1,1,189,0,0.555816," ","integrate(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{7} \, a c^{2} d x^{7} + \frac{1}{5} \, a d x^{5} - \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d"," ",0,"-1/7*a*c^2*d*x^7 + 1/5*a*d*x^5 - 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^2*d + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d","A",0
2,1,169,0,0.446840," ","integrate(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{6} \, a c^{2} d x^{6} + \frac{1}{4} \, a d x^{4} - \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d"," ",0,"-1/6*a*c^2*d*x^6 + 1/4*a*d*x^4 - 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*c^2*d + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d","A",0
3,1,148,0,0.533468," ","integrate(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{5} \, a c^{2} d x^{5} - \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d"," ",0,"-1/5*a*c^2*d*x^5 - 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^2*d + 1/3*a*d*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d","A",0
4,1,128,0,0.598116," ","integrate(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{4} \, a c^{2} d x^{4} - \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d"," ",0,"-1/4*a*c^2*d*x^4 - 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*c^2*d + 1/2*a*d*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d","A",0
5,1,97,0,0.527768," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{3} \, a c^{2} d x^{3} - \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d + a d x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d}{c}"," ",0,"-1/3*a*c^2*d*x^3 - 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^2*d + a*d*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d/c","A",0
6,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a c^{2} d x^{2} + a d \log\left(x\right) - \int \frac{{\left(b c^{2} d x^{2} - b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"-1/2*a*c^2*d*x^2 + a*d*log(x) - integrate((b*c^2*d*x^2 - b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
7,1,82,0,0.507794," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","-a c^{2} d x - {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b c d - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d - \frac{a d}{x}"," ",0,"-a*c^2*d*x - (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*c*d - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d - a*d/x","A",0
8,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","-b c^{2} d \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x} - a c^{2} d \log\left(x\right) - \frac{1}{2} \, b d {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a d}{2 \, x^{2}}"," ",0,"-b*c^2*d*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x) - a*c^2*d*log(x) - 1/2*b*d*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a*d/x^2","F",0
9,1,123,0,0.751785," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","{\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b c^{2} d - \frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d + \frac{a c^{2} d}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*c^2*d - 1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d + a*c^2*d/x - 1/3*a*d/x^3","A",0
10,1,328,0,0.475605," ","integrate(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a c^{4} d^{2} x^{9} - \frac{2}{7} \, a c^{2} d^{2} x^{7} + \frac{1}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{5} \, a d^{2} x^{5} - \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2}"," ",0,"1/9*a*c^4*d^2*x^9 - 2/7*a*c^2*d^2*x^7 + 1/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*c^4*d^2 + 1/5*a*d^2*x^5 - 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^2*d^2 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^2","B",0
11,1,298,0,0.530588," ","integrate(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{4} d^{2} x^{8} - \frac{1}{3} \, a c^{2} d^{2} x^{6} + \frac{1}{3072} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{4} \, a d^{2} x^{4} - \frac{1}{144} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2}"," ",0,"1/8*a*c^4*d^2*x^8 - 1/3*a*c^2*d^2*x^6 + 1/3072*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*c^4*d^2 + 1/4*a*d^2*x^4 - 1/144*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*c^2*d^2 + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2","A",0
12,1,267,0,0.488497," ","integrate(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{4} d^{2} x^{7} - \frac{2}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{4} d^{2} - \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2}"," ",0,"1/7*a*c^4*d^2*x^7 - 2/5*a*c^2*d^2*x^5 + 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^4*d^2 - 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^2*d^2 + 1/3*a*d^2*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2","A",0
13,1,237,0,0.538931," ","integrate(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{4} d^{2} x^{6} - \frac{1}{2} \, a c^{2} d^{2} x^{4} + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b c^{4} d^{2} - \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2}"," ",0,"1/6*a*c^4*d^2*x^6 - 1/2*a*c^2*d^2*x^4 + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*c^4*d^2 - 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*c^2*d^2 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2","B",0
14,1,196,0,0.502915," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{4} d^{2} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{4} d^{2} - \frac{2}{3} \, a c^{2} d^{2} x^{3} - \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d^{2} + a d^{2} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*c^4*d^2*x^5 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^4*d^2 - 2/3*a*c^2*d^2*x^3 - 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^2*d^2 + a*d^2*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2/c","A",0
15,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{4} d^{2} x^{4} - a c^{2} d^{2} x^{2} + a d^{2} \log\left(x\right) + \int \frac{{\left(b c^{4} d^{2} x^{4} - 2 \, b c^{2} d^{2} x^{2} + b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/4*a*c^4*d^2*x^4 - a*c^2*d^2*x^2 + a*d^2*log(x) + integrate((b*c^4*d^2*x^4 - 2*b*c^2*d^2*x^2 + b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
16,1,160,0,0.465273," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{4} d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{4} d^{2} - 2 \, a c^{2} d^{2} x - 2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b c d^{2} - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d^{2} - \frac{a d^{2}}{x}"," ",0,"1/3*a*c^4*d^2*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^4*d^2 - 2*a*c^2*d^2*x - 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*c*d^2 - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d^2 - a*d^2/x","A",0
17,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a c^{4} d^{2} x^{2} - 2 \, a c^{2} d^{2} \log\left(x\right) - \frac{1}{2} \, b d^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a d^{2}}{2 \, x^{2}} + \int \frac{{\left(b c^{4} d^{2} x^{2} - 2 \, b c^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/2*a*c^4*d^2*x^2 - 2*a*c^2*d^2*log(x) - 1/2*b*d^2*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a*d^2/x^2 + integrate((b*c^4*d^2*x^2 - 2*b*c^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
18,1,170,0,0.524838," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","a c^{4} d^{2} x + {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b c^{3} d^{2} + 2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b c^{2} d^{2} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d^{2} + \frac{2 \, a c^{2} d^{2}}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"a*c^4*d^2*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*c^3*d^2 + 2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*c^2*d^2 - 1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d^2 + 2*a*c^2*d^2/x - 1/3*a*d^2/x^3","A",0
19,1,479,0,0.503064," ","integrate(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{11} \, a c^{6} d^{3} x^{11} + \frac{1}{3} \, a c^{4} d^{3} x^{9} - \frac{3}{7} \, a c^{2} d^{3} x^{7} - \frac{1}{7623} \, {\left(693 \, x^{11} \arcsin\left(c x\right) + {\left(\frac{63 \, \sqrt{-c^{2} x^{2} + 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{-c^{2} x^{2} + 1}}{c^{12}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{945} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{5} \, a d^{3} x^{5} - \frac{3}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{3}"," ",0,"-1/11*a*c^6*d^3*x^11 + 1/3*a*c^4*d^3*x^9 - 3/7*a*c^2*d^3*x^7 - 1/7623*(693*x^11*arcsin(c*x) + (63*sqrt(-c^2*x^2 + 1)*x^10/c^2 + 70*sqrt(-c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(-c^2*x^2 + 1)*x^6/c^6 + 96*sqrt(-c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(-c^2*x^2 + 1)*x^2/c^10 + 256*sqrt(-c^2*x^2 + 1)/c^12)*c)*b*c^6*d^3 + 1/945*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*c^4*d^3 + 1/5*a*d^3*x^5 - 3/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^2*d^3 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^3","B",0
20,1,439,0,0.498189," ","integrate(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{10} \, a c^{6} d^{3} x^{10} + \frac{3}{8} \, a c^{4} d^{3} x^{8} - \frac{1}{2} \, a c^{2} d^{3} x^{6} - \frac{1}{12800} \, {\left(1280 \, x^{10} \arcsin\left(c x\right) + {\left(\frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{9}}{c^{2}} + \frac{144 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{6}} + \frac{210 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \arcsin\left(c x\right)}{c^{11}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{1024} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{4} \, a d^{3} x^{4} - \frac{1}{96} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{3}"," ",0,"-1/10*a*c^6*d^3*x^10 + 3/8*a*c^4*d^3*x^8 - 1/2*a*c^2*d^3*x^6 - 1/12800*(1280*x^10*arcsin(c*x) + (128*sqrt(-c^2*x^2 + 1)*x^9/c^2 + 144*sqrt(-c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(-c^2*x^2 + 1)*x^5/c^6 + 210*sqrt(-c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(-c^2*x^2 + 1)*x/c^10 - 315*arcsin(c*x)/c^11)*c)*b*c^6*d^3 + 1/1024*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*c^4*d^3 + 1/4*a*d^3*x^4 - 1/96*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*c^2*d^3 + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^3","B",0
21,1,398,0,0.455148," ","integrate(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{9} \, a c^{6} d^{3} x^{9} + \frac{3}{7} \, a c^{4} d^{3} x^{7} - \frac{1}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b c^{6} d^{3} - \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{3}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{4} d^{3} - \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3}"," ",0,"-1/9*a*c^6*d^3*x^9 + 3/7*a*c^4*d^3*x^7 - 1/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*c^6*d^3 - 3/5*a*c^2*d^3*x^5 + 3/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^4*d^3 - 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^2*d^3 + 1/3*a*d^3*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^3","B",0
22,1,358,0,0.467680," ","integrate(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{8} \, a c^{6} d^{3} x^{8} + \frac{1}{2} \, a c^{4} d^{3} x^{6} - \frac{1}{3072} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b c^{6} d^{3} - \frac{3}{4} \, a c^{2} d^{3} x^{4} + \frac{1}{96} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b c^{4} d^{3} - \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{3}"," ",0,"-1/8*a*c^6*d^3*x^8 + 1/2*a*c^4*d^3*x^6 - 1/3072*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*c^6*d^3 - 3/4*a*c^2*d^3*x^4 + 1/96*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*c^4*d^3 - 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*c^2*d^3 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^3","B",0
23,1,307,0,0.538802," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{7} \, a c^{6} d^{3} x^{7} + \frac{3}{5} \, a c^{4} d^{3} x^{5} - \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{4} d^{3} - a c^{2} d^{3} x^{3} - \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{2} d^{3} + a d^{3} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{3}}{c}"," ",0,"-1/7*a*c^6*d^3*x^7 + 3/5*a*c^4*d^3*x^5 - 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*c^6*d^3 + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^4*d^3 - a*c^2*d^3*x^3 - 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^2*d^3 + a*d^3*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3/c","A",0
24,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{6} \, a c^{6} d^{3} x^{6} + \frac{3}{4} \, a c^{4} d^{3} x^{4} - \frac{3}{2} \, a c^{2} d^{3} x^{2} + a d^{3} \log\left(x\right) - \int \frac{{\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"-1/6*a*c^6*d^3*x^6 + 3/4*a*c^4*d^3*x^4 - 3/2*a*c^2*d^3*x^2 + a*d^3*log(x) - integrate((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
25,1,250,0,0.484709," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{5} \, a c^{6} d^{3} x^{5} - \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b c^{6} d^{3} + a c^{4} d^{3} x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{4} d^{3} - 3 \, a c^{2} d^{3} x - 3 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b c d^{3} - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d^{3} - \frac{a d^{3}}{x}"," ",0,"-1/5*a*c^6*d^3*x^5 - 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*c^6*d^3 + a*c^4*d^3*x^3 + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^4*d^3 - 3*a*c^2*d^3*x - 3*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*c*d^3 - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d^3 - a*d^3/x","A",0
26,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a c^{6} d^{3} x^{4} + \frac{3}{2} \, a c^{4} d^{3} x^{2} - 3 \, a c^{2} d^{3} \log\left(x\right) - \frac{1}{2} \, b d^{3} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a d^{3}}{2 \, x^{2}} - \int \frac{{\left(b c^{6} d^{3} x^{4} - 3 \, b c^{4} d^{3} x^{2} + 3 \, b c^{2} d^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"-1/4*a*c^6*d^3*x^4 + 3/2*a*c^4*d^3*x^2 - 3*a*c^2*d^3*log(x) - 1/2*b*d^3*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a*d^3/x^2 - integrate((b*c^6*d^3*x^4 - 3*b*c^4*d^3*x^2 + 3*b*c^2*d^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
27,1,242,0,0.470774," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, a c^{6} d^{3} x^{3} - \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b c^{6} d^{3} + 3 \, a c^{4} d^{3} x + 3 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b c^{3} d^{3} + 3 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b c^{2} d^{3} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d^{3} + \frac{3 \, a c^{2} d^{3}}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"-1/3*a*c^6*d^3*x^3 - 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*c^6*d^3 + 3*a*c^4*d^3*x + 3*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*c^3*d^3 + 3*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*c^2*d^3 - 1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d^3 + 3*a*c^2*d^3/x - 1/3*a*d^3/x^3","A",0
28,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4} d} - \frac{3 \, \log\left(c x + 1\right)}{c^{5} d} + \frac{3 \, \log\left(c x - 1\right)}{c^{5} d}\right)} + \frac{-\frac{1}{3} \, {\left(c^{5} d {\left(\frac{2 \, {\left(c^{2} x^{2} + 2\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{5} d} + \frac{18 \, \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{5} d} + 3 \, \int -\frac{3 \, \sqrt{c x + 1} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{c^{6} d x^{2} - c^{4} d}\,{d x}\right)} + 6 \, {\left(c^{3} x^{3} + 3 \, c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 9 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + 9 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} b}{6 \, c^{5} d}"," ",0,"-1/6*a*(2*(c^2*x^3 + 3*x)/(c^4*d) - 3*log(c*x + 1)/(c^5*d) + 3*log(c*x - 1)/(c^5*d)) + 1/6*(6*c^5*d*integrate(-1/6*(2*c^3*x^3 + 6*c*x - 3*log(c*x + 1) + 3*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d*x^2 - c^4*d), x) - 2*(c^3*x^3 + 3*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*b/(c^5*d)","F",0
29,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x^{2}}{c^{2} d} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d}\right)} - \frac{{\left(c^{4} d \int \frac{c^{2} x^{2} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{7} d x^{4} - c^{5} d x^{2} - {\left(c^{5} d x^{2} - c^{3} d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} b}{2 \, c^{4} d}"," ",0,"-1/2*a*(x^2/(c^2*d) + log(c^2*x^2 - 1)/(c^4*d)) - 1/2*(2*c^4*d*integrate(1/2*(c^2*x^2*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/(c^7*d*x^4 - c^5*d*x^2 + (c^5*d*x^2 - c^3*d)*e^(log(c*x + 1) + log(-c*x + 1))), x) + c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*b/(c^4*d)","F",0
30,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, x}{c^{2} d} - \frac{\log\left(c x + 1\right)}{c^{3} d} + \frac{\log\left(c x - 1\right)}{c^{3} d}\right)} + \frac{-{\left(c^{3} d {\left(\frac{2 \, \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} d} + \int -\frac{\sqrt{c x + 1} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{c^{4} d x^{2} - c^{2} d}\,{d x}\right)} + 2 \, c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} b}{2 \, c^{3} d}"," ",0,"-1/2*a*(2*x/(c^2*d) - log(c*x + 1)/(c^3*d) + log(c*x - 1)/(c^3*d)) + 1/2*(2*c^3*d*integrate(-1/2*(2*c*x - log(c*x + 1) + log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d*x^2 - c^2*d), x) - 2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*b/(c^3*d)","F",0
31,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{{\left(c^{2} d \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{5} d x^{4} - c^{3} d x^{2} - {\left(c^{3} d x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} b}{2 \, c^{2} d} - \frac{a \log\left(c^{2} d x^{2} - d\right)}{2 \, c^{2} d}"," ",0,"-1/2*(2*c^2*d*integrate(1/2*(e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/(c^5*d*x^4 - c^3*d*x^2 + (c^3*d*x^2 - c*d)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*b/(c^2*d) - 1/2*a*log(c^2*d*x^2 - d)/(c^2*d)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)} + \frac{{\left(c d \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{c^{2} d x^{2} - d}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} b}{2 \, c d}"," ",0,"1/2*a*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d)) + 1/2*(2*c*d*integrate(1/2*sqrt(c*x + 1)*sqrt(-c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/(c^2*d*x^2 - d), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*b/(c*d)","F",0
33,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{d} + \frac{\log\left(c x - 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} - b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} d x^{3} - d x}\,{d x}"," ",0,"-1/2*a*(log(c*x + 1)/d + log(c*x - 1)/d - 2*log(x)/d) - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^3 - d*x), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(c x - 1\right)}{d} - \frac{2}{d x}\right)} + \frac{{\left(c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + d x \int \frac{{\left(c^{2} x \log\left(c x + 1\right) - c^{2} x \log\left(-c x + 1\right) - 2 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{3} - d x}\,{d x} - 2 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{2 \, d x}"," ",0,"1/2*a*(c*log(c*x + 1)/d - c*log(c*x - 1)/d - 2/(d*x)) + 1/2*(c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 2*d*x*integrate(1/2*(c^2*x*log(c*x + 1) - c^2*x*log(-c*x + 1) - 2*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^3 - d*x), x) - 2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(d*x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c x + 1\right)}{d} + \frac{c^{2} \log\left(c x - 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} + \frac{1}{d x^{2}}\right)} a - b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} d x^{5} - d x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(c*x + 1)/d + c^2*log(c*x - 1)/d - 2*c^2*log(x)/d + 1/(d*x^2))*a - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^5 - d*x^3), x)","F",0
36,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, c^{3} \log\left(c x + 1\right)}{d} - \frac{3 \, c^{3} \log\left(c x - 1\right)}{d} - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{d x^{3}}\right)} a + \frac{{\left(3 \, c^{3} x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, c^{3} x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + d x^{3} \int \frac{{\left(3 \, c^{4} x^{3} \log\left(c x + 1\right) - 3 \, c^{4} x^{3} \log\left(-c x + 1\right) - 6 \, c^{3} x^{2} - 2 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{5} - d x^{3}}\,{d x} - 2 \, {\left(3 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{6 \, d x^{3}}"," ",0,"1/6*(3*c^3*log(c*x + 1)/d - 3*c^3*log(c*x - 1)/d - 2*(3*c^2*x^2 + 1)/(d*x^3))*a + 1/6*(3*c^3*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*c^3*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 6*d*x^3*integrate(1/6*(3*c^4*x^3*log(c*x + 1) - 3*c^4*x^3*log(-c*x + 1) - 6*c^3*x^2 - 2*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^5 - d*x^3), x) - 2*(3*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(d*x^3)","F",0
