)} c^{4} d^{3} x^{4} + 17775 \, b^{2} c^{2} d^{3} x^{2} + 225 \, {\left(512 \, b^{2} c^{10} d^{3} x^{10} - 1920 \, b^{2} c^{8} d^{3} x^{8} + 2560 \, b^{2} c^{6} d^{3} x^{6} - 1280 \, b^{2} c^{4} d^{3} x^{4} + 79 \, b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 450 \, {\left(512 \, a b c^{10} d^{3} x^{10} - 1920 \, a b c^{8} d^{3} x^{8} + 2560 \, a b c^{6} d^{3} x^{6} - 1280 \, a b c^{4} d^{3} x^{4} + 79 \, a b d^{3}\right)} \arcsin\left(c x\right) + 30 \, {\left(768 \, a b c^{9} d^{3} x^{9} - 2736 \, a b c^{7} d^{3} x^{7} + 3208 \, a b c^{5} d^{3} x^{5} - 790 \, a b c^{3} d^{3} x^{3} - 1185 \, a b c d^{3} x + {\left(768 \, b^{2} c^{9} d^{3} x^{9} - 2736 \, b^{2} c^{7} d^{3} x^{7} + 3208 \, b^{2} c^{5} d^{3} x^{5} - 790 \, b^{2} c^{3} d^{3} x^{3} - 1185 \, b^{2} c d^{3} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{1152000 \, c^{4}}"," ",0,"-1/1152000*(2304*(50*a^2 - b^2)*c^10*d^3*x^10 - 540*(800*a^2 - 19*b^2)*c^8*d^3*x^8 + 40*(14400*a^2 - 401*b^2)*c^6*d^3*x^6 - 75*(3840*a^2 - 79*b^2)*c^4*d^3*x^4 + 17775*b^2*c^2*d^3*x^2 + 225*(512*b^2*c^10*d^3*x^10 - 1920*b^2*c^8*d^3*x^8 + 2560*b^2*c^6*d^3*x^6 - 1280*b^2*c^4*d^3*x^4 + 79*b^2*d^3)*arcsin(c*x)^2 + 450*(512*a*b*c^10*d^3*x^10 - 1920*a*b*c^8*d^3*x^8 + 2560*a*b*c^6*d^3*x^6 - 1280*a*b*c^4*d^3*x^4 + 79*a*b*d^3)*arcsin(c*x) + 30*(768*a*b*c^9*d^3*x^9 - 2736*a*b*c^7*d^3*x^7 + 3208*a*b*c^5*d^3*x^5 - 790*a*b*c^3*d^3*x^3 - 1185*a*b*c*d^3*x + (768*b^2*c^9*d^3*x^9 - 2736*b^2*c^7*d^3*x^7 + 3208*b^2*c^5*d^3*x^5 - 790*b^2*c^3*d^3*x^3 - 1185*b^2*c*d^3*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^4","A",0
176,1,372,0,0.637701," ","integrate(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{42875 \, {\left(81 \, a^{2} - 2 \, b^{2}\right)} c^{9} d^{3} x^{9} - 1125 \, {\left(11907 \, a^{2} - 374 \, b^{2}\right)} c^{7} d^{3} x^{7} + 189 \, {\left(99225 \, a^{2} - 4198 \, b^{2}\right)} c^{5} d^{3} x^{5} - 105 \, {\left(99225 \, a^{2} - 5258 \, b^{2}\right)} c^{3} d^{3} x^{3} + 3312540 \, b^{2} c d^{3} x + 99225 \, {\left(35 \, b^{2} c^{9} d^{3} x^{9} - 135 \, b^{2} c^{7} d^{3} x^{7} + 189 \, b^{2} c^{5} d^{3} x^{5} - 105 \, b^{2} c^{3} d^{3} x^{3}\right)} \arcsin\left(c x\right)^{2} + 198450 \, {\left(35 \, a b c^{9} d^{3} x^{9} - 135 \, a b c^{7} d^{3} x^{7} + 189 \, a b c^{5} d^{3} x^{5} - 105 \, a b c^{3} d^{3} x^{3}\right)} \arcsin\left(c x\right) + 630 \, {\left(1225 \, a b c^{8} d^{3} x^{8} - 4675 \, a b c^{6} d^{3} x^{6} + 6297 \, a b c^{4} d^{3} x^{4} - 2629 \, a b c^{2} d^{3} x^{2} - 5258 \, a b d^{3} + {\left(1225 \, b^{2} c^{8} d^{3} x^{8} - 4675 \, b^{2} c^{6} d^{3} x^{6} + 6297 \, b^{2} c^{4} d^{3} x^{4} - 2629 \, b^{2} c^{2} d^{3} x^{2} - 5258 \, b^{2} d^{3}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{31255875 \, c^{3}}"," ",0,"-1/31255875*(42875*(81*a^2 - 2*b^2)*c^9*d^3*x^9 - 1125*(11907*a^2 - 374*b^2)*c^7*d^3*x^7 + 189*(99225*a^2 - 4198*b^2)*c^5*d^3*x^5 - 105*(99225*a^2 - 5258*b^2)*c^3*d^3*x^3 + 3312540*b^2*c*d^3*x + 99225*(35*b^2*c^9*d^3*x^9 - 135*b^2*c^7*d^3*x^7 + 189*b^2*c^5*d^3*x^5 - 105*b^2*c^3*d^3*x^3)*arcsin(c*x)^2 + 198450*(35*a*b*c^9*d^3*x^9 - 135*a*b*c^7*d^3*x^7 + 189*a*b*c^5*d^3*x^5 - 105*a*b*c^3*d^3*x^3)*arcsin(c*x) + 630*(1225*a*b*c^8*d^3*x^8 - 4675*a*b*c^6*d^3*x^6 + 6297*a*b*c^4*d^3*x^4 - 2629*a*b*c^2*d^3*x^2 - 5258*a*b*d^3 + (1225*b^2*c^8*d^3*x^8 - 4675*b^2*c^6*d^3*x^6 + 6297*b^2*c^4*d^3*x^4 - 2629*b^2*c^2*d^3*x^2 - 5258*b^2*d^3)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^3","A",0
177,1,354,0,0.643550," ","integrate(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{36 \, {\left(32 \, a^{2} - b^{2}\right)} c^{8} d^{3} x^{8} - 8 \, {\left(576 \, a^{2} - 25 \, b^{2}\right)} c^{6} d^{3} x^{6} + 3 \, {\left(2304 \, a^{2} - 163 \, b^{2}\right)} c^{4} d^{3} x^{4} - 9 \, {\left(512 \, a^{2} - 93 \, b^{2}\right)} c^{2} d^{3} x^{2} + 9 \, {\left(128 \, b^{2} c^{8} d^{3} x^{8} - 512 \, b^{2} c^{6} d^{3} x^{6} + 768 \, b^{2} c^{4} d^{3} x^{4} - 512 \, b^{2} c^{2} d^{3} x^{2} + 93 \, b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 18 \, {\left(128 \, a b c^{8} d^{3} x^{8} - 512 \, a b c^{6} d^{3} x^{6} + 768 \, a b c^{4} d^{3} x^{4} - 512 \, a b c^{2} d^{3} x^{2} + 93 \, a b d^{3}\right)} \arcsin\left(c x\right) + 6 \, {\left(48 \, a b c^{7} d^{3} x^{7} - 200 \, a b c^{5} d^{3} x^{5} + 326 \, a b c^{3} d^{3} x^{3} - 279 \, a b c d^{3} x + {\left(48 \, b^{2} c^{7} d^{3} x^{7} - 200 \, b^{2} c^{5} d^{3} x^{5} + 326 \, b^{2} c^{3} d^{3} x^{3} - 279 \, b^{2} c d^{3} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{9216 \, c^{2}}"," ",0,"-1/9216*(36*(32*a^2 - b^2)*c^8*d^3*x^8 - 8*(576*a^2 - 25*b^2)*c^6*d^3*x^6 + 3*(2304*a^2 - 163*b^2)*c^4*d^3*x^4 - 9*(512*a^2 - 93*b^2)*c^2*d^3*x^2 + 9*(128*b^2*c^8*d^3*x^8 - 512*b^2*c^6*d^3*x^6 + 768*b^2*c^4*d^3*x^4 - 512*b^2*c^2*d^3*x^2 + 93*b^2*d^3)*arcsin(c*x)^2 + 18*(128*a*b*c^8*d^3*x^8 - 512*a*b*c^6*d^3*x^6 + 768*a*b*c^4*d^3*x^4 - 512*a*b*c^2*d^3*x^2 + 93*a*b*d^3)*arcsin(c*x) + 6*(48*a*b*c^7*d^3*x^7 - 200*a*b*c^5*d^3*x^5 + 326*a*b*c^3*d^3*x^3 - 279*a*b*c*d^3*x + (48*b^2*c^7*d^3*x^7 - 200*b^2*c^5*d^3*x^5 + 326*b^2*c^3*d^3*x^3 - 279*b^2*c*d^3*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^2","A",0
178,1,323,0,0.541797," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{1125 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{7} d^{3} x^{7} - 189 \, {\left(1225 \, a^{2} - 78 \, b^{2}\right)} c^{5} d^{3} x^{5} + 35 \, {\left(11025 \, a^{2} - 1514 \, b^{2}\right)} c^{3} d^{3} x^{3} - 105 \, {\left(3675 \, a^{2} - 4322 \, b^{2}\right)} c d^{3} x + 11025 \, {\left(5 \, b^{2} c^{7} d^{3} x^{7} - 21 \, b^{2} c^{5} d^{3} x^{5} + 35 \, b^{2} c^{3} d^{3} x^{3} - 35 \, b^{2} c d^{3} x\right)} \arcsin\left(c x\right)^{2} + 22050 \, {\left(5 \, a b c^{7} d^{3} x^{7} - 21 \, a b c^{5} d^{3} x^{5} + 35 \, a b c^{3} d^{3} x^{3} - 35 \, a b c d^{3} x\right)} \arcsin\left(c x\right) + 210 \, {\left(75 \, a b c^{6} d^{3} x^{6} - 351 \, a b c^{4} d^{3} x^{4} + 757 \, a b c^{2} d^{3} x^{2} - 2161 \, a b d^{3} + {\left(75 \, b^{2} c^{6} d^{3} x^{6} - 351 \, b^{2} c^{4} d^{3} x^{4} + 757 \, b^{2} c^{2} d^{3} x^{2} - 2161 \, b^{2} d^{3}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{385875 \, c}"," ",0,"-1/385875*(1125*(49*a^2 - 2*b^2)*c^7*d^3*x^7 - 189*(1225*a^2 - 78*b^2)*c^5*d^3*x^5 + 35*(11025*a^2 - 1514*b^2)*c^3*d^3*x^3 - 105*(3675*a^2 - 4322*b^2)*c*d^3*x + 11025*(5*b^2*c^7*d^3*x^7 - 21*b^2*c^5*d^3*x^5 + 35*b^2*c^3*d^3*x^3 - 35*b^2*c*d^3*x)*arcsin(c*x)^2 + 22050*(5*a*b*c^7*d^3*x^7 - 21*a*b*c^5*d^3*x^5 + 35*a*b*c^3*d^3*x^3 - 35*a*b*c*d^3*x)*arcsin(c*x) + 210*(75*a*b*c^6*d^3*x^6 - 351*a*b*c^4*d^3*x^4 + 757*a*b*c^2*d^3*x^2 - 2161*a*b*d^3 + (75*b^2*c^6*d^3*x^6 - 351*b^2*c^4*d^3*x^4 + 757*b^2*c^2*d^3*x^2 - 2161*b^2*d^3)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c","A",0
179,0,0,0,0.736043," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{6} d^{3} x^{6} - 3 \, a^{2} c^{4} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{2} - a^{2} d^{3} + {\left(b^{2} c^{6} d^{3} x^{6} - 3 \, b^{2} c^{4} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} d^{3} x^{6} - 3 \, a b c^{4} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{2} - a b d^{3}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral(-(a^2*c^6*d^3*x^6 - 3*a^2*c^4*d^3*x^4 + 3*a^2*c^2*d^3*x^2 - a^2*d^3 + (b^2*c^6*d^3*x^6 - 3*b^2*c^4*d^3*x^4 + 3*b^2*c^2*d^3*x^2 - b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*c^6*d^3*x^6 - 3*a*b*c^4*d^3*x^4 + 3*a*b*c^2*d^3*x^2 - a*b*d^3)*arcsin(c*x))/x, x)","F",0
180,0,0,0,1.020396," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{6} d^{3} x^{6} - 3 \, a^{2} c^{4} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{2} - a^{2} d^{3} + {\left(b^{2} c^{6} d^{3} x^{6} - 3 \, b^{2} c^{4} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} d^{3} x^{6} - 3 \, a b c^{4} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{2} - a b d^{3}\right)} \arcsin\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral(-(a^2*c^6*d^3*x^6 - 3*a^2*c^4*d^3*x^4 + 3*a^2*c^2*d^3*x^2 - a^2*d^3 + (b^2*c^6*d^3*x^6 - 3*b^2*c^4*d^3*x^4 + 3*b^2*c^2*d^3*x^2 - b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*c^6*d^3*x^6 - 3*a*b*c^4*d^3*x^4 + 3*a*b*c^2*d^3*x^2 - a*b*d^3)*arcsin(c*x))/x^2, x)","F",0
181,0,0,0,0.612192," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{6} d^{3} x^{6} - 3 \, a^{2} c^{4} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{2} - a^{2} d^{3} + {\left(b^{2} c^{6} d^{3} x^{6} - 3 \, b^{2} c^{4} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} d^{3} x^{6} - 3 \, a b c^{4} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{2} - a b d^{3}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a^2*c^6*d^3*x^6 - 3*a^2*c^4*d^3*x^4 + 3*a^2*c^2*d^3*x^2 - a^2*d^3 + (b^2*c^6*d^3*x^6 - 3*b^2*c^4*d^3*x^4 + 3*b^2*c^2*d^3*x^2 - b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*c^6*d^3*x^6 - 3*a*b*c^4*d^3*x^4 + 3*a*b*c^2*d^3*x^2 - a*b*d^3)*arcsin(c*x))/x^3, x)","F",0
182,0,0,0,0.734099," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c^{6} d^{3} x^{6} - 3 \, a^{2} c^{4} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{2} - a^{2} d^{3} + {\left(b^{2} c^{6} d^{3} x^{6} - 3 \, b^{2} c^{4} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} d^{3} x^{6} - 3 \, a b c^{4} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{2} - a b d^{3}\right)} \arcsin\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral(-(a^2*c^6*d^3*x^6 - 3*a^2*c^4*d^3*x^4 + 3*a^2*c^2*d^3*x^2 - a^2*d^3 + (b^2*c^6*d^3*x^6 - 3*b^2*c^4*d^3*x^4 + 3*b^2*c^2*d^3*x^2 - b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*c^6*d^3*x^6 - 3*a*b*c^4*d^3*x^4 + 3*a*b*c^2*d^3*x^2 - a*b*d^3)*arcsin(c*x))/x^4, x)","F",0
183,0,0,0,0.609628," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)/(c^2*d*x^2 - d), x)","F",0
184,0,0,0,1.147005," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3)/(c^2*d*x^2 - d), x)","F",0
185,0,0,0,0.610131," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)/(c^2*d*x^2 - d), x)","F",0
186,0,0,0,0.679295," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x)/(c^2*d*x^2 - d), x)","F",0
187,0,0,0,0.435864," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^2 - d), x)","F",0
188,0,0,0,0.754889," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{2} d x^{3} - d x}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^3 - d*x), x)","F",0
189,0,0,0,1.065679," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{2} d x^{4} - d x^{2}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^4 - d*x^2), x)","F",0
190,0,0,0,0.712362," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{2} d x^{5} - d x^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^5 - d*x^3), x)","F",0
191,0,0,0,2.959106," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{2} d x^{6} - d x^{4}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^6 - d*x^4), x)","F",0
192,0,0,0,0.702351," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
193,0,0,0,0.691038," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
194,0,0,0,1.201332," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
195,1,102,0,0.602153," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(c^{2} x^{2} - 1\right) - 2 \, {\left(b^{2} c x \arcsin\left(c x\right) + a b c x\right)} \sqrt{-c^{2} x^{2} + 1}}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"-1/2*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2 + (b^2*c^2*x^2 - b^2)*log(c^2*x^2 - 1) - 2*(b^2*c*x*arcsin(c*x) + a*b*c*x)*sqrt(-c^2*x^2 + 1))/(c^4*d^2*x^2 - c^2*d^2)","A",0
196,0,0,0,0.749158," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
197,0,0,0,1.007342," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
198,0,0,0,1.015651," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
199,0,0,0,0.832059," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
200,0,0,0,0.692166," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
201,0,0,0,0.583421," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
202,1,198,0,0.804737," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{2} - b^{2}\right)} c^{2} x^{2} + 3 \, {\left(2 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - 3 \, a^{2} + b^{2} + 6 \, {\left(2 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right) + 4 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} - 1\right) - 2 \, {\left(4 \, a b c^{3} x^{3} - 3 \, a b c x + {\left(4 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"1/12*((6*a^2 - b^2)*c^2*x^2 + 3*(2*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - 3*a^2 + b^2 + 6*(2*a*b*c^2*x^2 - a*b)*arcsin(c*x) + 4*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*log(c^2*x^2 - 1) - 2*(4*a*b*c^3*x^3 - 3*a*b*c*x + (4*b^2*c^3*x^3 - 3*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)","A",0
203,0,0,0,1.484333," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
204,1,165,0,3.229388," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} x^{2} - 3 \, b^{2} \arcsin\left(c x\right)^{2} - 6 \, a b \arcsin\left(c x\right) - 3 \, a^{2} - b^{2} + 2 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \log\left(c^{2} x^{2} - 1\right) - 2 \, {\left(2 \, a b c^{3} x^{3} - 3 \, a b c x + {\left(2 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"-1/12*(b^2*c^2*x^2 - 3*b^2*arcsin(c*x)^2 - 6*a*b*arcsin(c*x) - 3*a^2 - b^2 + 2*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*log(c^2*x^2 - 1) - 2*(2*a*b*c^3*x^3 - 3*a*b*c*x + (2*b^2*c^3*x^3 - 3*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)","A",0
205,0,0,0,3.706561," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
206,0,0,0,1.349356," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x)","F",0
207,0,0,0,1.488606," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x)","F",0
208,0,0,0,0.579574," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3), x)","F",0
209,0,0,0,0.997605," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{c^{6} d^{3} x^{10} - 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} - d^{3} x^{4}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^10 - 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 - d^3*x^4), x)","F",0
210,1,277,0,0.850993," ","integrate(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{30 \, {\left(9 \, a b c^{5} x^{5} - 5 \, a b c^{3} x^{3} - 30 \, a b c x + {\left(9 \, b^{2} c^{5} x^{5} - 5 \, b^{2} c^{3} x^{3} - 30 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(27 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{6} x^{6} - 4 \, {\left(225 \, a^{2} - 8 \, b^{2}\right)} c^{4} x^{4} - {\left(225 \, a^{2} - 878 \, b^{2}\right)} c^{2} x^{2} + 225 \, {\left(3 \, b^{2} c^{6} x^{6} - 4 \, b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2} + 2 \, b^{2}\right)} \arcsin\left(c x\right)^{2} + 450 \, a^{2} - 856 \, b^{2} + 450 \, {\left(3 \, a b c^{6} x^{6} - 4 \, a b c^{4} x^{4} - a b c^{2} x^{2} + 2 \, a b\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{3375 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"1/3375*(30*(9*a*b*c^5*x^5 - 5*a*b*c^3*x^3 - 30*a*b*c*x + (9*b^2*c^5*x^5 - 5*b^2*c^3*x^3 - 30*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (27*(25*a^2 - 2*b^2)*c^6*x^6 - 4*(225*a^2 - 8*b^2)*c^4*x^4 - (225*a^2 - 878*b^2)*c^2*x^2 + 225*(3*b^2*c^6*x^6 - 4*b^2*c^4*x^4 - b^2*c^2*x^2 + 2*b^2)*arcsin(c*x)^2 + 450*a^2 - 856*b^2 + 450*(3*a*b*c^6*x^6 - 4*a*b*c^4*x^4 - a*b*c^2*x^2 + 2*a*b)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
211,0,0,0,0.924632," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(-c^2*d*x^2 + d), x)","F",0
212,1,208,0,0.797908," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{6 \, {\left(a b c^{3} x^{3} - 3 \, a b c x + {\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left({\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{4} x^{4} - 2 \, {\left(9 \, a^{2} - 8 \, b^{2}\right)} c^{2} x^{2} + 9 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + 9 \, a^{2} - 14 \, b^{2} + 18 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{27 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"1/27*(6*(a*b*c^3*x^3 - 3*a*b*c*x + (b^2*c^3*x^3 - 3*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + ((9*a^2 - 2*b^2)*c^4*x^4 - 2*(9*a^2 - 8*b^2)*c^2*x^2 + 9*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + 9*a^2 - 14*b^2 + 18*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
213,0,0,0,0.791324," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
214,0,0,0,0.538019," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{x}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/x, x)","F",0
215,0,0,0,0.473818," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/x^2, x)","F",0
216,0,0,0,0.437186," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/x^3, x)","F",0
217,0,0,0,1.490546," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{x^{4}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/x^4, x)","F",0
218,1,360,0,0.594797," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{210 \, {\left(75 \, a b c^{7} d x^{7} - 168 \, a b c^{5} d x^{5} + 35 \, a b c^{3} d x^{3} + 210 \, a b c d x + {\left(75 \, b^{2} c^{7} d x^{7} - 168 \, b^{2} c^{5} d x^{5} + 35 \, b^{2} c^{3} d x^{3} + 210 \, b^{2} c d x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(1125 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{8} d x^{8} - 9 \, {\left(15925 \, a^{2} - 734 \, b^{2}\right)} c^{6} d x^{6} + {\left(99225 \, a^{2} - 998 \, b^{2}\right)} c^{4} d x^{4} + {\left(11025 \, a^{2} - 40742 \, b^{2}\right)} c^{2} d x^{2} + 11025 \, {\left(5 \, b^{2} c^{8} d x^{8} - 13 \, b^{2} c^{6} d x^{6} + 9 \, b^{2} c^{4} d x^{4} + b^{2} c^{2} d x^{2} - 2 \, b^{2} d\right)} \arcsin\left(c x\right)^{2} - 2 \, {\left(11025 \, a^{2} - 18692 \, b^{2}\right)} d + 22050 \, {\left(5 \, a b c^{8} d x^{8} - 13 \, a b c^{6} d x^{6} + 9 \, a b c^{4} d x^{4} + a b c^{2} d x^{2} - 2 \, a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{385875 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"-1/385875*(210*(75*a*b*c^7*d*x^7 - 168*a*b*c^5*d*x^5 + 35*a*b*c^3*d*x^3 + 210*a*b*c*d*x + (75*b^2*c^7*d*x^7 - 168*b^2*c^5*d*x^5 + 35*b^2*c^3*d*x^3 + 210*b^2*c*d*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (1125*(49*a^2 - 2*b^2)*c^8*d*x^8 - 9*(15925*a^2 - 734*b^2)*c^6*d*x^6 + (99225*a^2 - 998*b^2)*c^4*d*x^4 + (11025*a^2 - 40742*b^2)*c^2*d*x^2 + 11025*(5*b^2*c^8*d*x^8 - 13*b^2*c^6*d*x^6 + 9*b^2*c^4*d*x^4 + b^2*c^2*d*x^2 - 2*b^2*d)*arcsin(c*x)^2 - 2*(11025*a^2 - 18692*b^2)*d + 22050*(5*a*b*c^8*d*x^8 - 13*a*b*c^6*d*x^6 + 9*a*b*c^4*d*x^4 + a*b*c^2*d*x^2 - 2*a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
219,0,0,0,0.548477," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d x^{4} - a^{2} d x^{2} + {\left(b^{2} c^{2} d x^{4} - b^{2} d x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{4} - a b d x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^4 - a^2*d*x^2 + (b^2*c^2*d*x^4 - b^2*d*x^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^4 - a*b*d*x^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
220,1,295,0,0.636262," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{30 \, {\left(3 \, a b c^{5} d x^{5} - 10 \, a b c^{3} d x^{3} + 15 \, a b c d x + {\left(3 \, b^{2} c^{5} d x^{5} - 10 \, b^{2} c^{3} d x^{3} + 15 \, b^{2} c d x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(9 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{6} d x^{6} - {\left(675 \, a^{2} - 94 \, b^{2}\right)} c^{4} d x^{4} + {\left(675 \, a^{2} - 374 \, b^{2}\right)} c^{2} d x^{2} + 225 \, {\left(b^{2} c^{6} d x^{6} - 3 \, b^{2} c^{4} d x^{4} + 3 \, b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} - {\left(225 \, a^{2} - 298 \, b^{2}\right)} d + 450 \, {\left(a b c^{6} d x^{6} - 3 \, a b c^{4} d x^{4} + 3 \, a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{1125 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"-1/1125*(30*(3*a*b*c^5*d*x^5 - 10*a*b*c^3*d*x^3 + 15*a*b*c*d*x + (3*b^2*c^5*d*x^5 - 10*b^2*c^3*d*x^3 + 15*b^2*c*d*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (9*(25*a^2 - 2*b^2)*c^6*d*x^6 - (675*a^2 - 94*b^2)*c^4*d*x^4 + (675*a^2 - 374*b^2)*c^2*d*x^2 + 225*(b^2*c^6*d*x^6 - 3*b^2*c^4*d*x^4 + 3*b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 - (225*a^2 - 298*b^2)*d + 450*(a*b*c^6*d*x^6 - 3*a*b*c^4*d*x^4 + 3*a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
221,0,0,0,0.606472," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
222,0,0,0,0.485077," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x, x)","F",0
223,0,0,0,0.457816," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^2, x)","F",0
224,0,0,0,0.459025," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^3, x)","F",0
225,0,0,0,0.438757," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^4, x)","F",0