37,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{4 \, x}{c^{4} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - \frac{{\left(3 \, {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(2 \, c^{3} x^{3} - 3 \, c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)} \int \frac{{\left(4 \, c^{3} x^{3} - 6 \, c x - 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^6*d^2*x^2 - c^4*d^2) - 4*x/(c^4*d^2) + 3*log(c*x + 1)/(c^5*d^2) - 3*log(c*x - 1)/(c^5*d^2)) - 1/4*(3*(c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(2*c^3*x^3 - 3*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 4*(c^7*d^2*x^2 - c^5*d^2)*integrate(-1/4*(4*c^3*x^3 - 6*c*x - 3*(c^2*x^2 - 1)*log(c*x + 1) + 3*(c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x))*b/(c^7*d^2*x^2 - c^5*d^2)","F",0
38,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{1}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d^{2}}\right)} + \frac{{\left({\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)} \int \frac{{\left(c^{2} x^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{9} d^{2} x^{6} - 2 \, c^{7} d^{2} x^{4} + c^{5} d^{2} x^{2} - {\left(c^{7} d^{2} x^{4} - 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} - \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{2 \, {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)}}"," ",0,"-1/2*a*(1/(c^6*d^2*x^2 - c^4*d^2) - log(c^2*x^2 - 1)/(c^4*d^2)) + 1/2*((c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + (c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 2*(c^6*d^2*x^2 - c^4*d^2)*integrate(1/2*((c^2*x^2 - 1)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + (c^2*x^2 - 1)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1) - e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/(c^9*d^2*x^6 - 2*c^7*d^2*x^4 + c^5*d^2*x^2 + (c^7*d^2*x^4 - 2*c^5*d^2*x^2 + c^3*d^2)*e^(log(c*x + 1) + log(-c*x + 1))), x) - arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(c^6*d^2*x^2 - c^4*d^2)","F",0
39,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - \frac{{\left(2 \, c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)} \int \frac{{\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 1/4*(2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - (c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 4*(c^5*d^2*x^2 - c^3*d^2)*integrate(1/4*(2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x))*b/(c^5*d^2*x^2 - c^3*d^2)","F",0
40,1,136,0,0.477711," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(\frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x + c^{6} d^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x - c^{6} d^{4}}\right)} c^{2} - \frac{2 \, \arcsin\left(c x\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} b - \frac{a}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"1/4*((sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x + c^6*d^4) + sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x - c^6*d^4))*c^2 - 2*arcsin(c*x)/(c^4*d^2*x^2 - c^2*d^2))*b - 1/2*a/(c^4*d^2*x^2 - c^2*d^2)","B",0
41,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)} - \frac{{\left(2 \, c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + {\left(c^{3} d^{2} x^{2} - c d^{2}\right)} \int \frac{{\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{3} d^{2} x^{2} - c d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2)) - 1/4*(2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + (c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 4*(c^3*d^2*x^2 - c*d^2)*integrate(-1/4*(2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x))*b/(c^3*d^2*x^2 - c*d^2)","F",0
42,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{1}{c^{2} d^{2} x^{2} - d^{2}} + \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(c x - 1\right)}{d^{2}} - \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"-1/2*a*(1/(c^2*d^2*x^2 - d^2) + log(c*x + 1)/d^2 + log(c*x - 1)/d^2 - 2*log(x)/d^2) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{3} - d^{2} x} - \frac{3 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{3 \, c \log\left(c x - 1\right)}{d^{2}}\right)} + \frac{{\left(3 \, {\left(c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(3 \, c^{2} x^{2} - 2\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{2} d^{2} x^{3} - d^{2} x\right)} \int \frac{{\left(6 \, c^{3} x^{2} - 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(-c x + 1\right) - 4 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}\right)} b}{4 \, {\left(c^{2} d^{2} x^{3} - d^{2} x\right)}}"," ",0,"-1/4*a*(2*(3*c^2*x^2 - 2)/(c^2*d^2*x^3 - d^2*x) - 3*c*log(c*x + 1)/d^2 + 3*c*log(c*x - 1)/d^2) + 1/4*(3*(c^3*x^3 - c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(c^3*x^3 - c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(3*c^2*x^2 - 2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 4*(c^2*d^2*x^3 - d^2*x)*integrate(-1/4*(6*c^3*x^2 - 3*(c^4*x^3 - c^2*x)*log(c*x + 1) + 3*(c^4*x^3 - c^2*x)*log(-c*x + 1) - 4*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x))*b/(c^2*d^2*x^3 - d^2*x)","F",0
44,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c^{2} \log\left(c x - 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} + \frac{2 \, c^{2} x^{2} - 1}{c^{2} d^{2} x^{4} - d^{2} x^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*(2*c^2*log(c*x + 1)/d^2 + 2*c^2*log(c*x - 1)/d^2 - 4*c^2*log(x)/d^2 + (2*c^2*x^2 - 1)/(c^2*d^2*x^4 - d^2*x^2)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{15 \, c^{3} \log\left(c x + 1\right)}{d^{2}} - \frac{15 \, c^{3} \log\left(c x - 1\right)}{d^{2}} - \frac{2 \, {\left(15 \, c^{4} x^{4} - 10 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{5} - d^{2} x^{3}}\right)} a + \frac{{\left(15 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 15 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(15 \, c^{4} x^{4} - 10 \, c^{2} x^{2} - 2\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{2} d^{2} x^{5} - d^{2} x^{3}\right)} \int \frac{{\left(30 \, c^{5} x^{4} - 20 \, c^{3} x^{2} - 15 \, {\left(c^{6} x^{5} - c^{4} x^{3}\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{6} x^{5} - c^{4} x^{3}\right)} \log\left(-c x + 1\right) - 4 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}\right)} b}{12 \, {\left(c^{2} d^{2} x^{5} - d^{2} x^{3}\right)}}"," ",0,"1/12*(15*c^3*log(c*x + 1)/d^2 - 15*c^3*log(c*x - 1)/d^2 - 2*(15*c^4*x^4 - 10*c^2*x^2 - 2)/(c^2*d^2*x^5 - d^2*x^3))*a + 1/12*(15*(c^5*x^5 - c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 15*(c^5*x^5 - c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(15*c^4*x^4 - 10*c^2*x^2 - 2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 12*(c^2*d^2*x^5 - d^2*x^3)*integrate(-1/12*(30*c^5*x^4 - 20*c^3*x^2 - 15*(c^6*x^5 - c^4*x^3)*log(c*x + 1) + 15*(c^6*x^5 - c^4*x^3)*log(-c*x + 1) - 4*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x))*b/(c^2*d^2*x^5 - d^2*x^3)","F",0
46,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, a {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{{\left(3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + 2 \, {\left(5 \, c^{3} x^{3} - 3 \, c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}\right)} \int \frac{{\left(10 \, c^{3} x^{3} - 6 \, c x + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}}\,{d x}\right)} b}{16 \, {\left(c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}\right)}}"," ",0,"1/16*a*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3)) + 1/16*(3*(c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 2*(5*c^3*x^3 - 3*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 16*(c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3)*integrate(1/16*(10*c^3*x^3 - 6*c*x + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x))*b/(c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3)","F",0
47,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, c^{2} x^{2} - 1\right)} a}{4 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}} + \frac{{\left({\left(2 \, c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)} \int \frac{{\left(2 \, c^{2} x^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{11} d^{3} x^{8} - 3 \, c^{9} d^{3} x^{6} + 3 \, c^{7} d^{3} x^{4} - c^{5} d^{3} x^{2} - {\left(c^{9} d^{3} x^{6} - 3 \, c^{7} d^{3} x^{4} + 3 \, c^{5} d^{3} x^{2} - c^{3} d^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} b}{4 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"1/4*(2*c^2*x^2 - 1)*a/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 1/4*((2*c^2*x^2 - 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 4*(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)*integrate(1/4*(2*c^2*x^2 - 1)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^11*d^3*x^8 - 3*c^9*d^3*x^6 + 3*c^7*d^3*x^4 - c^5*d^3*x^2 + (c^9*d^3*x^6 - 3*c^7*d^3*x^4 + 3*c^5*d^3*x^2 - c^3*d^3)*e^(log(c*x + 1) + log(-c*x + 1))), x))*b/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)","F",0
48,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, a {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)} - \frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(c^{3} x^{3} + c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{7} d^{3} x^{4} - 2 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)} \int \frac{{\left(2 \, c^{3} x^{3} + 2 \, c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}}\,{d x}\right)} b}{16 \, {\left(c^{7} d^{3} x^{4} - 2 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)}}"," ",0,"1/16*a*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3)) - 1/16*((c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - (c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(c^3*x^3 + c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 16*(c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3)*integrate(-1/16*(2*c^3*x^3 + 2*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + (c^4*x^4 - 2*c^2*x^2 + 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x))*b/(c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3)","F",0
49,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{{\left({\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{9} d^{3} x^{8} - 3 \, c^{7} d^{3} x^{6} + 3 \, c^{5} d^{3} x^{4} - c^{3} d^{3} x^{2} - {\left(c^{7} d^{3} x^{6} - 3 \, c^{5} d^{3} x^{4} + 3 \, c^{3} d^{3} x^{2} - c d^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{4 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}} + \frac{a}{4 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"1/4*(4*(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)*integrate(1/4*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^9*d^3*x^8 - 3*c^7*d^3*x^6 + 3*c^5*d^3*x^4 - c^3*d^3*x^2 + (c^7*d^3*x^6 - 3*c^5*d^3*x^4 + 3*c^3*d^3*x^2 - c*d^3)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) + 1/4*a/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)","F",0
50,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, a {\left(\frac{2 \, {\left(3 \, c^{2} x^{3} - 5 \, x\right)}}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c d^{3}}\right)} + \frac{{\left(3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(3 \, c^{3} x^{3} - 5 \, c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)} \int \frac{{\left(6 \, c^{3} x^{3} - 10 \, c x - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x}\right)} b}{16 \, {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)}}"," ",0,"-1/16*a*(2*(3*c^2*x^3 - 5*x)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) - 3*log(c*x + 1)/(c*d^3) + 3*log(c*x - 1)/(c*d^3)) + 1/16*(3*(c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(3*c^3*x^3 - 5*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 16*(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3)*integrate(-1/16*(6*c^3*x^3 - 10*c*x - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x))*b/(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3)","F",0
51,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, c^{2} x^{2} - 3}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, \log\left(c x + 1\right)}{d^{3}} + \frac{2 \, \log\left(c x - 1\right)}{d^{3}} - \frac{4 \, \log\left(x\right)}{d^{3}}\right)} - b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}\,{d x}"," ",0,"-1/4*a*((2*c^2*x^2 - 3)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) + 2*log(c*x + 1)/d^3 + 2*log(c*x - 1)/d^3 - 4*log(x)/d^3) - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(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
52,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, a {\left(\frac{2 \, {\left(15 \, c^{4} x^{4} - 25 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x} - \frac{15 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{15 \, c \log\left(c x - 1\right)}{d^{3}}\right)} + \frac{{\left(15 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 15 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(15 \, c^{4} x^{4} - 25 \, c^{2} x^{2} + 8\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x\right)} \int \frac{{\left(30 \, c^{5} x^{4} - 50 \, c^{3} x^{2} - 15 \, {\left(c^{6} x^{5} - 2 \, c^{4} x^{3} + c^{2} x\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{6} x^{5} - 2 \, c^{4} x^{3} + c^{2} x\right)} \log\left(-c x + 1\right) + 16 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}\,{d x}\right)} b}{16 \, {\left(c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x\right)}}"," ",0,"-1/16*a*(2*(15*c^4*x^4 - 25*c^2*x^2 + 8)/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x) - 15*c*log(c*x + 1)/d^3 + 15*c*log(c*x - 1)/d^3) + 1/16*(15*(c^5*x^5 - 2*c^3*x^3 + c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 15*(c^5*x^5 - 2*c^3*x^3 + c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(15*c^4*x^4 - 25*c^2*x^2 + 8)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 16*(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x)*integrate(-1/16*(30*c^5*x^4 - 50*c^3*x^2 - 15*(c^6*x^5 - 2*c^4*x^3 + c^2*x)*log(c*x + 1) + 15*(c^6*x^5 - 2*c^4*x^3 + c^2*x)*log(-c*x + 1) + 16*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x))*b/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, c^{4} x^{4} - 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} - 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} + \frac{6 \, c^{2} \log\left(c x + 1\right)}{d^{3}} + \frac{6 \, c^{2} \log\left(c x - 1\right)}{d^{3}} - \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} - b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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}}\,{d x}"," ",0,"-1/4*a*((6*c^4*x^4 - 9*c^2*x^2 + 2)/(c^4*d^3*x^6 - 2*c^2*d^3*x^4 + d^3*x^2) + 6*c^2*log(c*x + 1)/d^3 + 6*c^2*log(c*x - 1)/d^3 - 12*c^2*log(x)/d^3) - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(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
54,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{48} \, a {\left(\frac{105 \, c^{3} \log\left(c x + 1\right)}{d^{3}} - \frac{105 \, c^{3} \log\left(c x - 1\right)}{d^{3}} - \frac{2 \, {\left(105 \, c^{6} x^{6} - 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\right)} + \frac{{\left(105 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 105 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(105 \, c^{6} x^{6} - 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} + 8\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}\right)} \int \frac{{\left(210 \, c^{7} x^{6} - 350 \, c^{5} x^{4} + 112 \, c^{3} x^{2} - 105 \, {\left(c^{8} x^{7} - 2 \, c^{6} x^{5} + c^{4} x^{3}\right)} \log\left(c x + 1\right) + 105 \, {\left(c^{8} x^{7} - 2 \, c^{6} x^{5} + c^{4} x^{3}\right)} \log\left(-c x + 1\right) + 16 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}\,{d x}\right)} b}{48 \, {\left(c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}\right)}}"," ",0,"1/48*a*(105*c^3*log(c*x + 1)/d^3 - 105*c^3*log(c*x - 1)/d^3 - 2*(105*c^6*x^6 - 175*c^4*x^4 + 56*c^2*x^2 + 8)/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)) + 1/48*(105*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 105*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(105*c^6*x^6 - 175*c^4*x^4 + 56*c^2*x^2 + 8)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 48*(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)*integrate(-1/48*(210*c^7*x^6 - 350*c^5*x^4 + 112*c^3*x^2 - 105*(c^8*x^7 - 2*c^6*x^5 + c^4*x^3)*log(c*x + 1) + 105*(c^8*x^7 - 2*c^6*x^5 + c^4*x^3)*log(-c*x + 1) + 16*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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))*b/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)","F",0
55,0,0,0,0.000000," ","integrate(x^4*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int \sqrt{c x + 1} \sqrt{-c x + 1} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} - \frac{1}{48} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}{c^{2} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4}} + \frac{6 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{4} d} - \frac{3 \, \sqrt{d} \arcsin\left(c x\right)}{c^{5}}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) - 1/48*(8*(-c^2*d*x^2 + d)^(3/2)*x^3/(c^2*d) - 3*sqrt(-c^2*d*x^2 + d)*x/c^4 + 6*(-c^2*d*x^2 + d)^(3/2)*x/(c^4*d) - 3*sqrt(d)*arcsin(c*x)/c^5)*a","F",0
56,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int \sqrt{c x + 1} \sqrt{-c x + 1} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{8} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)}"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/8*a*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3)","F",0
57,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a","F",0
58,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{2}}\,{d x} - {\left(c \sqrt{d} \arcsin\left(c x\right) + \frac{\sqrt{-c^{2} d x^{2} + d}}{x}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^2, x) - (c*sqrt(d)*arcsin(c*x) + sqrt(-c^2*d*x^2 + d)/x)*a","F",0
59,1,137,0,0.439123," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","\frac{{\left(\left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + c^{2} d^{\frac{3}{2}} \log\left(x^{2} - \frac{1}{c^{2}}\right) - \frac{\sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} d}{x^{2}}\right)} b c}{6 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \arcsin\left(c x\right)}{3 \, d x^{3}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, d x^{3}}"," ",0,"1/6*((-1)^(-2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(-2*c^2*d + 2*d/x^2) + c^2*d^(3/2)*log(x^2 - 1/c^2) - sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*d/x^2)*b*c/d - 1/3*(-c^2*d*x^2 + d)^(3/2)*b*arcsin(c*x)/(d*x^3) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a/(d*x^3)","A",0
60,1,140,0,0.534725," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(8 \, c^{4} \sqrt{d} \log\left(x\right) - \frac{2 \, c^{2} \sqrt{d} x^{2} - 3 \, \sqrt{d}}{x^{4}}\right)} b c - \frac{1}{15} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)} \arcsin\left(c x\right) - \frac{1}{15} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)}"," ",0,"-1/60*(8*c^4*sqrt(d)*log(x) - (2*c^2*sqrt(d)*x^2 - 3*sqrt(d))/x^4)*b*c - 1/15*b*(2*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(3/2)/(d*x^5))*arcsin(c*x) - 1/15*a*(2*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(3/2)/(d*x^5))","A",0
61,1,199,0,0.465049," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""maxima"")","-\frac{1}{420} \, {\left(32 \, c^{6} \sqrt{d} \log\left(x\right) - \frac{8 \, c^{4} \sqrt{d} x^{4} + 3 \, c^{2} \sqrt{d} x^{2} - 10 \, \sqrt{d}}{x^{6}}\right)} b c - \frac{1}{105} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4}}{d x^{3}} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{5}} + \frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{7}}\right)} b \arcsin\left(c x\right) - \frac{1}{105} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4}}{d x^{3}} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{5}} + \frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{7}}\right)} a"," ",0,"-1/420*(32*c^6*sqrt(d)*log(x) - (8*c^4*sqrt(d)*x^4 + 3*c^2*sqrt(d)*x^2 - 10*sqrt(d))/x^6)*b*c - 1/105*(8*(-c^2*d*x^2 + d)^(3/2)*c^4/(d*x^3) + 12*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^5) + 15*(-c^2*d*x^2 + d)^(3/2)/(d*x^7))*b*arcsin(c*x) - 1/105*(8*(-c^2*d*x^2 + d)^(3/2)*c^4/(d*x^3) + 12*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^5) + 15*(-c^2*d*x^2 + d)^(3/2)/(d*x^7))*a","A",0
62,1,197,0,0.609632," ","integrate(x^5*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{105} \, {\left(\frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{c^{2} d} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{6} d}\right)} b \arcsin\left(c x\right) - \frac{1}{105} \, {\left(\frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{c^{2} d} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{6} d}\right)} a - \frac{{\left(225 \, c^{6} \sqrt{d} x^{7} - 63 \, c^{4} \sqrt{d} x^{5} - 140 \, c^{2} \sqrt{d} x^{3} - 840 \, \sqrt{d} x\right)} b}{11025 \, c^{5}}"," ",0,"-1/105*(15*(-c^2*d*x^2 + d)^(3/2)*x^4/(c^2*d) + 12*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(3/2)/(c^6*d))*b*arcsin(c*x) - 1/105*(15*(-c^2*d*x^2 + d)^(3/2)*x^4/(c^2*d) + 12*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(3/2)/(c^6*d))*a - 1/11025*(225*c^6*sqrt(d)*x^7 - 63*c^4*sqrt(d)*x^5 - 140*c^2*sqrt(d)*x^3 - 840*sqrt(d)*x)*b/c^5","A",0