226,1,486,0,0.546856," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{126 \, {\left(49 \, a b c^{9} d^{2} x^{9} - 171 \, a b c^{7} d^{2} x^{7} + 189 \, a b c^{5} d^{2} x^{5} - 21 \, a b c^{3} d^{2} x^{3} - 126 \, a b c d^{2} x + {\left(49 \, b^{2} c^{9} d^{2} x^{9} - 171 \, b^{2} c^{7} d^{2} x^{7} + 189 \, b^{2} c^{5} d^{2} x^{5} - 21 \, b^{2} c^{3} d^{2} x^{3} - 126 \, b^{2} c d^{2} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(343 \, {\left(81 \, a^{2} - 2 \, b^{2}\right)} c^{10} d^{2} x^{10} - 2 \, {\left(51597 \, a^{2} - 1490 \, b^{2}\right)} c^{8} d^{2} x^{8} + 2 \, {\left(67473 \, a^{2} - 2152 \, b^{2}\right)} c^{6} d^{2} x^{6} - 4 \, {\left(15876 \, a^{2} - 53 \, b^{2}\right)} c^{4} d^{2} x^{4} - {\left(3969 \, a^{2} - 14078 \, b^{2}\right)} c^{2} d^{2} x^{2} + 2 \, {\left(3969 \, a^{2} - 6140 \, b^{2}\right)} d^{2} + 3969 \, {\left(7 \, b^{2} c^{10} d^{2} x^{10} - 26 \, b^{2} c^{8} d^{2} x^{8} + 34 \, b^{2} c^{6} d^{2} x^{6} - 16 \, b^{2} c^{4} d^{2} x^{4} - b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 7938 \, {\left(7 \, a b c^{10} d^{2} x^{10} - 26 \, a b c^{8} d^{2} x^{8} + 34 \, a b c^{6} d^{2} x^{6} - 16 \, a b c^{4} d^{2} x^{4} - a b c^{2} d^{2} x^{2} + 2 \, a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{250047 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"1/250047*(126*(49*a*b*c^9*d^2*x^9 - 171*a*b*c^7*d^2*x^7 + 189*a*b*c^5*d^2*x^5 - 21*a*b*c^3*d^2*x^3 - 126*a*b*c*d^2*x + (49*b^2*c^9*d^2*x^9 - 171*b^2*c^7*d^2*x^7 + 189*b^2*c^5*d^2*x^5 - 21*b^2*c^3*d^2*x^3 - 126*b^2*c*d^2*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (343*(81*a^2 - 2*b^2)*c^10*d^2*x^10 - 2*(51597*a^2 - 1490*b^2)*c^8*d^2*x^8 + 2*(67473*a^2 - 2152*b^2)*c^6*d^2*x^6 - 4*(15876*a^2 - 53*b^2)*c^4*d^2*x^4 - (3969*a^2 - 14078*b^2)*c^2*d^2*x^2 + 2*(3969*a^2 - 6140*b^2)*d^2 + 3969*(7*b^2*c^10*d^2*x^10 - 26*b^2*c^8*d^2*x^8 + 34*b^2*c^6*d^2*x^6 - 16*b^2*c^4*d^2*x^4 - b^2*c^2*d^2*x^2 + 2*b^2*d^2)*arcsin(c*x)^2 + 7938*(7*a*b*c^10*d^2*x^10 - 26*a*b*c^8*d^2*x^8 + 34*a*b*c^6*d^2*x^6 - 16*a*b*c^4*d^2*x^4 - a*b*c^2*d^2*x^2 + 2*a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*x^2 - c^4)","A",0
227,0,0,0,0.506887," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{4} d^{2} x^{6} - 2 \, a^{2} c^{2} d^{2} x^{4} + a^{2} d^{2} x^{2} + {\left(b^{2} c^{4} d^{2} x^{6} - 2 \, b^{2} c^{2} d^{2} x^{4} + b^{2} d^{2} x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{6} - 2 \, a b c^{2} d^{2} x^{4} + a b d^{2} x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^6 - 2*a^2*c^2*d^2*x^4 + a^2*d^2*x^2 + (b^2*c^4*d^2*x^6 - 2*b^2*c^2*d^2*x^4 + b^2*d^2*x^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^6 - 2*a*b*c^2*d^2*x^4 + a*b*d^2*x^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
228,1,405,0,0.473749," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{210 \, {\left(5 \, a b c^{7} d^{2} x^{7} - 21 \, a b c^{5} d^{2} x^{5} + 35 \, a b c^{3} d^{2} x^{3} - 35 \, a b c d^{2} x + {\left(5 \, b^{2} c^{7} d^{2} x^{7} - 21 \, b^{2} c^{5} d^{2} x^{5} + 35 \, b^{2} c^{3} d^{2} x^{3} - 35 \, b^{2} c d^{2} x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(75 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{8} d^{2} x^{8} - 12 \, {\left(1225 \, a^{2} - 71 \, b^{2}\right)} c^{6} d^{2} x^{6} + 2 \, {\left(11025 \, a^{2} - 1108 \, b^{2}\right)} c^{4} d^{2} x^{4} - 4 \, {\left(3675 \, a^{2} - 1459 \, b^{2}\right)} c^{2} d^{2} x^{2} + {\left(3675 \, a^{2} - 4322 \, b^{2}\right)} d^{2} + 3675 \, {\left(b^{2} c^{8} d^{2} x^{8} - 4 \, b^{2} c^{6} d^{2} x^{6} + 6 \, b^{2} c^{4} d^{2} x^{4} - 4 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 7350 \, {\left(a b c^{8} d^{2} x^{8} - 4 \, a b c^{6} d^{2} x^{6} + 6 \, a b c^{4} d^{2} x^{4} - 4 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{25725 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"1/25725*(210*(5*a*b*c^7*d^2*x^7 - 21*a*b*c^5*d^2*x^5 + 35*a*b*c^3*d^2*x^3 - 35*a*b*c*d^2*x + (5*b^2*c^7*d^2*x^7 - 21*b^2*c^5*d^2*x^5 + 35*b^2*c^3*d^2*x^3 - 35*b^2*c*d^2*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (75*(49*a^2 - 2*b^2)*c^8*d^2*x^8 - 12*(1225*a^2 - 71*b^2)*c^6*d^2*x^6 + 2*(11025*a^2 - 1108*b^2)*c^4*d^2*x^4 - 4*(3675*a^2 - 1459*b^2)*c^2*d^2*x^2 + (3675*a^2 - 4322*b^2)*d^2 + 3675*(b^2*c^8*d^2*x^8 - 4*b^2*c^6*d^2*x^6 + 6*b^2*c^4*d^2*x^4 - 4*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 7350*(a*b*c^8*d^2*x^8 - 4*a*b*c^6*d^2*x^6 + 6*a*b*c^4*d^2*x^4 - 4*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*x^2 - c^2)","A",0
229,0,0,0,0.468113," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d), x)","F",0
230,0,0,0,0.436724," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x, x)","F",0
231,0,0,0,0.498497," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^2, x)","F",0
232,0,0,0,0.481961," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^3, x)","F",0
233,0,0,0,0.487102," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)/x^4, x)","F",0
234,1,276,0,0.461249," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{30 \, {\left(9 \, a b c^{5} x^{5} + 20 \, a b c^{3} x^{3} + 120 \, a b c x + {\left(9 \, b^{2} c^{5} x^{5} + 20 \, b^{2} c^{3} x^{3} + 120 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left(27 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{6} x^{6} + {\left(225 \, a^{2} - 218 \, b^{2}\right)} c^{4} x^{4} + 4 \, {\left(225 \, a^{2} - 968 \, b^{2}\right)} c^{2} x^{2} + 225 \, {\left(3 \, b^{2} c^{6} x^{6} + b^{2} c^{4} x^{4} + 4 \, b^{2} c^{2} x^{2} - 8 \, b^{2}\right)} \arcsin\left(c x\right)^{2} - 1800 \, a^{2} + 4144 \, b^{2} + 450 \, {\left(3 \, a b c^{6} x^{6} + a b c^{4} x^{4} + 4 \, a b c^{2} x^{2} - 8 \, a b\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{3375 \, {\left(c^{8} d x^{2} - c^{6} d\right)}}"," ",0,"-1/3375*(30*(9*a*b*c^5*x^5 + 20*a*b*c^3*x^3 + 120*a*b*c*x + (9*b^2*c^5*x^5 + 20*b^2*c^3*x^3 + 120*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + (27*(25*a^2 - 2*b^2)*c^6*x^6 + (225*a^2 - 218*b^2)*c^4*x^4 + 4*(225*a^2 - 968*b^2)*c^2*x^2 + 225*(3*b^2*c^6*x^6 + b^2*c^4*x^4 + 4*b^2*c^2*x^2 - 8*b^2)*arcsin(c*x)^2 - 1800*a^2 + 4144*b^2 + 450*(3*a*b*c^6*x^6 + a*b*c^4*x^4 + 4*a*b*c^2*x^2 - 8*a*b)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^8*d*x^2 - c^6*d)","A",0
235,0,0,0,0.429907," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)*sqrt(-c^2*d*x^2 + d)/(c^2*d*x^2 - d), x)","F",0
236,1,210,0,0.452530," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, {\left(a b c^{3} x^{3} + 6 \, a b c x + {\left(b^{2} c^{3} x^{3} + 6 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} \sqrt{-c^{2} x^{2} + 1} + {\left({\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{4} x^{4} + {\left(9 \, a^{2} - 38 \, b^{2}\right)} c^{2} x^{2} + 9 \, {\left(b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2} - 2 \, b^{2}\right)} \arcsin\left(c x\right)^{2} - 18 \, a^{2} + 40 \, b^{2} + 18 \, {\left(a b c^{4} x^{4} + a b c^{2} x^{2} - 2 \, a b\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{27 \, {\left(c^{6} d x^{2} - c^{4} d\right)}}"," ",0,"-1/27*(6*(a*b*c^3*x^3 + 6*a*b*c*x + (b^2*c^3*x^3 + 6*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*sqrt(-c^2*x^2 + 1) + ((9*a^2 - 2*b^2)*c^4*x^4 + (9*a^2 - 38*b^2)*c^2*x^2 + 9*(b^2*c^4*x^4 + b^2*c^2*x^2 - 2*b^2)*arcsin(c*x)^2 - 18*a^2 + 40*b^2 + 18*(a*b*c^4*x^4 + a*b*c^2*x^2 - 2*a*b)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^6*d*x^2 - c^4*d)","A",0
237,0,0,0,0.428300," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(-c^2*d*x^2 + d)/(c^2*d*x^2 - d), x)","F",0
238,1,147,0,0.433081," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-c^{2} d x^{2} + d} {\left(b^{2} c x \arcsin\left(c x\right) + a b c x\right)} \sqrt{-c^{2} x^{2} + 1} + {\left({\left(a^{2} - 2 \, b^{2}\right)} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, b^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d x^{2} - c^{2} d}"," ",0,"-(2*sqrt(-c^2*d*x^2 + d)*(b^2*c*x*arcsin(c*x) + a*b*c*x)*sqrt(-c^2*x^2 + 1) + ((a^2 - 2*b^2)*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*b^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d))/(c^4*d*x^2 - c^2*d)","A",0
239,0,0,0,0.433147," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^2 - d), x)","F",0
240,0,0,0,0.430082," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{2} d x^{3} - d x}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^3 - d*x), x)","F",0
241,0,0,0,0.435723," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{2} d x^{4} - d x^{2}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^4 - d*x^2), x)","F",0
242,0,0,0,0.436161," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{2} d x^{5} - d x^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^5 - d*x^3), x)","F",0
243,0,0,0,0.469431," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{2} d x^{6} - d x^{4}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^2*d*x^6 - d*x^4), x)","F",0
244,0,0,0,0.490042," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{5} \arcsin\left(c x\right)^{2} + 2 \, a b x^{5} \arcsin\left(c x\right) + a^{2} x^{5}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^5*arcsin(c*x)^2 + 2*a*b*x^5*arcsin(c*x) + a^2*x^5)*sqrt(-c^2*d*x^2 + d)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
245,0,0,0,0.459450," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)*sqrt(-c^2*d*x^2 + d)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
246,0,0,0,0.475305," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3)*sqrt(-c^2*d*x^2 + d)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
247,0,0,0,0.433889," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(-c^2*d*x^2 + d)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
248,0,0,0,0.438788," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x\right)}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
249,0,0,0,0.446021," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
250,0,0,0,0.433520," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
251,0,0,0,0.445638," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x)","F",0
252,0,0,0,0.425122," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
253,0,0,0,0.443421," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
254,0,0,0,0.455668," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{5} \arcsin\left(c x\right)^{2} + 2 \, a b x^{5} \arcsin\left(c x\right) + a^{2} x^{5}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^5*arcsin(c*x)^2 + 2*a*b*x^5*arcsin(c*x) + a^2*x^5)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
255,0,0,0,0.435968," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
256,0,0,0,0.447480," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
257,0,0,0,0.463487," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{-c^{2} d x^{2} + d}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(-c^2*d*x^2 + d)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
258,0,0,0,0.444959," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x\right)}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
259,0,0,0,0.475312," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
260,0,0,0,0.487766," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x)","F",0
261,0,0,0,0.471926," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x)","F",0
262,0,0,0,0.502288," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3), x)","F",0
263,0,0,0,0.543035," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)}}{c^{6} d^{3} x^{10} - 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} - d^{3} x^{4}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(c^6*d^3*x^10 - 3*c^4*d^3*x^8 + 3*c^2*d^3*x^6 - d^3*x^4), x)","F",0
264,1,84,0,0.465423," ","integrate(x^4*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{8 \, \arcsin\left(a x\right)^{3} + {\left(8 \, a^{4} x^{4} + 24 \, a^{2} x^{2} - 15\right)} \arcsin\left(a x\right) + {\left(2 \, a^{3} x^{3} - 8 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arcsin\left(a x\right)^{2} + 15 \, a x\right)} \sqrt{-a^{2} x^{2} + 1}}{64 \, a^{5}}"," ",0,"1/64*(8*arcsin(a*x)^3 + (8*a^4*x^4 + 24*a^2*x^2 - 15)*arcsin(a*x) + (2*a^3*x^3 - 8*(2*a^3*x^3 + 3*a*x)*arcsin(a*x)^2 + 15*a*x)*sqrt(-a^2*x^2 + 1))/a^5","A",0
265,1,64,0,0.472639," ","integrate(x^3*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{6 \, {\left(a^{3} x^{3} + 6 \, a x\right)} \arcsin\left(a x\right) + {\left(2 \, a^{2} x^{2} - 9 \, {\left(a^{2} x^{2} + 2\right)} \arcsin\left(a x\right)^{2} + 40\right)} \sqrt{-a^{2} x^{2} + 1}}{27 \, a^{4}}"," ",0,"1/27*(6*(a^3*x^3 + 6*a*x)*arcsin(a*x) + (2*a^2*x^2 - 9*(a^2*x^2 + 2)*arcsin(a*x)^2 + 40)*sqrt(-a^2*x^2 + 1))/a^4","A",0
266,1,59,0,0.443983," ","integrate(x^2*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \arcsin\left(a x\right)^{3} + 3 \, {\left(2 \, a^{2} x^{2} - 1\right)} \arcsin\left(a x\right) - 3 \, \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x \arcsin\left(a x\right)^{2} - a x\right)}}{12 \, a^{3}}"," ",0,"1/12*(2*arcsin(a*x)^3 + 3*(2*a^2*x^2 - 1)*arcsin(a*x) - 3*sqrt(-a^2*x^2 + 1)*(2*a*x*arcsin(a*x)^2 - a*x))/a^3","A",0
267,1,35,0,0.445364," ","integrate(x*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a x \arcsin\left(a x\right) - \sqrt{-a^{2} x^{2} + 1} {\left(\arcsin\left(a x\right)^{2} - 2\right)}}{a^{2}}"," ",0,"(2*a*x*arcsin(a*x) - sqrt(-a^2*x^2 + 1)*(arcsin(a*x)^2 - 2))/a^2","A",0
268,1,11,0,0.432338," ","integrate(arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\arcsin\left(a x\right)^{3}}{3 \, a}"," ",0,"1/3*arcsin(a*x)^3/a","A",0
269,0,0,0,0.469717," ","integrate(arcsin(a*x)^2/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{2}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^2/(a^2*x^3 - x), x)","F",0
270,0,0,0,0.476894," ","integrate(arcsin(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{2}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^2/(a^2*x^4 - x^2), x)","F",0
271,0,0,0,0.482950," ","integrate(arcsin(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{2}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^2/(a^2*x^5 - x^3), x)","F",0
272,0,0,0,0.424911," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{2}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^2/(a^2*c*x^2 - c), x)","F",0
273,0,0,0,0.482567," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{2}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^2/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
274,0,0,0,0.465128," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{2}}{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^2/(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3), x)","F",0
275,0,0,0,0.492305," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{2}}{a^{8} c^{4} x^{8} - 4 \, a^{6} c^{4} x^{6} + 6 \, a^{4} c^{4} x^{4} - 4 \, a^{2} c^{4} x^{2} + c^{4}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^2/(a^8*c^4*x^8 - 4*a^6*c^4*x^6 + 6*a^4*c^4*x^4 - 4*a^2*c^4*x^2 + c^4), x)","F",0
276,0,0,0,0.563467," ","integrate(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{6} d^{3} x^{6} - 3 \, a^{2} c^{4} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{2} - a^{2} d^{3} + {\left(b^{2} c^{6} d^{3} x^{6} - 3 \, b^{2} c^{4} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{2} - b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} d^{3} x^{6} - 3 \, a b c^{4} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{2} - a b d^{3}\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral(-(a^2*c^6*d^3*x^6 - 3*a^2*c^4*d^3*x^4 + 3*a^2*c^2*d^3*x^2 - a^2*d^3 + (b^2*c^6*d^3*x^6 - 3*b^2*c^4*d^3*x^4 + 3*b^2*c^2*d^3*x^2 - b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*c^6*d^3*x^6 - 3*a*b*c^4*d^3*x^4 + 3*a*b*c^2*d^3*x^2 - a*b*d^3)*arcsin(c*x))*x^m, x)","F",0
277,0,0,0,0.477632," ","integrate(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*x^m, x)","F",0
278,0,0,0,0.493725," ","integrate(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} x^{m}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*x^m, x)","F",0
279,0,0,0,0.457818," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^2*d*x^2 - d), x)","F",0
280,0,0,0,0.457830," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
281,0,0,0,1.193140," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
282,0,0,0,0.545576," ","integrate(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{4} d^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} x^{m}, x\right)"," ",0,"integral((a^2*c^4*d^2*x^4 - 2*a^2*c^2*d^2*x^2 + a^2*d^2 + (b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*x^m, x)","F",0
283,0,0,0,0.462057," ","integrate(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d x^{2} - a^{2} d + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} d x^{2} + d} x^{m}, x\right)"," ",0,"integral(-(a^2*c^2*d*x^2 - a^2*d + (b^2*c^2*d*x^2 - b^2*d)*arcsin(c*x)^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arcsin(c*x))*sqrt(-c^2*d*x^2 + d)*x^m, x)","F",0
284,0,0,0,0.432109," ","integrate(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m, x)","F",0
285,0,0,0,0.445060," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{2} d x^{2} - d}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^2*d*x^2 - d), x)","F",0
286,0,0,0,0.482845," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
287,0,0,0,0.458930," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} x^{m}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}, x\right)"," ",0,"integral(-sqrt(-c^2*d*x^2 + d)*(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*x^m/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x)","F",0
288,0,0,0,0.478583," ","integrate(x^m*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \arcsin\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)^2/(a^2*x^2 - 1), x)","F",0
289,1,202,0,0.455703," ","integrate((-a^2*c*x^2+c)^3*arcsin(a*x)^3,x, algorithm=""fricas"")","-\frac{385875 \, {\left(5 \, a^{7} c^{3} x^{7} - 21 \, a^{5} c^{3} x^{5} + 35 \, a^{3} c^{3} x^{3} - 35 \, a c^{3} x\right)} \arcsin\left(a x\right)^{3} - 210 \, {\left(1125 \, a^{7} c^{3} x^{7} - 7371 \, a^{5} c^{3} x^{5} + 26495 \, a^{3} c^{3} x^{3} - 226905 \, a c^{3} x\right)} \arcsin\left(a x\right) - {\left(33750 \, a^{6} c^{3} x^{6} - 269082 \, a^{4} c^{3} x^{4} + 1495874 \, a^{2} c^{3} x^{2} - 44658302 \, c^{3} - 11025 \, {\left(75 \, a^{6} c^{3} x^{6} - 351 \, a^{4} c^{3} x^{4} + 757 \, a^{2} c^{3} x^{2} - 2161 \, c^{3}\right)} \arcsin\left(a x\right)^{2}\right)} \sqrt{-a^{2} x^{2} + 1}}{13505625 \, a}"," ",0,"-1/13505625*(385875*(5*a^7*c^3*x^7 - 21*a^5*c^3*x^5 + 35*a^3*c^3*x^3 - 35*a*c^3*x)*arcsin(a*x)^3 - 210*(1125*a^7*c^3*x^7 - 7371*a^5*c^3*x^5 + 26495*a^3*c^3*x^3 - 226905*a*c^3*x)*arcsin(a*x) - (33750*a^6*c^3*x^6 - 269082*a^4*c^3*x^4 + 1495874*a^2*c^3*x^2 - 44658302*c^3 - 11025*(75*a^6*c^3*x^6 - 351*a^4*c^3*x^4 + 757*a^2*c^3*x^2 - 2161*c^3)*arcsin(a*x)^2)*sqrt(-a^2*x^2 + 1))/a","A",0
290,1,158,0,0.477474," ","integrate((-a^2*c*x^2+c)^2*arcsin(a*x)^3,x, algorithm=""fricas"")","\frac{1125 \, {\left(3 \, a^{5} c^{2} x^{5} - 10 \, a^{3} c^{2} x^{3} + 15 \, a c^{2} x\right)} \arcsin\left(a x\right)^{3} - 30 \, {\left(27 \, a^{5} c^{2} x^{5} - 190 \, a^{3} c^{2} x^{3} + 2235 \, a c^{2} x\right)} \arcsin\left(a x\right) - {\left(162 \, a^{4} c^{2} x^{4} - 1684 \, a^{2} c^{2} x^{2} - 225 \, {\left(9 \, a^{4} c^{2} x^{4} - 38 \, a^{2} c^{2} x^{2} + 149 \, c^{2}\right)} \arcsin\left(a x\right)^{2} + 63682 \, c^{2}\right)} \sqrt{-a^{2} x^{2} + 1}}{16875 \, a}"," ",0,"1/16875*(1125*(3*a^5*c^2*x^5 - 10*a^3*c^2*x^3 + 15*a*c^2*x)*arcsin(a*x)^3 - 30*(27*a^5*c^2*x^5 - 190*a^3*c^2*x^3 + 2235*a*c^2*x)*arcsin(a*x) - (162*a^4*c^2*x^4 - 1684*a^2*c^2*x^2 - 225*(9*a^4*c^2*x^4 - 38*a^2*c^2*x^2 + 149*c^2)*arcsin(a*x)^2 + 63682*c^2)*sqrt(-a^2*x^2 + 1))/a","A",0
291,1,95,0,0.455125," ","integrate((-a^2*c*x^2+c)*arcsin(a*x)^3,x, algorithm=""fricas"")","-\frac{9 \, {\left(a^{3} c x^{3} - 3 \, a c x\right)} \arcsin\left(a x\right)^{3} - 6 \, {\left(a^{3} c x^{3} - 21 \, a c x\right)} \arcsin\left(a x\right) - {\left(2 \, a^{2} c x^{2} - 9 \, {\left(a^{2} c x^{2} - 7 \, c\right)} \arcsin\left(a x\right)^{2} - 122 \, c\right)} \sqrt{-a^{2} x^{2} + 1}}{27 \, a}"," ",0,"-1/27*(9*(a^3*c*x^3 - 3*a*c*x)*arcsin(a*x)^3 - 6*(a^3*c*x^3 - 21*a*c*x)*arcsin(a*x) - (2*a^2*c*x^2 - 9*(a^2*c*x^2 - 7*c)*arcsin(a*x)^2 - 122*c)*sqrt(-a^2*x^2 + 1))/a","A",0
292,0,0,0,0.453188," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\arcsin\left(a x\right)^{3}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(-arcsin(a*x)^3/(a^2*c*x^2 - c), x)","F",0
293,0,0,0,0.463249," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arcsin\left(a x\right)^{3}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(arcsin(a*x)^3/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
294,0,0,0,0.474698," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\arcsin\left(a x\right)^{3}}{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}, x\right)"," ",0,"integral(-arcsin(a*x)^3/(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3), x)","F",0
295,0,0,0,0.449397," ","integrate((-a^2*c*x^2+c)^(5/2)*arcsin(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3, x)","F",0
296,0,0,0,0.464326," ","integrate((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}, x\right)"," ",0,"integral(-(a^2*c*x^2 - c)*sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3, x)","F",0
297,0,0,0,0.451563," ","integrate((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3, x)","F",0
298,0,0,0,0.446878," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3/(a^2*c*x^2 - c), x)","F",0
299,0,0,0,0.443926," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}}{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3/(a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2), x)","F",0
300,0,0,0,0.495485," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}}{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3/(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3), x)","F",0