63,1,138,0,0.506020," ","integrate(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{15} \, b {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \arcsin\left(c x\right) - \frac{1}{15} \, a {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} - \frac{{\left(9 \, c^{4} \sqrt{d} x^{5} - 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} b}{225 \, c^{3}}"," ",0,"-1/15*b*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsin(c*x) - 1/15*a*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d)) - 1/225*(9*c^4*sqrt(d)*x^5 - 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*b/c^3","A",0
64,1,75,0,0.467825," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \arcsin\left(c x\right)}{3 \, c^{2} d} - \frac{{\left(c^{2} d^{\frac{3}{2}} x^{3} - 3 \, d^{\frac{3}{2}} x\right)} b}{9 \, c d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, c^{2} d}"," ",0,"-1/3*(-c^2*d*x^2 + d)^(3/2)*b*arcsin(c*x)/(c^2*d) - 1/9*(c^2*d^(3/2)*x^3 - 3*d^(3/2)*x)*b/(c*d) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a/(c^2*d)","A",0
65,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x} - {\left(\sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x) - (sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d))*a","F",0
66,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x} + \frac{1}{2} \, {\left(c^{2} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{2} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^3, x) + 1/2*(c^2*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^2 - (-c^2*d*x^2 + d)^(3/2)/(d*x^2))*a","F",0
67,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{5}}\,{d x} + \frac{1}{8} \, {\left(c^{4} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{4} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{4}}\right)} a"," ",0,"b*sqrt(d)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^5, x) + 1/8*(c^4*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^4 - (-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^2) - 2*(-c^2*d*x^2 + d)^(3/2)/(d*x^4))*a","F",0
68,0,0,0,0.000000," ","integrate(x^4*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int -{\left(c^{2} d x^{6} - d x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} - \frac{1}{128} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}{c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{4}} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{4} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{4}} - \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{5}}\right)} a"," ",0,"b*sqrt(d)*integrate(-(c^2*d*x^6 - d*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) - 1/128*(16*(-c^2*d*x^2 + d)^(5/2)*x^3/(c^2*d) - 2*(-c^2*d*x^2 + d)^(3/2)*x/c^4 + 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^4*d) - 3*sqrt(-c^2*d*x^2 + d)*d*x/c^4 - 3*d^(3/2)*arcsin(c*x)/c^5)*a","F",0
69,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int -{\left(c^{2} d x^{4} - d x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{48} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)}"," ",0,"b*sqrt(d)*integrate(-(c^2*d*x^4 - d*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/48*a*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3)","F",0
70,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int -{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a"," ",0,"b*sqrt(d)*integrate(-(c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a","F",0
71,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","-b \sqrt{d} \int \frac{{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{2}}\,{d x} - \frac{1}{2} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d x + 3 \, c d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a"," ",0,"-b*sqrt(d)*integrate((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^2, x) - 1/2*(3*sqrt(-c^2*d*x^2 + d)*c^2*d*x + 3*c*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)/x)*a","F",0
72,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","-b \sqrt{d} \int \frac{{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{4}}\,{d x} + \frac{1}{3} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d x + 3 \, c^{3} d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{x} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a"," ",0,"-b*sqrt(d)*integrate((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^4, x) + 1/3*(3*sqrt(-c^2*d*x^2 + d)*c^4*d*x + 3*c^3*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)*c^2/x - (-c^2*d*x^2 + d)^(5/2)/(d*x^3))*a","F",0
73,1,172,0,0.722174," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""maxima"")","-\frac{{\left(2 \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{4} d^{\frac{5}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + 2 \, c^{4} d^{\frac{5}{2}} \log\left(x^{2} - \frac{1}{c^{2}}\right) - \frac{3 \, \sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} c^{2} d^{2}}{x^{2}} + \frac{\sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} d^{2}}{x^{4}}\right)} b c}{20 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b \arcsin\left(c x\right)}{5 \, d x^{5}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, d x^{5}}"," ",0,"-1/20*(2*(-1)^(-2*c^2*d*x^2 + 2*d)*c^4*d^(5/2)*log(-2*c^2*d + 2*d/x^2) + 2*c^4*d^(5/2)*log(x^2 - 1/c^2) - 3*sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*c^2*d^2/x^2 + sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*d^2/x^4)*b*c/d - 1/5*(-c^2*d*x^2 + d)^(5/2)*b*arcsin(c*x)/(d*x^5) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a/(d*x^5)","A",0
74,1,151,0,0.557347," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{210} \, {\left(12 \, c^{6} d^{\frac{3}{2}} \log\left(x\right) - \frac{3 \, c^{4} d^{\frac{3}{2}} x^{4} - 12 \, c^{2} d^{\frac{3}{2}} x^{2} + 5 \, d^{\frac{3}{2}}}{x^{6}}\right)} b c - \frac{1}{35} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{5}} + \frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)} \arcsin\left(c x\right) - \frac{1}{35} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{5}} + \frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)}"," ",0,"1/210*(12*c^6*d^(3/2)*log(x) - (3*c^4*d^(3/2)*x^4 - 12*c^2*d^(3/2)*x^2 + 5*d^(3/2))/x^6)*b*c - 1/35*b*(2*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^5) + 5*(-c^2*d*x^2 + d)^(5/2)/(d*x^7))*arcsin(c*x) - 1/35*a*(2*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^5) + 5*(-c^2*d*x^2 + d)^(5/2)/(d*x^7))","A",0
75,1,210,0,0.527016," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^10,x, algorithm=""maxima"")","\frac{1}{7560} \, {\left(192 \, c^{8} d^{\frac{3}{2}} \log\left(x\right) - \frac{48 \, c^{6} d^{\frac{3}{2}} x^{6} + 18 \, c^{4} d^{\frac{3}{2}} x^{4} - 200 \, c^{2} d^{\frac{3}{2}} x^{2} + 105 \, d^{\frac{3}{2}}}{x^{8}}\right)} b c - \frac{1}{315} \, b {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{5}} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{7}} + \frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{9}}\right)} \arcsin\left(c x\right) - \frac{1}{315} \, a {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{5}} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{7}} + \frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{9}}\right)}"," ",0,"1/7560*(192*c^8*d^(3/2)*log(x) - (48*c^6*d^(3/2)*x^6 + 18*c^4*d^(3/2)*x^4 - 200*c^2*d^(3/2)*x^2 + 105*d^(3/2))/x^8)*b*c - 1/315*b*(8*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^5) + 20*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^7) + 35*(-c^2*d*x^2 + d)^(5/2)/(d*x^9))*arcsin(c*x) - 1/315*a*(8*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^5) + 20*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^7) + 35*(-c^2*d*x^2 + d)^(5/2)/(d*x^9))","A",0
76,1,269,0,0.473071," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^12,x, algorithm=""maxima"")","\frac{1}{6930} \, {\left(96 \, c^{10} d^{\frac{3}{2}} \log\left(x\right) - \frac{24 \, c^{8} d^{\frac{3}{2}} x^{8} + 9 \, c^{6} d^{\frac{3}{2}} x^{6} + 5 \, c^{4} d^{\frac{3}{2}} x^{4} - 105 \, c^{2} d^{\frac{3}{2}} x^{2} + 63 \, d^{\frac{3}{2}}}{x^{10}}\right)} b c - \frac{1}{1155} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{6}}{d x^{5}} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{7}} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{9}} + \frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{11}}\right)} b \arcsin\left(c x\right) - \frac{1}{1155} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{6}}{d x^{5}} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{7}} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{9}} + \frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{11}}\right)} a"," ",0,"1/6930*(96*c^10*d^(3/2)*log(x) - (24*c^8*d^(3/2)*x^8 + 9*c^6*d^(3/2)*x^6 + 5*c^4*d^(3/2)*x^4 - 105*c^2*d^(3/2)*x^2 + 63*d^(3/2))/x^10)*b*c - 1/1155*(16*(-c^2*d*x^2 + d)^(5/2)*c^6/(d*x^5) + 40*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^7) + 70*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^9) + 105*(-c^2*d*x^2 + d)^(5/2)/(d*x^11))*b*arcsin(c*x) - 1/1155*(16*(-c^2*d*x^2 + d)^(5/2)*c^6/(d*x^5) + 40*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^7) + 70*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^9) + 105*(-c^2*d*x^2 + d)^(5/2)/(d*x^11))*a","A",0
77,1,267,0,0.987674," ","integrate(x^7*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{1155} \, {\left(\frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{6}}{c^{2} d} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{4} d} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{8} d}\right)} b \arcsin\left(c x\right) - \frac{1}{1155} \, {\left(\frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{6}}{c^{2} d} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{4} d} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{8} d}\right)} a + \frac{{\left(33075 \, c^{10} d^{\frac{3}{2}} x^{11} - 53900 \, c^{8} d^{\frac{3}{2}} x^{9} + 2475 \, c^{6} d^{\frac{3}{2}} x^{7} + 4158 \, c^{4} d^{\frac{3}{2}} x^{5} + 9240 \, c^{2} d^{\frac{3}{2}} x^{3} + 55440 \, d^{\frac{3}{2}} x\right)} b}{4002075 \, c^{7}}"," ",0,"-1/1155*(105*(-c^2*d*x^2 + d)^(5/2)*x^6/(c^2*d) + 70*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^4*d) + 40*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(5/2)/(c^8*d))*b*arcsin(c*x) - 1/1155*(105*(-c^2*d*x^2 + d)^(5/2)*x^6/(c^2*d) + 70*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^4*d) + 40*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(5/2)/(c^8*d))*a + 1/4002075*(33075*c^10*d^(3/2)*x^11 - 53900*c^8*d^(3/2)*x^9 + 2475*c^6*d^(3/2)*x^7 + 4158*c^4*d^(3/2)*x^5 + 9240*c^2*d^(3/2)*x^3 + 55440*d^(3/2)*x)*b/c^7","A",0
78,1,208,0,0.558012," ","integrate(x^5*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{315} \, {\left(\frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{2} d} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{6} d}\right)} b \arcsin\left(c x\right) - \frac{1}{315} \, {\left(\frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{2} d} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{6} d}\right)} a + \frac{{\left(1225 \, c^{8} d^{\frac{3}{2}} x^{9} - 2250 \, c^{6} d^{\frac{3}{2}} x^{7} + 189 \, c^{4} d^{\frac{3}{2}} x^{5} + 420 \, c^{2} d^{\frac{3}{2}} x^{3} + 2520 \, d^{\frac{3}{2}} x\right)} b}{99225 \, c^{5}}"," ",0,"-1/315*(35*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^2*d) + 20*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(5/2)/(c^6*d))*b*arcsin(c*x) - 1/315*(35*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^2*d) + 20*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(5/2)/(c^6*d))*a + 1/99225*(1225*c^8*d^(3/2)*x^9 - 2250*c^6*d^(3/2)*x^7 + 189*c^4*d^(3/2)*x^5 + 420*c^2*d^(3/2)*x^3 + 2520*d^(3/2)*x)*b/c^5","A",0
79,1,149,0,0.511527," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b \arcsin\left(c x\right) - \frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a + \frac{{\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} - 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} + 210 \, d^{\frac{3}{2}} x\right)} b}{3675 \, c^{3}}"," ",0,"-1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*b*arcsin(c*x) - 1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a + 1/3675*(75*c^6*d^(3/2)*x^7 - 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 + 210*d^(3/2)*x)*b/c^3","A",0
80,1,87,0,0.572637," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b \arcsin\left(c x\right)}{5 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, c^{2} d} + \frac{{\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} - 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} b}{75 \, c d}"," ",0,"-1/5*(-c^2*d*x^2 + d)^(5/2)*b*arcsin(c*x)/(c^2*d) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a/(c^2*d) + 1/75*(3*c^4*d^(5/2)*x^5 - 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*b/(c*d)","A",0
81,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","-b \sqrt{d} \int \frac{{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x} - \frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{-c^{2} d x^{2} + d} d\right)} a"," ",0,"-b*sqrt(d)*integrate((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x) - 1/3*(3*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2) - 3*sqrt(-c^2*d*x^2 + d)*d)*a","F",0
82,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","-b \sqrt{d} \int \frac{{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x} + \frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a"," ",0,"-b*sqrt(d)*integrate((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^3, x) + 1/2*(3*c^2*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(-c^2*d*x^2 + d)*c^2*d - (-c^2*d*x^2 + d)^(5/2)/(d*x^2))*a","F",0
83,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""maxima"")","-b \sqrt{d} \int \frac{{\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{5}}\,{d x} - \frac{1}{8} \, {\left(3 \, c^{4} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{4}}\right)} a"," ",0,"-b*sqrt(d)*integrate((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^5, x) - 1/8*(3*c^4*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^4 - 3*sqrt(-c^2*d*x^2 + d)*c^4*d - (-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^2) + 2*(-c^2*d*x^2 + d)^(5/2)/(d*x^4))*a","F",0
84,0,0,0,0.000000," ","integrate(x^4*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int {\left(c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} - \frac{1}{1280} \, {\left(\frac{128 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{3}}{c^{2} d} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{4}} + \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{4} d} - \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{4}} - \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{4}} - \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{5}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) - 1/1280*(128*(-c^2*d*x^2 + d)^(7/2)*x^3/(c^2*d) - 8*(-c^2*d*x^2 + d)^(5/2)*x/c^4 + 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^4*d) - 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^4 - 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^4 - 15*d^(5/2)*arcsin(c*x)/c^5)*a","F",0
85,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int {\left(c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{384} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/384*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a","F",0
86,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \int {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a","F",0
87,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{2}}\,{d x} - \frac{1}{8} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} x + 15 \, c d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{x}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^2, x) - 1/8*(10*(-c^2*d*x^2 + d)^(3/2)*c^2*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2*x + 15*c*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)/x)*a","F",0
88,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{4}}\,{d x} + \frac{1}{6} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} x + 15 \, c^{3} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{3}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^4, x) + 1/6*(10*(-c^2*d*x^2 + d)^(3/2)*c^4*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2*x + 15*c^3*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^2/x - 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^3))*a","F",0
89,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^6,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{6}}\,{d x} - \frac{1}{15} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{6} d^{2} x + 15 \, c^{5} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{5}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^6, x) - 1/15*(10*(-c^2*d*x^2 + d)^(3/2)*c^6*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^6*d^2*x + 15*c^5*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^4/x - 2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^5))*a","F",0
90,1,205,0,0.455662," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^8,x, algorithm=""maxima"")","\frac{{\left(6 \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{6} d^{\frac{7}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + 6 \, c^{6} d^{\frac{7}{2}} \log\left(x^{2} - \frac{1}{c^{2}}\right) - \frac{11 \, \sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} c^{4} d^{3}}{x^{2}} + \frac{7 \, \sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} c^{2} d^{3}}{x^{4}} - \frac{2 \, \sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} d^{3}}{x^{6}}\right)} b c}{84 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b \arcsin\left(c x\right)}{7 \, d x^{7}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a}{7 \, d x^{7}}"," ",0,"1/84*(6*(-1)^(-2*c^2*d*x^2 + 2*d)*c^6*d^(7/2)*log(-2*c^2*d + 2*d/x^2) + 6*c^6*d^(7/2)*log(x^2 - 1/c^2) - 11*sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*c^4*d^3/x^2 + 7*sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*c^2*d^3/x^4 - 2*sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*d^3/x^6)*b*c/d - 1/7*(-c^2*d*x^2 + d)^(7/2)*b*arcsin(c*x)/(d*x^7) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a/(d*x^7)","A",0
91,1,162,0,0.536353," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^10,x, algorithm=""maxima"")","-\frac{1}{1512} \, {\left(48 \, c^{8} d^{\frac{5}{2}} \log\left(x\right) - \frac{12 \, c^{6} d^{\frac{5}{2}} x^{6} - 90 \, c^{4} d^{\frac{5}{2}} x^{4} + 76 \, c^{2} d^{\frac{5}{2}} x^{2} - 21 \, d^{\frac{5}{2}}}{x^{8}}\right)} b c - \frac{1}{63} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{7}} + \frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{9}}\right)} \arcsin\left(c x\right) - \frac{1}{63} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{7}} + \frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{9}}\right)}"," ",0,"-1/1512*(48*c^8*d^(5/2)*log(x) - (12*c^6*d^(5/2)*x^6 - 90*c^4*d^(5/2)*x^4 + 76*c^2*d^(5/2)*x^2 - 21*d^(5/2))/x^8)*b*c - 1/63*b*(2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^7) + 7*(-c^2*d*x^2 + d)^(7/2)/(d*x^9))*arcsin(c*x) - 1/63*a*(2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^7) + 7*(-c^2*d*x^2 + d)^(7/2)/(d*x^9))","A",0
92,1,221,0,0.796960," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^12,x, algorithm=""maxima"")","-\frac{1}{83160} \, {\left(960 \, c^{10} d^{\frac{5}{2}} \log\left(x\right) - \frac{240 \, c^{8} d^{\frac{5}{2}} x^{8} + 90 \, c^{6} d^{\frac{5}{2}} x^{6} - 2260 \, c^{4} d^{\frac{5}{2}} x^{4} + 2415 \, c^{2} d^{\frac{5}{2}} x^{2} - 756 \, d^{\frac{5}{2}}}{x^{10}}\right)} b c - \frac{1}{693} \, b {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{4}}{d x^{7}} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{9}} + \frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{11}}\right)} \arcsin\left(c x\right) - \frac{1}{693} \, a {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{4}}{d x^{7}} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{9}} + \frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{11}}\right)}"," ",0,"-1/83160*(960*c^10*d^(5/2)*log(x) - (240*c^8*d^(5/2)*x^8 + 90*c^6*d^(5/2)*x^6 - 2260*c^4*d^(5/2)*x^4 + 2415*c^2*d^(5/2)*x^2 - 756*d^(5/2))/x^10)*b*c - 1/693*b*(8*(-c^2*d*x^2 + d)^(7/2)*c^4/(d*x^7) + 28*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^9) + 63*(-c^2*d*x^2 + d)^(7/2)/(d*x^11))*arcsin(c*x) - 1/693*a*(8*(-c^2*d*x^2 + d)^(7/2)*c^4/(d*x^7) + 28*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^9) + 63*(-c^2*d*x^2 + d)^(7/2)/(d*x^11))","A",0