301,0,0,0,0.475539," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}}{a^{8} c^{4} x^{8} - 4 \, a^{6} c^{4} x^{6} + 6 \, a^{4} c^{4} x^{4} - 4 \, a^{2} c^{4} x^{2} + c^{4}}, x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3/(a^8*c^4*x^8 - 4*a^6*c^4*x^6 + 6*a^4*c^4*x^4 - 4*a^2*c^4*x^2 + c^4), x)","F",0
302,0,0,0,0.475133," ","integrate(x^m*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \arcsin\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)^3/(a^2*x^2 - 1), x)","F",0
303,1,111,0,0.463257," ","integrate(x^4*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, a^{4} x^{4} + 45 \, a^{2} x^{2} - 12 \, \arcsin\left(a x\right)^{4} - 3 \, {\left(8 \, a^{4} x^{4} + 24 \, a^{2} x^{2} - 15\right)} \arcsin\left(a x\right)^{2} + 2 \, \sqrt{-a^{2} x^{2} + 1} {\left(8 \, {\left(2 \, a^{3} x^{3} + 3 \, a x\right)} \arcsin\left(a x\right)^{3} - 3 \, {\left(2 \, a^{3} x^{3} + 15 \, a x\right)} \arcsin\left(a x\right)\right)}}{128 \, a^{5}}"," ",0,"-1/128*(3*a^4*x^4 + 45*a^2*x^2 - 12*arcsin(a*x)^4 - 3*(8*a^4*x^4 + 24*a^2*x^2 - 15)*arcsin(a*x)^2 + 2*sqrt(-a^2*x^2 + 1)*(8*(2*a^3*x^3 + 3*a*x)*arcsin(a*x)^3 - 3*(2*a^3*x^3 + 15*a*x)*arcsin(a*x)))/a^5","A",0
304,1,85,0,0.428181," ","integrate(x^3*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, a^{3} x^{3} - 9 \, {\left(a^{3} x^{3} + 6 \, a x\right)} \arcsin\left(a x\right)^{2} + 120 \, a x + 3 \, \sqrt{-a^{2} x^{2} + 1} {\left(3 \, {\left(a^{2} x^{2} + 2\right)} \arcsin\left(a x\right)^{3} - 2 \, {\left(a^{2} x^{2} + 20\right)} \arcsin\left(a x\right)\right)}}{27 \, a^{4}}"," ",0,"-1/27*(2*a^3*x^3 - 9*(a^3*x^3 + 6*a*x)*arcsin(a*x)^2 + 120*a*x + 3*sqrt(-a^2*x^2 + 1)*(3*(a^2*x^2 + 2)*arcsin(a*x)^3 - 2*(a^2*x^2 + 20)*arcsin(a*x)))/a^4","A",0
305,1,73,0,0.464648," ","integrate(x^2*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, a^{2} x^{2} - \arcsin\left(a x\right)^{4} - 3 \, {\left(2 \, a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)^{2} + 2 \, {\left(2 \, a x \arcsin\left(a x\right)^{3} - 3 \, a x \arcsin\left(a x\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{8 \, a^{3}}"," ",0,"-1/8*(3*a^2*x^2 - arcsin(a*x)^4 - 3*(2*a^2*x^2 - 1)*arcsin(a*x)^2 + 2*(2*a*x*arcsin(a*x)^3 - 3*a*x*arcsin(a*x))*sqrt(-a^2*x^2 + 1))/a^3","A",0
306,1,46,0,0.483516," ","integrate(x*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{3 \, a x \arcsin\left(a x\right)^{2} - 6 \, a x - \sqrt{-a^{2} x^{2} + 1} {\left(\arcsin\left(a x\right)^{3} - 6 \, \arcsin\left(a x\right)\right)}}{a^{2}}"," ",0,"(3*a*x*arcsin(a*x)^2 - 6*a*x - sqrt(-a^2*x^2 + 1)*(arcsin(a*x)^3 - 6*arcsin(a*x)))/a^2","A",0
307,1,11,0,0.434516," ","integrate(arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\arcsin\left(a x\right)^{4}}{4 \, a}"," ",0,"1/4*arcsin(a*x)^4/a","A",0
308,0,0,0,0.455899," ","integrate(arcsin(a*x)^3/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{3}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^3/(a^2*x^3 - x), x)","F",0
309,0,0,0,0.444472," ","integrate(arcsin(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{3}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^3/(a^2*x^4 - x^2), x)","F",0
310,0,0,0,0.467573," ","integrate(arcsin(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{3}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^3/(a^2*x^5 - x^3), x)","F",0
311,0,0,0,0.413545," ","integrate((-a^2*c*x^2+c)^3/arcsin(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}{\arcsin\left(a x\right)}, x\right)"," ",0,"integral(-(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)/arcsin(a*x), x)","F",0
312,0,0,0,0.440725," ","integrate((-a^2*c*x^2+c)^2/arcsin(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}{\arcsin\left(a x\right)}, x\right)"," ",0,"integral((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)/arcsin(a*x), x)","F",0
313,0,0,0,0.469306," ","integrate((-a^2*c*x^2+c)/arcsin(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c x^{2} - c}{\arcsin\left(a x\right)}, x\right)"," ",0,"integral(-(a^2*c*x^2 - c)/arcsin(a*x), x)","F",0
314,0,0,0,0.631557," ","integrate(1/(-a^2*c*x^2+c)/arcsin(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} c x^{2} - c\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-1/((a^2*c*x^2 - c)*arcsin(a*x)), x)","F",0
315,0,0,0,0.513078," ","integrate(1/(-a^2*c*x^2+c)^2/arcsin(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(1/((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*arcsin(a*x)), x)","F",0
316,0,0,0,0.463965," ","integrate(x^4*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{4}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^4/(b*arcsin(c*x) + a), x)","F",0
317,0,0,0,0.437780," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^3/(b*arcsin(c*x) + a), x)","F",0
318,0,0,0,0.684964," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^2/(b*arcsin(c*x) + a), x)","F",0
319,0,0,0,0.458765," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x/(b*arcsin(c*x) + a), x)","F",0
320,-1,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,0,0,0,1.243518," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b x \arcsin\left(c x\right) + a x}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b*x*arcsin(c*x) + a*x), x)","F",0
322,0,0,0,2.364108," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b x^{2} \arcsin\left(c x\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b*x^2*arcsin(c*x) + a*x^2), x)","F",0
323,0,0,0,0.679021," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b x^{3} \arcsin\left(c x\right) + a x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b*x^3*arcsin(c*x) + a*x^3), x)","F",0
324,0,0,0,2.938376," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b x^{4} \arcsin\left(c x\right) + a x^{4}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b*x^4*arcsin(c*x) + a*x^4), x)","F",0
325,0,0,0,1.298882," ","integrate(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{5} - x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(-(c^2*x^5 - x^3)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
326,0,0,0,0.722911," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{4} - x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(-(c^2*x^4 - x^2)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
327,0,0,0,0.682432," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{3} - x\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(-(c^2*x^3 - x)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
328,0,0,0,0.521735," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b*arcsin(c*x) + a), x)","F",0
329,0,0,0,1.326529," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b x \arcsin\left(c x\right) + a x}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b*x*arcsin(c*x) + a*x), x)","F",0
330,0,0,0,0.511004," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b x^{2} \arcsin\left(c x\right) + a x^{2}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b*x^2*arcsin(c*x) + a*x^2), x)","F",0
331,0,0,0,0.538508," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b x^{3} \arcsin\left(c x\right) + a x^{3}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b*x^3*arcsin(c*x) + a*x^3), x)","F",0
332,0,0,0,1.836154," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b x^{4} \arcsin\left(c x\right) + a x^{4}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b*x^4*arcsin(c*x) + a*x^4), x)","F",0
333,0,0,0,0.787708," ","integrate(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{7} - 2 \, c^{2} x^{5} + x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((c^4*x^7 - 2*c^2*x^5 + x^3)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
334,0,0,0,0.530490," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{6} - 2 \, c^{2} x^{4} + x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((c^4*x^6 - 2*c^2*x^4 + x^2)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
335,0,0,0,1.083452," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{5} - 2 \, c^{2} x^{3} + x\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((c^4*x^5 - 2*c^2*x^3 + x)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
336,0,0,0,2.059505," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
337,0,0,0,1.002998," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b x \arcsin\left(c x\right) + a x}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b*x*arcsin(c*x) + a*x), x)","F",0
338,0,0,0,1.147388," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b x^{2} \arcsin\left(c x\right) + a x^{2}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b*x^2*arcsin(c*x) + a*x^2), x)","F",0
339,0,0,0,3.637523," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b x^{3} \arcsin\left(c x\right) + a x^{3}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b*x^3*arcsin(c*x) + a*x^3), x)","F",0
340,0,0,0,1.051039," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b x^{4} \arcsin\left(c x\right) + a x^{4}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b*x^4*arcsin(c*x) + a*x^4), x)","F",0
341,0,0,0,0.577292," ","integrate(x^4/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{4}}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^4/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
342,0,0,0,0.568217," ","integrate(x^3/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{3}}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^3/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
343,0,0,0,1.773570," ","integrate(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
344,0,0,0,2.061101," ","integrate(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
345,0,0,0,0.699474," ","integrate(x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
346,1,11,0,2.436723," ","integrate(1/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(-\arcsin\left(a x\right)\right)}{a}"," ",0,"log(-arcsin(a*x))/a","A",0
347,0,0,0,1.004968," ","integrate(1/x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x^{3} - x\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^2*x^3 - x)*arcsin(a*x)), x)","F",0
348,0,0,0,0.642076," ","integrate(1/x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x^{4} - x^{2}\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^2*x^4 - x^2)*arcsin(a*x)), x)","F",0
349,0,0,0,1.125671," ","integrate(x^5/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{5}}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^5/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
350,0,0,0,0.568094," ","integrate(x^4/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{4}}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^4/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
351,0,0,0,0.650546," ","integrate(x^3/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^3/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
352,0,0,0,0.497416," ","integrate(x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^2/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
353,0,0,0,0.650345," ","integrate(x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
354,1,19,0,0.604029," ","integrate(1/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\log\left(-b \arcsin\left(c x\right) - a\right)}{b c}"," ",0,"log(-b*arcsin(c*x) - a)/(b*c)","A",0
355,0,0,0,0.527353," ","integrate(1/x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{2} x^{3} - a x + {\left(b c^{2} x^{3} - b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a*c^2*x^3 - a*x + (b*c^2*x^3 - b*x)*arcsin(c*x)), x)","F",0
356,0,0,0,0.670593," ","integrate(1/x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{2} x^{4} - a x^{2} + {\left(b c^{2} x^{4} - b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a*c^2*x^4 - a*x^2 + (b*c^2*x^4 - b*x^2)*arcsin(c*x)), x)","F",0
357,0,0,0,0.507395," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^2/(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a), x)","F",0
358,0,0,0,0.645218," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x/(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a), x)","F",0
359,0,0,0,1.126828," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a), x)","F",0
360,0,0,0,0.480460," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{4} x^{5} - 2 \, a c^{2} x^{3} + a x + {\left(b c^{4} x^{5} - 2 \, b c^{2} x^{3} + b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a*c^4*x^5 - 2*a*c^2*x^3 + a*x + (b*c^4*x^5 - 2*b*c^2*x^3 + b*x)*arcsin(c*x)), x)","F",0
361,0,0,0,0.394962," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{4} x^{6} - 2 \, a c^{2} x^{4} + a x^{2} + {\left(b c^{4} x^{6} - 2 \, b c^{2} x^{4} + b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a*c^4*x^6 - 2*a*c^2*x^4 + a*x^2 + (b*c^4*x^6 - 2*b*c^2*x^4 + b*x^2)*arcsin(c*x)), x)","F",0
362,0,0,0,0.405000," ","integrate(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a c^{6} x^{6} - 3 \, a c^{4} x^{4} + 3 \, a c^{2} x^{2} + {\left(b c^{6} x^{6} - 3 \, b c^{4} x^{4} + 3 \, b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^2/(a*c^6*x^6 - 3*a*c^4*x^4 + 3*a*c^2*x^2 + (b*c^6*x^6 - 3*b*c^4*x^4 + 3*b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
363,0,0,0,0.640269," ","integrate(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x}{a c^{6} x^{6} - 3 \, a c^{4} x^{4} + 3 \, a c^{2} x^{2} + {\left(b c^{6} x^{6} - 3 \, b c^{4} x^{4} + 3 \, b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x/(a*c^6*x^6 - 3*a*c^4*x^4 + 3*a*c^2*x^2 + (b*c^6*x^6 - 3*b*c^4*x^4 + 3*b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
364,0,0,0,1.633718," ","integrate(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{6} x^{6} - 3 \, a c^{4} x^{4} + 3 \, a c^{2} x^{2} + {\left(b c^{6} x^{6} - 3 \, b c^{4} x^{4} + 3 \, b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a*c^6*x^6 - 3*a*c^4*x^4 + 3*a*c^2*x^2 + (b*c^6*x^6 - 3*b*c^4*x^4 + 3*b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
365,0,0,0,2.097488," ","integrate(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{6} x^{7} - 3 \, a c^{4} x^{5} + 3 \, a c^{2} x^{3} - a x + {\left(b c^{6} x^{7} - 3 \, b c^{4} x^{5} + 3 \, b c^{2} x^{3} - b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a*c^6*x^7 - 3*a*c^4*x^5 + 3*a*c^2*x^3 - a*x + (b*c^6*x^7 - 3*b*c^4*x^5 + 3*b*c^2*x^3 - b*x)*arcsin(c*x)), x)","F",0
366,0,0,0,0.444449," ","integrate(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a c^{6} x^{8} - 3 \, a c^{4} x^{6} + 3 \, a c^{2} x^{4} - a x^{2} + {\left(b c^{6} x^{8} - 3 \, b c^{4} x^{6} + 3 \, b c^{2} x^{4} - b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a*c^6*x^8 - 3*a*c^4*x^6 + 3*a*c^2*x^4 - a*x^2 + (b*c^6*x^8 - 3*b*c^4*x^6 + 3*b*c^2*x^4 - b*x^2)*arcsin(c*x)), x)","F",0
367,0,0,0,0.409956," ","integrate(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1} x^{m}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)*x^m/(b*arcsin(c*x) + a), x)","F",0
368,0,0,0,0.423203," ","integrate(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{2} - 1\right)} \sqrt{-c^{2} x^{2} + 1} x^{m}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(-(c^2*x^2 - 1)*sqrt(-c^2*x^2 + 1)*x^m/(b*arcsin(c*x) + a), x)","F",0
369,0,0,0,0.406194," ","integrate(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^m/(b*arcsin(c*x) + a), x)","F",0
370,0,0,0,0.444280," ","integrate(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^m/(a*c^2*x^2 + (b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
371,0,0,0,0.505476," ","integrate(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a c^{4} x^{4} - 2 \, a c^{2} x^{2} + {\left(b c^{4} x^{4} - 2 \, b c^{2} x^{2} + b\right)} \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^m/(a*c^4*x^4 - 2*a*c^2*x^2 + (b*c^4*x^4 - 2*b*c^2*x^2 + b)*arcsin(c*x) + a), x)","F",0
372,0,0,0,0.512932," ","integrate(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a c^{6} x^{6} - 3 \, a c^{4} x^{4} + 3 \, a c^{2} x^{2} + {\left(b c^{6} x^{6} - 3 \, b c^{4} x^{4} + 3 \, b c^{2} x^{2} - b\right)} \arcsin\left(c x\right) - a}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^m/(a*c^6*x^6 - 3*a*c^4*x^4 + 3*a*c^2*x^2 + (b*c^6*x^6 - 3*b*c^4*x^4 + 3*b*c^2*x^2 - b)*arcsin(c*x) - a), x)","F",0
373,0,0,0,0.473193," ","integrate(x^m/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{{\left(a^{2} x^{2} - 1\right)} \arcsin\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^m/((a^2*x^2 - 1)*arcsin(a*x)), x)","F",0
374,0,0,0,0.550280," ","integrate((-a^2*c*x^2+c)^3/arcsin(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}}{\arcsin\left(a x\right)^{2}}, x\right)"," ",0,"integral(-(a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)/arcsin(a*x)^2, x)","F",0
375,0,0,0,0.403196," ","integrate((-a^2*c*x^2+c)^2/arcsin(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}}{\arcsin\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)/arcsin(a*x)^2, x)","F",0
376,0,0,0,0.447791," ","integrate((-a^2*c*x^2+c)/arcsin(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} c x^{2} - c}{\arcsin\left(a x\right)^{2}}, x\right)"," ",0,"integral(-(a^2*c*x^2 - c)/arcsin(a*x)^2, x)","F",0
377,0,0,0,0.444180," ","integrate(1/(-a^2*c*x^2+c)/arcsin(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} c x^{2} - c\right)} \arcsin\left(a x\right)^{2}}, x\right)"," ",0,"integral(-1/((a^2*c*x^2 - c)*arcsin(a*x)^2), x)","F",0
378,0,0,0,0.488838," ","integrate(1/(-a^2*c*x^2+c)^2/arcsin(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \arcsin\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*arcsin(a*x)^2), x)","F",0
379,1,21,0,0.389528," ","integrate(1/(-x^2+1)/arcsin(x)^2-x/(-x^2+1)^(3/2)/arcsin(x),x, algorithm=""fricas"")","\frac{\sqrt{-x^{2} + 1}}{{\left(x^{2} - 1\right)} \arcsin\left(x\right)}"," ",0,"sqrt(-x^2 + 1)/((x^2 - 1)*arcsin(x))","A",0
380,0,0,0,0.530736," ","integrate(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^m/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
381,0,0,0,0.525154," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^3/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
382,0,0,0,0.535995," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^2/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
383,0,0,0,0.565475," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
384,0,0,0,0.498024," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
385,0,0,0,0.428038," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x), x)","F",0
386,0,0,0,0.423949," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2), x)","F",0
387,0,0,0,0.586663," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3), x)","F",0
388,0,0,0,0.476301," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4), x)","F",0
389,0,0,0,0.505274," ","integrate(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{2} - 1\right)} \sqrt{-c^{2} x^{2} + 1} x^{m}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(-(c^2*x^2 - 1)*sqrt(-c^2*x^2 + 1)*x^m/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
390,0,0,0,0.563788," ","integrate(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{5} - x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(-(c^2*x^5 - x^3)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
391,0,0,0,0.501919," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{4} - x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(-(c^2*x^4 - x^2)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
392,0,0,0,0.426998," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} x^{3} - x\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(-(c^2*x^3 - x)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
393,0,0,0,0.403236," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
394,0,0,0,0.396775," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x), x)","F",0
395,0,0,0,0.536367," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2), x)","F",0
396,0,0,0,0.427131," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3), x)","F",0
397,0,0,0,0.450407," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}, x\right)"," ",0,"integral((-c^2*x^2 + 1)^(3/2)/(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4), x)","F",0
398,0,0,0,0.436474," ","integrate(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1} x^{m}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)*x^m/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
399,0,0,0,0.430154," ","integrate(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{7} - 2 \, c^{2} x^{5} + x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((c^4*x^7 - 2*c^2*x^5 + x^3)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
400,0,0,0,0.404043," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{6} - 2 \, c^{2} x^{4} + x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((c^4*x^6 - 2*c^2*x^4 + x^2)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
401,0,0,0,0.411914," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{5} - 2 \, c^{2} x^{3} + x\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((c^4*x^5 - 2*c^2*x^3 + x)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
402,0,0,0,0.404924," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
403,0,0,0,0.424280," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x), x)","F",0
404,0,0,0,0.393578," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2), x)","F",0
405,0,0,0,0.409734," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{3} \arcsin\left(c x\right)^{2} + 2 \, a b x^{3} \arcsin\left(c x\right) + a^{2} x^{3}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b^2*x^3*arcsin(c*x)^2 + 2*a*b*x^3*arcsin(c*x) + a^2*x^3), x)","F",0
406,0,0,0,0.417623," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \sqrt{-c^{2} x^{2} + 1}}{b^{2} x^{4} \arcsin\left(c x\right)^{2} + 2 \, a b x^{4} \arcsin\left(c x\right) + a^{2} x^{4}}, x\right)"," ",0,"integral((c^4*x^4 - 2*c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(b^2*x^4*arcsin(c*x)^2 + 2*a*b*x^4*arcsin(c*x) + a^2*x^4), x)","F",0
407,0,0,0,0.506255," ","integrate(x^m/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^m/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
408,0,0,0,0.405009," ","integrate(x^5/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{5}}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^5/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
409,0,0,0,0.402828," ","integrate(x^4/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{4}}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^4/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
410,0,0,0,0.418711," ","integrate(x^3/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^3/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
411,0,0,0,0.402531," ","integrate(x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^2/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
412,0,0,0,0.460730," ","integrate(x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
413,1,18,0,0.509028," ","integrate(1/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{b^{2} c \arcsin\left(c x\right) + a b c}"," ",0,"-1/(b^2*c*arcsin(c*x) + a*b*c)","A",0
414,0,0,0,0.410572," ","integrate(1/x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{2} x^{3} - a^{2} x + {\left(b^{2} c^{2} x^{3} - b^{2} x\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} x^{3} - a b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a^2*c^2*x^3 - a^2*x + (b^2*c^2*x^3 - b^2*x)*arcsin(c*x)^2 + 2*(a*b*c^2*x^3 - a*b*x)*arcsin(c*x)), x)","F",0
415,0,0,0,0.417134," ","integrate(1/x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{2} x^{4} - a^{2} x^{2} + {\left(b^{2} c^{2} x^{4} - b^{2} x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} x^{4} - a b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a^2*c^2*x^4 - a^2*x^2 + (b^2*c^2*x^4 - b^2*x^2)*arcsin(c*x)^2 + 2*(a*b*c^2*x^4 - a*b*x^2)*arcsin(c*x)), x)","F",0
416,0,0,0,0.447731," ","integrate(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a^{2} c^{4} x^{4} - 2 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^m/(a^2*c^4*x^4 - 2*a^2*c^2*x^2 + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + a^2 + 2*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x)), x)","F",0
417,0,0,0,0.447099," ","integrate(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{a^{2} c^{4} x^{4} - 2 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^3/(a^2*c^4*x^4 - 2*a^2*c^2*x^2 + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + a^2 + 2*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x)), x)","F",0
418,0,0,0,0.462385," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a^{2} c^{4} x^{4} - 2 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x^2/(a^2*c^4*x^4 - 2*a^2*c^2*x^2 + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + a^2 + 2*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x)), x)","F",0
419,0,0,0,0.441067," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{a^{2} c^{4} x^{4} - 2 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)*x/(a^2*c^4*x^4 - 2*a^2*c^2*x^2 + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + a^2 + 2*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x)), x)","F",0
420,0,0,0,0.415465," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{4} x^{4} - 2 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + a^{2} + 2 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a^2*c^4*x^4 - 2*a^2*c^2*x^2 + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + a^2 + 2*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x)), x)","F",0
421,0,0,0,0.419431," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{4} x^{5} - 2 \, a^{2} c^{2} x^{3} + a^{2} x + {\left(b^{2} c^{4} x^{5} - 2 \, b^{2} c^{2} x^{3} + b^{2} x\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} x^{5} - 2 \, a b c^{2} x^{3} + a b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a^2*c^4*x^5 - 2*a^2*c^2*x^3 + a^2*x + (b^2*c^4*x^5 - 2*b^2*c^2*x^3 + b^2*x)*arcsin(c*x)^2 + 2*(a*b*c^4*x^5 - 2*a*b*c^2*x^3 + a*b*x)*arcsin(c*x)), x)","F",0
422,0,0,0,0.461350," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{4} x^{6} - 2 \, a^{2} c^{2} x^{4} + a^{2} x^{2} + {\left(b^{2} c^{4} x^{6} - 2 \, b^{2} c^{2} x^{4} + b^{2} x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} x^{6} - 2 \, a b c^{2} x^{4} + a b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/(a^2*c^4*x^6 - 2*a^2*c^2*x^4 + a^2*x^2 + (b^2*c^4*x^6 - 2*b^2*c^2*x^4 + b^2*x^2)*arcsin(c*x)^2 + 2*(a*b*c^4*x^6 - 2*a*b*c^2*x^4 + a*b*x^2)*arcsin(c*x)), x)","F",0
423,0,0,0,0.443010," ","integrate(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{a^{2} c^{6} x^{6} - 3 \, a^{2} c^{4} x^{4} + 3 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^m/(a^2*c^6*x^6 - 3*a^2*c^4*x^4 + 3*a^2*c^2*x^2 + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
424,0,0,0,0.671127," ","integrate(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{a^{2} c^{6} x^{6} - 3 \, a^{2} c^{4} x^{4} + 3 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^3/(a^2*c^6*x^6 - 3*a^2*c^4*x^4 + 3*a^2*c^2*x^2 + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
425,0,0,0,0.436189," ","integrate(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{a^{2} c^{6} x^{6} - 3 \, a^{2} c^{4} x^{4} + 3 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x^2/(a^2*c^6*x^6 - 3*a^2*c^4*x^4 + 3*a^2*c^2*x^2 + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
426,0,0,0,0.599950," ","integrate(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1} x}{a^{2} c^{6} x^{6} - 3 \, a^{2} c^{4} x^{4} + 3 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)*x/(a^2*c^6*x^6 - 3*a^2*c^4*x^4 + 3*a^2*c^2*x^2 + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
427,0,0,0,0.428919," ","integrate(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{6} x^{6} - 3 \, a^{2} c^{4} x^{4} + 3 \, a^{2} c^{2} x^{2} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a^2*c^6*x^6 - 3*a^2*c^4*x^4 + 3*a^2*c^2*x^2 + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*arcsin(c*x)), x)","F",0
428,0,0,0,0.409176," ","integrate(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{6} x^{7} - 3 \, a^{2} c^{4} x^{5} + 3 \, a^{2} c^{2} x^{3} - a^{2} x + {\left(b^{2} c^{6} x^{7} - 3 \, b^{2} c^{4} x^{5} + 3 \, b^{2} c^{2} x^{3} - b^{2} x\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} x^{7} - 3 \, a b c^{4} x^{5} + 3 \, a b c^{2} x^{3} - a b x\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a^2*c^6*x^7 - 3*a^2*c^4*x^5 + 3*a^2*c^2*x^3 - a^2*x + (b^2*c^6*x^7 - 3*b^2*c^4*x^5 + 3*b^2*c^2*x^3 - b^2*x)*arcsin(c*x)^2 + 2*(a*b*c^6*x^7 - 3*a*b*c^4*x^5 + 3*a*b*c^2*x^3 - a*b*x)*arcsin(c*x)), x)","F",0
429,0,0,0,0.405352," ","integrate(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{2} x^{2} + 1}}{a^{2} c^{6} x^{8} - 3 \, a^{2} c^{4} x^{6} + 3 \, a^{2} c^{2} x^{4} - a^{2} x^{2} + {\left(b^{2} c^{6} x^{8} - 3 \, b^{2} c^{4} x^{6} + 3 \, b^{2} c^{2} x^{4} - b^{2} x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{6} x^{8} - 3 \, a b c^{4} x^{6} + 3 \, a b c^{2} x^{4} - a b x^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(-sqrt(-c^2*x^2 + 1)/(a^2*c^6*x^8 - 3*a^2*c^4*x^6 + 3*a^2*c^2*x^4 - a^2*x^2 + (b^2*c^6*x^8 - 3*b^2*c^4*x^6 + 3*b^2*c^2*x^4 - b^2*x^2)*arcsin(c*x)^2 + 2*(a*b*c^6*x^8 - 3*a*b*c^4*x^6 + 3*a*b*c^2*x^4 - a*b*x^2)*arcsin(c*x)), x)","F",0
430,1,11,0,0.508821," ","integrate(1/arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{1}{2 \, a \arcsin\left(a x\right)^{2}}"," ",0,"-1/2/(a*arcsin(a*x)^2)","A",0
431,-2,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
432,-2,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
433,-2,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
434,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
435,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/x/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
436,-2,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
437,-2,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
438,-2,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
439,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
440,-2,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/x/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
441,-2,0,0,0.000000," ","integrate(x*arcsin(x)^(3/2)/(-x^2+1)^2-3/8*x/(-x^2+1)/arcsin(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
442,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
443,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
444,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
445,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
446,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
447,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
448,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
449,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
450,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
451,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
452,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
453,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(5/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
454,-2,0,0,0.000000," ","integrate(arcsin(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
455,-2,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arcsin(x/a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
456,-2,0,0,0.000000," ","integrate((a^2-x^2)^(1/2)*arcsin(x/a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
457,1,36,0,0.387647," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(1/2),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{-\arctan\left(-\frac{x}{\sqrt{a^{2} - x^{2}}}\right)} \arctan\left(-\frac{x}{\sqrt{a^{2} - x^{2}}}\right)"," ",0,"-2/3*sqrt(-arctan(-x/sqrt(a^2 - x^2)))*arctan(-x/sqrt(a^2 - x^2))","A",0
458,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
459,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
460,-2,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arcsin(x/a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
461,-2,0,0,0.000000," ","integrate((a^2-x^2)^(1/2)*arcsin(x/a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
462,1,38,0,0.454596," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{-\arctan\left(-\frac{x}{\sqrt{a^{2} - x^{2}}}\right)} \arctan\left(-\frac{x}{\sqrt{a^{2} - x^{2}}}\right)^{2}"," ",0,"2/5*sqrt(-arctan(-x/sqrt(a^2 - x^2)))*arctan(-x/sqrt(a^2 - x^2))^2","A",0
463,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
464,-2,0,0,0.000000," ","integrate(x/(-x^2+1)^(1/2)/arcsin(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
465,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
466,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
467,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
468,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
469,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
470,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
471,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
472,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
473,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
474,1,48,0,0.396512," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{{\left(a^{3} c x^{2} - a c\right)} \sqrt{\arcsin\left(a x\right)}}"," ",0,"2*sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/((a^3*c*x^2 - a*c)*sqrt(arcsin(a*x)))","A",0
475,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
476,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
477,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
478,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
479,1,48,0,0.478155," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-a^{2} c x^{2} + c} \sqrt{-a^{2} x^{2} + 1}}{3 \, {\left(a^{3} c x^{2} - a c\right)} \arcsin\left(a x\right)^{\frac{3}{2}}}"," ",0,"2/3*sqrt(-a^2*c*x^2 + c)*sqrt(-a^2*x^2 + 1)/((a^3*c*x^2 - a*c)*arcsin(a*x)^(3/2))","A",0
480,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
481,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
482,0,0,0,0.477003," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x^{2}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n*x^2, x)","F",0
483,0,0,0,0.457678," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n*x, x)","F",0
484,0,0,0,0.609730," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
485,0,0,0,0.548241," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x, x)","F",0
486,0,0,0,0.448622," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
487,0,0,0,0.446801," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} d x^{4} - d x^{2}\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral(-(c^2*d*x^4 - d*x^2)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
488,0,0,0,0.434468," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} d x^{3} - d x\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral(-(c^2*d*x^3 - d*x)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
489,0,0,0,0.473264," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n, x)","F",0
490,0,0,0,0.450378," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}, x\right)"," ",0,"integral((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n/x, x)","F",0
491,0,0,0,0.457251," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
492,0,0,0,0.439222," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral((c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
493,0,0,0,0.433761," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral((c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
494,0,0,0,0.476498," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}, x\right)"," ",0,"integral((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
495,0,0,0,0.435396," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}, x\right)"," ",0,"integral((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x, x)","F",0
496,0,0,0,0.456772," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}, x\right)"," ",0,"integral((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
497,0,0,0,0.431596," ","integrate(x^m*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \arcsin\left(a x\right)^{n}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^m*arcsin(a*x)^n/(a^2*x^2 - 1), x)","F",0
498,0,0,0,0.441659," ","integrate(x^3*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{3} \arcsin\left(a x\right)^{n}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^3*arcsin(a*x)^n/(a^2*x^2 - 1), x)","F",0
499,0,0,0,0.433755," ","integrate(x^2*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \arcsin\left(a x\right)^{n}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2*arcsin(a*x)^n/(a^2*x^2 - 1), x)","F",0
500,0,0,0,0.469316," ","integrate(x*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x \arcsin\left(a x\right)^{n}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x*arcsin(a*x)^n/(a^2*x^2 - 1), x)","F",0
501,1,18,0,0.426327," ","integrate(arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\arcsin\left(a x\right)^{n} \arcsin\left(a x\right)}{a n + a}"," ",0,"arcsin(a*x)^n*arcsin(a*x)/(a*n + a)","A",0
502,0,0,0,0.436799," ","integrate(arcsin(a*x)^n/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{n}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^n/(a^2*x^3 - x), x)","F",0
503,0,0,0,0.433221," ","integrate(arcsin(a*x)^n/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{n}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^n/(a^2*x^4 - x^2), x)","F",0
504,0,0,0,0.435055," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral((a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
505,0,0,0,0.441968," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c d x + a d + {\left(b c d x + b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral((a*c*d*x + a*d + (b*c*d*x + b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
506,0,0,0,0.409295," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a), x)","F",0
507,0,0,0,0.547894," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral(sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/sqrt(c*d*x + d), x)","F",0
508,0,0,0,0.478801," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral(sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
509,1,520,0,0.624414," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{3} d x^{3} + b c^{2} d x^{2} - b c d x - b d\right)} \sqrt{\frac{f}{d}} \log\left(\frac{c^{6} f x^{6} + 4 \, c^{5} f x^{5} + 5 \, c^{4} f x^{4} - 4 \, c^{2} f x^{2} - 4 \, c f x + {\left(c^{4} x^{4} + 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} + 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{\frac{f}{d}} - 2 \, f}{c^{4} x^{4} + 2 \, c^{3} x^{3} - 2 \, c x - 1}\right) + 2 \, {\left(a c^{2} x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b c x - 2 \, a c x + {\left(b c^{2} x^{2} - 2 \, b c x + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{6 \, {\left(c^{4} d^{3} x^{3} + c^{3} d^{3} x^{2} - c^{2} d^{3} x - c d^{3}\right)}}, -\frac{{\left(b c^{3} d x^{3} + b c^{2} d x^{2} - b c d x - b d\right)} \sqrt{-\frac{f}{d}} \arctan\left(\frac{{\left(c^{2} x^{2} + 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-\frac{f}{d}}}{c^{4} f x^{4} + 2 \, c^{3} f x^{3} - c^{2} f x^{2} - 2 \, c f x}\right) - {\left(a c^{2} x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b c x - 2 \, a c x + {\left(b c^{2} x^{2} - 2 \, b c x + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{3 \, {\left(c^{4} d^{3} x^{3} + c^{3} d^{3} x^{2} - c^{2} d^{3} x - c d^{3}\right)}}\right]"," ",0,"[1/6*((b*c^3*d*x^3 + b*c^2*d*x^2 - b*c*d*x - b*d)*sqrt(f/d)*log((c^6*f*x^6 + 4*c^5*f*x^5 + 5*c^4*f*x^4 - 4*c^2*f*x^2 - 4*c*f*x + (c^4*x^4 + 4*c^3*x^3 + 6*c^2*x^2 + 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(f/d) - 2*f)/(c^4*x^4 + 2*c^3*x^3 - 2*c*x - 1)) + 2*(a*c^2*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*c*x - 2*a*c*x + (b*c^2*x^2 - 2*b*c*x + b)*arcsin(c*x) + a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d^3*x^3 + c^3*d^3*x^2 - c^2*d^3*x - c*d^3), -1/3*((b*c^3*d*x^3 + b*c^2*d*x^2 - b*c*d*x - b*d)*sqrt(-f/d)*arctan((c^2*x^2 + 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-f/d)/(c^4*f*x^4 + 2*c^3*f*x^3 - c^2*f*x^2 - 2*c*f*x)) - (a*c^2*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*c*x - 2*a*c*x + (b*c^2*x^2 - 2*b*c*x + b)*arcsin(c*x) + a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d^3*x^3 + c^3*d^3*x^2 - c^2*d^3*x - c*d^3)]","A",0
510,0,0,0,0.569460," ","integrate((c*d*x+d)^(5/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{3} d^{2} f x^{3} + a c^{2} d^{2} f x^{2} - a c d^{2} f x - a d^{2} f + {\left(b c^{3} d^{2} f x^{3} + b c^{2} d^{2} f x^{2} - b c d^{2} f x - b d^{2} f\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral(-(a*c^3*d^2*f*x^3 + a*c^2*d^2*f*x^2 - a*c*d^2*f*x - a*d^2*f + (b*c^3*d^2*f*x^3 + b*c^2*d^2*f*x^2 - b*c*d^2*f*x - b*d^2*f)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
511,0,0,0,0.476195," ","integrate((c*d*x+d)^(3/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} d f x^{2} - a d f + {\left(b c^{2} d f x^{2} - b d f\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral(-(a*c^2*d*f*x^2 - a*d*f + (b*c^2*d*f*x^2 - b*d*f)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
512,0,0,0,0.420905," ","integrate((c*d*x+d)^(1/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c f x - a f + {\left(b c f x - b f\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral(-(a*c*f*x - a*f + (b*c*f*x - b*f)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
513,0,0,0,0.451231," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c f x - a f + {\left(b c f x - b f\right)} \arcsin\left(c x\right)\right)} \sqrt{-c f x + f}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral(-(a*c*f*x - a*f + (b*c*f*x - b*f)*arcsin(c*x))*sqrt(-c*f*x + f)/sqrt(c*d*x + d), x)","F",0
514,0,0,0,0.457457," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c f x - a f + {\left(b c f x - b f\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral(-(a*c*f*x - a*f + (b*c*f*x - b*f)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
515,0,0,0,0.516116," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c f x - a f + {\left(b c f x - b f\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral(-(a*c*f*x - a*f + (b*c*f*x - b*f)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
516,0,0,0,0.510676," ","integrate((c*d*x+d)^(5/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{4} d^{2} f^{2} x^{4} - 2 \, a c^{2} d^{2} f^{2} x^{2} + a d^{2} f^{2} + {\left(b c^{4} d^{2} f^{2} x^{4} - 2 \, b c^{2} d^{2} f^{2} x^{2} + b d^{2} f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral((a*c^4*d^2*f^2*x^4 - 2*a*c^2*d^2*f^2*x^2 + a*d^2*f^2 + (b*c^4*d^2*f^2*x^4 - 2*b*c^2*d^2*f^2*x^2 + b*d^2*f^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