93,1,219,0,0.552826," ","integrate(x^5*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{693} \, {\left(\frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{2} d} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{6} d}\right)} b \arcsin\left(c x\right) - \frac{1}{693} \, {\left(\frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{2} d} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{6} d}\right)} a - \frac{{\left(19845 \, c^{10} d^{\frac{5}{2}} x^{11} - 61985 \, c^{8} d^{\frac{5}{2}} x^{9} + 55935 \, c^{6} d^{\frac{5}{2}} x^{7} - 2079 \, c^{4} d^{\frac{5}{2}} x^{5} - 4620 \, c^{2} d^{\frac{5}{2}} x^{3} - 27720 \, d^{\frac{5}{2}} x\right)} b}{2401245 \, c^{5}}"," ",0,"-1/693*(63*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^2*d) + 28*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(7/2)/(c^6*d))*b*arcsin(c*x) - 1/693*(63*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^2*d) + 28*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(7/2)/(c^6*d))*a - 1/2401245*(19845*c^10*d^(5/2)*x^11 - 61985*c^8*d^(5/2)*x^9 + 55935*c^6*d^(5/2)*x^7 - 2079*c^4*d^(5/2)*x^5 - 4620*c^2*d^(5/2)*x^3 - 27720*d^(5/2)*x)*b/c^5","A",0
94,1,160,0,0.424142," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b \arcsin\left(c x\right) - \frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a - \frac{{\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} - 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} - 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} b}{3969 \, c^{3}}"," ",0,"-1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*b*arcsin(c*x) - 1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a - 1/3969*(49*c^8*d^(5/2)*x^9 - 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 - 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*b/c^3","A",0
95,1,98,0,0.496277," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b \arcsin\left(c x\right)}{7 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a}{7 \, c^{2} d} - \frac{{\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} - 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} - 35 \, d^{\frac{7}{2}} x\right)} b}{245 \, c d}"," ",0,"-1/7*(-c^2*d*x^2 + d)^(7/2)*b*arcsin(c*x)/(c^2*d) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a/(c^2*d) - 1/245*(5*c^6*d^(7/2)*x^7 - 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 - 35*d^(7/2)*x)*b/(c*d)","A",0
96,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x} - \frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x) - 1/15*(15*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2) - 5*(-c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(-c^2*d*x^2 + d)*d^2)*a","F",0
97,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x} + \frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^3, x) + 1/6*(15*c^2*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^2 - 5*(-c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^2))*a","F",0
98,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^5,x, algorithm=""maxima"")","b \sqrt{d} \int \frac{{\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{5}}\,{d x} - \frac{1}{8} \, {\left(15 \, c^{4} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{4}}\right)} a"," ",0,"b*sqrt(d)*integrate((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^5, x) - 1/8*(15*c^4*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^4 - 5*(-c^2*d*x^2 + d)^(3/2)*c^4*d - 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^2) + 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^4))*a","F",0
99,1,30,0,0.557747," ","integrate(arcsin(x)*(-x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{2} + \frac{1}{2} \, {\left(\sqrt{-x^{2} + 1} x + \arcsin\left(x\right)\right)} \arcsin\left(x\right) - \frac{1}{4} \, \arcsin\left(x\right)^{2}"," ",0,"-1/4*x^2 + 1/2*(sqrt(-x^2 + 1)*x + arcsin(x))*arcsin(x) - 1/4*arcsin(x)^2","A",0
100,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))*(-pi*c^2*x^2+pi)^(1/2),x, algorithm=""maxima"")","\sqrt{\pi} b \int \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{2} \, {\left(\sqrt{\pi - \pi c^{2} x^{2}} x + \frac{\sqrt{\pi} \arcsin\left(c x\right)}{c}\right)} a"," ",0,"sqrt(pi)*b*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/2*(sqrt(pi - pi*c^2*x^2)*x + sqrt(pi)*arcsin(c*x)/c)*a","F",0
101,1,85,0,0.496866," ","integrate(x^4*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{x^{4}}{a^{2}} + \frac{3 \, x^{2}}{a^{4}} - \frac{3 \, \arcsin\left(a x\right)^{2}}{a^{6}}\right)} a - \frac{1}{8} \, {\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1} x^{3}}{a^{2}} + \frac{3 \, \sqrt{-a^{2} x^{2} + 1} x}{a^{4}} - \frac{3 \, \arcsin\left(a x\right)}{a^{5}}\right)} \arcsin\left(a x\right)"," ",0,"1/16*(x^4/a^2 + 3*x^2/a^4 - 3*arcsin(a*x)^2/a^6)*a - 1/8*(2*sqrt(-a^2*x^2 + 1)*x^3/a^2 + 3*sqrt(-a^2*x^2 + 1)*x/a^4 - 3*arcsin(a*x)/a^5)*arcsin(a*x)","A",0
102,1,61,0,0.484204," ","integrate(x^3*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{9} \, a {\left(\frac{x^{3}}{a^{2}} + \frac{6 \, x}{a^{4}}\right)} - \frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \arcsin\left(a x\right)"," ",0,"1/9*a*(x^3/a^2 + 6*x/a^4) - 1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arcsin(a*x)","A",0
103,1,56,0,0.506882," ","integrate(x^2*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{x^{2}}{a^{2}} - \frac{\arcsin\left(a x\right)^{2}}{a^{4}}\right)} - \frac{1}{2} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x}{a^{2}} - \frac{\arcsin\left(a x\right)}{a^{3}}\right)} \arcsin\left(a x\right)"," ",0,"1/4*a*(x^2/a^2 - arcsin(a*x)^2/a^4) - 1/2*(sqrt(-a^2*x^2 + 1)*x/a^2 - arcsin(a*x)/a^3)*arcsin(a*x)","A",0
104,1,27,0,0.488971," ","integrate(x*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{x}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{a^{2}}"," ",0,"x/a - sqrt(-a^2*x^2 + 1)*arcsin(a*x)/a^2","A",0
105,1,11,0,0.551242," ","integrate(arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{2}}{2 \, a}"," ",0,"1/2*arcsin(a*x)^2/a","A",0
106,0,0,0,0.000000," ","integrate(arcsin(a*x)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsin(a*x)/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
107,1,26,0,0.537816," ","integrate(arcsin(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","a \log\left(x\right) - \frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{x}"," ",0,"a*log(x) - sqrt(-a^2*x^2 + 1)*arcsin(a*x)/x","A",0
108,0,0,0,0.000000," ","integrate(arcsin(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsin(a*x)/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
109,1,180,0,0.597199," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} b \arcsin\left(c x\right) - \frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a + \frac{{\left(9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x\right)} b}{225 \, c^{5} \sqrt{d}}"," ",0,"-1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*b*arcsin(c*x) - 1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a + 1/225*(9*c^4*x^5 + 20*c^2*x^3 + 120*x)*b/(c^5*sqrt(d))","A",0
110,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} x^{3}}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4} d} - \frac{3 \, \arcsin\left(c x\right)}{c^{5} \sqrt{d}}\right)} + \frac{b \int \frac{x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}}{\sqrt{d}}"," ",0,"-1/8*a*(2*sqrt(-c^2*d*x^2 + d)*x^3/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*x/(c^4*d) - 3*arcsin(c*x)/(c^5*sqrt(d))) + b*integrate(x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
111,1,121,0,0.425875," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} + \frac{{\left(c^{2} x^{3} + 6 \, x\right)} b}{9 \, c^{3} \sqrt{d}}"," ",0,"-1/3*b*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arcsin(c*x) - 1/3*a*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d)) + 1/9*(c^2*x^3 + 6*x)*b/(c^3*sqrt(d))","A",0
112,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + \frac{b \int \frac{x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}}{\sqrt{d}}"," ",0,"-1/2*a*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + b*integrate(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
113,1,58,0,0.490496," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b x}{c \sqrt{d}} - \frac{\sqrt{-c^{2} d x^{2} + d} b \arcsin\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a}{c^{2} d}"," ",0,"b*x/(c*sqrt(d)) - sqrt(-c^2*d*x^2 + d)*b*arcsin(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a/(c^2*d)","A",0
114,1,28,0,0.433868," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b \arcsin\left(c x\right)^{2}}{2 \, c \sqrt{d}} + \frac{a \arcsin\left(c x\right)}{c \sqrt{d}}"," ",0,"1/2*b*arcsin(c*x)^2/(c*sqrt(d)) + a*arcsin(c*x)/(c*sqrt(d))","A",0
115,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1} x}\,{d x}}{\sqrt{d}} - \frac{a \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)*x), x)/sqrt(d) - a*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d)","F",0
116,1,104,0,0.605472," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \sqrt{d} \log\left(x^{2} - \frac{1}{c^{2}}\right)\right)} b c}{2 \, d} - \frac{\sqrt{-c^{2} d x^{2} + d} b \arcsin\left(c x\right)}{d x} - \frac{\sqrt{-c^{2} d x^{2} + d} a}{d x}"," ",0,"-1/2*((-1)^(-2*c^2*d*x^2 + 2*d)*sqrt(d)*log(-2*c^2*d + 2*d/x^2) + sqrt(d)*log(x^2 - 1/c^2))*b*c/d - sqrt(-c^2*d*x^2 + d)*b*arcsin(c*x)/(d*x) - sqrt(-c^2*d*x^2 + d)*a/(d*x)","A",0
117,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{2}}\right)} a + \frac{b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1} x^{3}}\,{d x}}{\sqrt{d}}"," ",0,"-1/2*(c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) + sqrt(-c^2*d*x^2 + d)/(d*x^2))*a + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^3), x)/sqrt(d)","F",0
118,1,124,0,0.745700," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{4 \, c^{2} \log\left(x\right)}{\sqrt{d}} - \frac{1}{\sqrt{d} x^{2}}\right)} b c - \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)}"," ",0,"1/6*(4*c^2*log(x)/sqrt(d) - 1/(sqrt(d)*x^2))*b*c - 1/3*b*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))*arcsin(c*x) - 1/3*a*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))","A",0
119,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{x^{4}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \frac{4 \, x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{-c^{2} d x^{2} + d} c^{6} d}\right)} - \frac{\frac{1}{30} \, {\left(\sqrt{c x + 1} \sqrt{-c x + 1} c^{6} d^{2} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 25 \, c^{2} x^{3} - 45 \, x\right)}}{c^{5} d^{2}} + \frac{45 \, \log\left(c x + 1\right)}{c^{6} d^{2}} - \frac{45 \, \log\left(c x - 1\right)}{c^{6} d^{2}}\right)} + 30 \, {\left(c^{4} x^{4} + 4 \, c^{2} x^{2} - 8\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{3 \, \sqrt{c x + 1} \sqrt{-c x + 1} c^{6} d^{\frac{3}{2}}}"," ",0,"-1/3*a*(x^4/(sqrt(-c^2*d*x^2 + d)*c^2*d) + 4*x^2/(sqrt(-c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(-c^2*d*x^2 + d)*c^6*d)) - 1/3*(3*sqrt(c*x + 1)*sqrt(-c*x + 1)*c^6*d^2*integrate(1/3*(c^4*x^6 + 4*c^2*x^4 - 8*x^2)/(c^7*d^2*x^4 - c^5*d^2*x^2 + (c^5*d^2*x^2 - c^3*d^2)*e^(log(c*x + 1) + log(-c*x + 1))), x) + (c^4*x^4 + 4*c^2*x^2 - 8)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(sqrt(c*x + 1)*sqrt(-c*x + 1)*c^6*d^(3/2))","F",0
120,-1,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,1,142,0,0.668390," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, b c {\left(\frac{2 \, x}{c^{4} d^{\frac{3}{2}}} + \frac{\log\left(c x + 1\right)}{c^{5} d^{\frac{3}{2}}} - \frac{\log\left(c x - 1\right)}{c^{5} d^{\frac{3}{2}}}\right)} - b {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} \arcsin\left(c x\right) - a {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)}"," ",0,"-1/2*b*c*(2*x/(c^4*d^(3/2)) + log(c*x + 1)/(c^5*d^(3/2)) - log(c*x - 1)/(c^5*d^(3/2))) - b*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))*arcsin(c*x) - a*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))","A",0
122,-1,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{\frac{1}{2} \, {\left(\sqrt{c x + 1} \sqrt{-c x + 1} c^{3} d^{2} {\left(\frac{2 \, x}{c^{2} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + 2 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{\sqrt{c x + 1} \sqrt{-c x + 1} c^{2} d^{\frac{3}{2}}} + \frac{a}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"(sqrt(c*x + 1)*sqrt(-c*x + 1)*c^3*d^2*integrate(x^2/(c^4*d^2*x^4 - c^2*d^2*x^2 + (c^2*d^2*x^2 - d^2)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(sqrt(c*x + 1)*sqrt(-c*x + 1)*c^2*d^(3/2)) + a/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
124,1,62,0,0.657340," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{b x \arcsin\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{b \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, c d^{\frac{3}{2}}}"," ",0,"b*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/2*b*log(x^2 - 1/c^2)/(c*d^(3/2))","A",0
125,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d}\right)} - \frac{\frac{b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} \sqrt{-c x + 1} x}\,{d x}}{d}}{\sqrt{d}}"," ",0,"-a*(log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 1/(sqrt(-c^2*d*x^2 + d)*d)) - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^2*d*x^3 - d*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
126,1,129,0,0.430218," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, b c {\left(\frac{\log\left(c x + 1\right)}{d^{\frac{3}{2}}} + \frac{\log\left(c x - 1\right)}{d^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{d^{\frac{3}{2}}}\right)} + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} b \arcsin\left(c x\right) + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a"," ",0,"1/2*b*c*(log(c*x + 1)/d^(3/2) + log(c*x - 1)/d^(3/2) + 2*log(x)/d^(3/2)) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*b*arcsin(c*x) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a","A",0
127,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{3 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{2}}\right)} a - \frac{\frac{b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} \sqrt{-c x + 1} x^{3}}\,{d x}}{d}}{\sqrt{d}}"," ",0,"-1/2*(3*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 3*c^2/(sqrt(-c^2*d*x^2 + d)*d) + 1/(sqrt(-c^2*d*x^2 + d)*d*x^2))*a - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^2*d*x^5 - d*x^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
128,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{4 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{3}}\right)} a - \frac{-\frac{1}{6} \, b {\left(\frac{3 \, c^{3} \log\left(c x + 1\right) + 3 \, c^{3} \log\left(c x - 1\right) + 10 \, c^{3} \log\left(x\right) - \frac{c}{x^{2}}}{d} + \frac{2 \, {\left(8 \, c^{4} x^{4} - 4 \, c^{2} x^{2} - 1\right)} \arctan\left(\frac{c x}{\sqrt{c x + 1} \sqrt{-c x + 1}}\right)}{\sqrt{c x + 1} \sqrt{-c x + 1} d x^{3}}\right)}}{\sqrt{d}}"," ",0,"1/3*(8*c^4*x/(sqrt(-c^2*d*x^2 + d)*d) - 4*c^2/(sqrt(-c^2*d*x^2 + d)*d*x) - 1/(sqrt(-c^2*d*x^2 + d)*d*x^3))*a - b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^2*d*x^6 - d*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
129,-1,0,0,0.000000," ","integrate(x^6*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, x^{4}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{12 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)} + \frac{\frac{1}{4} \, {\left({\left(c^{8} d^{3} x^{2} - c^{6} d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} {\left(\frac{2 \, x}{c^{7} d^{3} x^{2} - c^{5} d^{3}} + \frac{4 \, {\left(c^{2} x^{3} - 6 \, x\right)}}{c^{5} d^{3}} + \frac{13 \, \log\left(c x + 1\right)}{c^{6} d^{3}} - \frac{13 \, \log\left(c x - 1\right)}{c^{6} d^{3}}\right)} + 4 \, {\left(3 \, c^{4} x^{4} - 12 \, c^{2} x^{2} + 8\right)} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{3 \, {\left(c^{8} d^{3} x^{2} - c^{6} d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}"," ",0,"-1/3*a*(3*x^4/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 12*x^2/((-c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((-c^2*d*x^2 + d)^(3/2)*c^6*d)) + 1/3*(3*(c^8*d^3*x^2 - c^6*d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*sqrt(d)*integrate(1/3*(3*c^4*x^6 - 12*c^2*x^4 + 8*x^2)/(c^9*d^3*x^6 - 2*c^7*d^3*x^4 + c^5*d^3*x^2 + (c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3)*e^(log(c*x + 1) + log(-c*x + 1))), x) + (3*c^4*x^4 - 12*c^2*x^2 + 8)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/((c^8*d^3*x^2 - c^6*d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1))","F",0
131,-1,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,1,160,0,0.572161," ","integrate(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{12} \, b c {\left(\frac{2 \, x}{c^{6} d^{\frac{5}{2}} x^{2} - c^{4} d^{\frac{5}{2}}} + \frac{5 \, \log\left(c x + 1\right)}{c^{5} d^{\frac{5}{2}}} - \frac{5 \, \log\left(c x - 1\right)}{c^{5} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)}"," ",0,"1/12*b*c*(2*x/(c^6*d^(5/2)*x^2 - c^4*d^(5/2)) + 5*log(c*x + 1)/(c^5*d^(5/2)) - 5*log(c*x - 1)/(c^5*d^(5/2))) + 1/3*b*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d))*arcsin(c*x) + 1/3*a*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d))","A",0
133,1,153,0,0.710118," ","integrate(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{c^{6} d^{\frac{5}{2}} x^{2} - c^{4} d^{\frac{5}{2}}} - \frac{\log\left(c x + 1\right)}{c^{4} d^{\frac{5}{2}}} - \frac{\log\left(c x - 1\right)}{c^{4} d^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)}"," ",0,"1/6*b*c*(1/(c^6*d^(5/2)*x^2 - c^4*d^(5/2)) - log(c*x + 1)/(c^4*d^(5/2)) - log(c*x - 1)/(c^4*d^(5/2))) - 1/3*b*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d))*arcsin(c*x) - 1/3*a*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d))","A",0
134,-1,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,1,141,0,0.712501," ","integrate((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)}"," ",0,"1/6*b*c*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 1/3*b*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))","A",0
136,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \frac{\frac{b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{5}{2}} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1} x}\,{d x}}{d^{2}}}{\sqrt{d}}"," ",0,"-1/3*a*(3*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 3/(sqrt(-c^2*d*x^2 + d)*d^2) - 1/((-c^2*d*x^2 + d)^(3/2)*d)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
137,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{8 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + \frac{\frac{1}{6} \, b {\left(\frac{c}{c^{2} d^{2} x^{2} - d^{2}} + \frac{2 \, {\left(8 \, c^{4} x^{4} - 12 \, c^{2} x^{2} + 3\right)} \arctan\left(\frac{c x}{\sqrt{c x + 1} \sqrt{-c x + 1}}\right)}{{\left(c^{2} d^{2} x^{3} - d^{2} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1}} + \frac{5 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{5 \, c \log\left(c x - 1\right)}{d^{2}} + \frac{6 \, c \log\left(x\right)}{d^{2}}\right)}}{\sqrt{d}}"," ",0,"1/3*a*(8*c^2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 4*c^2*x/((-c^2*d*x^2 + d)^(3/2)*d) - 3/((-c^2*d*x^2 + d)^(3/2)*d*x)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
138,-1,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,1,255,0,1.333510," ","integrate((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{8 \, c^{2} \log\left(c x + 1\right)}{d^{\frac{5}{2}}} + \frac{8 \, c^{2} \log\left(c x - 1\right)}{d^{\frac{5}{2}}} + \frac{16 \, c^{2} \log\left(x\right)}{d^{\frac{5}{2}}} + \frac{1}{c^{2} d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}}\right)} + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} b \arcsin\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a"," ",0,"1/6*b*c*(8*c^2*log(c*x + 1)/d^(5/2) + 8*c^2*log(c*x - 1)/d^(5/2) + 16*c^2*log(x)/d^(5/2) + 1/(c^2*d^(5/2)*x^4 - d^(5/2)*x^2)) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*b*arcsin(c*x) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a","A",0
140,1,149,0,1.063174," ","integrate(arcsin(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{1}{60} \, a {\left(\frac{3}{{\left(a^{6} c^{\frac{5}{2}} x^{4} - 2 \, a^{4} c^{\frac{5}{2}} x^{2} + a^{2} c^{\frac{5}{2}}\right)} c} - \frac{8}{{\left(a^{4} c^{\frac{3}{2}} x^{2} - a^{2} c^{\frac{3}{2}}\right)} c^{2}} + \frac{16 \, \log\left(x^{2} - \frac{1}{a^{2}}\right)}{a^{2} c^{\frac{7}{2}}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \arcsin\left(a x\right)"," ",0,"-1/60*a*(3/((a^6*c^(5/2)*x^4 - 2*a^4*c^(5/2)*x^2 + a^2*c^(5/2))*c) - 8/((a^4*c^(3/2)*x^2 - a^2*c^(3/2))*c^2) + 16*log(x^2 - 1/a^2)/(a^2*c^(7/2))) + 1/15*(8*x/(sqrt(-a^2*c*x^2 + c)*c^3) + 4*x/((-a^2*c*x^2 + c)^(3/2)*c^2) + 3*x/((-a^2*c*x^2 + c)^(5/2)*c))*arcsin(a*x)","A",0
141,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((f*x)^(3/2)*(b*arcsin(c*x) + a)/sqrt(-c^2*x^2 + 1), x)","F",0
142,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((f*x)^(3/2)*(b*arcsin(c*x) + a)/sqrt(-c^2*d*x^2 + d), x)","F",0
143,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","-\frac{a c^{6} d^{3} x^{m + 7}}{m + 7} + \frac{3 \, a c^{4} d^{3} x^{m + 5}}{m + 5} - \frac{3 \, a c^{2} d^{3} x^{m + 3}}{m + 3} + \frac{a d^{3} x^{m + 1}}{m + 1} - \frac{{\left({\left(b c^{6} d^{3} m^{3} + 9 \, b c^{6} d^{3} m^{2} + 23 \, b c^{6} d^{3} m + 15 \, b c^{6} d^{3}\right)} x^{7} - 3 \, {\left(b c^{4} d^{3} m^{3} + 11 \, b c^{4} d^{3} m^{2} + 31 \, b c^{4} d^{3} m + 21 \, b c^{4} d^{3}\right)} x^{5} + 3 \, {\left(b c^{2} d^{3} m^{3} + 13 \, b c^{2} d^{3} m^{2} + 47 \, b c^{2} d^{3} m + 35 \, b c^{2} d^{3}\right)} x^{3} - {\left(b d^{3} m^{3} + 15 \, b d^{3} m^{2} + 71 \, b d^{3} m + 105 \, b d^{3}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left({\left(b c^{7} d^{3} m^{3} + 9 \, b c^{7} d^{3} m^{2} + 23 \, b c^{7} d^{3} m + 15 \, b c^{7} d^{3}\right)} x^{7} - 3 \, {\left(b c^{5} d^{3} m^{3} + 11 \, b c^{5} d^{3} m^{2} + 31 \, b c^{5} d^{3} m + 21 \, b c^{5} d^{3}\right)} x^{5} + 3 \, {\left(b c^{3} d^{3} m^{3} + 13 \, b c^{3} d^{3} m^{2} + 47 \, b c^{3} d^{3} m + 35 \, b c^{3} d^{3}\right)} x^{3} - {\left(b c d^{3} m^{3} + 15 \, b c d^{3} m^{2} + 71 \, b c d^{3} m + 105 \, b c d^{3}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m}}{m^{4} + 16 \, m^{3} - {\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"-a*c^6*d^3*x^(m + 7)/(m + 7) + 3*a*c^4*d^3*x^(m + 5)/(m + 5) - 3*a*c^2*d^3*x^(m + 3)/(m + 3) + a*d^3*x^(m + 1)/(m + 1) - (((b*c^6*d^3*m^3 + 9*b*c^6*d^3*m^2 + 23*b*c^6*d^3*m + 15*b*c^6*d^3)*x^7 - 3*(b*c^4*d^3*m^3 + 11*b*c^4*d^3*m^2 + 31*b*c^4*d^3*m + 21*b*c^4*d^3)*x^5 + 3*(b*c^2*d^3*m^3 + 13*b*c^2*d^3*m^2 + 47*b*c^2*d^3*m + 35*b*c^2*d^3)*x^3 - (b*d^3*m^3 + 15*b*d^3*m^2 + 71*b*d^3*m + 105*b*d^3)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(-((b*c^7*d^3*m^3 + 9*b*c^7*d^3*m^2 + 23*b*c^7*d^3*m + 15*b*c^7*d^3)*x^7 - 3*(b*c^5*d^3*m^3 + 11*b*c^5*d^3*m^2 + 31*b*c^5*d^3*m + 21*b*c^5*d^3)*x^5 + 3*(b*c^3*d^3*m^3 + 13*b*c^3*d^3*m^2 + 47*b*c^3*d^3*m + 35*b*c^3*d^3)*x^3 - (b*c*d^3*m^3 + 15*b*c*d^3*m^2 + 71*b*c*d^3*m + 105*b*c*d^3)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m/(m^4 + 16*m^3 - (c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
144,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{a c^{4} d^{2} x^{m + 5}}{m + 5} - \frac{2 \, a c^{2} d^{2} x^{m + 3}}{m + 3} + \frac{a d^{2} x^{m + 1}}{m + 1} + \frac{{\left({\left(b c^{4} d^{2} m^{2} + 4 \, b c^{4} d^{2} m + 3 \, b c^{4} d^{2}\right)} x^{5} - 2 \, {\left(b c^{2} d^{2} m^{2} + 6 \, b c^{2} d^{2} m + 5 \, b c^{2} d^{2}\right)} x^{3} + {\left(b d^{2} m^{2} + 8 \, b d^{2} m + 15 \, b d^{2}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left({\left(b c^{5} d^{2} m^{2} + 4 \, b c^{5} d^{2} m + 3 \, b c^{5} d^{2}\right)} x^{5} - 2 \, {\left(b c^{3} d^{2} m^{2} + 6 \, b c^{3} d^{2} m + 5 \, b c^{3} d^{2}\right)} x^{3} + {\left(b c d^{2} m^{2} + 8 \, b c d^{2} m + 15 \, b c d^{2}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m}}{m^{3} - {\left(c^{2} m^{3} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 15 \, c^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"a*c^4*d^2*x^(m + 5)/(m + 5) - 2*a*c^2*d^2*x^(m + 3)/(m + 3) + a*d^2*x^(m + 1)/(m + 1) + (((b*c^4*d^2*m^2 + 4*b*c^4*d^2*m + 3*b*c^4*d^2)*x^5 - 2*(b*c^2*d^2*m^2 + 6*b*c^2*d^2*m + 5*b*c^2*d^2)*x^3 + (b*d^2*m^2 + 8*b*d^2*m + 15*b*d^2)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (m^3 + 9*m^2 + 23*m + 15)*integrate(-((b*c^5*d^2*m^2 + 4*b*c^5*d^2*m + 3*b*c^5*d^2)*x^5 - 2*(b*c^3*d^2*m^2 + 6*b*c^3*d^2*m + 5*b*c^3*d^2)*x^3 + (b*c*d^2*m^2 + 8*b*c*d^2*m + 15*b*c*d^2)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m/(m^3 - (c^2*m^3 + 9*c^2*m^2 + 23*c^2*m + 15*c^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
145,-1,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-integrate((b*arcsin(c*x) + a)*x^m/(c^2*d*x^2 - d), x)","F",0
147,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*x^m/(c^2*d*x^2 - d)^2, x)","F",0
148,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{{\left(c^{2} d x^{2} - d\right)}^{3}}\,{d x}"," ",0,"-integrate((b*arcsin(c*x) + a)*x^m/(c^2*d*x^2 - d)^3, x)","F",0
149,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)*x^m, x)","F",0
150,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)*x^m, x)","F",0
151,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)} x^{m}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)*x^m, x)","F",0
152,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*x^m/sqrt(-c^2*d*x^2 + d), x)","F",0
153,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*x^m/(-c^2*d*x^2 + d)^(3/2), x)","F",0
154,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} x^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*x^m/(-c^2*d*x^2 + d)^(5/2), x)","F",0
155,0,0,0,0.000000," ","integrate(x^m*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arcsin\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsin(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
156,1,453,0,0.465029," ","integrate(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{7} \, b^{2} c^{2} d x^{7} \arcsin\left(c x\right)^{2} - \frac{1}{7} \, a^{2} c^{2} d x^{7} + \frac{1}{5} \, b^{2} d x^{5} \arcsin\left(c x\right)^{2} + \frac{1}{5} \, a^{2} d x^{5} - \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d + \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d"," ",0,"-1/7*b^2*c^2*d*x^7*arcsin(c*x)^2 - 1/7*a^2*c^2*d*x^7 + 1/5*b^2*d*x^5*arcsin(c*x)^2 + 1/5*a^2*d*x^5 - 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d - 2/25725*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^2*d + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*d + 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*d","A",0
157,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} c^{2} d x^{6} + \frac{1}{4} \, a^{2} d x^{4} - \frac{1}{144} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b d - \frac{1}{12} \, {\left(2 \, b^{2} c^{2} d x^{6} - 3 \, b^{2} d x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - \int \frac{{\left(2 \, b^{2} c^{3} d x^{6} - 3 \, b^{2} c d x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{6 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-1/6*a^2*c^2*d*x^6 + 1/4*a^2*d*x^4 - 1/144*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*c^2*d + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*d - 1/12*(2*b^2*c^2*d*x^6 - 3*b^2*d*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - integrate(1/6*(2*b^2*c^3*d*x^6 - 3*b^2*c*d*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
158,1,354,0,0.448794," ","integrate(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{5} \, b^{2} c^{2} d x^{5} \arcsin\left(c x\right)^{2} - \frac{1}{5} \, a^{2} c^{2} d x^{5} + \frac{1}{3} \, b^{2} d x^{3} \arcsin\left(c x\right)^{2} - \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d + \frac{1}{3} \, a^{2} d x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d + \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d"," ",0,"-1/5*b^2*c^2*d*x^5*arcsin(c*x)^2 - 1/5*a^2*c^2*d*x^5 + 1/3*b^2*d*x^3*arcsin(c*x)^2 - 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d - 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d + 1/3*a^2*d*x^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*d + 2/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d","A",0
159,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} c^{2} d x^{4} - \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d + \frac{1}{2} \, a^{2} d x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d - \frac{1}{4} \, {\left(b^{2} c^{2} d x^{4} - 2 \, b^{2} d x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - \int \frac{{\left(b^{2} c^{3} d x^{4} - 2 \, b^{2} c d x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{2 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-1/4*a^2*c^2*d*x^4 - 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*c^2*d + 1/2*a^2*d*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d - 1/4*(b^2*c^2*d*x^4 - 2*b^2*d*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - integrate(1/2*(b^2*c^3*d*x^4 - 2*b^2*c*d*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
160,1,233,0,0.428979," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{3} \, b^{2} c^{2} d x^{3} \arcsin\left(c x\right)^{2} - \frac{1}{3} \, a^{2} c^{2} d x^{3} - \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} c^{2} d + b^{2} d x \arcsin\left(c x\right)^{2} - 2 \, b^{2} d {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d}{c}"," ",0,"-1/3*b^2*c^2*d*x^3*arcsin(c*x)^2 - 1/3*a^2*c^2*d*x^3 - 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^2*d - 2/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*c^2*d + b^2*d*x*arcsin(c*x)^2 - 2*b^2*d*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d/c","B",0
161,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} c^{2} d x^{2} + a^{2} d \log\left(x\right) - \int \frac{{\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"-1/2*a^2*c^2*d*x^2 + a^2*d*log(x) - integrate(((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/x, x)","F",0
162,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-b^{2} c^{2} d x \arcsin\left(c x\right)^{2} + 2 \, b^{2} c^{2} d {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} - a^{2} c^{2} d x - 2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b c d - 2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b d - \frac{{\left(2 \, c x \int \frac{\sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} {\left(c x - 1\right)} x}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}\right)} b^{2} d}{x} - \frac{a^{2} d}{x}"," ",0,"-b^2*c^2*d*x*arcsin(c*x)^2 + 2*b^2*c^2*d*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) - a^2*c^2*d*x - 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*c*d - 2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*d - (2*c*x*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^3 - x), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)*b^2*d/x - a^2*d/x","F",0
163,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","-a^{2} c^{2} d \log\left(x\right) - a b d {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d}{2 \, x^{2}} - \int \frac{2 \, a b c^{2} d x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{x^{3}}\,{d x}"," ",0,"-a^2*c^2*d*log(x) - a*b*d*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a^2*d/x^2 - integrate((2*a*b*c^2*d*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/x^3, x)","F",0
164,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b c^{2} d - \frac{1}{3} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} a b d + \frac{a^{2} c^{2} d}{x} - \frac{a^{2} d}{3 \, x^{3}} + \frac{2 \, x^{3} \int \frac{{\left(3 \, b^{2} c^{3} d x^{2} - b^{2} c d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x} + {\left(3 \, b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{3 \, x^{3}}"," ",0,"2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*c^2*d - 1/3*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*a*b*d + a^2*c^2*d/x - 1/3*a^2*d/x^3 + 1/3*(3*x^3*integrate(2/3*(3*b^2*c^3*d*x^2 - b^2*c*d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^5 - x^3), x) + (3*b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/x^3","F",0
165,1,781,0,0.770964," ","integrate(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{9} \, b^{2} c^{4} d^{2} x^{9} \arcsin\left(c x\right)^{2} + \frac{1}{9} \, a^{2} c^{4} d^{2} x^{9} - \frac{2}{7} \, b^{2} c^{2} d^{2} x^{7} \arcsin\left(c x\right)^{2} - \frac{2}{7} \, a^{2} c^{2} d^{2} x^{7} + \frac{1}{5} \, b^{2} d^{2} x^{5} \arcsin\left(c x\right)^{2} + \frac{2}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{4} d^{2} + \frac{2}{893025} \, {\left(315 \, {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c \arcsin\left(c x\right) - \frac{1225 \, c^{8} x^{9} + 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} + 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{4} d^{2} + \frac{1}{5} \, a^{2} d^{2} x^{5} - \frac{4}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d^{2} - \frac{4}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d^{2} + \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d^{2}"," ",0,"1/9*b^2*c^4*d^2*x^9*arcsin(c*x)^2 + 1/9*a^2*c^4*d^2*x^9 - 2/7*b^2*c^2*d^2*x^7*arcsin(c*x)^2 - 2/7*a^2*c^2*d^2*x^7 + 1/5*b^2*d^2*x^5*arcsin(c*x)^2 + 2/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*a*b*c^4*d^2 + 2/893025*(315*(35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c*arcsin(c*x) - (1225*c^8*x^9 + 1800*c^6*x^7 + 3024*c^4*x^5 + 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^4*d^2 + 1/5*a^2*d^2*x^5 - 4/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d^2 - 4/25725*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^2*d^2 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*d^2 + 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*d^2","B",0
166,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} c^{4} d^{2} x^{8} - \frac{1}{3} \, a^{2} c^{2} d^{2} x^{6} + \frac{1}{1536} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{4} d^{2} + \frac{1}{4} \, a^{2} d^{2} x^{4} - \frac{1}{72} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b d^{2} + \frac{1}{24} \, {\left(3 \, b^{2} c^{4} d^{2} x^{8} - 8 \, b^{2} c^{2} d^{2} x^{6} + 6 \, b^{2} d^{2} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(3 \, b^{2} c^{5} d^{2} x^{8} - 8 \, b^{2} c^{3} d^{2} x^{6} + 6 \, b^{2} c d^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{12 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/8*a^2*c^4*d^2*x^8 - 1/3*a^2*c^2*d^2*x^6 + 1/1536*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*a*b*c^4*d^2 + 1/4*a^2*d^2*x^4 - 1/72*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*c^2*d^2 + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*d^2 + 1/24*(3*b^2*c^4*d^2*x^8 - 8*b^2*c^2*d^2*x^6 + 6*b^2*d^2*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/12*(3*b^2*c^5*d^2*x^8 - 8*b^2*c^3*d^2*x^6 + 6*b^2*c*d^2*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
167,1,634,0,0.755306," ","integrate(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} c^{4} d^{2} x^{7} \arcsin\left(c x\right)^{2} + \frac{1}{7} \, a^{2} c^{4} d^{2} x^{7} - \frac{2}{5} \, b^{2} c^{2} d^{2} x^{5} \arcsin\left(c x\right)^{2} - \frac{2}{5} \, a^{2} c^{2} d^{2} x^{5} + \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{4} d^{2} + \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{4} d^{2} + \frac{1}{3} \, b^{2} d^{2} x^{3} \arcsin\left(c x\right)^{2} - \frac{4}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d^{2} - \frac{4}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d^{2} + \frac{1}{3} \, a^{2} d^{2} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{2} + \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d^{2}"," ",0,"1/7*b^2*c^4*d^2*x^7*arcsin(c*x)^2 + 1/7*a^2*c^4*d^2*x^7 - 2/5*b^2*c^2*d^2*x^5*arcsin(c*x)^2 - 2/5*a^2*c^2*d^2*x^5 + 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^4*d^2 + 2/25725*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^4*d^2 + 1/3*b^2*d^2*x^3*arcsin(c*x)^2 - 4/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d^2 - 4/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d^2 + 1/3*a^2*d^2*x^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*d^2 + 2/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d^2","B",0
168,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} c^{4} d^{2} x^{6} - \frac{1}{2} \, a^{2} c^{2} d^{2} x^{4} + \frac{1}{144} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{4} d^{2} - \frac{1}{8} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d^{2} + \frac{1}{2} \, a^{2} d^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d^{2} + \frac{1}{6} \, {\left(b^{2} c^{4} d^{2} x^{6} - 3 \, b^{2} c^{2} d^{2} x^{4} + 3 \, b^{2} d^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + \int \frac{{\left(b^{2} c^{5} d^{2} x^{6} - 3 \, b^{2} c^{3} d^{2} x^{4} + 3 \, b^{2} c d^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/6*a^2*c^4*d^2*x^6 - 1/2*a^2*c^2*d^2*x^4 + 1/144*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*c^4*d^2 - 1/8*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*c^2*d^2 + 1/2*a^2*d^2*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d^2 + 1/6*(b^2*c^4*d^2*x^6 - 3*b^2*c^2*d^2*x^4 + 3*b^2*d^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + integrate(1/3*(b^2*c^5*d^2*x^6 - 3*b^2*c^3*d^2*x^4 + 3*b^2*c*d^2*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
169,1,465,0,0.686316," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} c^{4} d^{2} x^{5} \arcsin\left(c x\right)^{2} + \frac{1}{5} \, a^{2} c^{4} d^{2} x^{5} - \frac{2}{3} \, b^{2} c^{2} d^{2} x^{3} \arcsin\left(c x\right)^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{4} d^{2} + \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{4} d^{2} - \frac{2}{3} \, a^{2} c^{2} d^{2} x^{3} - \frac{4}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d^{2} - \frac{4}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} c^{2} d^{2} + b^{2} d^{2} x \arcsin\left(c x\right)^{2} - 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d^{2}}{c}"," ",0,"1/5*b^2*c^4*d^2*x^5*arcsin(c*x)^2 + 1/5*a^2*c^4*d^2*x^5 - 2/3*b^2*c^2*d^2*x^3*arcsin(c*x)^2 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^4*d^2 + 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*c^4*d^2 - 2/3*a^2*c^2*d^2*x^3 - 4/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^2*d^2 - 4/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*c^2*d^2 + b^2*d^2*x*arcsin(c*x)^2 - 2*b^2*d^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d^2/c","B",0
170,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} c^{4} d^{2} x^{4} - a^{2} c^{2} d^{2} x^{2} + a^{2} d^{2} \log\left(x\right) + \int \frac{{\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/4*a^2*c^4*d^2*x^4 - a^2*c^2*d^2*x^2 + a^2*d^2*log(x) + integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/x, x)","F",0
171,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} c^{4} d^{2} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{4} d^{2} - 2 \, b^{2} c^{2} d^{2} x \arcsin\left(c x\right)^{2} + 4 \, b^{2} c^{2} d^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} - 2 \, a^{2} c^{2} d^{2} x - 4 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b c d^{2} - 2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b d^{2} - \frac{a^{2} d^{2}}{x} + \frac{{\left(b^{2} c^{4} d^{2} x^{4} - 3 \, b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, x \int \frac{{\left(b^{2} c^{5} d^{2} x^{4} - 3 \, b^{2} c d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{3} - x}\,{d x}}{3 \, x}"," ",0,"1/3*a^2*c^4*d^2*x^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^4*d^2 - 2*b^2*c^2*d^2*x*arcsin(c*x)^2 + 4*b^2*c^2*d^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) - 2*a^2*c^2*d^2*x - 4*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*c*d^2 - 2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*d^2 - a^2*d^2/x + 1/3*((b^2*c^4*d^2*x^4 - 3*b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 3*x*integrate(2/3*(b^2*c^5*d^2*x^4 - 3*b^2*c*d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^3 - x), x))/x","F",0
172,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} c^{4} d^{2} x^{2} - 2 \, a^{2} c^{2} d^{2} \log\left(x\right) - a b d^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d^{2}}{2 \, x^{2}} + \int \frac{{\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{4} d^{2} x^{4} - 2 \, a b c^{2} d^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x}"," ",0,"1/2*a^2*c^4*d^2*x^2 - 2*a^2*c^2*d^2*log(x) - a*b*d^2*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a^2*d^2/x^2 + integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/x^3, x)","F",0
173,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","b^{2} c^{4} d^{2} x \arcsin\left(c x\right)^{2} - 2 \, b^{2} c^{4} d^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} c^{4} d^{2} x + 2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b c^{3} d^{2} + 4 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b c^{2} d^{2} - \frac{1}{3} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} a b d^{2} + \frac{2 \, a^{2} c^{2} d^{2}}{x} - \frac{a^{2} d^{2}}{3 \, x^{3}} + \frac{2 \, x^{3} \int \frac{{\left(6 \, b^{2} c^{3} d^{2} x^{2} - b^{2} c d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x} + {\left(6 \, b^{2} c^{2} d^{2} x^{2} - b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{3 \, x^{3}}"," ",0,"b^2*c^4*d^2*x*arcsin(c*x)^2 - 2*b^2*c^4*d^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*c^4*d^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*c^3*d^2 + 4*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*c^2*d^2 - 1/3*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*a*b*d^2 + 2*a^2*c^2*d^2/x - 1/3*a^2*d^2/x^3 + 1/3*(3*x^3*integrate(2/3*(6*b^2*c^3*d^2*x^2 - b^2*c*d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^5 - x^3), x) + (6*b^2*c^2*d^2*x^2 - b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/x^3","F",0