517,0,0,0,0.510594," ","integrate((c*d*x+d)^(3/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{3} d f^{2} x^{3} - a c^{2} d f^{2} x^{2} - a c d f^{2} x + a d f^{2} + {\left(b c^{3} d f^{2} x^{3} - b c^{2} d f^{2} x^{2} - b c d f^{2} x + b d f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral((a*c^3*d*f^2*x^3 - a*c^2*d*f^2*x^2 - a*c*d*f^2*x + a*d*f^2 + (b*c^3*d*f^2*x^3 - b*c^2*d*f^2*x^2 - b*c*d*f^2*x + b*d*f^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
518,0,0,0,0.427464," ","integrate((c*d*x+d)^(1/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a c^{2} f^{2} x^{2} - 2 \, a c f^{2} x + a f^{2} + {\left(b c^{2} f^{2} x^{2} - 2 \, b c f^{2} x + b f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}, x\right)"," ",0,"integral((a*c^2*f^2*x^2 - 2*a*c*f^2*x + a*f^2 + (b*c^2*f^2*x^2 - 2*b*c*f^2*x + b*f^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f), x)","F",0
519,0,0,0,0.434500," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{2} f^{2} x^{2} - 2 \, a c f^{2} x + a f^{2} + {\left(b c^{2} f^{2} x^{2} - 2 \, b c f^{2} x + b f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c f x + f}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral((a*c^2*f^2*x^2 - 2*a*c*f^2*x + a*f^2 + (b*c^2*f^2*x^2 - 2*b*c*f^2*x + b*f^2)*arcsin(c*x))*sqrt(-c*f*x + f)/sqrt(c*d*x + d), x)","F",0
520,0,0,0,0.424151," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{2} f^{2} x^{2} - 2 \, a c f^{2} x + a f^{2} + {\left(b c^{2} f^{2} x^{2} - 2 \, b c f^{2} x + b f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((a*c^2*f^2*x^2 - 2*a*c*f^2*x + a*f^2 + (b*c^2*f^2*x^2 - 2*b*c*f^2*x + b*f^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
521,0,0,0,0.472437," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{2} f^{2} x^{2} - 2 \, a c f^{2} x + a f^{2} + {\left(b c^{2} f^{2} x^{2} - 2 \, b c f^{2} x + b f^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((a*c^2*f^2*x^2 - 2*a*c*f^2*x + a*f^2 + (b*c^2*f^2*x^2 - 2*b*c*f^2*x + b*f^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
522,0,0,0,0.418120," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c f x - f}, x\right)"," ",0,"integral(-(a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c*f*x - f), x)","F",0
523,0,0,0,0.425142," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c d x + a d + {\left(b c d x + b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c f x - f}, x\right)"," ",0,"integral(-(a*c*d*x + a*d + (b*c*d*x + b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c*f*x - f), x)","F",0
524,0,0,0,0.412247," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c f x - f}, x\right)"," ",0,"integral(-sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c*f*x - f), x)","F",0
525,0,0,0,0.431210," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d f x^{2} - d f}, x\right)"," ",0,"integral(-sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^2*d*f*x^2 - d*f), x)","F",0
526,1,348,0,0.484576," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c x + b\right)} \sqrt{d f} \log\left(\frac{c^{6} d f x^{6} + 4 \, c^{5} d f x^{5} + 5 \, c^{4} d f x^{4} - 4 \, c^{2} d f x^{2} - 4 \, c d f x - {\left(c^{4} x^{4} + 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} + 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{d f} - 2 \, d f}{c^{4} x^{4} + 2 \, c^{3} x^{3} - 2 \, c x - 1}\right) - 2 \, \sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{2 \, {\left(c^{2} d^{2} f x + c d^{2} f\right)}}, \frac{{\left(b c x + b\right)} \sqrt{-d f} \arctan\left(\frac{{\left(c^{2} x^{2} + 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-d f}}{c^{4} d f x^{4} + 2 \, c^{3} d f x^{3} - c^{2} d f x^{2} - 2 \, c d f x}\right) - \sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d^{2} f x + c d^{2} f}\right]"," ",0,"[1/2*((b*c*x + b)*sqrt(d*f)*log((c^6*d*f*x^6 + 4*c^5*d*f*x^5 + 5*c^4*d*f*x^4 - 4*c^2*d*f*x^2 - 4*c*d*f*x - (c^4*x^4 + 4*c^3*x^3 + 6*c^2*x^2 + 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(d*f) - 2*d*f)/(c^4*x^4 + 2*c^3*x^3 - 2*c*x - 1)) - 2*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a))/(c^2*d^2*f*x + c*d^2*f), ((b*c*x + b)*sqrt(-d*f)*arctan((c^2*x^2 + 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-d*f)/(c^4*d*f*x^4 + 2*c^3*d*f*x^3 - c^2*d*f*x^2 - 2*c*d*f*x)) - sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a))/(c^2*d^2*f*x + c*d^2*f)]","A",0
527,1,525,0,0.550119," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{3} x^{3} + b c^{2} x^{2} - b c x - b\right)} \sqrt{d f} \log\left(\frac{c^{6} d f x^{6} + 4 \, c^{5} d f x^{5} + 5 \, c^{4} d f x^{4} - 4 \, c^{2} d f x^{2} - 4 \, c d f x - {\left(c^{4} x^{4} + 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} + 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{d f} - 2 \, d f}{c^{4} x^{4} + 2 \, c^{3} x^{3} - 2 \, c x - 1}\right) - 2 \, {\left(a c^{2} x^{2} + \sqrt{-c^{2} x^{2} + 1} b c x + a c x + {\left(b c^{2} x^{2} + b c x - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{6 \, {\left(c^{4} d^{3} f x^{3} + c^{3} d^{3} f x^{2} - c^{2} d^{3} f x - c d^{3} f\right)}}, \frac{{\left(b c^{3} x^{3} + b c^{2} x^{2} - b c x - b\right)} \sqrt{-d f} \arctan\left(\frac{{\left(c^{2} x^{2} + 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-d f}}{c^{4} d f x^{4} + 2 \, c^{3} d f x^{3} - c^{2} d f x^{2} - 2 \, c d f x}\right) - {\left(a c^{2} x^{2} + \sqrt{-c^{2} x^{2} + 1} b c x + a c x + {\left(b c^{2} x^{2} + b c x - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{3 \, {\left(c^{4} d^{3} f x^{3} + c^{3} d^{3} f x^{2} - c^{2} d^{3} f x - c d^{3} f\right)}}\right]"," ",0,"[1/6*((b*c^3*x^3 + b*c^2*x^2 - b*c*x - b)*sqrt(d*f)*log((c^6*d*f*x^6 + 4*c^5*d*f*x^5 + 5*c^4*d*f*x^4 - 4*c^2*d*f*x^2 - 4*c*d*f*x - (c^4*x^4 + 4*c^3*x^3 + 6*c^2*x^2 + 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(d*f) - 2*d*f)/(c^4*x^4 + 2*c^3*x^3 - 2*c*x - 1)) - 2*(a*c^2*x^2 + sqrt(-c^2*x^2 + 1)*b*c*x + a*c*x + (b*c^2*x^2 + b*c*x - 2*b)*arcsin(c*x) - 2*a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d^3*f*x^3 + c^3*d^3*f*x^2 - c^2*d^3*f*x - c*d^3*f), 1/3*((b*c^3*x^3 + b*c^2*x^2 - b*c*x - b)*sqrt(-d*f)*arctan((c^2*x^2 + 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-d*f)/(c^4*d*f*x^4 + 2*c^3*d*f*x^3 - c^2*d*f*x^2 - 2*c*d*f*x)) - (a*c^2*x^2 + sqrt(-c^2*x^2 + 1)*b*c*x + a*c*x + (b*c^2*x^2 + b*c*x - 2*b)*arcsin(c*x) - 2*a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d^3*f*x^3 + c^3*d^3*f*x^2 - c^2*d^3*f*x - c*d^3*f)]","A",0
528,0,0,0,0.430441," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{2} f^{2} x^{2} - 2 \, c f^{2} x + f^{2}}, x\right)"," ",0,"integral((a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^2*f^2*x^2 - 2*c*f^2*x + f^2), x)","F",0
529,0,0,0,0.454596," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a c d x + a d + {\left(b c d x + b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{2} f^{2} x^{2} - 2 \, c f^{2} x + f^{2}}, x\right)"," ",0,"integral((a*c*d*x + a*d + (b*c*d*x + b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^2*f^2*x^2 - 2*c*f^2*x + f^2), x)","F",0
530,0,0,0,0.425154," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} f^{2} x^{2} - 2 \, c f^{2} x + f^{2}}, x\right)"," ",0,"integral(sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^2*f^2*x^2 - 2*c*f^2*x + f^2), x)","F",0
531,1,354,0,0.484532," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c x - b\right)} \sqrt{d f} \log\left(\frac{c^{6} d f x^{6} - 4 \, c^{5} d f x^{5} + 5 \, c^{4} d f x^{4} - 4 \, c^{2} d f x^{2} + 4 \, c d f x - {\left(c^{4} x^{4} - 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} - 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{d f} - 2 \, d f}{c^{4} x^{4} - 2 \, c^{3} x^{3} + 2 \, c x - 1}\right) - 2 \, \sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{2 \, {\left(c^{2} d f^{2} x - c d f^{2}\right)}}, \frac{{\left(b c x - b\right)} \sqrt{-d f} \arctan\left(\frac{{\left(c^{2} x^{2} - 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-d f}}{c^{4} d f x^{4} - 2 \, c^{3} d f x^{3} - c^{2} d f x^{2} + 2 \, c d f x}\right) - \sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{2} d f^{2} x - c d f^{2}}\right]"," ",0,"[1/2*((b*c*x - b)*sqrt(d*f)*log((c^6*d*f*x^6 - 4*c^5*d*f*x^5 + 5*c^4*d*f*x^4 - 4*c^2*d*f*x^2 + 4*c*d*f*x - (c^4*x^4 - 4*c^3*x^3 + 6*c^2*x^2 - 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(d*f) - 2*d*f)/(c^4*x^4 - 2*c^3*x^3 + 2*c*x - 1)) - 2*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a))/(c^2*d*f^2*x - c*d*f^2), ((b*c*x - b)*sqrt(-d*f)*arctan((c^2*x^2 - 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-d*f)/(c^4*d*f*x^4 - 2*c^3*d*f*x^3 - c^2*d*f*x^2 + 2*c*d*f*x)) - sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a))/(c^2*d*f^2*x - c*d*f^2)]","A",0
532,0,0,0,0.536653," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{4} d^{2} f^{2} x^{4} - 2 \, c^{2} d^{2} f^{2} x^{2} + d^{2} f^{2}}, x\right)"," ",0,"integral(sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^4*d^2*f^2*x^4 - 2*c^2*d^2*f^2*x^2 + d^2*f^2), x)","F",0
533,0,0,0,0.672677," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{5} d^{3} f^{2} x^{5} + c^{4} d^{3} f^{2} x^{4} - 2 \, c^{3} d^{3} f^{2} x^{3} - 2 \, c^{2} d^{3} f^{2} x^{2} + c d^{3} f^{2} x + d^{3} f^{2}}, x\right)"," ",0,"integral(sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^5*d^3*f^2*x^5 + c^4*d^3*f^2*x^4 - 2*c^3*d^3*f^2*x^3 - 2*c^2*d^3*f^2*x^2 + c*d^3*f^2*x + d^3*f^2), x)","F",0
534,0,0,0,0.840723," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{3} f^{3} x^{3} - 3 \, c^{2} f^{3} x^{2} + 3 \, c f^{3} x - f^{3}}, x\right)"," ",0,"integral(-(a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^3*f^3*x^3 - 3*c^2*f^3*x^2 + 3*c*f^3*x - f^3), x)","F",0
535,0,0,0,1.239692," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a c d x + a d + {\left(b c d x + b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{c^{3} f^{3} x^{3} - 3 \, c^{2} f^{3} x^{2} + 3 \, c f^{3} x - f^{3}}, x\right)"," ",0,"integral(-(a*c*d*x + a*d + (b*c*d*x + b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*f*x + f)/(c^3*f^3*x^3 - 3*c^2*f^3*x^2 + 3*c*f^3*x - f^3), x)","F",0
536,1,520,0,0.623802," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{3} f x^{3} - b c^{2} f x^{2} - b c f x + b f\right)} \sqrt{\frac{d}{f}} \log\left(\frac{c^{6} d x^{6} - 4 \, c^{5} d x^{5} + 5 \, c^{4} d x^{4} - 4 \, c^{2} d x^{2} + 4 \, c d x + {\left(c^{4} x^{4} - 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} - 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{\frac{d}{f}} - 2 \, d}{c^{4} x^{4} - 2 \, c^{3} x^{3} + 2 \, c x - 1}\right) + 2 \, {\left(a c^{2} x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b c x + 2 \, a c x + {\left(b c^{2} x^{2} + 2 \, b c x + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{6 \, {\left(c^{4} f^{3} x^{3} - c^{3} f^{3} x^{2} - c^{2} f^{3} x + c f^{3}\right)}}, -\frac{{\left(b c^{3} f x^{3} - b c^{2} f x^{2} - b c f x + b f\right)} \sqrt{-\frac{d}{f}} \arctan\left(\frac{{\left(c^{2} x^{2} - 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-\frac{d}{f}}}{c^{4} d x^{4} - 2 \, c^{3} d x^{3} - c^{2} d x^{2} + 2 \, c d x}\right) - {\left(a c^{2} x^{2} - 2 \, \sqrt{-c^{2} x^{2} + 1} b c x + 2 \, a c x + {\left(b c^{2} x^{2} + 2 \, b c x + b\right)} \arcsin\left(c x\right) + a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{3 \, {\left(c^{4} f^{3} x^{3} - c^{3} f^{3} x^{2} - c^{2} f^{3} x + c f^{3}\right)}}\right]"," ",0,"[1/6*((b*c^3*f*x^3 - b*c^2*f*x^2 - b*c*f*x + b*f)*sqrt(d/f)*log((c^6*d*x^6 - 4*c^5*d*x^5 + 5*c^4*d*x^4 - 4*c^2*d*x^2 + 4*c*d*x + (c^4*x^4 - 4*c^3*x^3 + 6*c^2*x^2 - 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(d/f) - 2*d)/(c^4*x^4 - 2*c^3*x^3 + 2*c*x - 1)) + 2*(a*c^2*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*c*x + 2*a*c*x + (b*c^2*x^2 + 2*b*c*x + b)*arcsin(c*x) + a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*f^3*x^3 - c^3*f^3*x^2 - c^2*f^3*x + c*f^3), -1/3*((b*c^3*f*x^3 - b*c^2*f*x^2 - b*c*f*x + b*f)*sqrt(-d/f)*arctan((c^2*x^2 - 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-d/f)/(c^4*d*x^4 - 2*c^3*d*x^3 - c^2*d*x^2 + 2*c*d*x)) - (a*c^2*x^2 - 2*sqrt(-c^2*x^2 + 1)*b*c*x + 2*a*c*x + (b*c^2*x^2 + 2*b*c*x + b)*arcsin(c*x) + a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*f^3*x^3 - c^3*f^3*x^2 - c^2*f^3*x + c*f^3)]","A",0
537,1,527,0,0.639826," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(b c^{3} x^{3} - b c^{2} x^{2} - b c x + b\right)} \sqrt{d f} \log\left(\frac{c^{6} d f x^{6} - 4 \, c^{5} d f x^{5} + 5 \, c^{4} d f x^{4} - 4 \, c^{2} d f x^{2} + 4 \, c d f x - {\left(c^{4} x^{4} - 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} - 4 \, c x\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{d f} - 2 \, d f}{c^{4} x^{4} - 2 \, c^{3} x^{3} + 2 \, c x - 1}\right) - 2 \, {\left(a c^{2} x^{2} + \sqrt{-c^{2} x^{2} + 1} b c x - a c x + {\left(b c^{2} x^{2} - b c x - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{6 \, {\left(c^{4} d f^{3} x^{3} - c^{3} d f^{3} x^{2} - c^{2} d f^{3} x + c d f^{3}\right)}}, \frac{{\left(b c^{3} x^{3} - b c^{2} x^{2} - b c x + b\right)} \sqrt{-d f} \arctan\left(\frac{{\left(c^{2} x^{2} - 2 \, c x + 2\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{c d x + d} \sqrt{-c f x + f} \sqrt{-d f}}{c^{4} d f x^{4} - 2 \, c^{3} d f x^{3} - c^{2} d f x^{2} + 2 \, c d f x}\right) - {\left(a c^{2} x^{2} + \sqrt{-c^{2} x^{2} + 1} b c x - a c x + {\left(b c^{2} x^{2} - b c x - 2 \, b\right)} \arcsin\left(c x\right) - 2 \, a\right)} \sqrt{c d x + d} \sqrt{-c f x + f}}{3 \, {\left(c^{4} d f^{3} x^{3} - c^{3} d f^{3} x^{2} - c^{2} d f^{3} x + c d f^{3}\right)}}\right]"," ",0,"[1/6*((b*c^3*x^3 - b*c^2*x^2 - b*c*x + b)*sqrt(d*f)*log((c^6*d*f*x^6 - 4*c^5*d*f*x^5 + 5*c^4*d*f*x^4 - 4*c^2*d*f*x^2 + 4*c*d*f*x - (c^4*x^4 - 4*c^3*x^3 + 6*c^2*x^2 - 4*c*x)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(d*f) - 2*d*f)/(c^4*x^4 - 2*c^3*x^3 + 2*c*x - 1)) - 2*(a*c^2*x^2 + sqrt(-c^2*x^2 + 1)*b*c*x - a*c*x + (b*c^2*x^2 - b*c*x - 2*b)*arcsin(c*x) - 2*a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d*f^3*x^3 - c^3*d*f^3*x^2 - c^2*d*f^3*x + c*d*f^3), 1/3*((b*c^3*x^3 - b*c^2*x^2 - b*c*x + b)*sqrt(-d*f)*arctan((c^2*x^2 - 2*c*x + 2)*sqrt(-c^2*x^2 + 1)*sqrt(c*d*x + d)*sqrt(-c*f*x + f)*sqrt(-d*f)/(c^4*d*f*x^4 - 2*c^3*d*f*x^3 - c^2*d*f*x^2 + 2*c*d*f*x)) - (a*c^2*x^2 + sqrt(-c^2*x^2 + 1)*b*c*x - a*c*x + (b*c^2*x^2 - b*c*x - 2*b)*arcsin(c*x) - 2*a)*sqrt(c*d*x + d)*sqrt(-c*f*x + f))/(c^4*d*f^3*x^3 - c^3*d*f^3*x^2 - c^2*d*f^3*x + c*d*f^3)]","A",0
538,0,0,0,0.725960," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{5} d^{2} f^{3} x^{5} - c^{4} d^{2} f^{3} x^{4} - 2 \, c^{3} d^{2} f^{3} x^{3} + 2 \, c^{2} d^{2} f^{3} x^{2} + c d^{2} f^{3} x - d^{2} f^{3}}, x\right)"," ",0,"integral(-sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^5*d^2*f^3*x^5 - c^4*d^2*f^3*x^4 - 2*c^3*d^2*f^3*x^3 + 2*c^2*d^2*f^3*x^2 + c*d^2*f^3*x - d^2*f^3), x)","F",0
539,0,0,0,0.600513," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c d x + d} \sqrt{-c f x + f} {\left(b \arcsin\left(c x\right) + a\right)}}{c^{6} d^{3} f^{3} x^{6} - 3 \, c^{4} d^{3} f^{3} x^{4} + 3 \, c^{2} d^{3} f^{3} x^{2} - d^{3} f^{3}}, x\right)"," ",0,"integral(-sqrt(c*d*x + d)*sqrt(-c*f*x + f)*(b*arcsin(c*x) + a)/(c^6*d^3*f^3*x^6 - 3*c^4*d^3*f^3*x^4 + 3*c^2*d^3*f^3*x^2 - d^3*f^3), x)","F",0
540,0,0,0,0.424313," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
541,0,0,0,0.420736," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arcsin(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
542,0,0,0,1.396359," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
543,0,0,0,0.489127," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{-c e x + e}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(-c*e*x + e)/sqrt(c*d*x + d), x)","F",0
544,0,0,0,0.660096," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
545,0,0,0,0.472821," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
546,0,0,0,0.467509," ","integrate((c*d*x+d)^(5/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{3} d^{2} e x^{3} + a^{2} c^{2} d^{2} e x^{2} - a^{2} c d^{2} e x - a^{2} d^{2} e + {\left(b^{2} c^{3} d^{2} e x^{3} + b^{2} c^{2} d^{2} e x^{2} - b^{2} c d^{2} e x - b^{2} d^{2} e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{2} e x^{3} + a b c^{2} d^{2} e x^{2} - a b c d^{2} e x - a b d^{2} e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral(-(a^2*c^3*d^2*e*x^3 + a^2*c^2*d^2*e*x^2 - a^2*c*d^2*e*x - a^2*d^2*e + (b^2*c^3*d^2*e*x^3 + b^2*c^2*d^2*e*x^2 - b^2*c*d^2*e*x - b^2*d^2*e)*arcsin(c*x)^2 + 2*(a*b*c^3*d^2*e*x^3 + a*b*c^2*d^2*e*x^2 - a*b*c*d^2*e*x - a*b*d^2*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
547,0,0,0,0.437895," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d e x^{2} - a^{2} d e + {\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral(-(a^2*c^2*d*e*x^2 - a^2*d*e + (b^2*c^2*d*e*x^2 - b^2*d*e)*arcsin(c*x)^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
548,0,0,0,0.459477," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c e x - a^{2} e + {\left(b^{2} c e x - b^{2} e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral(-(a^2*c*e*x - a^2*e + (b^2*c*e*x - b^2*e)*arcsin(c*x)^2 + 2*(a*b*c*e*x - a*b*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
549,0,0,0,0.625890," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c e x - a^{2} e + {\left(b^{2} c e x - b^{2} e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arcsin\left(c x\right)\right)} \sqrt{-c e x + e}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral(-(a^2*c*e*x - a^2*e + (b^2*c*e*x - b^2*e)*arcsin(c*x)^2 + 2*(a*b*c*e*x - a*b*e)*arcsin(c*x))*sqrt(-c*e*x + e)/sqrt(c*d*x + d), x)","F",0
550,0,0,0,0.498138," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c e x - a^{2} e + {\left(b^{2} c e x - b^{2} e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral(-(a^2*c*e*x - a^2*e + (b^2*c*e*x - b^2*e)*arcsin(c*x)^2 + 2*(a*b*c*e*x - a*b*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
551,0,0,0,0.493686," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c e x - a^{2} e + {\left(b^{2} c e x - b^{2} e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral(-(a^2*c*e*x - a^2*e + (b^2*c*e*x - b^2*e)*arcsin(c*x)^2 + 2*(a*b*c*e*x - a*b*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
552,0,0,0,0.424343," ","integrate((c*d*x+d)^(5/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{4} d^{2} e^{2} x^{4} - 2 \, a^{2} c^{2} d^{2} e^{2} x^{2} + a^{2} d^{2} e^{2} + {\left(b^{2} c^{4} d^{2} e^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} e^{2} x^{2} + b^{2} d^{2} e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{4} d^{2} e^{2} x^{4} - 2 \, a b c^{2} d^{2} e^{2} x^{2} + a b d^{2} e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((a^2*c^4*d^2*e^2*x^4 - 2*a^2*c^2*d^2*e^2*x^2 + a^2*d^2*e^2 + (b^2*c^4*d^2*e^2*x^4 - 2*b^2*c^2*d^2*e^2*x^2 + b^2*d^2*e^2)*arcsin(c*x)^2 + 2*(a*b*c^4*d^2*e^2*x^4 - 2*a*b*c^2*d^2*e^2*x^2 + a*b*d^2*e^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
553,0,0,0,0.437119," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{3} d e^{2} x^{3} - a^{2} c^{2} d e^{2} x^{2} - a^{2} c d e^{2} x + a^{2} d e^{2} + {\left(b^{2} c^{3} d e^{2} x^{3} - b^{2} c^{2} d e^{2} x^{2} - b^{2} c d e^{2} x + b^{2} d e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d e^{2} x^{3} - a b c^{2} d e^{2} x^{2} - a b c d e^{2} x + a b d e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((a^2*c^3*d*e^2*x^3 - a^2*c^2*d*e^2*x^2 - a^2*c*d*e^2*x + a^2*d*e^2 + (b^2*c^3*d*e^2*x^3 - b^2*c^2*d*e^2*x^2 - b^2*c*d*e^2*x + b^2*d*e^2)*arcsin(c*x)^2 + 2*(a*b*c^3*d*e^2*x^3 - a*b*c^2*d*e^2*x^2 - a*b*c*d*e^2*x + a*b*d*e^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
554,0,0,0,0.425875," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c^{2} e^{2} x^{2} - 2 \, a^{2} c e^{2} x + a^{2} e^{2} + {\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((a^2*c^2*e^2*x^2 - 2*a^2*c*e^2*x + a^2*e^2 + (b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arcsin(c*x)^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
555,0,0,0,0.503941," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{2} e^{2} x^{2} - 2 \, a^{2} c e^{2} x + a^{2} e^{2} + {\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c e x + e}}{\sqrt{c d x + d}}, x\right)"," ",0,"integral((a^2*c^2*e^2*x^2 - 2*a^2*c*e^2*x + a^2*e^2 + (b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arcsin(c*x)^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arcsin(c*x))*sqrt(-c*e*x + e)/sqrt(c*d*x + d), x)","F",0
556,0,0,0,0.463763," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{2} e^{2} x^{2} - 2 \, a^{2} c e^{2} x + a^{2} e^{2} + {\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((a^2*c^2*e^2*x^2 - 2*a^2*c*e^2*x + a^2*e^2 + (b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arcsin(c*x)^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
557,0,0,0,0.509789," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{2} e^{2} x^{2} - 2 \, a^{2} c e^{2} x + a^{2} e^{2} + {\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((a^2*c^2*e^2*x^2 - 2*a^2*c*e^2*x + a^2*e^2 + (b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arcsin(c*x)^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