174,1,1141,0,0.723010," ","integrate(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{11} \, b^{2} c^{6} d^{3} x^{11} \arcsin\left(c x\right)^{2} - \frac{1}{11} \, a^{2} c^{6} d^{3} x^{11} + \frac{1}{3} \, b^{2} c^{4} d^{3} x^{9} \arcsin\left(c x\right)^{2} + \frac{1}{3} \, a^{2} c^{4} d^{3} x^{9} - \frac{3}{7} \, b^{2} c^{2} d^{3} x^{7} \arcsin\left(c x\right)^{2} - \frac{3}{7} \, a^{2} c^{2} d^{3} x^{7} - \frac{2}{7623} \, {\left(693 \, x^{11} \arcsin\left(c x\right) + {\left(\frac{63 \, \sqrt{-c^{2} x^{2} + 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{-c^{2} x^{2} + 1}}{c^{12}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{26413695} \, {\left(3465 \, {\left(\frac{63 \, \sqrt{-c^{2} x^{2} + 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{-c^{2} x^{2} + 1}}{c^{12}}\right)} c \arcsin\left(c x\right) - \frac{19845 \, c^{10} x^{11} + 26950 \, c^{8} x^{9} + 39600 \, c^{6} x^{7} + 66528 \, c^{4} x^{5} + 147840 \, c^{2} x^{3} + 887040 \, x}{c^{10}}\right)} b^{2} c^{6} d^{3} + \frac{1}{5} \, b^{2} d^{3} x^{5} \arcsin\left(c x\right)^{2} + \frac{2}{945} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{4} d^{3} + \frac{2}{297675} \, {\left(315 \, {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c \arcsin\left(c x\right) - \frac{1225 \, c^{8} x^{9} + 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} + 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{4} d^{3} + \frac{1}{5} \, a^{2} d^{3} x^{5} - \frac{6}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{2} d^{3} - \frac{2}{8575} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{2} d^{3} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d^{3} + \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d^{3}"," ",0,"-1/11*b^2*c^6*d^3*x^11*arcsin(c*x)^2 - 1/11*a^2*c^6*d^3*x^11 + 1/3*b^2*c^4*d^3*x^9*arcsin(c*x)^2 + 1/3*a^2*c^4*d^3*x^9 - 3/7*b^2*c^2*d^3*x^7*arcsin(c*x)^2 - 3/7*a^2*c^2*d^3*x^7 - 2/7623*(693*x^11*arcsin(c*x) + (63*sqrt(-c^2*x^2 + 1)*x^10/c^2 + 70*sqrt(-c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(-c^2*x^2 + 1)*x^6/c^6 + 96*sqrt(-c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(-c^2*x^2 + 1)*x^2/c^10 + 256*sqrt(-c^2*x^2 + 1)/c^12)*c)*a*b*c^6*d^3 - 2/26413695*(3465*(63*sqrt(-c^2*x^2 + 1)*x^10/c^2 + 70*sqrt(-c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(-c^2*x^2 + 1)*x^6/c^6 + 96*sqrt(-c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(-c^2*x^2 + 1)*x^2/c^10 + 256*sqrt(-c^2*x^2 + 1)/c^12)*c*arcsin(c*x) - (19845*c^10*x^11 + 26950*c^8*x^9 + 39600*c^6*x^7 + 66528*c^4*x^5 + 147840*c^2*x^3 + 887040*x)/c^10)*b^2*c^6*d^3 + 1/5*b^2*d^3*x^5*arcsin(c*x)^2 + 2/945*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*a*b*c^4*d^3 + 2/297675*(315*(35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c*arcsin(c*x) - (1225*c^8*x^9 + 1800*c^6*x^7 + 3024*c^4*x^5 + 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^4*d^3 + 1/5*a^2*d^3*x^5 - 6/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^2*d^3 - 2/8575*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^2*d^3 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*d^3 + 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*d^3","B",0
175,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{10} \, a^{2} c^{6} d^{3} x^{10} + \frac{3}{8} \, a^{2} c^{4} d^{3} x^{8} - \frac{1}{2} \, a^{2} c^{2} d^{3} x^{6} - \frac{1}{6400} \, {\left(1280 \, x^{10} \arcsin\left(c x\right) + {\left(\frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{9}}{c^{2}} + \frac{144 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{6}} + \frac{210 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \arcsin\left(c x\right)}{c^{11}}\right)} c\right)} a b c^{6} d^{3} + \frac{1}{512} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{4} d^{3} + \frac{1}{4} \, a^{2} d^{3} x^{4} - \frac{1}{48} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{2} d^{3} + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b d^{3} - \frac{1}{40} \, {\left(4 \, b^{2} c^{6} d^{3} x^{10} - 15 \, b^{2} c^{4} d^{3} x^{8} + 20 \, b^{2} c^{2} d^{3} x^{6} - 10 \, b^{2} d^{3} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - \int \frac{{\left(4 \, b^{2} c^{7} d^{3} x^{10} - 15 \, b^{2} c^{5} d^{3} x^{8} + 20 \, b^{2} c^{3} d^{3} x^{6} - 10 \, b^{2} c d^{3} x^{4}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{20 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-1/10*a^2*c^6*d^3*x^10 + 3/8*a^2*c^4*d^3*x^8 - 1/2*a^2*c^2*d^3*x^6 - 1/6400*(1280*x^10*arcsin(c*x) + (128*sqrt(-c^2*x^2 + 1)*x^9/c^2 + 144*sqrt(-c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(-c^2*x^2 + 1)*x^5/c^6 + 210*sqrt(-c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(-c^2*x^2 + 1)*x/c^10 - 315*arcsin(c*x)/c^11)*c)*a*b*c^6*d^3 + 1/512*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*a*b*c^4*d^3 + 1/4*a^2*d^3*x^4 - 1/48*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*c^2*d^3 + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*d^3 - 1/40*(4*b^2*c^6*d^3*x^10 - 15*b^2*c^4*d^3*x^8 + 20*b^2*c^2*d^3*x^6 - 10*b^2*d^3*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - integrate(1/20*(4*b^2*c^7*d^3*x^10 - 15*b^2*c^5*d^3*x^8 + 20*b^2*c^3*d^3*x^6 - 10*b^2*c*d^3*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
176,1,946,0,0.944406," ","integrate(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{9} \, b^{2} c^{6} d^{3} x^{9} \arcsin\left(c x\right)^{2} - \frac{1}{9} \, a^{2} c^{6} d^{3} x^{9} + \frac{3}{7} \, b^{2} c^{4} d^{3} x^{7} \arcsin\left(c x\right)^{2} + \frac{3}{7} \, a^{2} c^{4} d^{3} x^{7} - \frac{3}{5} \, b^{2} c^{2} d^{3} x^{5} \arcsin\left(c x\right)^{2} - \frac{2}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{893025} \, {\left(315 \, {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c \arcsin\left(c x\right) - \frac{1225 \, c^{8} x^{9} + 1800 \, c^{6} x^{7} + 3024 \, c^{4} x^{5} + 6720 \, c^{2} x^{3} + 40320 \, x}{c^{8}}\right)} b^{2} c^{6} d^{3} - \frac{3}{5} \, a^{2} c^{2} d^{3} x^{5} + \frac{6}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{4} d^{3} + \frac{2}{8575} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{4} d^{3} + \frac{1}{3} \, b^{2} d^{3} x^{3} \arcsin\left(c x\right)^{2} - \frac{2}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{2} d^{3} - \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{2} d^{3} + \frac{1}{3} \, a^{2} d^{3} x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{3} + \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d^{3}"," ",0,"-1/9*b^2*c^6*d^3*x^9*arcsin(c*x)^2 - 1/9*a^2*c^6*d^3*x^9 + 3/7*b^2*c^4*d^3*x^7*arcsin(c*x)^2 + 3/7*a^2*c^4*d^3*x^7 - 3/5*b^2*c^2*d^3*x^5*arcsin(c*x)^2 - 2/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*a*b*c^6*d^3 - 2/893025*(315*(35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c*arcsin(c*x) - (1225*c^8*x^9 + 1800*c^6*x^7 + 3024*c^4*x^5 + 6720*c^2*x^3 + 40320*x)/c^8)*b^2*c^6*d^3 - 3/5*a^2*c^2*d^3*x^5 + 6/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^4*d^3 + 2/8575*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^4*d^3 + 1/3*b^2*d^3*x^3*arcsin(c*x)^2 - 2/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^2*d^3 - 2/375*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*c^2*d^3 + 1/3*a^2*d^3*x^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*d^3 + 2/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d^3","B",0
177,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} c^{6} d^{3} x^{8} + \frac{1}{2} \, a^{2} c^{4} d^{3} x^{6} - \frac{1}{1536} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} a b c^{6} d^{3} - \frac{3}{4} \, a^{2} c^{2} d^{3} x^{4} + \frac{1}{48} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} a b c^{4} d^{3} - \frac{3}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} a b c^{2} d^{3} + \frac{1}{2} \, a^{2} d^{3} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} a b d^{3} - \frac{1}{8} \, {\left(b^{2} c^{6} d^{3} x^{8} - 4 \, b^{2} c^{4} d^{3} x^{6} + 6 \, b^{2} c^{2} d^{3} x^{4} - 4 \, b^{2} d^{3} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - \int \frac{{\left(b^{2} c^{7} d^{3} x^{8} - 4 \, b^{2} c^{5} d^{3} x^{6} + 6 \, b^{2} c^{3} d^{3} x^{4} - 4 \, b^{2} c d^{3} x^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"-1/8*a^2*c^6*d^3*x^8 + 1/2*a^2*c^4*d^3*x^6 - 1/1536*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*a*b*c^6*d^3 - 3/4*a^2*c^2*d^3*x^4 + 1/48*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*a*b*c^4*d^3 - 3/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*a*b*c^2*d^3 + 1/2*a^2*d^3*x^2 + 1/2*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*a*b*d^3 - 1/8*(b^2*c^6*d^3*x^8 - 4*b^2*c^4*d^3*x^6 + 6*b^2*c^2*d^3*x^4 - 4*b^2*d^3*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - integrate(1/4*(b^2*c^7*d^3*x^8 - 4*b^2*c^5*d^3*x^6 + 6*b^2*c^3*d^3*x^4 - 4*b^2*c*d^3*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^2 - 1), x)","F",0
178,1,729,0,0.719775," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{7} \, b^{2} c^{6} d^{3} x^{7} \arcsin\left(c x\right)^{2} - \frac{1}{7} \, a^{2} c^{6} d^{3} x^{7} + \frac{3}{5} \, b^{2} c^{4} d^{3} x^{5} \arcsin\left(c x\right)^{2} + \frac{3}{5} \, a^{2} c^{4} d^{3} x^{5} - \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b c^{6} d^{3} - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} c^{6} d^{3} - b^{2} c^{2} d^{3} x^{3} \arcsin\left(c x\right)^{2} + \frac{2}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{4} d^{3} + \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} c^{4} d^{3} - a^{2} c^{2} d^{3} x^{3} - \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{2} d^{3} - \frac{2}{9} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} c^{2} d^{3} + b^{2} d^{3} x \arcsin\left(c x\right)^{2} - 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d^{3}}{c}"," ",0,"-1/7*b^2*c^6*d^3*x^7*arcsin(c*x)^2 - 1/7*a^2*c^6*d^3*x^7 + 3/5*b^2*c^4*d^3*x^5*arcsin(c*x)^2 + 3/5*a^2*c^4*d^3*x^5 - 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*c^6*d^3 - 2/25725*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*c^6*d^3 - b^2*c^2*d^3*x^3*arcsin(c*x)^2 + 2/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^4*d^3 + 2/375*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*c^4*d^3 - a^2*c^2*d^3*x^3 - 2/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^2*d^3 - 2/9*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*c^2*d^3 + b^2*d^3*x*arcsin(c*x)^2 - 2*b^2*d^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d^3*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d^3/c","B",0
179,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} c^{6} d^{3} x^{6} + \frac{3}{4} \, a^{2} c^{4} d^{3} x^{4} - \frac{3}{2} \, a^{2} c^{2} d^{3} x^{2} + a^{2} d^{3} \log\left(x\right) - \int \frac{{\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"-1/6*a^2*c^6*d^3*x^6 + 3/4*a^2*c^4*d^3*x^4 - 3/2*a^2*c^2*d^3*x^2 + a^2*d^3*log(x) - integrate(((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/x, x)","F",0
180,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{5} \, a^{2} c^{6} d^{3} x^{5} - \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b c^{6} d^{3} + a^{2} c^{4} d^{3} x^{3} + \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{4} d^{3} - 3 \, b^{2} c^{2} d^{3} x \arcsin\left(c x\right)^{2} + 6 \, b^{2} c^{2} d^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} - 3 \, a^{2} c^{2} d^{3} x - 6 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b c d^{3} - 2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b d^{3} - \frac{a^{2} d^{3}}{x} - \frac{{\left(b^{2} c^{6} d^{3} x^{6} - 5 \, b^{2} c^{4} d^{3} x^{4} + 5 \, b^{2} d^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, x \int \frac{{\left(b^{2} c^{7} d^{3} x^{6} - 5 \, b^{2} c^{5} d^{3} x^{4} + 5 \, b^{2} c d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{3} - x}\,{d x}}{5 \, x}"," ",0,"-1/5*a^2*c^6*d^3*x^5 - 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*c^6*d^3 + a^2*c^4*d^3*x^3 + 2/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^4*d^3 - 3*b^2*c^2*d^3*x*arcsin(c*x)^2 + 6*b^2*c^2*d^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) - 3*a^2*c^2*d^3*x - 6*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*c*d^3 - 2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*d^3 - a^2*d^3/x - 1/5*((b^2*c^6*d^3*x^6 - 5*b^2*c^4*d^3*x^4 + 5*b^2*d^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 5*x*integrate(2/5*(b^2*c^7*d^3*x^6 - 5*b^2*c^5*d^3*x^4 + 5*b^2*c*d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^3 - x), x))/x","F",0
181,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} c^{6} d^{3} x^{4} + \frac{3}{2} \, a^{2} c^{4} d^{3} x^{2} - 3 \, a^{2} c^{2} d^{3} \log\left(x\right) - a b d^{3} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} - \frac{a^{2} d^{3}}{2 \, x^{2}} - \int \frac{{\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/4*a^2*c^6*d^3*x^4 + 3/2*a^2*c^4*d^3*x^2 - 3*a^2*c^2*d^3*log(x) - a*b*d^3*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) - 1/2*a^2*d^3/x^2 - integrate(((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/x^3, x)","F",0
182,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} c^{6} d^{3} x^{3} - \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b c^{6} d^{3} + 3 \, b^{2} c^{4} d^{3} x \arcsin\left(c x\right)^{2} - 6 \, b^{2} c^{4} d^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + 3 \, a^{2} c^{4} d^{3} x + 6 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b c^{3} d^{3} + 6 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} a b c^{2} d^{3} - \frac{1}{3} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} a b d^{3} + \frac{3 \, a^{2} c^{2} d^{3}}{x} - \frac{a^{2} d^{3}}{3 \, x^{3}} - \frac{2 \, x^{3} \int \frac{{\left(b^{2} c^{7} d^{3} x^{6} - 9 \, b^{2} c^{3} d^{3} x^{2} + b^{2} c d^{3}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x} + {\left(b^{2} c^{6} d^{3} x^{6} - 9 \, b^{2} c^{2} d^{3} x^{2} + b^{2} d^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{3 \, x^{3}}"," ",0,"-1/3*a^2*c^6*d^3*x^3 - 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*c^6*d^3 + 3*b^2*c^4*d^3*x*arcsin(c*x)^2 - 6*b^2*c^4*d^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + 3*a^2*c^4*d^3*x + 6*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*c^3*d^3 + 6*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*a*b*c^2*d^3 - 1/3*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*a*b*d^3 + 3*a^2*c^2*d^3/x - 1/3*a^2*d^3/x^3 - 1/3*(3*x^3*integrate(2/3*(b^2*c^7*d^3*x^6 - 9*b^2*c^3*d^3*x^2 + b^2*c*d^3)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*x^5 - x^3), x) + (b^2*c^6*d^3*x^6 - 9*b^2*c^2*d^3*x^2 + b^2*d^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/x^3","F",0
183,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4} d} - \frac{3 \, \log\left(c x + 1\right)}{c^{5} d} + \frac{3 \, \log\left(c x - 1\right)}{c^{5} d}\right)} + \frac{-2 \, c^{5} d \int \frac{6 \, a b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(3 \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(b^{2} c^{3} x^{3} + 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d x^{2} - c^{4} d}\,{d x} + 3 \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(b^{2} c^{3} x^{3} + 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{6 \, c^{5} d}"," ",0,"-1/6*a^2*(2*(c^2*x^3 + 3*x)/(c^4*d) - 3*log(c*x + 1)/(c^5*d) + 3*log(c*x - 1)/(c^5*d)) + 1/6*(6*c^5*d*integrate(-1/3*(6*a*b*c^4*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(b^2*c^3*x^3 + 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^6*d*x^2 - c^4*d), x) + 3*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(b^2*c^3*x^3 + 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/(c^5*d)","F",0
184,-1,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{2 \, x}{c^{2} d} - \frac{\log\left(c x + 1\right)}{c^{3} d} + \frac{\log\left(c x - 1\right)}{c^{3} d}\right)} - \frac{2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, c^{3} d \int \frac{2 \, a b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d x^{2} - c^{2} d}\,{d x} - b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) + b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right)}{2 \, c^{3} d}"," ",0,"-1/2*a^2*(2*x/(c^2*d) - log(c*x + 1)/(c^3*d) + log(c*x - 1)/(c^3*d)) - 1/2*(2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - 2*c^3*d*integrate(-(2*a*b*c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d*x^2 - c^2*d), x) - b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) + b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1))/(c^3*d)","F",0
186,-1,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)} + \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, c d \int \frac{2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{2} - d}\,{d x}}{2 \, c d}"," ",0,"1/2*a^2*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d)) + 1/2*(b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) + 2*c*d*integrate(-(2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^2 - d), x))/(c*d)","F",0
188,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{d} + \frac{\log\left(c x - 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} - \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} d x^{3} - d x}\,{d x}"," ",0,"-1/2*a^2*(log(c*x + 1)/d + log(c*x - 1)/d - 2*log(x)/d) - integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^2*d*x^3 - d*x), x)","F",0
189,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(c x - 1\right)}{d} - \frac{2}{d x}\right)} + \frac{b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, d x \int \frac{2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(b^{2} c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - b^{2} c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{4} - d x^{2}}\,{d x}}{2 \, d x}"," ",0,"1/2*a^2*(c*log(c*x + 1)/d - c*log(c*x - 1)/d - 2/(d*x)) + 1/2*(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*d*x*integrate(-(2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (b^2*c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - b^2*c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^4 - d*x^2), x))/(d*x)","F",0
190,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c x + 1\right)}{d} + \frac{c^{2} \log\left(c x - 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} + \frac{1}{d x^{2}}\right)} a^{2} - \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} d x^{5} - d x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(c*x + 1)/d + c^2*log(c*x - 1)/d - 2*c^2*log(x)/d + 1/(d*x^2))*a^2 - integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^2*d*x^5 - d*x^3), x)","F",0
191,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, c^{3} \log\left(c x + 1\right)}{d} - \frac{3 \, c^{3} \log\left(c x - 1\right)}{d} - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{d x^{3}}\right)} a^{2} + \frac{3 \, b^{2} c^{3} x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, b^{2} c^{3} x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, d x^{3} \int \frac{6 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(3 \, b^{2} c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, b^{2} c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{6} - d x^{4}}\,{d x} - 2 \, {\left(3 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{6 \, d x^{3}}"," ",0,"1/6*(3*c^3*log(c*x + 1)/d - 3*c^3*log(c*x - 1)/d - 2*(3*c^2*x^2 + 1)/(d*x^3))*a^2 + 1/6*(3*b^2*c^3*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*b^2*c^3*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) + 6*d*x^3*integrate(-1/3*(6*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*b^2*c^4*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*b^2*c^4*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(3*b^2*c^3*x^3 + b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d*x^6 - d*x^4), x) - 2*(3*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2)/(d*x^3)","F",0
192,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{2 \, x}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{4 \, x}{c^{4} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - \frac{3 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)} \int \frac{4 \, a b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(3 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(2 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}}\,{d x}}{4 \, {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)}}"," ",0,"-1/4*a^2*(2*x/(c^6*d^2*x^2 - c^4*d^2) - 4*x/(c^4*d^2) + 3*log(c*x + 1)/(c^5*d^2) - 3*log(c*x - 1)/(c^5*d^2)) - 1/4*(3*(b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*(b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(2*b^2*c^3*x^3 - 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 4*(c^7*d^2*x^2 - c^5*d^2)*integrate(-1/2*(4*a*b*c^4*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*(b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(2*b^2*c^3*x^3 - 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x))/(c^7*d^2*x^2 - c^5*d^2)","F",0
193,-1,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - \frac{2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)} \int \frac{4 \, a b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x}}{4 \, {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)}}"," ",0,"-1/4*a^2*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 1/4*(2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) + 4*(c^5*d^2*x^2 - c^3*d^2)*integrate(-1/2*(4*a*b*c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x))/(c^5*d^2*x^2 - c^3*d^2)","F",0
195,1,293,0,0.930456," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(\frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x + c^{6} d^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x - c^{6} d^{4}}\right)} c^{2} - \frac{2 \, \arcsin\left(c x\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} a b - \frac{1}{2} \, {\left(c^{3} {\left(\frac{\log\left(c x + 1\right)}{c^{5} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x + c^{6} d^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x - c^{6} d^{4}}\right)} c^{2} \arcsin\left(c x\right)\right)} b^{2} - \frac{b^{2} \arcsin\left(c x\right)^{2}}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}} - \frac{a^{2}}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"1/2*((sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x + c^6*d^4) + sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x - c^6*d^4))*c^2 - 2*arcsin(c*x)/(c^4*d^2*x^2 - c^2*d^2))*a*b - 1/2*(c^3*(log(c*x + 1)/(c^5*d^2) + log(c*x - 1)/(c^5*d^2)) - (sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x + c^6*d^4) + sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x - c^6*d^4))*c^2*arcsin(c*x))*b^2 - 1/2*b^2*arcsin(c*x)^2/(c^4*d^2*x^2 - c^2*d^2) - 1/2*a^2/(c^4*d^2*x^2 - c^2*d^2)","B",0
196,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)} - \frac{2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(c^{3} d^{2} x^{2} - c d^{2}\right)} \int \frac{4 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(2 \, b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}}{4 \, {\left(c^{3} d^{2} x^{2} - c d^{2}\right)}}"," ",0,"-1/4*a^2*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2)) - 1/4*(2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 4*(c^3*d^2*x^2 - c*d^2)*integrate(1/2*(4*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (2*b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x))/(c^3*d^2*x^2 - c*d^2)","F",0
197,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{1}{c^{2} d^{2} x^{2} - d^{2}} + \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(c x - 1\right)}{d^{2}} - \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"-1/2*a^2*(1/(c^2*d^2*x^2 - d^2) + log(c*x + 1)/d^2 + log(c*x - 1)/d^2 - 2*log(x)/d^2) + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
198,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{3} - d^{2} x} - \frac{3 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{3 \, c \log\left(c x - 1\right)}{d^{2}}\right)} + \frac{3 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{2} x^{2} - 2 \, b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(c^{2} d^{2} x^{3} - d^{2} x\right)} \int \frac{4 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(3 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{3} x^{3} - 2 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}}\,{d x}}{4 \, {\left(c^{2} d^{2} x^{3} - d^{2} x\right)}}"," ",0,"-1/4*a^2*(2*(3*c^2*x^2 - 2)/(c^2*d^2*x^3 - d^2*x) - 3*c*log(c*x + 1)/d^2 + 3*c*log(c*x - 1)/d^2) + 1/4*(3*(b^2*c^3*x^3 - b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*(b^2*c^3*x^3 - b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(3*b^2*c^2*x^2 - 2*b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 4*(c^2*d^2*x^3 - d^2*x)*integrate(1/2*(4*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (3*(b^2*c^4*x^4 - b^2*c^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(b^2*c^4*x^4 - b^2*c^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(3*b^2*c^3*x^3 - 2*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x))/(c^2*d^2*x^3 - d^2*x)","F",0
199,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c^{2} \log\left(c x - 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} + \frac{2 \, c^{2} x^{2} - 1}{c^{2} d^{2} x^{4} - d^{2} x^{2}}\right)} + \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a^2*(2*c^2*log(c*x + 1)/d^2 + 2*c^2*log(c*x - 1)/d^2 - 4*c^2*log(x)/d^2 + (2*c^2*x^2 - 1)/(c^2*d^2*x^4 - d^2*x^2)) + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
200,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{15 \, c^{3} \log\left(c x + 1\right)}{d^{2}} - \frac{15 \, c^{3} \log\left(c x - 1\right)}{d^{2}} - \frac{2 \, {\left(15 \, c^{4} x^{4} - 10 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{5} - d^{2} x^{3}}\right)} a^{2} + \frac{15 \, {\left(b^{2} c^{5} x^{5} - b^{2} c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 15 \, {\left(b^{2} c^{5} x^{5} - b^{2} c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(15 \, b^{2} c^{4} x^{4} - 10 \, b^{2} c^{2} x^{2} - 2 \, b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(c^{2} d^{2} x^{5} - d^{2} x^{3}\right)} \int \frac{12 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(15 \, {\left(b^{2} c^{6} x^{6} - b^{2} c^{4} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 15 \, {\left(b^{2} c^{6} x^{6} - b^{2} c^{4} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(15 \, b^{2} c^{5} x^{5} - 10 \, b^{2} c^{3} x^{3} - 2 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}\,{d x}}{12 \, {\left(c^{2} d^{2} x^{5} - d^{2} x^{3}\right)}}"," ",0,"1/12*(15*c^3*log(c*x + 1)/d^2 - 15*c^3*log(c*x - 1)/d^2 - 2*(15*c^4*x^4 - 10*c^2*x^2 - 2)/(c^2*d^2*x^5 - d^2*x^3))*a^2 + 1/12*(15*(b^2*c^5*x^5 - b^2*c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 15*(b^2*c^5*x^5 - b^2*c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(15*b^2*c^4*x^4 - 10*b^2*c^2*x^2 - 2*b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 12*(c^2*d^2*x^5 - d^2*x^3)*integrate(1/6*(12*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (15*(b^2*c^6*x^6 - b^2*c^4*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 15*(b^2*c^6*x^6 - b^2*c^4*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(15*b^2*c^5*x^5 - 10*b^2*c^3*x^3 - 2*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x))/(c^2*d^2*x^5 - d^2*x^3)","F",0
201,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, a^{2} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) + 2 \, {\left(5 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}\right)} \int \frac{16 \, a b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) + 2 \, {\left(5 \, b^{2} c^{3} x^{3} - 3 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}}\,{d x}}{16 \, {\left(c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}\right)}}"," ",0,"1/16*a^2*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3)) + 1/16*(3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) + 2*(5*b^2*c^3*x^3 - 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 16*(c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3)*integrate(-1/8*(16*a*b*c^4*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) + 2*(5*b^2*c^3*x^3 - 3*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x))/(c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3)","F",0
202,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{{\left(2 \, c^{2} x^{2} - 1\right)} a^{2}}{4 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}} + \frac{{\left(2 \, b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)} \int \frac{4 \, a b c^{3} x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(2 \, b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{9} d^{3} x^{6} - 3 \, c^{7} d^{3} x^{4} + 3 \, c^{5} d^{3} x^{2} - c^{3} d^{3}}\,{d x}}{4 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"1/4*(2*c^2*x^2 - 1)*a^2/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 1/4*((2*b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 4*(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)*integrate(-1/2*(4*a*b*c^3*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (2*b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^9*d^3*x^6 - 3*c^7*d^3*x^4 + 3*c^5*d^3*x^2 - c^3*d^3), x))/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)","F",0
203,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, a^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)} - \frac{{\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(c^{7} d^{3} x^{4} - 2 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)} \int \frac{16 \, a b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left({\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(b^{2} c^{3} x^{3} + b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}}\,{d x}}{16 \, {\left(c^{7} d^{3} x^{4} - 2 \, c^{5} d^{3} x^{2} + c^{3} d^{3}\right)}}"," ",0,"1/16*a^2*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3)) - 1/16*((b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(b^2*c^3*x^3 + b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 16*(c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3)*integrate(1/8*(16*a*b*c^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + ((b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(b^2*c^3*x^3 + b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x))/(c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3)","F",0
204,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{a^{2}}{4 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}} + \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)} \int \frac{4 \, a b c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - \sqrt{c x + 1} \sqrt{-c x + 1} b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{7} d^{3} x^{6} - 3 \, c^{5} d^{3} x^{4} + 3 \, c^{3} d^{3} x^{2} - c d^{3}}\,{d x}}{4 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"1/4*a^2/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) + 1/4*(b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 4*(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)*integrate(-1/2*(4*a*b*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^7*d^3*x^6 - 3*c^5*d^3*x^4 + 3*c^3*d^3*x^2 - c*d^3), x))/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)","F",0
205,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, a^{2} {\left(\frac{2 \, {\left(3 \, c^{2} x^{3} - 5 \, x\right)}}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c d^{3}}\right)} + \frac{3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{3} x^{3} - 5 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)} \int \frac{16 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(3 \, b^{2} c^{3} x^{3} - 5 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x}}{16 \, {\left(c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}\right)}}"," ",0,"-1/16*a^2*(2*(3*c^2*x^3 - 5*x)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) - 3*log(c*x + 1)/(c*d^3) + 3*log(c*x - 1)/(c*d^3)) + 1/16*(3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(3*b^2*c^3*x^3 - 5*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 16*(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3)*integrate(-1/8*(16*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 3*(b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(3*b^2*c^3*x^3 - 5*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x))/(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3)","F",0
206,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{2 \, c^{2} x^{2} - 3}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, \log\left(c x + 1\right)}{d^{3}} + \frac{2 \, \log\left(c x - 1\right)}{d^{3}} - \frac{4 \, \log\left(x\right)}{d^{3}}\right)} - \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}\,{d x}"," ",0,"-1/4*a^2*((2*c^2*x^2 - 3)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) + 2*log(c*x + 1)/d^3 + 2*log(c*x - 1)/d^3 - 4*log(x)/d^3) - integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(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
207,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, a^{2} {\left(\frac{2 \, {\left(15 \, c^{4} x^{4} - 25 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x} - \frac{15 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{15 \, c \log\left(c x - 1\right)}{d^{3}}\right)} + \frac{15 \, {\left(b^{2} c^{5} x^{5} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 15 \, {\left(b^{2} c^{5} x^{5} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(15 \, b^{2} c^{4} x^{4} - 25 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x\right)} \int \frac{16 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(15 \, {\left(b^{2} c^{6} x^{6} - 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 15 \, {\left(b^{2} c^{6} x^{6} - 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(15 \, b^{2} c^{5} x^{5} - 25 \, b^{2} c^{3} x^{3} + 8 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}\,{d x}}{16 \, {\left(c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x\right)}}"," ",0,"-1/16*a^2*(2*(15*c^4*x^4 - 25*c^2*x^2 + 8)/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x) - 15*c*log(c*x + 1)/d^3 + 15*c*log(c*x - 1)/d^3) + 1/16*(15*(b^2*c^5*x^5 - 2*b^2*c^3*x^3 + b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 15*(b^2*c^5*x^5 - 2*b^2*c^3*x^3 + b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(15*b^2*c^4*x^4 - 25*b^2*c^2*x^2 + 8*b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 16*(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x)*integrate(-1/8*(16*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (15*(b^2*c^6*x^6 - 2*b^2*c^4*x^4 + b^2*c^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 15*(b^2*c^6*x^6 - 2*b^2*c^4*x^4 + b^2*c^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(15*b^2*c^5*x^5 - 25*b^2*c^3*x^3 + 8*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(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))/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x)","F",0
208,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} {\left(\frac{6 \, c^{4} x^{4} - 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} - 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} + \frac{6 \, c^{2} \log\left(c x + 1\right)}{d^{3}} + \frac{6 \, c^{2} \log\left(c x - 1\right)}{d^{3}} - \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} - \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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}}\,{d x}"," ",0,"-1/4*a^2*((6*c^4*x^4 - 9*c^2*x^2 + 2)/(c^4*d^3*x^6 - 2*c^2*d^3*x^4 + d^3*x^2) + 6*c^2*log(c*x + 1)/d^3 + 6*c^2*log(c*x - 1)/d^3 - 12*c^2*log(x)/d^3) - integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(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
209,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{48} \, a^{2} {\left(\frac{105 \, c^{3} \log\left(c x + 1\right)}{d^{3}} - \frac{105 \, c^{3} \log\left(c x - 1\right)}{d^{3}} - \frac{2 \, {\left(105 \, c^{6} x^{6} - 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\right)} + \frac{105 \, {\left(b^{2} c^{7} x^{7} - 2 \, b^{2} c^{5} x^{5} + b^{2} c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(c x + 1\right) - 105 \, {\left(b^{2} c^{7} x^{7} - 2 \, b^{2} c^{5} x^{5} + b^{2} c^{3} x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} \log\left(-c x + 1\right) - 2 \, {\left(105 \, b^{2} c^{6} x^{6} - 175 \, b^{2} c^{4} x^{4} + 56 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}\right)} \int \frac{48 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(105 \, {\left(b^{2} c^{8} x^{8} - 2 \, b^{2} c^{6} x^{6} + b^{2} c^{4} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 105 \, {\left(b^{2} c^{8} x^{8} - 2 \, b^{2} c^{6} x^{6} + b^{2} c^{4} x^{4}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right) - 2 \, {\left(105 \, b^{2} c^{7} x^{7} - 175 \, b^{2} c^{5} x^{5} + 56 \, b^{2} c^{3} x^{3} + 8 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{10} - 3 \, c^{4} d^{3} x^{8} + 3 \, c^{2} d^{3} x^{6} - d^{3} x^{4}}\,{d x}}{48 \, {\left(c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}\right)}}"," ",0,"1/48*a^2*(105*c^3*log(c*x + 1)/d^3 - 105*c^3*log(c*x - 1)/d^3 - 2*(105*c^6*x^6 - 175*c^4*x^4 + 56*c^2*x^2 + 8)/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)) + 1/48*(105*(b^2*c^7*x^7 - 2*b^2*c^5*x^5 + b^2*c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(c*x + 1) - 105*(b^2*c^7*x^7 - 2*b^2*c^5*x^5 + b^2*c^3*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2*log(-c*x + 1) - 2*(105*b^2*c^6*x^6 - 175*b^2*c^4*x^4 + 56*b^2*c^2*x^2 + 8*b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 48*(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)*integrate(-1/24*(48*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (105*(b^2*c^8*x^8 - 2*b^2*c^6*x^6 + b^2*c^4*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(c*x + 1) - 105*(b^2*c^8*x^8 - 2*b^2*c^6*x^6 + b^2*c^4*x^4)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))*log(-c*x + 1) - 2*(105*b^2*c^7*x^7 - 175*b^2*c^5*x^5 + 56*b^2*c^3*x^3 + 8*b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1))/(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))/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3)","F",0
210,1,311,0,1.061278," ","integrate(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{15} \, b^{2} {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \arcsin\left(c x\right)^{2} - \frac{2}{15} \, a b {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \arcsin\left(c x\right) - \frac{1}{15} \, a^{2} {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} - \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{-c^{2} x^{2} + 1} c^{2} \sqrt{d} x^{4} + 11 \, \sqrt{-c^{2} x^{2} + 1} \sqrt{d} x^{2} - \frac{428 \, \sqrt{-c^{2} x^{2} + 1} \sqrt{d}}{c^{2}}}{c^{2}} + \frac{15 \, {\left(9 \, c^{4} \sqrt{d} x^{5} - 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(9 \, c^{4} \sqrt{d} x^{5} - 5 \, c^{2} \sqrt{d} x^{3} - 30 \, \sqrt{d} x\right)} a b}{225 \, c^{3}}"," ",0,"-1/15*b^2*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsin(c*x)^2 - 2/15*a*b*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arcsin(c*x) - 1/15*a^2*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d)) - 2/3375*b^2*((27*sqrt(-c^2*x^2 + 1)*c^2*sqrt(d)*x^4 + 11*sqrt(-c^2*x^2 + 1)*sqrt(d)*x^2 - 428*sqrt(-c^2*x^2 + 1)*sqrt(d)/c^2)/c^2 + 15*(9*c^4*sqrt(d)*x^5 - 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*arcsin(c*x)/c^3) - 2/225*(9*c^4*sqrt(d)*x^5 - 5*c^2*sqrt(d)*x^3 - 30*sqrt(d)*x)*a*b/c^3","A",0
211,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)} + \sqrt{d} \int {\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/8*a^2*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3) + sqrt(d)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
212,1,188,0,0.522758," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{2}{27} \, b^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}} x^{2} - \frac{7 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}}}{c^{2}}}{d} + \frac{3 \, {\left(c^{2} d^{\frac{3}{2}} x^{3} - 3 \, d^{\frac{3}{2}} x\right)} \arcsin\left(c x\right)}{c d}\right)} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \arcsin\left(c x\right)^{2}}{3 \, c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \arcsin\left(c x\right)}{3 \, c^{2} d} - \frac{2 \, {\left(c^{2} d^{\frac{3}{2}} x^{3} - 3 \, d^{\frac{3}{2}} x\right)} a b}{9 \, c d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, c^{2} d}"," ",0,"-2/27*b^2*((sqrt(-c^2*x^2 + 1)*d^(3/2)*x^2 - 7*sqrt(-c^2*x^2 + 1)*d^(3/2)/c^2)/d + 3*(c^2*d^(3/2)*x^3 - 3*d^(3/2)*x)*arcsin(c*x)/(c*d)) - 1/3*(-c^2*d*x^2 + d)^(3/2)*b^2*arcsin(c*x)^2/(c^2*d) - 2/3*(-c^2*d*x^2 + d)^(3/2)*a*b*arcsin(c*x)/(c^2*d) - 2/9*(c^2*d^(3/2)*x^3 - 3*d^(3/2)*x)*a*b/(c*d) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a^2/(c^2*d)","A",0
213,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a^{2} + \sqrt{d} \int {\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
214,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d}\right)} a^{2} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x}\,{d x}"," ",0,"-(sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d))*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x, x)","F",0
215,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-{\left(c \sqrt{d} \arcsin\left(c x\right) + \frac{\sqrt{-c^{2} d x^{2} + d}}{x}\right)} a^{2} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{2}}\,{d x}"," ",0,"-(c*sqrt(d)*arcsin(c*x) + sqrt(-c^2*d*x^2 + d)/x)*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^2, x)","F",0
216,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c^{2} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{2} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a^{2} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{3}}\,{d x}"," ",0,"1/2*(c^2*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^2 - (-c^2*d*x^2 + d)^(3/2)/(d*x^2))*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^3, x)","F",0
217,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{{\left(\left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + c^{2} d^{\frac{3}{2}} \log\left(x^{2} - \frac{1}{c^{2}}\right) - \frac{\sqrt{c^{4} d x^{4} - 2 \, c^{2} d x^{2} + d} d}{x^{2}}\right)} a b c}{3 \, d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \arcsin\left(c x\right)}{3 \, d x^{3}} + \frac{{\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, \sqrt{d} x^{3} \int \frac{{\left(c^{3} x^{2} - c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x^{3}}\,{d x}\right)} b^{2}}{3 \, x^{3}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, d x^{3}}"," ",0,"1/3*((-1)^(-2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(-2*c^2*d + 2*d/x^2) + c^2*d^(3/2)*log(x^2 - 1/c^2) - sqrt(c^4*d*x^4 - 2*c^2*d*x^2 + d)*d/x^2)*a*b*c/d - 2/3*(-c^2*d*x^2 + d)^(3/2)*a*b*arcsin(c*x)/(d*x^3) + 1/3*((c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - sqrt(d)*x^3*integrate(2*(c^3*x^2 - c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x^3, x))*b^2/x^3 - 1/3*(-c^2*d*x^2 + d)^(3/2)*a^2/(d*x^3)","F",0