558,0,0,0,0.459469," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c e x - e}, x\right)"," ",0,"integral(-(a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c*e*x - e), x)","F",0
559,0,0,0,0.478740," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c e x - e}, x\right)"," ",0,"integral(-(a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arcsin(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c*e*x - e), x)","F",0
560,0,0,0,0.430396," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c e x - e}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c*e*x - e), x)","F",0
561,0,0,0,0.489201," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d e x^{2} - d e}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d*e*x^2 - d*e), x)","F",0
562,0,0,0,0.453545," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} d^{2} e x^{3} + c^{2} d^{2} e x^{2} - c d^{2} e x - d^{2} e}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*d^2*e*x^3 + c^2*d^2*e*x^2 - c*d^2*e*x - d^2*e), x)","F",0
563,0,0,0,1.130522," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{3} e x^{4} + 2 \, c^{3} d^{3} e x^{3} - 2 \, c d^{3} e x - d^{3} e}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^3*e*x^4 + 2*c^3*d^3*e*x^3 - 2*c*d^3*e*x - d^3*e), x)","F",0
564,0,0,0,1.060889," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
565,0,0,0,1.602765," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arcsin(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
566,0,0,0,1.160365," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
567,0,0,0,0.513703," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} d e^{2} x^{3} - c^{2} d e^{2} x^{2} - c d e^{2} x + d e^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*d*e^2*x^3 - c^2*d*e^2*x^2 - c*d*e^2*x + d*e^2), x)","F",0
568,0,0,0,0.712762," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x)","F",0
569,0,0,0,0.476680," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{5} d^{3} e^{2} x^{5} + c^{4} d^{3} e^{2} x^{4} - 2 \, c^{3} d^{3} e^{2} x^{3} - 2 \, c^{2} d^{3} e^{2} x^{2} + c d^{3} e^{2} x + d^{3} e^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^5*d^3*e^2*x^5 + c^4*d^3*e^2*x^4 - 2*c^3*d^3*e^2*x^3 - 2*c^2*d^3*e^2*x^2 + c*d^3*e^2*x + d^3*e^2), x)","F",0
570,0,0,0,0.442774," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} e^{3} x^{3} - 3 \, c^{2} e^{3} x^{2} + 3 \, c e^{3} x - e^{3}}, x\right)"," ",0,"integral(-(a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*e^3*x^3 - 3*c^2*e^3*x^2 + 3*c*e^3*x - e^3), x)","F",0
571,0,0,0,0.521940," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} e^{3} x^{3} - 3 \, c^{2} e^{3} x^{2} + 3 \, c e^{3} x - e^{3}}, x\right)"," ",0,"integral(-(a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arcsin(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*e^3*x^3 - 3*c^2*e^3*x^2 + 3*c*e^3*x - e^3), x)","F",0
572,0,0,0,0.496509," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{3} e^{3} x^{3} - 3 \, c^{2} e^{3} x^{2} + 3 \, c e^{3} x - e^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^3*e^3*x^3 - 3*c^2*e^3*x^2 + 3*c*e^3*x - e^3), x)","F",0
573,0,0,0,0.472758," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d e^{3} x^{4} - 2 \, c^{3} d e^{3} x^{3} + 2 \, c d e^{3} x - d e^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d*e^3*x^4 - 2*c^3*d*e^3*x^3 + 2*c*d*e^3*x - d*e^3), x)","F",0
574,0,0,0,0.450397," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{5} d^{2} e^{3} x^{5} - c^{4} d^{2} e^{3} x^{4} - 2 \, c^{3} d^{2} e^{3} x^{3} + 2 \, c^{2} d^{2} e^{3} x^{2} + c d^{2} e^{3} x - d^{2} e^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^5*d^2*e^3*x^5 - c^4*d^2*e^3*x^4 - 2*c^3*d^2*e^3*x^3 + 2*c^2*d^2*e^3*x^2 + c*d^2*e^3*x - d^2*e^3), x)","F",0
575,0,0,0,0.438132," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{6} d^{3} e^{3} x^{6} - 3 \, c^{4} d^{3} e^{3} x^{4} + 3 \, c^{2} d^{3} e^{3} x^{2} - d^{3} e^{3}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^6*d^3*e^3*x^6 - 3*c^4*d^3*e^3*x^4 + 3*c^2*d^3*e^3*x^2 - d^3*e^3), x)","F",0
576,0,0,0,0.444431," ","integrate(x^2*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
577,1,197,0,0.438860," ","integrate(x*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{{\left({\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{4} x^{4} - 2 \, {\left(9 \, a^{2} - 8 \, b^{2}\right)} c^{2} x^{2} + 9 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arcsin\left(c x\right)^{2} + 9 \, a^{2} - 14 \, b^{2} + 18 \, {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \arcsin\left(c x\right) + 6 \, {\left(a b c^{3} x^{3} - 3 \, a b c x + {\left(b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{27 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"1/27*((9*a^2 - 2*b^2)*c^4*x^4 - 2*(9*a^2 - 8*b^2)*c^2*x^2 + 9*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arcsin(c*x)^2 + 9*a^2 - 14*b^2 + 18*(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*arcsin(c*x) + 6*(a*b*c^3*x^3 - 3*a*b*c*x + (b^2*c^3*x^3 - 3*b^2*c*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*x^2 - c^2)","A",0
578,0,0,0,0.412748," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
579,0,0,0,0.474647," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{x}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/x, x)","F",0
580,0,0,0,0.435910," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{x^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/x^2, x)","F",0
581,0,0,0,0.620767," ","integrate(x^2*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d e x^{4} - a^{2} d e x^{2} + {\left(b^{2} c^{2} d e x^{4} - b^{2} d e x^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d e x^{4} - a b d e x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral(-(a^2*c^2*d*e*x^4 - a^2*d*e*x^2 + (b^2*c^2*d*e*x^4 - b^2*d*e*x^2)*arcsin(c*x)^2 + 2*(a*b*c^2*d*e*x^4 - a*b*d*e*x^2)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
582,1,302,0,0.730213," ","integrate(x*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{6} d e x^{6} - {\left(675 \, a^{2} - 94 \, b^{2}\right)} c^{4} d e x^{4} + {\left(675 \, a^{2} - 374 \, b^{2}\right)} c^{2} d e x^{2} - {\left(225 \, a^{2} - 298 \, b^{2}\right)} d e + 225 \, {\left(b^{2} c^{6} d e x^{6} - 3 \, b^{2} c^{4} d e x^{4} + 3 \, b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arcsin\left(c x\right)^{2} + 450 \, {\left(a b c^{6} d e x^{6} - 3 \, a b c^{4} d e x^{4} + 3 \, a b c^{2} d e x^{2} - a b d e\right)} \arcsin\left(c x\right) + 30 \, {\left(3 \, a b c^{5} d e x^{5} - 10 \, a b c^{3} d e x^{3} + 15 \, a b c d e x + {\left(3 \, b^{2} c^{5} d e x^{5} - 10 \, b^{2} c^{3} d e x^{3} + 15 \, b^{2} c d e x\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{1125 \, {\left(c^{4} x^{2} - c^{2}\right)}}"," ",0,"-1/1125*(9*(25*a^2 - 2*b^2)*c^6*d*e*x^6 - (675*a^2 - 94*b^2)*c^4*d*e*x^4 + (675*a^2 - 374*b^2)*c^2*d*e*x^2 - (225*a^2 - 298*b^2)*d*e + 225*(b^2*c^6*d*e*x^6 - 3*b^2*c^4*d*e*x^4 + 3*b^2*c^2*d*e*x^2 - b^2*d*e)*arcsin(c*x)^2 + 450*(a*b*c^6*d*e*x^6 - 3*a*b*c^4*d*e*x^4 + 3*a*b*c^2*d*e*x^2 - a*b*d*e)*arcsin(c*x) + 30*(3*a*b*c^5*d*e*x^5 - 10*a*b*c^3*d*e*x^3 + 15*a*b*c*d*e*x + (3*b^2*c^5*d*e*x^5 - 10*b^2*c^3*d*e*x^3 + 15*b^2*c*d*e*x)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*x^2 - c^2)","A",0
583,0,0,0,0.630682," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c^{2} d e x^{2} - a^{2} d e + {\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}, x\right)"," ",0,"integral(-(a^2*c^2*d*e*x^2 - a^2*d*e + (b^2*c^2*d*e*x^2 - b^2*d*e)*arcsin(c*x)^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e), x)","F",0
584,0,0,0,0.680475," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d e x^{2} - a^{2} d e + {\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{x}, x\right)"," ",0,"integral(-(a^2*c^2*d*e*x^2 - a^2*d*e + (b^2*c^2*d*e*x^2 - b^2*d*e)*arcsin(c*x)^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/x, x)","F",0
585,0,0,0,0.430281," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} c^{2} d e x^{2} - a^{2} d e + {\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arcsin\left(c x\right)\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{x^{2}}, x\right)"," ",0,"integral(-(a^2*c^2*d*e*x^2 - a^2*d*e + (b^2*c^2*d*e*x^2 - b^2*d*e)*arcsin(c*x)^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arcsin(c*x))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/x^2, x)","F",0
586,0,0,0,0.573586," ","integrate(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d e x^{2} - d e}, x\right)"," ",0,"integral(-(b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d*e*x^2 - d*e), x)","F",0
587,1,138,0,0.527446," ","integrate(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","-\frac{{\left({\left(a^{2} - 2 \, b^{2}\right)} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arcsin\left(c x\right)^{2} - a^{2} + 2 \, b^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \arcsin\left(c x\right) + 2 \, {\left(b^{2} c x \arcsin\left(c x\right) + a b c x\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d e x^{2} - c^{2} d e}"," ",0,"-((a^2 - 2*b^2)*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arcsin(c*x)^2 - a^2 + 2*b^2 + 2*(a*b*c^2*x^2 - a*b)*arcsin(c*x) + 2*(b^2*c*x*arcsin(c*x) + a*b*c*x)*sqrt(-c^2*x^2 + 1))*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d*e*x^2 - c^2*d*e)","A",0
588,0,0,0,0.779798," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d e x^{2} - d e}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d*e*x^2 - d*e), x)","F",0
589,0,0,0,0.547445," ","integrate((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d e x^{3} - d e x}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d*e*x^3 - d*e*x), x)","F",0
590,0,0,0,0.660349," ","integrate((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{2} d e x^{4} - d e x^{2}}, x\right)"," ",0,"integral(-(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^2*d*e*x^4 - d*e*x^2), x)","F",0
591,0,0,0,1.241560," ","integrate(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} \arcsin\left(c x\right)^{2} + 2 \, a b x^{2} \arcsin\left(c x\right) + a^{2} x^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}, x\right)"," ",0,"integral((b^2*x^2*arcsin(c*x)^2 + 2*a*b*x^2*arcsin(c*x) + a^2*x^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x)","F",0
592,0,0,0,0.504339," ","integrate(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x \arcsin\left(c x\right)^{2} + 2 \, a b x \arcsin\left(c x\right) + a^{2} x\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}, x\right)"," ",0,"integral((b^2*x*arcsin(c*x)^2 + 2*a*b*x*arcsin(c*x) + a^2*x)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x)","F",0
593,0,0,0,0.778068," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x)","F",0
594,0,0,0,0.700231," ","integrate((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{5} - 2 \, c^{2} d^{2} e^{2} x^{3} + d^{2} e^{2} x}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^5 - 2*c^2*d^2*e^2*x^3 + d^2*e^2*x), x)","F",0
595,0,0,0,0.566588," ","integrate((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{c d x + d} \sqrt{-c e x + e}}{c^{4} d^{2} e^{2} x^{6} - 2 \, c^{2} d^{2} e^{2} x^{4} + d^{2} e^{2} x^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(c*d*x + d)*sqrt(-c*e*x + e)/(c^4*d^2*e^2*x^6 - 2*c^2*d^2*e^2*x^4 + d^2*e^2*x^2), x)","F",0
596,1,128,0,0.602076," ","integrate(x^4*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{525 \, a c^{7} e x^{7} + 735 \, a c^{7} d x^{5} + 105 \, {\left(5 \, b c^{7} e x^{7} + 7 \, b c^{7} d x^{5}\right)} \arcsin\left(c x\right) + {\left(75 \, b c^{6} e x^{6} + 3 \, {\left(49 \, b c^{6} d + 30 \, b c^{4} e\right)} x^{4} + 392 \, b c^{2} d + 4 \, {\left(49 \, b c^{4} d + 30 \, b c^{2} e\right)} x^{2} + 240 \, b e\right)} \sqrt{-c^{2} x^{2} + 1}}{3675 \, c^{7}}"," ",0,"1/3675*(525*a*c^7*e*x^7 + 735*a*c^7*d*x^5 + 105*(5*b*c^7*e*x^7 + 7*b*c^7*d*x^5)*arcsin(c*x) + (75*b*c^6*e*x^6 + 3*(49*b*c^6*d + 30*b*c^4*e)*x^4 + 392*b*c^2*d + 4*(49*b*c^4*d + 30*b*c^2*e)*x^2 + 240*b*e)*sqrt(-c^2*x^2 + 1))/c^7","A",0
597,1,124,0,0.543277," ","integrate(x^3*(e*x^2+d)*(a+b*arcsin(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)} \arcsin\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)*arcsin(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
598,1,107,0,0.631369," ","integrate(x^2*(e*x^2+d)*(a+b*arcsin(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)} \arcsin\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)*arcsin(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
599,1,102,0,0.642204," ","integrate(x*(e*x^2+d)*(a+b*arcsin(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)} \arcsin\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)*arcsin(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
600,1,82,0,0.938489," ","integrate((e*x^2+d)*(a+b*arcsin(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)} \arcsin\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)*arcsin(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
601,0,0,0,0.669541," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsin(c*x))/x, x)","F",0
602,1,103,0,0.873747," ","integrate((e*x^2+d)*(a+b*arcsin(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 e x^{2} - b c d\right)} \arcsin\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*e*x^2 - b*c*d)*arcsin(c*x))/(c*x)","A",0
603,0,0,0,0.548019," ","integrate((e*x^2+d)*(a+b*arcsin(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)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsin(c*x))/x^3, x)","F",0
604,1,115,0,0.787587," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","-\frac{{\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} + b d\right)} \arcsin\left(c x\right)}{12 \, x^{3}}"," ",0,"-1/12*((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)*arcsin(c*x))/x^3","A",0
605,1,219,0,0.596790," ","integrate(x^4*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{11025 \, a c^{9} e^{2} x^{9} + 28350 \, a c^{9} d e x^{7} + 19845 \, a c^{9} d^{2} x^{5} + 315 \, {\left(35 \, b c^{9} e^{2} x^{9} + 90 \, b c^{9} d e x^{7} + 63 \, b c^{9} d^{2} x^{5}\right)} \arcsin\left(c x\right) + {\left(1225 \, b c^{8} e^{2} x^{8} + 10584 \, b c^{4} d^{2} + 50 \, {\left(81 \, b c^{8} d e + 28 \, b c^{6} e^{2}\right)} x^{6} + 12960 \, b c^{2} d e + 3 \, {\left(1323 \, b c^{8} d^{2} + 1620 \, b c^{6} d e + 560 \, b c^{4} e^{2}\right)} x^{4} + 4480 \, b e^{2} + 4 \, {\left(1323 \, b c^{6} d^{2} + 1620 \, b c^{4} d e + 560 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{99225 \, c^{9}}"," ",0,"1/99225*(11025*a*c^9*e^2*x^9 + 28350*a*c^9*d*e*x^7 + 19845*a*c^9*d^2*x^5 + 315*(35*b*c^9*e^2*x^9 + 90*b*c^9*d*e*x^7 + 63*b*c^9*d^2*x^5)*arcsin(c*x) + (1225*b*c^8*e^2*x^8 + 10584*b*c^4*d^2 + 50*(81*b*c^8*d*e + 28*b*c^6*e^2)*x^6 + 12960*b*c^2*d*e + 3*(1323*b*c^8*d^2 + 1620*b*c^6*d*e + 560*b*c^4*e^2)*x^4 + 4480*b*e^2 + 4*(1323*b*c^6*d^2 + 1620*b*c^4*d*e + 560*b*c^2*e^2)*x^2)*sqrt(-c^2*x^2 + 1))/c^9","A",0
606,1,215,0,0.420965," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{1152 \, a c^{8} e^{2} x^{8} + 3072 \, a c^{8} d e x^{6} + 2304 \, a c^{8} d^{2} x^{4} + 3 \, {\left(384 \, b c^{8} e^{2} x^{8} + 1024 \, b c^{8} d e x^{6} + 768 \, b c^{8} d^{2} x^{4} - 288 \, b c^{4} d^{2} - 320 \, b c^{2} d e - 105 \, b e^{2}\right)} \arcsin\left(c x\right) + {\left(144 \, b c^{7} e^{2} x^{7} + 8 \, {\left(64 \, b c^{7} d e + 21 \, b c^{5} e^{2}\right)} x^{5} + 2 \, {\left(288 \, b c^{7} d^{2} + 320 \, b c^{5} d e + 105 \, b c^{3} e^{2}\right)} x^{3} + 3 \, {\left(288 \, b c^{5} d^{2} + 320 \, b c^{3} d e + 105 \, b c e^{2}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{9216 \, c^{8}}"," ",0,"1/9216*(1152*a*c^8*e^2*x^8 + 3072*a*c^8*d*e*x^6 + 2304*a*c^8*d^2*x^4 + 3*(384*b*c^8*e^2*x^8 + 1024*b*c^8*d*e*x^6 + 768*b*c^8*d^2*x^4 - 288*b*c^4*d^2 - 320*b*c^2*d*e - 105*b*e^2)*arcsin(c*x) + (144*b*c^7*e^2*x^7 + 8*(64*b*c^7*d*e + 21*b*c^5*e^2)*x^5 + 2*(288*b*c^7*d^2 + 320*b*c^5*d*e + 105*b*c^3*e^2)*x^3 + 3*(288*b*c^5*d^2 + 320*b*c^3*d*e + 105*b*c*e^2)*x)*sqrt(-c^2*x^2 + 1))/c^8","A",0
607,1,186,0,0.527704," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{1575 \, a c^{7} e^{2} x^{7} + 4410 \, a c^{7} d e x^{5} + 3675 \, a c^{7} d^{2} x^{3} + 105 \, {\left(15 \, b c^{7} e^{2} x^{7} + 42 \, b c^{7} d e x^{5} + 35 \, b c^{7} d^{2} x^{3}\right)} \arcsin\left(c x\right) + {\left(225 \, b c^{6} e^{2} x^{6} + 2450 \, b c^{4} d^{2} + 2352 \, b c^{2} d e + 18 \, {\left(49 \, b c^{6} d e + 15 \, b c^{4} e^{2}\right)} x^{4} + 720 \, b e^{2} + {\left(1225 \, b c^{6} d^{2} + 1176 \, b c^{4} d e + 360 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{11025 \, c^{7}}"," ",0,"1/11025*(1575*a*c^7*e^2*x^7 + 4410*a*c^7*d*e*x^5 + 3675*a*c^7*d^2*x^3 + 105*(15*b*c^7*e^2*x^7 + 42*b*c^7*d*e*x^5 + 35*b*c^7*d^2*x^3)*arcsin(c*x) + (225*b*c^6*e^2*x^6 + 2450*b*c^4*d^2 + 2352*b*c^2*d*e + 18*(49*b*c^6*d*e + 15*b*c^4*e^2)*x^4 + 720*b*e^2 + (1225*b*c^6*d^2 + 1176*b*c^4*d*e + 360*b*c^2*e^2)*x^2)*sqrt(-c^2*x^2 + 1))/c^7","A",0
608,1,183,0,0.684535," ","integrate(x*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{48 \, a c^{6} e^{2} x^{6} + 144 \, a c^{6} d e x^{4} + 144 \, a c^{6} d^{2} x^{2} + 3 \, {\left(16 \, b c^{6} e^{2} x^{6} + 48 \, b c^{6} d e x^{4} + 48 \, b c^{6} d^{2} x^{2} - 24 \, b c^{4} d^{2} - 18 \, b c^{2} d e - 5 \, b e^{2}\right)} \arcsin\left(c x\right) + {\left(8 \, b c^{5} e^{2} x^{5} + 2 \, {\left(18 \, b c^{5} d e + 5 \, b c^{3} e^{2}\right)} x^{3} + 3 \, {\left(24 \, b c^{5} d^{2} + 18 \, b c^{3} d e + 5 \, b c e^{2}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{288 \, c^{6}}"," ",0,"1/288*(48*a*c^6*e^2*x^6 + 144*a*c^6*d*e*x^4 + 144*a*c^6*d^2*x^2 + 3*(16*b*c^6*e^2*x^6 + 48*b*c^6*d*e*x^4 + 48*b*c^6*d^2*x^2 - 24*b*c^4*d^2 - 18*b*c^2*d*e - 5*b*e^2)*arcsin(c*x) + (8*b*c^5*e^2*x^5 + 2*(18*b*c^5*d*e + 5*b*c^3*e^2)*x^3 + 3*(24*b*c^5*d^2 + 18*b*c^3*d*e + 5*b*c*e^2)*x)*sqrt(-c^2*x^2 + 1))/c^6","A",0
609,1,151,0,0.659272," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{45 \, a c^{5} e^{2} x^{5} + 150 \, a c^{5} d e x^{3} + 225 \, a c^{5} d^{2} x + 15 \, {\left(3 \, b c^{5} e^{2} x^{5} + 10 \, b c^{5} d e x^{3} + 15 \, b c^{5} d^{2} x\right)} \arcsin\left(c x\right) + {\left(9 \, b c^{4} e^{2} x^{4} + 225 \, b c^{4} d^{2} + 100 \, b c^{2} d e + 24 \, b e^{2} + 2 \, {\left(25 \, b c^{4} d e + 6 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{225 \, c^{5}}"," ",0,"1/225*(45*a*c^5*e^2*x^5 + 150*a*c^5*d*e*x^3 + 225*a*c^5*d^2*x + 15*(3*b*c^5*e^2*x^5 + 10*b*c^5*d*e*x^3 + 15*b*c^5*d^2*x)*arcsin(c*x) + (9*b*c^4*e^2*x^4 + 225*b*c^4*d^2 + 100*b*c^2*d*e + 24*b*e^2 + 2*(25*b*c^4*d*e + 6*b*c^2*e^2)*x^2)*sqrt(-c^2*x^2 + 1))/c^5","A",0
610,0,0,0,0.663748," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsin(c*x))/x, x)","F",0
611,1,172,0,0.676770," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","\frac{6 \, a c^{3} e^{2} x^{4} - 9 \, b c^{4} d^{2} x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + 9 \, b c^{4} d^{2} x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 36 \, a c^{3} d e x^{2} - 18 \, a c^{3} d^{2} + 6 \, {\left(b c^{3} e^{2} x^{4} + 6 \, b c^{3} d e x^{2} - 3 \, b c^{3} d^{2}\right)} \arcsin\left(c x\right) + 2 \, {\left(b c^{2} e^{2} x^{3} + 2 \, {\left(9 \, b c^{2} d e + b e^{2}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{18 \, c^{3} x}"," ",0,"1/18*(6*a*c^3*e^2*x^4 - 9*b*c^4*d^2*x*log(sqrt(-c^2*x^2 + 1) + 1) + 9*b*c^4*d^2*x*log(sqrt(-c^2*x^2 + 1) - 1) + 36*a*c^3*d*e*x^2 - 18*a*c^3*d^2 + 6*(b*c^3*e^2*x^4 + 6*b*c^3*d*e*x^2 - 3*b*c^3*d^2)*arcsin(c*x) + 2*(b*c^2*e^2*x^3 + 2*(9*b*c^2*d*e + b*e^2)*x)*sqrt(-c^2*x^2 + 1))/(c^3*x)","A",0
612,0,0,0,2.061702," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsin(c*x))/x^3, x)","F",0
613,1,174,0,0.736716," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","\frac{12 \, a c e^{2} x^{4} - 24 \, a c d e x^{2} - {\left(b c^{4} d^{2} + 12 \, b c^{2} d e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + {\left(b c^{4} d^{2} + 12 \, b c^{2} d e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) - 4 \, a c d^{2} + 4 \, {\left(3 \, b c e^{2} x^{4} - 6 \, b c d e x^{2} - b c d^{2}\right)} \arcsin\left(c x\right) - 2 \, {\left(b c^{2} d^{2} x - 6 \, b e^{2} x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{12 \, c x^{3}}"," ",0,"1/12*(12*a*c*e^2*x^4 - 24*a*c*d*e*x^2 - (b*c^4*d^2 + 12*b*c^2*d*e)*x^3*log(sqrt(-c^2*x^2 + 1) + 1) + (b*c^4*d^2 + 12*b*c^2*d*e)*x^3*log(sqrt(-c^2*x^2 + 1) - 1) - 4*a*c*d^2 + 4*(3*b*c*e^2*x^4 - 6*b*c*d*e*x^2 - b*c*d^2)*arcsin(c*x) - 2*(b*c^2*d^2*x - 6*b*e^2*x^3)*sqrt(-c^2*x^2 + 1))/(c*x^3)","A",0
614,1,322,0,0.688263," ","integrate(x^4*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{363825 \, a c^{11} e^{3} x^{11} + 1334025 \, a c^{11} d e^{2} x^{9} + 1715175 \, a c^{11} d^{2} e x^{7} + 800415 \, a c^{11} d^{3} x^{5} + 3465 \, {\left(105 \, b c^{11} e^{3} x^{11} + 385 \, b c^{11} d e^{2} x^{9} + 495 \, b c^{11} d^{2} e x^{7} + 231 \, b c^{11} d^{3} x^{5}\right)} \arcsin\left(c x\right) + {\left(33075 \, b c^{10} e^{3} x^{10} + 426888 \, b c^{6} d^{3} + 1225 \, {\left(121 \, b c^{10} d e^{2} + 30 \, b c^{8} e^{3}\right)} x^{8} + 784080 \, b c^{4} d^{2} e + 25 \, {\left(9801 \, b c^{10} d^{2} e + 6776 \, b c^{8} d e^{2} + 1680 \, b c^{6} e^{3}\right)} x^{6} + 542080 \, b c^{2} d e^{2} + 3 \, {\left(53361 \, b c^{10} d^{3} + 98010 \, b c^{8} d^{2} e + 67760 \, b c^{6} d e^{2} + 16800 \, b c^{4} e^{3}\right)} x^{4} + 134400 \, b e^{3} + 4 \, {\left(53361 \, b c^{8} d^{3} + 98010 \, b c^{6} d^{2} e + 67760 \, b c^{4} d e^{2} + 16800 \, b c^{2} e^{3}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{4002075 \, c^{11}}"," ",0,"1/4002075*(363825*a*c^11*e^3*x^11 + 1334025*a*c^11*d*e^2*x^9 + 1715175*a*c^11*d^2*e*x^7 + 800415*a*c^11*d^3*x^5 + 3465*(105*b*c^11*e^3*x^11 + 385*b*c^11*d*e^2*x^9 + 495*b*c^11*d^2*e*x^7 + 231*b*c^11*d^3*x^5)*arcsin(c*x) + (33075*b*c^10*e^3*x^10 + 426888*b*c^6*d^3 + 1225*(121*b*c^10*d*e^2 + 30*b*c^8*e^3)*x^8 + 784080*b*c^4*d^2*e + 25*(9801*b*c^10*d^2*e + 6776*b*c^8*d*e^2 + 1680*b*c^6*e^3)*x^6 + 542080*b*c^2*d*e^2 + 3*(53361*b*c^10*d^3 + 98010*b*c^8*d^2*e + 67760*b*c^6*d*e^2 + 16800*b*c^4*e^3)*x^4 + 134400*b*e^3 + 4*(53361*b*c^8*d^3 + 98010*b*c^6*d^2*e + 67760*b*c^4*d*e^2 + 16800*b*c^2*e^3)*x^2)*sqrt(-c^2*x^2 + 1))/c^11","A",0
615,1,318,0,0.574338," ","integrate(x^3*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{7680 \, a c^{10} e^{3} x^{10} + 28800 \, a c^{10} d e^{2} x^{8} + 38400 \, a c^{10} d^{2} e x^{6} + 19200 \, a c^{10} d^{3} x^{4} + 15 \, {\left(512 \, b c^{10} e^{3} x^{10} + 1920 \, b c^{10} d e^{2} x^{8} + 2560 \, b c^{10} d^{2} e x^{6} + 1280 \, b c^{10} d^{3} x^{4} - 480 \, b c^{6} d^{3} - 800 \, b c^{4} d^{2} e - 525 \, b c^{2} d e^{2} - 126 \, b e^{3}\right)} \arcsin\left(c x\right) + {\left(768 \, b c^{9} e^{3} x^{9} + 144 \, {\left(25 \, b c^{9} d e^{2} + 6 \, b c^{7} e^{3}\right)} x^{7} + 8 \, {\left(800 \, b c^{9} d^{2} e + 525 \, b c^{7} d e^{2} + 126 \, b c^{5} e^{3}\right)} x^{5} + 10 \, {\left(480 \, b c^{9} d^{3} + 800 \, b c^{7} d^{2} e + 525 \, b c^{5} d e^{2} + 126 \, b c^{3} e^{3}\right)} x^{3} + 15 \, {\left(480 \, b c^{7} d^{3} + 800 \, b c^{5} d^{2} e + 525 \, b c^{3} d e^{2} + 126 \, b c e^{3}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{76800 \, c^{10}}"," ",0,"1/76800*(7680*a*c^10*e^3*x^10 + 28800*a*c^10*d*e^2*x^8 + 38400*a*c^10*d^2*e*x^6 + 19200*a*c^10*d^3*x^4 + 15*(512*b*c^10*e^3*x^10 + 1920*b*c^10*d*e^2*x^8 + 2560*b*c^10*d^2*e*x^6 + 1280*b*c^10*d^3*x^4 - 480*b*c^6*d^3 - 800*b*c^4*d^2*e - 525*b*c^2*d*e^2 - 126*b*e^3)*arcsin(c*x) + (768*b*c^9*e^3*x^9 + 144*(25*b*c^9*d*e^2 + 6*b*c^7*e^3)*x^7 + 8*(800*b*c^9*d^2*e + 525*b*c^7*d*e^2 + 126*b*c^5*e^3)*x^5 + 10*(480*b*c^9*d^3 + 800*b*c^7*d^2*e + 525*b*c^5*d*e^2 + 126*b*c^3*e^3)*x^3 + 15*(480*b*c^7*d^3 + 800*b*c^5*d^2*e + 525*b*c^3*d*e^2 + 126*b*c*e^3)*x)*sqrt(-c^2*x^2 + 1))/c^10","A",0
616,1,277,0,0.421050," ","integrate(x^2*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{11025 \, a c^{9} e^{3} x^{9} + 42525 \, a c^{9} d e^{2} x^{7} + 59535 \, a c^{9} d^{2} e x^{5} + 33075 \, a c^{9} d^{3} x^{3} + 315 \, {\left(35 \, b c^{9} e^{3} x^{9} + 135 \, b c^{9} d e^{2} x^{7} + 189 \, b c^{9} d^{2} e x^{5} + 105 \, b c^{9} d^{3} x^{3}\right)} \arcsin\left(c x\right) + {\left(1225 \, b c^{8} e^{3} x^{8} + 22050 \, b c^{6} d^{3} + 31752 \, b c^{4} d^{2} e + 25 \, {\left(243 \, b c^{8} d e^{2} + 56 \, b c^{6} e^{3}\right)} x^{6} + 19440 \, b c^{2} d e^{2} + 3 \, {\left(3969 \, b c^{8} d^{2} e + 2430 \, b c^{6} d e^{2} + 560 \, b c^{4} e^{3}\right)} x^{4} + 4480 \, b e^{3} + {\left(11025 \, b c^{8} d^{3} + 15876 \, b c^{6} d^{2} e + 9720 \, b c^{4} d e^{2} + 2240 \, b c^{2} e^{3}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{99225 \, c^{9}}"," ",0,"1/99225*(11025*a*c^9*e^3*x^9 + 42525*a*c^9*d*e^2*x^7 + 59535*a*c^9*d^2*e*x^5 + 33075*a*c^9*d^3*x^3 + 315*(35*b*c^9*e^3*x^9 + 135*b*c^9*d*e^2*x^7 + 189*b*c^9*d^2*e*x^5 + 105*b*c^9*d^3*x^3)*arcsin(c*x) + (1225*b*c^8*e^3*x^8 + 22050*b*c^6*d^3 + 31752*b*c^4*d^2*e + 25*(243*b*c^8*d*e^2 + 56*b*c^6*e^3)*x^6 + 19440*b*c^2*d*e^2 + 3*(3969*b*c^8*d^2*e + 2430*b*c^6*d*e^2 + 560*b*c^4*e^3)*x^4 + 4480*b*e^3 + (11025*b*c^8*d^3 + 15876*b*c^6*d^2*e + 9720*b*c^4*d*e^2 + 2240*b*c^2*e^3)*x^2)*sqrt(-c^2*x^2 + 1))/c^9","A",0
617,1,274,0,0.679328," ","integrate(x*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{384 \, a c^{8} e^{3} x^{8} + 1536 \, a c^{8} d e^{2} x^{6} + 2304 \, a c^{8} d^{2} e x^{4} + 1536 \, a c^{8} d^{3} x^{2} + 3 \, {\left(128 \, b c^{8} e^{3} x^{8} + 512 \, b c^{8} d e^{2} x^{6} + 768 \, b c^{8} d^{2} e x^{4} + 512 \, b c^{8} d^{3} x^{2} - 256 \, b c^{6} d^{3} - 288 \, b c^{4} d^{2} e - 160 \, b c^{2} d e^{2} - 35 \, b e^{3}\right)} \arcsin\left(c x\right) + {\left(48 \, b c^{7} e^{3} x^{7} + 8 \, {\left(32 \, b c^{7} d e^{2} + 7 \, b c^{5} e^{3}\right)} x^{5} + 2 \, {\left(288 \, b c^{7} d^{2} e + 160 \, b c^{5} d e^{2} + 35 \, b c^{3} e^{3}\right)} x^{3} + 3 \, {\left(256 \, b c^{7} d^{3} + 288 \, b c^{5} d^{2} e + 160 \, b c^{3} d e^{2} + 35 \, b c e^{3}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{3072 \, c^{8}}"," ",0,"1/3072*(384*a*c^8*e^3*x^8 + 1536*a*c^8*d*e^2*x^6 + 2304*a*c^8*d^2*e*x^4 + 1536*a*c^8*d^3*x^2 + 3*(128*b*c^8*e^3*x^8 + 512*b*c^8*d*e^2*x^6 + 768*b*c^8*d^2*e*x^4 + 512*b*c^8*d^3*x^2 - 256*b*c^6*d^3 - 288*b*c^4*d^2*e - 160*b*c^2*d*e^2 - 35*b*e^3)*arcsin(c*x) + (48*b*c^7*e^3*x^7 + 8*(32*b*c^7*d*e^2 + 7*b*c^5*e^3)*x^5 + 2*(288*b*c^7*d^2*e + 160*b*c^5*d*e^2 + 35*b*c^3*e^3)*x^3 + 3*(256*b*c^7*d^3 + 288*b*c^5*d^2*e + 160*b*c^3*d*e^2 + 35*b*c*e^3)*x)*sqrt(-c^2*x^2 + 1))/c^8","A",0
618,1,229,0,0.668495," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{525 \, a c^{7} e^{3} x^{7} + 2205 \, a c^{7} d e^{2} x^{5} + 3675 \, a c^{7} d^{2} e x^{3} + 3675 \, a c^{7} d^{3} x + 105 \, {\left(5 \, b c^{7} e^{3} x^{7} + 21 \, b c^{7} d e^{2} x^{5} + 35 \, b c^{7} d^{2} e x^{3} + 35 \, b c^{7} d^{3} x\right)} \arcsin\left(c x\right) + {\left(75 \, b c^{6} e^{3} x^{6} + 3675 \, b c^{6} d^{3} + 2450 \, b c^{4} d^{2} e + 1176 \, b c^{2} d e^{2} + 9 \, {\left(49 \, b c^{6} d e^{2} + 10 \, b c^{4} e^{3}\right)} x^{4} + 240 \, b e^{3} + {\left(1225 \, b c^{6} d^{2} e + 588 \, b c^{4} d e^{2} + 120 \, b c^{2} e^{3}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{3675 \, c^{7}}"," ",0,"1/3675*(525*a*c^7*e^3*x^7 + 2205*a*c^7*d*e^2*x^5 + 3675*a*c^7*d^2*e*x^3 + 3675*a*c^7*d^3*x + 105*(5*b*c^7*e^3*x^7 + 21*b*c^7*d*e^2*x^5 + 35*b*c^7*d^2*e*x^3 + 35*b*c^7*d^3*x)*arcsin(c*x) + (75*b*c^6*e^3*x^6 + 3675*b*c^6*d^3 + 2450*b*c^4*d^2*e + 1176*b*c^2*d*e^2 + 9*(49*b*c^6*d*e^2 + 10*b*c^4*e^3)*x^4 + 240*b*e^3 + (1225*b*c^6*d^2*e + 588*b*c^4*d*e^2 + 120*b*c^2*e^3)*x^2)*sqrt(-c^2*x^2 + 1))/c^7","A",0
619,0,0,0,0.528518," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arcsin\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arcsin(c*x))/x, x)","F",0
620,1,239,0,0.763119," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x, algorithm=""fricas"")","\frac{30 \, a c^{5} e^{3} x^{6} + 150 \, a c^{5} d e^{2} x^{4} - 75 \, b c^{6} d^{3} x \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + 75 \, b c^{6} d^{3} x \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 450 \, a c^{5} d^{2} e x^{2} - 150 \, a c^{5} d^{3} + 30 \, {\left(b c^{5} e^{3} x^{6} + 5 \, b c^{5} d e^{2} x^{4} + 15 \, b c^{5} d^{2} e x^{2} - 5 \, b c^{5} d^{3}\right)} \arcsin\left(c x\right) + 2 \, {\left(3 \, b c^{4} e^{3} x^{5} + {\left(25 \, b c^{4} d e^{2} + 4 \, b c^{2} e^{3}\right)} x^{3} + {\left(225 \, b c^{4} d^{2} e + 50 \, b c^{2} d e^{2} + 8 \, b e^{3}\right)} x\right)} \sqrt{-c^{2} x^{2} + 1}}{150 \, c^{5} x}"," ",0,"1/150*(30*a*c^5*e^3*x^6 + 150*a*c^5*d*e^2*x^4 - 75*b*c^6*d^3*x*log(sqrt(-c^2*x^2 + 1) + 1) + 75*b*c^6*d^3*x*log(sqrt(-c^2*x^2 + 1) - 1) + 450*a*c^5*d^2*e*x^2 - 150*a*c^5*d^3 + 30*(b*c^5*e^3*x^6 + 5*b*c^5*d*e^2*x^4 + 15*b*c^5*d^2*e*x^2 - 5*b*c^5*d^3)*arcsin(c*x) + 2*(3*b*c^4*e^3*x^5 + (25*b*c^4*d*e^2 + 4*b*c^2*e^3)*x^3 + (225*b*c^4*d^2*e + 50*b*c^2*d*e^2 + 8*b*e^3)*x)*sqrt(-c^2*x^2 + 1))/(c^5*x)","A",0
621,0,0,0,0.619372," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arcsin\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arcsin(c*x))/x^3, x)","F",0
622,1,246,0,0.867540," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x, algorithm=""fricas"")","\frac{12 \, a c^{3} e^{3} x^{6} + 108 \, a c^{3} d e^{2} x^{4} - 108 \, a c^{3} d^{2} e x^{2} - 12 \, a c^{3} d^{3} - 3 \, {\left(b c^{6} d^{3} + 18 \, b c^{4} d^{2} e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} + 1\right) + 3 \, {\left(b c^{6} d^{3} + 18 \, b c^{4} d^{2} e\right)} x^{3} \log\left(\sqrt{-c^{2} x^{2} + 1} - 1\right) + 12 \, {\left(b c^{3} e^{3} x^{6} + 9 \, b c^{3} d e^{2} x^{4} - 9 \, b c^{3} d^{2} e x^{2} - b c^{3} d^{3}\right)} \arcsin\left(c x\right) + 2 \, {\left(2 \, b c^{2} e^{3} x^{5} - 3 \, b c^{4} d^{3} x + 2 \, {\left(27 \, b c^{2} d e^{2} + 2 \, b e^{3}\right)} x^{3}\right)} \sqrt{-c^{2} x^{2} + 1}}{36 \, c^{3} x^{3}}"," ",0,"1/36*(12*a*c^3*e^3*x^6 + 108*a*c^3*d*e^2*x^4 - 108*a*c^3*d^2*e*x^2 - 12*a*c^3*d^3 - 3*(b*c^6*d^3 + 18*b*c^4*d^2*e)*x^3*log(sqrt(-c^2*x^2 + 1) + 1) + 3*(b*c^6*d^3 + 18*b*c^4*d^2*e)*x^3*log(sqrt(-c^2*x^2 + 1) - 1) + 12*(b*c^3*e^3*x^6 + 9*b*c^3*d*e^2*x^4 - 9*b*c^3*d^2*e*x^2 - b*c^3*d^3)*arcsin(c*x) + 2*(2*b*c^2*e^3*x^5 - 3*b*c^4*d^3*x + 2*(27*b*c^2*d*e^2 + 2*b*e^3)*x^3)*sqrt(-c^2*x^2 + 1))/(c^3*x^3)","A",0
623,1,321,0,0.602900," ","integrate((e*x^2+d)^4*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","\frac{11025 \, a c^{9} e^{4} x^{9} + 56700 \, a c^{9} d e^{3} x^{7} + 119070 \, a c^{9} d^{2} e^{2} x^{5} + 132300 \, a c^{9} d^{3} e x^{3} + 99225 \, a c^{9} d^{4} x + 315 \, {\left(35 \, b c^{9} e^{4} x^{9} + 180 \, b c^{9} d e^{3} x^{7} + 378 \, b c^{9} d^{2} e^{2} x^{5} + 420 \, b c^{9} d^{3} e x^{3} + 315 \, b c^{9} d^{4} x\right)} \arcsin\left(c x\right) + {\left(1225 \, b c^{8} e^{4} x^{8} + 99225 \, b c^{8} d^{4} + 88200 \, b c^{6} d^{3} e + 63504 \, b c^{4} d^{2} e^{2} + 25920 \, b c^{2} d e^{3} + 100 \, {\left(81 \, b c^{8} d e^{3} + 14 \, b c^{6} e^{4}\right)} x^{6} + 4480 \, b e^{4} + 6 \, {\left(3969 \, b c^{8} d^{2} e^{2} + 1620 \, b c^{6} d e^{3} + 280 \, b c^{4} e^{4}\right)} x^{4} + 4 \, {\left(11025 \, b c^{8} d^{3} e + 7938 \, b c^{6} d^{2} e^{2} + 3240 \, b c^{4} d e^{3} + 560 \, b c^{2} e^{4}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}}{99225 \, c^{9}}"," ",0,"1/99225*(11025*a*c^9*e^4*x^9 + 56700*a*c^9*d*e^3*x^7 + 119070*a*c^9*d^2*e^2*x^5 + 132300*a*c^9*d^3*e*x^3 + 99225*a*c^9*d^4*x + 315*(35*b*c^9*e^4*x^9 + 180*b*c^9*d*e^3*x^7 + 378*b*c^9*d^2*e^2*x^5 + 420*b*c^9*d^3*e*x^3 + 315*b*c^9*d^4*x)*arcsin(c*x) + (1225*b*c^8*e^4*x^8 + 99225*b*c^8*d^4 + 88200*b*c^6*d^3*e + 63504*b*c^4*d^2*e^2 + 25920*b*c^2*d*e^3 + 100*(81*b*c^8*d*e^3 + 14*b*c^6*e^4)*x^6 + 4480*b*e^4 + 6*(3969*b*c^8*d^2*e^2 + 1620*b*c^6*d*e^3 + 280*b*c^4*e^4)*x^4 + 4*(11025*b*c^8*d^3*e + 7938*b*c^6*d^2*e^2 + 3240*b*c^4*d*e^3 + 560*b*c^2*e^4)*x^2)*sqrt(-c^2*x^2 + 1))/c^9","A",0
624,0,0,0,0.525343," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \arcsin\left(c x\right) + a x^{4}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^4*arcsin(c*x) + a*x^4)/(e*x^2 + d), x)","F",0
625,0,0,0,0.733270," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arcsin\left(c x\right) + a x^{3}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^3*arcsin(c*x) + a*x^3)/(e*x^2 + d), x)","F",0
626,0,0,0,0.538283," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arcsin\left(c x\right) + a x^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arcsin(c*x) + a*x^2)/(e*x^2 + d), x)","F",0
627,0,0,0,0.588454," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \arcsin\left(c x\right) + a x}{e x^{2} + d}, x\right)"," ",0,"integral((b*x*arcsin(c*x) + a*x)/(e*x^2 + d), x)","F",0
628,0,0,0,0.504711," ","integrate((a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e*x^2 + d), x)","F",0
629,0,0,0,0.628144," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e x^{3} + d x}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e*x^3 + d*x), x)","F",0
630,0,0,0,0.738828," ","integrate((a+b*arcsin(c*x))/x^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
631,0,0,0,0.533014," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e*x^5 + d*x^3), x)","F",0
632,0,0,0,0.657181," ","integrate((a+b*arcsin(c*x))/x^4/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e x^{6} + d x^{4}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e*x^6 + d*x^4), x)","F",0
633,0,0,0,0.567021," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \arcsin\left(c x\right) + a x^{3}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^3*arcsin(c*x) + a*x^3)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
634,1,395,0,0.652871," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{2} d^{2} + 4 \, a d e + {\left(b c e x^{2} + b c d\right)} \sqrt{-c^{2} d^{2} - d e} \log\left(\frac{{\left(8 \, c^{4} d^{2} + 8 \, c^{2} d e + e^{2}\right)} x^{4} - 2 \, {\left(4 \, c^{2} d^{2} + 3 \, d e\right)} x^{2} - 4 \, \sqrt{-c^{2} d^{2} - d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{3} - d x\right)} + d^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 4 \, {\left(b c^{2} d^{2} + b d e\right)} \arcsin\left(c x\right)}{8 \, {\left(c^{2} d^{3} e + d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} + d e^{3}\right)} x^{2}\right)}}, -\frac{2 \, a c^{2} d^{2} + 2 \, a d e + {\left(b c e x^{2} + b c d\right)} \sqrt{c^{2} d^{2} + d e} \arctan\left(\frac{\sqrt{c^{2} d^{2} + d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{2} - d\right)}}{2 \, {\left({\left(c^{4} d^{2} + c^{2} d e\right)} x^{3} - {\left(c^{2} d^{2} + d e\right)} x\right)}}\right) + 2 \, {\left(b c^{2} d^{2} + b d e\right)} \arcsin\left(c x\right)}{4 \, {\left(c^{2} d^{3} e + d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} + d e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/8*(4*a*c^2*d^2 + 4*a*d*e + (b*c*e*x^2 + b*c*d)*sqrt(-c^2*d^2 - d*e)*log(((8*c^4*d^2 + 8*c^2*d*e + e^2)*x^4 - 2*(4*c^2*d^2 + 3*d*e)*x^2 - 4*sqrt(-c^2*d^2 - d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^3 - d*x) + d^2)/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 4*(b*c^2*d^2 + b*d*e)*arcsin(c*x))/(c^2*d^3*e + d^2*e^2 + (c^2*d^2*e^2 + d*e^3)*x^2), -1/4*(2*a*c^2*d^2 + 2*a*d*e + (b*c*e*x^2 + b*c*d)*sqrt(c^2*d^2 + d*e)*arctan(1/2*sqrt(c^2*d^2 + d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^2 - d)/((c^4*d^2 + c^2*d*e)*x^3 - (c^2*d^2 + d*e)*x)) + 2*(b*c^2*d^2 + b*d*e)*arcsin(c*x))/(c^2*d^3*e + d^2*e^2 + (c^2*d^2*e^2 + d*e^3)*x^2)]","B",0
635,0,0,0,0.732092," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
636,0,0,0,0.668556," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
637,0,0,0,0.593074," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \arcsin\left(c x\right) + a x^{4}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^4*arcsin(c*x) + a*x^4)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
638,0,0,0,0.703375," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arcsin\left(c x\right) + a x^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arcsin(c*x) + a*x^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
639,0,0,0,0.627547," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
640,0,0,0,0.850469," ","integrate((a+b*arcsin(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
641,0,0,0,0.749161," ","integrate(x^5*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \arcsin\left(c x\right) + a x^{5}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^5*arcsin(c*x) + a*x^5)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
642,1,921,0,1.168664," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, a c^{4} d^{4} + 16 \, a c^{2} d^{3} e + 8 \, a d^{2} e^{2} + 16 \, {\left(a c^{4} d^{3} e + 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} + 3 \, b c d^{2} e + {\left(2 \, b c^{3} d e^{2} + 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e + 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d^{2} - d e} \log\left(\frac{{\left(8 \, c^{4} d^{2} + 8 \, c^{2} d e + e^{2}\right)} x^{4} - 2 \, {\left(4 \, c^{2} d^{2} + 3 \, d e\right)} x^{2} - 4 \, \sqrt{-c^{2} d^{2} - d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{3} - d x\right)} + d^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 8 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arcsin\left(c x\right) + 4 \, \sqrt{-c^{2} x^{2} + 1} {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)}}{32 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} + 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}, -\frac{4 \, a c^{4} d^{4} + 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{3} e + 2 \, a c^{2} d^{2} e^{2} + a d e^{3}\right)} x^{2} + {\left(2 \, b c^{3} d^{3} + 3 \, b c d^{2} e + {\left(2 \, b c^{3} d e^{2} + 3 \, b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e + 3 \, b c d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d^{2} + d e} \arctan\left(\frac{\sqrt{c^{2} d^{2} + d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{2} - d\right)}}{2 \, {\left({\left(c^{4} d^{2} + c^{2} d e\right)} x^{3} - {\left(c^{2} d^{2} + d e\right)} x\right)}}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \arcsin\left(c x\right) + 2 \, \sqrt{-c^{2} x^{2} + 1} {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)}}{16 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} + 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/32*(8*a*c^4*d^4 + 16*a*c^2*d^3*e + 8*a*d^2*e^2 + 16*(a*c^4*d^3*e + 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 + (2*b*c^3*d^3 + 3*b*c*d^2*e + (2*b*c^3*d*e^2 + 3*b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e + 3*b*c*d*e^2)*x^2)*sqrt(-c^2*d^2 - d*e)*log(((8*c^4*d^2 + 8*c^2*d*e + e^2)*x^4 - 2*(4*c^2*d^2 + 3*d*e)*x^2 - 4*sqrt(-c^2*d^2 - d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^3 - d*x) + d^2)/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 8*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arcsin(c*x) + 4*sqrt(-c^2*x^2 + 1)*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x))/(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 + 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^2), -1/16*(4*a*c^4*d^4 + 8*a*c^2*d^3*e + 4*a*d^2*e^2 + 8*(a*c^4*d^3*e + 2*a*c^2*d^2*e^2 + a*d*e^3)*x^2 + (2*b*c^3*d^3 + 3*b*c*d^2*e + (2*b*c^3*d*e^2 + 3*b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e + 3*b*c*d*e^2)*x^2)*sqrt(c^2*d^2 + d*e)*arctan(1/2*sqrt(c^2*d^2 + d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^2 - d)/((c^4*d^2 + c^2*d*e)*x^3 - (c^2*d^2 + d*e)*x)) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*arcsin(c*x) + 2*sqrt(-c^2*x^2 + 1)*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x))/(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 + 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^2)]","B",0
643,1,783,0,0.720940," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{8 \, a c^{4} d^{4} + 16 \, a c^{2} d^{3} e + 8 \, a d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} + b c d^{2} e + {\left(2 \, b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d^{2} - d e} \log\left(\frac{{\left(8 \, c^{4} d^{2} + 8 \, c^{2} d e + e^{2}\right)} x^{4} - 2 \, {\left(4 \, c^{2} d^{2} + 3 \, d e\right)} x^{2} - 4 \, \sqrt{-c^{2} d^{2} - d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{3} - d x\right)} + d^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\right) + 8 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \arcsin\left(c x\right) - 4 \, \sqrt{-c^{2} x^{2} + 1} {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)}}{32 \, {\left(c^{4} d^{6} e + 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}, -\frac{4 \, a c^{4} d^{4} + 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{2} + {\left(2 \, b c^{3} d^{3} + b c d^{2} e + {\left(2 \, b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(2 \, b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d^{2} + d e} \arctan\left(\frac{\sqrt{c^{2} d^{2} + d e} \sqrt{-c^{2} x^{2} + 1} {\left({\left(2 \, c^{2} d + e\right)} x^{2} - d\right)}}{2 \, {\left({\left(c^{4} d^{2} + c^{2} d e\right)} x^{3} - {\left(c^{2} d^{2} + d e\right)} x\right)}}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \arcsin\left(c x\right) - 2 \, \sqrt{-c^{2} x^{2} + 1} {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)}}{16 \, {\left(c^{4} d^{6} e + 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/32*(8*a*c^4*d^4 + 16*a*c^2*d^3*e + 8*a*d^2*e^2 + (2*b*c^3*d^3 + b*c*d^2*e + (2*b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(-c^2*d^2 - d*e)*log(((8*c^4*d^2 + 8*c^2*d*e + e^2)*x^4 - 2*(4*c^2*d^2 + 3*d*e)*x^2 - 4*sqrt(-c^2*d^2 - d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^3 - d*x) + d^2)/(e^2*x^4 + 2*d*e*x^2 + d^2)) + 8*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*arcsin(c*x) - 4*sqrt(-c^2*x^2 + 1)*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x))/(c^4*d^6*e + 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4)*x^2), -1/16*(4*a*c^4*d^4 + 8*a*c^2*d^3*e + 4*a*d^2*e^2 + (2*b*c^3*d^3 + b*c*d^2*e + (2*b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(2*b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(c^2*d^2 + d*e)*arctan(1/2*sqrt(c^2*d^2 + d*e)*sqrt(-c^2*x^2 + 1)*((2*c^2*d + e)*x^2 - d)/((c^4*d^2 + c^2*d*e)*x^3 - (c^2*d^2 + d*e)*x)) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*arcsin(c*x) - 2*sqrt(-c^2*x^2 + 1)*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x))/(c^4*d^6*e + 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4)*x^2)]","B",0
644,0,0,0,0.757160," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
645,0,0,0,0.838543," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
646,0,0,0,0.517182," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \arcsin\left(c x\right) + a x^{4}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^4*arcsin(c*x) + a*x^4)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
647,0,0,0,0.632411," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \arcsin\left(c x\right) + a x^{2}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^2*arcsin(c*x) + a*x^2)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
648,0,0,0,0.844060," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
649,0,0,0,0.547809," ","integrate((e*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsin(c*x) + a), x)","F",0
650,0,0,0,0.617826," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \arcsin\left(c x\right) + a}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
651,1,294,0,1.063901," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b e x^{2} + b d\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{-e} + e^{2}\right) - 4 \, {\left(b e x \arcsin\left(c x\right) + a e x\right)} \sqrt{e x^{2} + d}}{4 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}, \frac{{\left(b e x^{2} + b d\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{2} + c^{2} d - e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(b e x \arcsin\left(c x\right) + a e x\right)} \sqrt{e x^{2} + d}}{2 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}\right]"," ",0,"[-1/4*((b*e*x^2 + b*d)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 + 4*(2*c^3*e*x^2 + c^3*d - c*e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(-e) + e^2) - 4*(b*e*x*arcsin(c*x) + a*e*x)*sqrt(e*x^2 + d))/(d*e^2*x^2 + d^2*e), 1/2*((b*e*x^2 + b*d)*sqrt(e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(b*e*x*arcsin(c*x) + a*e*x)*sqrt(e*x^2 + d))/(d*e^2*x^2 + d^2*e)]","B",0
652,1,683,0,0.736417," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{-e} + e^{2}\right) - 2 \, {\left(2 \, {\left(a c^{2} d e^{2} + a e^{3}\right)} x^{3} + 3 \, {\left(a c^{2} d^{2} e + a d e^{2}\right)} x + {\left(2 \, {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x\right)} \arcsin\left(c x\right) + {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}, \frac{{\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{2} + c^{2} d - e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, {\left(a c^{2} d e^{2} + a e^{3}\right)} x^{3} + 3 \, {\left(a c^{2} d^{2} e + a d e^{2}\right)} x + {\left(2 \, {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{3} + 3 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x\right)} \arcsin\left(c x\right) + {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{e x^{2} + d}}{3 \, {\left(c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/6*((b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 + 4*(2*c^3*e*x^2 + c^3*d - c*e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(-e) + e^2) - 2*(2*(a*c^2*d*e^2 + a*e^3)*x^3 + 3*(a*c^2*d^2*e + a*d*e^2)*x + (2*(b*c^2*d*e^2 + b*e^3)*x^3 + 3*(b*c^2*d^2*e + b*d*e^2)*x)*arcsin(c*x) + (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(-c^2*x^2 + 1))*sqrt(e*x^2 + d))/(c^2*d^5*e + d^4*e^2 + (c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^2*d^4*e^2 + d^3*e^3)*x^2), 1/3*((b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (2*(a*c^2*d*e^2 + a*e^3)*x^3 + 3*(a*c^2*d^2*e + a*d*e^2)*x + (2*(b*c^2*d*e^2 + b*e^3)*x^3 + 3*(b*c^2*d^2*e + b*d*e^2)*x)*arcsin(c*x) + (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(-c^2*x^2 + 1))*sqrt(e*x^2 + d))/(c^2*d^5*e + d^4*e^2 + (c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^2*d^4*e^2 + d^3*e^3)*x^2)]","B",0
653,1,1321,0,0.759221," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(7/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(b c^{4} d^{5} + 2 \, b c^{2} d^{4} e + {\left(b c^{4} d^{2} e^{3} + 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} + 3 \, {\left(b c^{4} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} + 3 \, {\left(b c^{4} d^{4} e + 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} + 4 \, {\left(2 \, c^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{-e} + e^{2}\right) - {\left(8 \, {\left(a c^{4} d^{2} e^{3} + 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{5} + 20 \, {\left(a c^{4} d^{3} e^{2} + 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{3} + 15 \, {\left(a c^{4} d^{4} e + 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x + {\left(8 \, {\left(b c^{4} d^{2} e^{3} + 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{5} + 20 \, {\left(b c^{4} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{3} + 15 \, {\left(b c^{4} d^{4} e + 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x\right)} \arcsin\left(c x\right) + {\left(7 \, b c^{3} d^{4} e + 5 \, b c d^{3} e^{2} + 2 \, {\left(3 \, b c^{3} d^{2} e^{3} + 2 \, b c d e^{4}\right)} x^{4} + {\left(13 \, b c^{3} d^{3} e^{2} + 9 \, b c d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{e x^{2} + d}}{15 \, {\left(c^{4} d^{8} e + 2 \, c^{2} d^{7} e^{2} + d^{6} e^{3} + {\left(c^{4} d^{5} e^{4} + 2 \, c^{2} d^{4} e^{5} + d^{3} e^{6}\right)} x^{6} + 3 \, {\left(c^{4} d^{6} e^{3} + 2 \, c^{2} d^{5} e^{4} + d^{4} e^{5}\right)} x^{4} + 3 \, {\left(c^{4} d^{7} e^{2} + 2 \, c^{2} d^{6} e^{3} + d^{5} e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left(b c^{4} d^{5} + 2 \, b c^{2} d^{4} e + {\left(b c^{4} d^{2} e^{3} + 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{6} + b d^{3} e^{2} + 3 \, {\left(b c^{4} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{4} + 3 \, {\left(b c^{4} d^{4} e + 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{2} + c^{2} d - e\right)} \sqrt{-c^{2} x^{2} + 1} \sqrt{e x^{2} + d} \sqrt{e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + {\left(8 \, {\left(a c^{4} d^{2} e^{3} + 2 \, a c^{2} d e^{4} + a e^{5}\right)} x^{5} + 20 \, {\left(a c^{4} d^{3} e^{2} + 2 \, a c^{2} d^{2} e^{3} + a d e^{4}\right)} x^{3} + 15 \, {\left(a c^{4} d^{4} e + 2 \, a c^{2} d^{3} e^{2} + a d^{2} e^{3}\right)} x + {\left(8 \, {\left(b c^{4} d^{2} e^{3} + 2 \, b c^{2} d e^{4} + b e^{5}\right)} x^{5} + 20 \, {\left(b c^{4} d^{3} e^{2} + 2 \, b c^{2} d^{2} e^{3} + b d e^{4}\right)} x^{3} + 15 \, {\left(b c^{4} d^{4} e + 2 \, b c^{2} d^{3} e^{2} + b d^{2} e^{3}\right)} x\right)} \arcsin\left(c x\right) + {\left(7 \, b c^{3} d^{4} e + 5 \, b c d^{3} e^{2} + 2 \, {\left(3 \, b c^{3} d^{2} e^{3} + 2 \, b c d e^{4}\right)} x^{4} + {\left(13 \, b c^{3} d^{3} e^{2} + 9 \, b c d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-c^{2} x^{2} + 1}\right)} \sqrt{e x^{2} + d}}{15 \, {\left(c^{4} d^{8} e + 2 \, c^{2} d^{7} e^{2} + d^{6} e^{3} + {\left(c^{4} d^{5} e^{4} + 2 \, c^{2} d^{4} e^{5} + d^{3} e^{6}\right)} x^{6} + 3 \, {\left(c^{4} d^{6} e^{3} + 2 \, c^{2} d^{5} e^{4} + d^{4} e^{5}\right)} x^{4} + 3 \, {\left(c^{4} d^{7} e^{2} + 2 \, c^{2} d^{6} e^{3} + d^{5} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/15*(2*(b*c^4*d^5 + 2*b*c^2*d^4*e + (b*c^4*d^2*e^3 + 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 + 3*(b*c^4*d^3*e^2 + 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 + 3*(b*c^4*d^4*e + 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 + 4*(2*c^3*e*x^2 + c^3*d - c*e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(-e) + e^2) - (8*(a*c^4*d^2*e^3 + 2*a*c^2*d*e^4 + a*e^5)*x^5 + 20*(a*c^4*d^3*e^2 + 2*a*c^2*d^2*e^3 + a*d*e^4)*x^3 + 15*(a*c^4*d^4*e + 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x + (8*(b*c^4*d^2*e^3 + 2*b*c^2*d*e^4 + b*e^5)*x^5 + 20*(b*c^4*d^3*e^2 + 2*b*c^2*d^2*e^3 + b*d*e^4)*x^3 + 15*(b*c^4*d^4*e + 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x)*arcsin(c*x) + (7*b*c^3*d^4*e + 5*b*c*d^3*e^2 + 2*(3*b*c^3*d^2*e^3 + 2*b*c*d*e^4)*x^4 + (13*b*c^3*d^3*e^2 + 9*b*c*d^2*e^3)*x^2)*sqrt(-c^2*x^2 + 1))*sqrt(e*x^2 + d))/(c^4*d^8*e + 2*c^2*d^7*e^2 + d^6*e^3 + (c^4*d^5*e^4 + 2*c^2*d^4*e^5 + d^3*e^6)*x^6 + 3*(c^4*d^6*e^3 + 2*c^2*d^5*e^4 + d^4*e^5)*x^4 + 3*(c^4*d^7*e^2 + 2*c^2*d^6*e^3 + d^5*e^4)*x^2), 1/15*(4*(b*c^4*d^5 + 2*b*c^2*d^4*e + (b*c^4*d^2*e^3 + 2*b*c^2*d*e^4 + b*e^5)*x^6 + b*d^3*e^2 + 3*(b*c^4*d^3*e^2 + 2*b*c^2*d^2*e^3 + b*d*e^4)*x^4 + 3*(b*c^4*d^4*e + 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(-c^2*x^2 + 1)*sqrt(e*x^2 + d)*sqrt(e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + (8*(a*c^4*d^2*e^3 + 2*a*c^2*d*e^4 + a*e^5)*x^5 + 20*(a*c^4*d^3*e^2 + 2*a*c^2*d^2*e^3 + a*d*e^4)*x^3 + 15*(a*c^4*d^4*e + 2*a*c^2*d^3*e^2 + a*d^2*e^3)*x + (8*(b*c^4*d^2*e^3 + 2*b*c^2*d*e^4 + b*e^5)*x^5 + 20*(b*c^4*d^3*e^2 + 2*b*c^2*d^2*e^3 + b*d*e^4)*x^3 + 15*(b*c^4*d^4*e + 2*b*c^2*d^3*e^2 + b*d^2*e^3)*x)*arcsin(c*x) + (7*b*c^3*d^4*e + 5*b*c*d^3*e^2 + 2*(3*b*c^3*d^2*e^3 + 2*b*c*d*e^4)*x^4 + (13*b*c^3*d^3*e^2 + 9*b*c*d^2*e^3)*x^2)*sqrt(-c^2*x^2 + 1))*sqrt(e*x^2 + d))/(c^4*d^8*e + 2*c^2*d^7*e^2 + d^6*e^3 + (c^4*d^5*e^4 + 2*c^2*d^4*e^5 + d^3*e^6)*x^6 + 3*(c^4*d^6*e^3 + 2*c^2*d^5*e^4 + d^4*e^5)*x^4 + 3*(c^4*d^7*e^2 + 2*c^2*d^6*e^3 + d^5*e^4)*x^2)]","B",0
654,0,0,0,0.719568," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arcsin\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arcsin(c*x))*(f*x)^m, x)","F",0
655,0,0,0,0.830366," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arcsin\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsin(c*x))*(f*x)^m, x)","F",0
656,0,0,0,0.837569," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arcsin\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsin(c*x))*(f*x)^m, x)","F",0
657,0,0,0,1.243036," ","integrate((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arcsin\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
658,0,0,0,0.494425," ","integrate((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \arcsin\left(c x\right) + a\right)} \left(f x\right)^{m}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsin(c*x) + a)*(f*x)^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
659,1,555,0,1.281056," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{1125 \, {\left(49 \, a^{2} - 2 \, b^{2}\right)} c^{7} e^{3} x^{7} + 189 \, {\left(49 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{7} d e^{2} - 20 \, b^{2} c^{5} e^{3}\right)} x^{5} + 35 \, {\left(1225 \, {\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{7} d^{2} e - 1176 \, b^{2} c^{5} d e^{2} - 240 \, b^{2} c^{3} e^{3}\right)} x^{3} + 11025 \, {\left(5 \, b^{2} c^{7} e^{3} x^{7} + 21 \, b^{2} c^{7} d e^{2} x^{5} + 35 \, b^{2} c^{7} d^{2} e x^{3} + 35 \, b^{2} c^{7} d^{3} x\right)} \arcsin\left(c x\right)^{2} + 105 \, {\left(3675 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{7} d^{3} - 4900 \, b^{2} c^{5} d^{2} e - 2352 \, b^{2} c^{3} d e^{2} - 480 \, b^{2} c e^{3}\right)} x + 22050 \, {\left(5 \, a b c^{7} e^{3} x^{7} + 21 \, a b c^{7} d e^{2} x^{5} + 35 \, a b c^{7} d^{2} e x^{3} + 35 \, a b c^{7} d^{3} x\right)} \arcsin\left(c x\right) + 210 \, {\left(75 \, a b c^{6} e^{3} x^{6} + 3675 \, a b c^{6} d^{3} + 2450 \, a b c^{4} d^{2} e + 1176 \, a b c^{2} d e^{2} + 240 \, a b e^{3} + 9 \, {\left(49 \, a b c^{6} d e^{2} + 10 \, a b c^{4} e^{3}\right)} x^{4} + {\left(1225 \, a b c^{6} d^{2} e + 588 \, a b c^{4} d e^{2} + 120 \, a b c^{2} e^{3}\right)} x^{2} + {\left(75 \, b^{2} c^{6} e^{3} x^{6} + 3675 \, b^{2} c^{6} d^{3} + 2450 \, b^{2} c^{4} d^{2} e + 1176 \, b^{2} c^{2} d e^{2} + 240 \, b^{2} e^{3} + 9 \, {\left(49 \, b^{2} c^{6} d e^{2} + 10 \, b^{2} c^{4} e^{3}\right)} x^{4} + {\left(1225 \, b^{2} c^{6} d^{2} e + 588 \, b^{2} c^{4} d e^{2} + 120 \, b^{2} c^{2} e^{3}\right)} x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{385875 \, c^{7}}"," ",0,"1/385875*(1125*(49*a^2 - 2*b^2)*c^7*e^3*x^7 + 189*(49*(25*a^2 - 2*b^2)*c^7*d*e^2 - 20*b^2*c^5*e^3)*x^5 + 35*(1225*(9*a^2 - 2*b^2)*c^7*d^2*e - 1176*b^2*c^5*d*e^2 - 240*b^2*c^3*e^3)*x^3 + 11025*(5*b^2*c^7*e^3*x^7 + 21*b^2*c^7*d*e^2*x^5 + 35*b^2*c^7*d^2*e*x^3 + 35*b^2*c^7*d^3*x)*arcsin(c*x)^2 + 105*(3675*(a^2 - 2*b^2)*c^7*d^3 - 4900*b^2*c^5*d^2*e - 2352*b^2*c^3*d*e^2 - 480*b^2*c*e^3)*x + 22050*(5*a*b*c^7*e^3*x^7 + 21*a*b*c^7*d*e^2*x^5 + 35*a*b*c^7*d^2*e*x^3 + 35*a*b*c^7*d^3*x)*arcsin(c*x) + 210*(75*a*b*c^6*e^3*x^6 + 3675*a*b*c^6*d^3 + 2450*a*b*c^4*d^2*e + 1176*a*b*c^2*d*e^2 + 240*a*b*e^3 + 9*(49*a*b*c^6*d*e^2 + 10*a*b*c^4*e^3)*x^4 + (1225*a*b*c^6*d^2*e + 588*a*b*c^4*d*e^2 + 120*a*b*c^2*e^3)*x^2 + (75*b^2*c^6*e^3*x^6 + 3675*b^2*c^6*d^3 + 2450*b^2*c^4*d^2*e + 1176*b^2*c^2*d*e^2 + 240*b^2*e^3 + 9*(49*b^2*c^6*d*e^2 + 10*b^2*c^4*e^3)*x^4 + (1225*b^2*c^6*d^2*e + 588*b^2*c^4*d*e^2 + 120*b^2*c^2*e^3)*x^2)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^7","A",0
660,1,349,0,0.990710," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{27 \, {\left(25 \, a^{2} - 2 \, b^{2}\right)} c^{5} e^{2} x^{5} + 10 \, {\left(25 \, {\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{5} d e - 12 \, b^{2} c^{3} e^{2}\right)} x^{3} + 225 \, {\left(3 \, b^{2} c^{5} e^{2} x^{5} + 10 \, b^{2} c^{5} d e x^{3} + 15 \, b^{2} c^{5} d^{2} x\right)} \arcsin\left(c x\right)^{2} + 15 \, {\left(225 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{5} d^{2} - 200 \, b^{2} c^{3} d e - 48 \, b^{2} c e^{2}\right)} x + 450 \, {\left(3 \, a b c^{5} e^{2} x^{5} + 10 \, a b c^{5} d e x^{3} + 15 \, a b c^{5} d^{2} x\right)} \arcsin\left(c x\right) + 30 \, {\left(9 \, a b c^{4} e^{2} x^{4} + 225 \, a b c^{4} d^{2} + 100 \, a b c^{2} d e + 24 \, a b e^{2} + 2 \, {\left(25 \, a b c^{4} d e + 6 \, a b c^{2} e^{2}\right)} x^{2} + {\left(9 \, b^{2} c^{4} e^{2} x^{4} + 225 \, b^{2} c^{4} d^{2} + 100 \, b^{2} c^{2} d e + 24 \, b^{2} e^{2} + 2 \, {\left(25 \, b^{2} c^{4} d e + 6 \, b^{2} c^{2} e^{2}\right)} x^{2}\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{3375 \, c^{5}}"," ",0,"1/3375*(27*(25*a^2 - 2*b^2)*c^5*e^2*x^5 + 10*(25*(9*a^2 - 2*b^2)*c^5*d*e - 12*b^2*c^3*e^2)*x^3 + 225*(3*b^2*c^5*e^2*x^5 + 10*b^2*c^5*d*e*x^3 + 15*b^2*c^5*d^2*x)*arcsin(c*x)^2 + 15*(225*(a^2 - 2*b^2)*c^5*d^2 - 200*b^2*c^3*d*e - 48*b^2*c*e^2)*x + 450*(3*a*b*c^5*e^2*x^5 + 10*a*b*c^5*d*e*x^3 + 15*a*b*c^5*d^2*x)*arcsin(c*x) + 30*(9*a*b*c^4*e^2*x^4 + 225*a*b*c^4*d^2 + 100*a*b*c^2*d*e + 24*a*b*e^2 + 2*(25*a*b*c^4*d*e + 6*a*b*c^2*e^2)*x^2 + (9*b^2*c^4*e^2*x^4 + 225*b^2*c^4*d^2 + 100*b^2*c^2*d*e + 24*b^2*e^2 + 2*(25*b^2*c^4*d*e + 6*b^2*c^2*e^2)*x^2)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^5","A",0
661,1,177,0,0.880597," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{{\left(9 \, a^{2} - 2 \, b^{2}\right)} c^{3} e x^{3} + 9 \, {\left(b^{2} c^{3} e x^{3} + 3 \, b^{2} c^{3} d x\right)} \arcsin\left(c x\right)^{2} + 3 \, {\left(9 \, {\left(a^{2} - 2 \, b^{2}\right)} c^{3} d - 4 \, b^{2} c e\right)} x + 18 \, {\left(a b c^{3} e x^{3} + 3 \, a b c^{3} d x\right)} \arcsin\left(c x\right) + 6 \, {\left(a b c^{2} e x^{2} + 9 \, a b c^{2} d + 2 \, a b e + {\left(b^{2} c^{2} e x^{2} + 9 \, b^{2} c^{2} d + 2 \, b^{2} e\right)} \arcsin\left(c x\right)\right)} \sqrt{-c^{2} x^{2} + 1}}{27 \, c^{3}}"," ",0,"1/27*((9*a^2 - 2*b^2)*c^3*e*x^3 + 9*(b^2*c^3*e*x^3 + 3*b^2*c^3*d*x)*arcsin(c*x)^2 + 3*(9*(a^2 - 2*b^2)*c^3*d - 4*b^2*c*e)*x + 18*(a*b*c^3*e*x^3 + 3*a*b*c^3*d*x)*arcsin(c*x) + 6*(a*b*c^2*e*x^2 + 9*a*b*c^2*d + 2*a*b*e + (b^2*c^2*e*x^2 + 9*b^2*c^2*d + 2*b^2*e)*arcsin(c*x))*sqrt(-c^2*x^2 + 1))/c^3","A",0
662,1,65,0,0.616219," ","integrate((a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","\frac{b^{2} c x \arcsin\left(c x\right)^{2} + 2 \, a b c x \arcsin\left(c x\right) + {\left(a^{2} - 2 \, b^{2}\right)} c x + 2 \, \sqrt{-c^{2} x^{2} + 1} {\left(b^{2} \arcsin\left(c x\right) + a b\right)}}{c}"," ",0,"(b^2*c*x*arcsin(c*x)^2 + 2*a*b*c*x*arcsin(c*x) + (a^2 - 2*b^2)*c*x + 2*sqrt(-c^2*x^2 + 1)*(b^2*arcsin(c*x) + a*b))/c","A",0
663,0,0,0,0.686351," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/(e*x^2 + d), x)","F",0
664,0,0,0,0.814073," ","integrate((e*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(e*x^2 + d), x)","F",0
665,0,0,0,0.666867," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)/sqrt(e*x^2 + d), x)","F",0
666,0,0,0,0.550415," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{e x^{2} + d}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
667,0,0,0,0.583118," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2)*sqrt(e*x^2 + d)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
668,0,0,0,0.522573," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^2 + d^2)/(b*arcsin(c*x) + a), x)","F",0
669,0,0,0,0.767493," ","integrate((e*x^2+d)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral((e*x^2 + d)/(b*arcsin(c*x) + a), x)","F",0
670,0,0,0,0.583270," ","integrate(1/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(1/(b*arcsin(c*x) + a), x)","F",0
671,0,0,0,0.440405," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(1/(a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsin(c*x)), x)","F",0
672,0,0,0,0.707761," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(1/(a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsin(c*x)), x)","F",0
673,0,0,0,1.026735," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{b \arcsin\left(c x\right) + a}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(b*arcsin(c*x) + a), x)","F",0
674,0,0,0,0.677887," ","integrate(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsin(c*x)), x)","F",0
675,0,0,0,0.562685," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsin(c*x)), x)","F",0
676,0,0,0,0.745005," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arcsin(c*x)), x)","F",0
677,0,0,0,0.562497," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^2 + d^2)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
678,0,0,0,0.687580," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((e*x^2 + d)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
679,0,0,0,0.597142," ","integrate(1/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(1/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
680,0,0,0,0.547750," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(1/(a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arcsin(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arcsin(c*x)), x)","F",0
681,0,0,0,0.578315," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(1/(a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arcsin(c*x)), x)","F",0
682,0,0,0,0.466284," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{b^{2} \arcsin\left(c x\right)^{2} + 2 \, a b \arcsin\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(b^2*arcsin(c*x)^2 + 2*a*b*arcsin(c*x) + a^2), x)","F",0
683,0,0,0,0.671221," ","integrate(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a^{2} e x^{2} + a^{2} d + {\left(b^{2} e x^{2} + b^{2} d\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b e x^{2} + a b d\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a^2*e*x^2 + a^2*d + (b^2*e*x^2 + b^2*d)*arcsin(c*x)^2 + 2*(a*b*e*x^2 + a*b*d)*arcsin(c*x)), x)","F",0
684,0,0,0,0.508125," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a^{2} e^{2} x^{4} + 2 \, a^{2} d e x^{2} + a^{2} d^{2} + {\left(b^{2} e^{2} x^{4} + 2 \, b^{2} d e x^{2} + b^{2} d^{2}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b e^{2} x^{4} + 2 \, a b d e x^{2} + a b d^{2}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a^2*e^2*x^4 + 2*a^2*d*e*x^2 + a^2*d^2 + (b^2*e^2*x^4 + 2*b^2*d*e*x^2 + b^2*d^2)*arcsin(c*x)^2 + 2*(a*b*e^2*x^4 + 2*a*b*d*e*x^2 + a*b*d^2)*arcsin(c*x)), x)","F",0
685,0,0,0,0.497841," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d}}{a^{2} e^{3} x^{6} + 3 \, a^{2} d e^{2} x^{4} + 3 \, a^{2} d^{2} e x^{2} + a^{2} d^{3} + {\left(b^{2} e^{3} x^{6} + 3 \, b^{2} d e^{2} x^{4} + 3 \, b^{2} d^{2} e x^{2} + b^{2} d^{3}\right)} \arcsin\left(c x\right)^{2} + 2 \, {\left(a b e^{3} x^{6} + 3 \, a b d e^{2} x^{4} + 3 \, a b d^{2} e x^{2} + a b d^{3}\right)} \arcsin\left(c x\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)/(a^2*e^3*x^6 + 3*a^2*d*e^2*x^4 + 3*a^2*d^2*e*x^2 + a^2*d^3 + (b^2*e^3*x^6 + 3*b^2*d*e^2*x^4 + 3*b^2*d^2*e*x^2 + b^2*d^3)*arcsin(c*x)^2 + 2*(a*b*e^3*x^6 + 3*a*b*d*e^2*x^4 + 3*a*b*d^2*e*x^2 + a*b*d^3)*arcsin(c*x)), x)","F",0
686,-2,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
687,-2,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
688,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
689,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
690,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2)/(e*x^2+d)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
691,-2,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
692,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
693,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2)/(e*x^2+d),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
694,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2)/(e*x^2+d)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
695,-2,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
696,-2,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
697,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
698,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
699,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
700,-2,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
701,-2,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
702,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
703,-2,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