218,1,356,0,1.536922," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b^{2} \arcsin\left(c x\right)^{2} - \frac{2}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a b \arcsin\left(c x\right) - \frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a^{2} + \frac{2}{385875} \, b^{2} {\left(\frac{1125 \, \sqrt{-c^{2} x^{2} + 1} c^{4} d^{\frac{3}{2}} x^{6} - 2178 \, \sqrt{-c^{2} x^{2} + 1} c^{2} d^{\frac{3}{2}} x^{4} - 1679 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}} x^{2} + \frac{18692 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}}}{c^{2}}}{c^{2}} + \frac{105 \, {\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} - 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} + 210 \, d^{\frac{3}{2}} x\right)} \arcsin\left(c x\right)}{c^{3}}\right)} + \frac{2 \, {\left(75 \, c^{6} d^{\frac{3}{2}} x^{7} - 168 \, c^{4} d^{\frac{3}{2}} x^{5} + 35 \, c^{2} d^{\frac{3}{2}} x^{3} + 210 \, d^{\frac{3}{2}} x\right)} a b}{3675 \, c^{3}}"," ",0,"-1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*b^2*arcsin(c*x)^2 - 2/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a*b*arcsin(c*x) - 1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a^2 + 2/385875*b^2*((1125*sqrt(-c^2*x^2 + 1)*c^4*d^(3/2)*x^6 - 2178*sqrt(-c^2*x^2 + 1)*c^2*d^(3/2)*x^4 - 1679*sqrt(-c^2*x^2 + 1)*d^(3/2)*x^2 + 18692*sqrt(-c^2*x^2 + 1)*d^(3/2)/c^2)/c^2 + 105*(75*c^6*d^(3/2)*x^7 - 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 + 210*d^(3/2)*x)*arcsin(c*x)/c^3) + 2/3675*(75*c^6*d^(3/2)*x^7 - 168*c^4*d^(3/2)*x^5 + 35*c^2*d^(3/2)*x^3 + 210*d^(3/2)*x)*a*b/c^3","A",0
219,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, a^{2} {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} + \sqrt{d} \int -{\left({\left(b^{2} c^{2} d x^{4} - b^{2} d x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{4} - a b d x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/48*a^2*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3) + sqrt(d)*integrate(-((b^2*c^2*d*x^4 - b^2*d*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^4 - a*b*d*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
220,1,236,0,0.935746," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \arcsin\left(c x\right)^{2}}{5 \, c^{2} d} + \frac{2}{1125} \, b^{2} {\left(\frac{9 \, \sqrt{-c^{2} x^{2} + 1} c^{2} d^{\frac{5}{2}} x^{4} - 38 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}} x^{2} + \frac{149 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}}}{c^{2}}}{d} + \frac{15 \, {\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} - 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} \arcsin\left(c x\right)}{c d}\right)} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \arcsin\left(c x\right)}{5 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a^{2}}{5 \, c^{2} d} + \frac{2 \, {\left(3 \, c^{4} d^{\frac{5}{2}} x^{5} - 10 \, c^{2} d^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} x\right)} a b}{75 \, c d}"," ",0,"-1/5*(-c^2*d*x^2 + d)^(5/2)*b^2*arcsin(c*x)^2/(c^2*d) + 2/1125*b^2*((9*sqrt(-c^2*x^2 + 1)*c^2*d^(5/2)*x^4 - 38*sqrt(-c^2*x^2 + 1)*d^(5/2)*x^2 + 149*sqrt(-c^2*x^2 + 1)*d^(5/2)/c^2)/d + 15*(3*c^4*d^(5/2)*x^5 - 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*arcsin(c*x)/(c*d)) - 2/5*(-c^2*d*x^2 + d)^(5/2)*a*b*arcsin(c*x)/(c^2*d) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a^2/(c^2*d) + 2/75*(3*c^4*d^(5/2)*x^5 - 10*c^2*d^(5/2)*x^3 + 15*d^(5/2)*x)*a*b/(c*d)","A",0
221,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a^{2} + \sqrt{d} \int -{\left({\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a^2 + sqrt(d)*integrate(-((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
222,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{-c^{2} d x^{2} + d} d\right)} a^{2} - \sqrt{d} \int \frac{{\left({\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2) - 3*sqrt(-c^2*d*x^2 + d)*d)*a^2 - sqrt(d)*integrate(((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x, x)","F",0
223,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d x + 3 \, c d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a^{2} - \sqrt{d} \int \frac{{\left({\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{2}}\,{d x}"," ",0,"-1/2*(3*sqrt(-c^2*d*x^2 + d)*c^2*d*x + 3*c*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)/x)*a^2 - sqrt(d)*integrate(((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^2, x)","F",0
224,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a^{2} - \sqrt{d} \int \frac{{\left({\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(-c^2*d*x^2 + d)*c^2*d - (-c^2*d*x^2 + d)^(5/2)/(d*x^2))*a^2 - sqrt(d)*integrate(((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^3, x)","F",0
225,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d x + 3 \, c^{3} d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{x} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a^{2} - \sqrt{d} \int \frac{{\left({\left(b^{2} c^{2} d x^{2} - b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d x^{2} - a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{4}}\,{d x}"," ",0,"1/3*(3*sqrt(-c^2*d*x^2 + d)*c^4*d*x + 3*c^3*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)*c^2/x - (-c^2*d*x^2 + d)^(5/2)/(d*x^3))*a^2 - sqrt(d)*integrate(((b^2*c^2*d*x^2 - b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*x^2 - a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^4, x)","F",0
226,1,401,0,0.682862," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b^{2} \arcsin\left(c x\right)^{2} - \frac{2}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a b \arcsin\left(c x\right) - \frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a^{2} - \frac{2}{250047} \, b^{2} {\left(\frac{343 \, \sqrt{-c^{2} x^{2} + 1} c^{6} d^{\frac{5}{2}} x^{8} - 1147 \, \sqrt{-c^{2} x^{2} + 1} c^{4} d^{\frac{5}{2}} x^{6} + 1005 \, \sqrt{-c^{2} x^{2} + 1} c^{2} d^{\frac{5}{2}} x^{4} + 899 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}} x^{2} - \frac{6140 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}}}{c^{2}}}{c^{2}} + \frac{63 \, {\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} - 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} - 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} \arcsin\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(49 \, c^{8} d^{\frac{5}{2}} x^{9} - 171 \, c^{6} d^{\frac{5}{2}} x^{7} + 189 \, c^{4} d^{\frac{5}{2}} x^{5} - 21 \, c^{2} d^{\frac{5}{2}} x^{3} - 126 \, d^{\frac{5}{2}} x\right)} a b}{3969 \, c^{3}}"," ",0,"-1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*b^2*arcsin(c*x)^2 - 2/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a*b*arcsin(c*x) - 1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a^2 - 2/250047*b^2*((343*sqrt(-c^2*x^2 + 1)*c^6*d^(5/2)*x^8 - 1147*sqrt(-c^2*x^2 + 1)*c^4*d^(5/2)*x^6 + 1005*sqrt(-c^2*x^2 + 1)*c^2*d^(5/2)*x^4 + 899*sqrt(-c^2*x^2 + 1)*d^(5/2)*x^2 - 6140*sqrt(-c^2*x^2 + 1)*d^(5/2)/c^2)/c^2 + 63*(49*c^8*d^(5/2)*x^9 - 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 - 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*arcsin(c*x)/c^3) - 2/3969*(49*c^8*d^(5/2)*x^9 - 171*c^6*d^(5/2)*x^7 + 189*c^4*d^(5/2)*x^5 - 21*c^2*d^(5/2)*x^3 - 126*d^(5/2)*x)*a*b/c^3","A",0
227,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{384} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a^{2} + \sqrt{d} \int {\left({\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/384*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^6 - 2*b^2*c^2*d^2*x^4 + b^2*d^2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
228,1,281,0,0.557897," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b^{2} \arcsin\left(c x\right)^{2}}{7 \, c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a b \arcsin\left(c x\right)}{7 \, c^{2} d} - \frac{2}{25725} \, b^{2} {\left(\frac{75 \, \sqrt{-c^{2} x^{2} + 1} c^{4} d^{\frac{7}{2}} x^{6} - 351 \, \sqrt{-c^{2} x^{2} + 1} c^{2} d^{\frac{7}{2}} x^{4} + 757 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{7}{2}} x^{2} - \frac{2161 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{7}{2}}}{c^{2}}}{d} + \frac{105 \, {\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} - 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} - 35 \, d^{\frac{7}{2}} x\right)} \arcsin\left(c x\right)}{c d}\right)} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2}}{7 \, c^{2} d} - \frac{2 \, {\left(5 \, c^{6} d^{\frac{7}{2}} x^{7} - 21 \, c^{4} d^{\frac{7}{2}} x^{5} + 35 \, c^{2} d^{\frac{7}{2}} x^{3} - 35 \, d^{\frac{7}{2}} x\right)} a b}{245 \, c d}"," ",0,"-1/7*(-c^2*d*x^2 + d)^(7/2)*b^2*arcsin(c*x)^2/(c^2*d) - 2/7*(-c^2*d*x^2 + d)^(7/2)*a*b*arcsin(c*x)/(c^2*d) - 2/25725*b^2*((75*sqrt(-c^2*x^2 + 1)*c^4*d^(7/2)*x^6 - 351*sqrt(-c^2*x^2 + 1)*c^2*d^(7/2)*x^4 + 757*sqrt(-c^2*x^2 + 1)*d^(7/2)*x^2 - 2161*sqrt(-c^2*x^2 + 1)*d^(7/2)/c^2)/d + 105*(5*c^6*d^(7/2)*x^7 - 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 - 35*d^(7/2)*x)*arcsin(c*x)/(c*d)) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a^2/(c^2*d) - 2/245*(5*c^6*d^(7/2)*x^7 - 21*c^4*d^(7/2)*x^5 + 35*c^2*d^(7/2)*x^3 - 35*d^(7/2)*x)*a*b/(c*d)","A",0
229,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a^{2} + \sqrt{d} \int {\left({\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
230,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2}\right)} a^{2} + \sqrt{d} \int \frac{{\left({\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x}\,{d x}"," ",0,"-1/15*(15*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2) - 5*(-c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(-c^2*d*x^2 + d)*d^2)*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x, x)","F",0
231,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} x + 15 \, c d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{x}\right)} a^{2} + \sqrt{d} \int \frac{{\left({\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{2}}\,{d x}"," ",0,"-1/8*(10*(-c^2*d*x^2 + d)^(3/2)*c^2*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2*x + 15*c*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)/x)*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^2, x)","F",0
232,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a^{2} + \sqrt{d} \int \frac{{\left({\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{3}}\,{d x}"," ",0,"1/6*(15*c^2*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^2 - 5*(-c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^2))*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^3, x)","F",0
233,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} x + 15 \, c^{3} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{3}}\right)} a^{2} + \sqrt{d} \int \frac{{\left({\left(b^{2} c^{4} d^{2} x^{4} - 2 \, b^{2} c^{2} d^{2} x^{2} + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{4}}\,{d x}"," ",0,"1/6*(10*(-c^2*d*x^2 + d)^(3/2)*c^4*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2*x + 15*c^3*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^2/x - 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^3))*a^2 + sqrt(d)*integrate(((b^2*c^4*d^2*x^4 - 2*b^2*c^2*d^2*x^2 + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^4*d^2*x^4 - 2*a*b*c^2*d^2*x^2 + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^4, x)","F",0
234,1,365,0,1.469731," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} b^{2} \arcsin\left(c x\right)^{2} - \frac{2}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a b \arcsin\left(c x\right) - \frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a^{2} + \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{-c^{2} x^{2} + 1} c^{2} x^{4} + 136 \, \sqrt{-c^{2} x^{2} + 1} x^{2} + \frac{2072 \, \sqrt{-c^{2} x^{2} + 1}}{c^{2}}}{c^{4} \sqrt{d}} + \frac{15 \, {\left(9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x\right)} \arcsin\left(c x\right)}{c^{5} \sqrt{d}}\right)} + \frac{2 \, {\left(9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x\right)} a b}{225 \, c^{5} \sqrt{d}}"," ",0,"-1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*b^2*arcsin(c*x)^2 - 2/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a*b*arcsin(c*x) - 1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a^2 + 2/3375*b^2*((27*sqrt(-c^2*x^2 + 1)*c^2*x^4 + 136*sqrt(-c^2*x^2 + 1)*x^2 + 2072*sqrt(-c^2*x^2 + 1)/c^2)/(c^4*sqrt(d)) + 15*(9*c^4*x^5 + 20*c^2*x^3 + 120*x)*arcsin(c*x)/(c^5*sqrt(d))) + 2/225*(9*c^4*x^5 + 20*c^2*x^3 + 120*x)*a*b/(c^5*sqrt(d))","A",0
235,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} x^{3}}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4} d} - \frac{3 \, \arcsin\left(c x\right)}{c^{5} \sqrt{d}}\right)} - \sqrt{d} \int \frac{{\left(b^{2} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-1/8*a^2*(2*sqrt(-c^2*d*x^2 + d)*x^3/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*x/(c^4*d) - 3*arcsin(c*x)/(c^5*sqrt(d))) - sqrt(d)*integrate((b^2*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^2 - d), x)","F",0
236,1,251,0,0.556854," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \arcsin\left(c x\right)^{2} - \frac{2}{3} \, a b {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} + \frac{2}{27} \, b^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2} + \frac{20 \, \sqrt{-c^{2} x^{2} + 1}}{c^{2}}}{c^{2} \sqrt{d}} + \frac{3 \, {\left(c^{2} x^{3} + 6 \, x\right)} \arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + \frac{2 \, {\left(c^{2} x^{3} + 6 \, x\right)} a b}{9 \, c^{3} \sqrt{d}}"," ",0,"-1/3*b^2*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arcsin(c*x)^2 - 2/3*a*b*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arcsin(c*x) - 1/3*a^2*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d)) + 2/27*b^2*((sqrt(-c^2*x^2 + 1)*x^2 + 20*sqrt(-c^2*x^2 + 1)/c^2)/(c^2*sqrt(d)) + 3*(c^2*x^3 + 6*x)*arcsin(c*x)/(c^3*sqrt(d))) + 2/9*(c^2*x^3 + 6*x)*a*b/(c^3*sqrt(d))","A",0
237,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} - \sqrt{d} \int \frac{{\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-1/2*a^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) - sqrt(d)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^2 - d), x)","F",0
238,1,130,0,0.602444," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","2 \, b^{2} {\left(\frac{x \arcsin\left(c x\right)}{c \sqrt{d}} + \frac{\sqrt{-c^{2} x^{2} + 1}}{c^{2} \sqrt{d}}\right)} + \frac{2 \, a b x}{c \sqrt{d}} - \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} \arcsin\left(c x\right)^{2}}{c^{2} d} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \arcsin\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a^{2}}{c^{2} d}"," ",0,"2*b^2*(x*arcsin(c*x)/(c*sqrt(d)) + sqrt(-c^2*x^2 + 1)/(c^2*sqrt(d))) + 2*a*b*x/(c*sqrt(d)) - sqrt(-c^2*d*x^2 + d)*b^2*arcsin(c*x)^2/(c^2*d) - 2*sqrt(-c^2*d*x^2 + d)*a*b*arcsin(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a^2/(c^2*d)","A",0
239,1,47,0,0.610462," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \arcsin\left(c x\right)^{3}}{3 \, c \sqrt{d}} + \frac{a b \arcsin\left(c x\right)^{2}}{c \sqrt{d}} + \frac{a^{2} \arcsin\left(c x\right)}{c \sqrt{d}}"," ",0,"1/3*b^2*arcsin(c*x)^3/(c*sqrt(d)) + a*b*arcsin(c*x)^2/(c*sqrt(d)) + a^2*arcsin(c*x)/(c*sqrt(d))","A",0
240,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} - \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{3} - d x}\,{d x}"," ",0,"-a^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) - sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^3 - d*x), x)","F",0
241,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \sqrt{d} \log\left(x^{2} - \frac{1}{c^{2}}\right)\right)} a b c}{d} + \frac{-\frac{\frac{1}{4} \, {\left(7 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 4 \, x \int \frac{9 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 14 \, {\left(c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{2} x^{4} - x^{2}\right)}}\,{d x}\right)} b^{2}}{4 \, x}}{\sqrt{d}} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \arcsin\left(c x\right)}{d x} - \frac{\sqrt{-c^{2} d x^{2} + d} a^{2}}{d x}"," ",0,"-((-1)^(-2*c^2*d*x^2 + 2*d)*sqrt(d)*log(-2*c^2*d + 2*d/x^2) + sqrt(d)*log(x^2 - 1/c^2))*a*b*c/d + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2), x)/sqrt(d) - 2*sqrt(-c^2*d*x^2 + d)*a*b*arcsin(c*x)/(d*x) - sqrt(-c^2*d*x^2 + d)*a^2/(d*x)","F",0
242,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{2}}\right)} a^{2} - \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{5} - d x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) + sqrt(-c^2*d*x^2 + d)/(d*x^2))*a^2 - sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^5 - d*x^3), x)","F",0
243,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{4 \, c^{2} \log\left(x\right)}{\sqrt{d}} - \frac{1}{\sqrt{d} x^{2}}\right)} a b c - \frac{2}{3} \, a b {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} + \frac{-\frac{-\frac{1}{4} \, {\left(4 \, {\left(2 \, c^{4} x^{4} - c^{2} x^{2} - 1\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - {\left(3 \, {\left(2 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 4 \, x^{3} \int \frac{27 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 14 \, {\left(2 \, c^{5} x^{5} - c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{2} x^{6} - x^{4}\right)}}\,{d x}\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\right)} b^{2}}{12 \, \sqrt{c x + 1} \sqrt{-c x + 1} x^{3}}}{\sqrt{d}}"," ",0,"1/3*(4*c^2*log(x)/sqrt(d) - 1/(sqrt(d)*x^2))*a*b*c - 2/3*a*b*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))*arcsin(c*x) - 1/3*a^2*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^4), x)/sqrt(d)","F",0
244,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{x^{4}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \frac{4 \, x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{-c^{2} d x^{2} + d} c^{6} d}\right)} + \frac{{\left(b^{2} c^{4} x^{4} + 4 \, b^{2} c^{2} x^{2} - 8 \, b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{4} x^{4} + 4 \, a b c^{2} x^{2} - 8 \, a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + \frac{1}{6} \, {\left(12 \, a b c^{3} x^{3} + 6 \, a b c x - 4 \, {\left(b^{2} c^{5} x^{5} + 14 \, b^{2} c^{3} x^{3} - 15 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 12 \, {\left(c^{8} d^{2} x^{2} - c^{6} d^{2}\right)} \int \frac{6 \, a b c^{6} x^{6} + 24 \, a b c^{4} x^{4} - 48 \, a b c^{2} x^{2} + 9 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - 9 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right) + 2 \, {\left(b^{2} c^{5} x^{5} + 14 \, b^{2} c^{3} x^{3} - 15 \, b^{2} c x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{6 \, {\left(c^{11} d^{2} x^{6} - 2 \, c^{9} d^{2} x^{4} + c^{7} d^{2} x^{2} + {\left(c^{9} d^{2} x^{4} - 2 \, c^{7} d^{2} x^{2} + c^{5} d^{2}\right)} e^{\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)}\right)}}\,{d x} - 9 \, {\left(5 \, a b c^{2} x^{2} - 5 \, a b + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \log\left(c x + 1\right) + 9 \, {\left(5 \, a b c^{2} x^{2} - 5 \, a b + 2 \, {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \log\left(-c x + 1\right)\right)} \sqrt{d}}{3 \, {\left(c^{8} d^{2} x^{2} - c^{6} d^{2}\right)}}"," ",0,"-1/3*a^2*(x^4/(sqrt(-c^2*d*x^2 + d)*c^2*d) + 4*x^2/(sqrt(-c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(-c^2*d*x^2 + d)*c^6*d)) + 1/3*((b^2*c^4*x^4 + 4*b^2*c^2*x^2 - 8*b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 3*(c^8*d^2*x^2 - c^6*d^2)*integrate(2/3*(3*sqrt(c*x + 1)*sqrt(-c*x + 1)*a*b*c^5*sqrt(d)*x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (b^2*c^6*x^6 + 3*b^2*c^4*x^4 - 12*b^2*c^2*x^2 + 8*b^2)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^9*d^2*x^4 - 2*c^7*d^2*x^2 + c^5*d^2), x))/(c^8*d^2*x^2 - c^6*d^2)","F",0
245,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{x^{3}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{3 \, x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + \sqrt{d} \int \frac{{\left(b^{2} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a^2*(x^3/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 3*x/(sqrt(-c^2*d*x^2 + d)*c^4*d) + 3*arcsin(c*x)/(c^5*d^(3/2))) + sqrt(d)*integrate((b^2*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
246,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a b c {\left(\frac{2 \, x}{c^{4} d^{\frac{3}{2}}} + \frac{\log\left(c x + 1\right)}{c^{5} d^{\frac{3}{2}}} - \frac{\log\left(c x - 1\right)}{c^{5} d^{\frac{3}{2}}}\right)} - 2 \, a b {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} \arcsin\left(c x\right) - a^{2} {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} + \frac{\frac{1}{3} \, {\left(3 \, {\left(c^{2} x^{2} - 2\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - \frac{{\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)} {\left(c^{4} d^{2} \int \frac{2 \, {\left(c^{3} x^{3} - 3 \, c x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + 3 \, e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - 3 \, e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{7} d^{2} x^{4} - c^{5} d^{2} x^{2} - {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + 2 \, {\left(c^{3} x^{3} - 3 \, c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + 3 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(c x + 1\right) - 3 \, \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) \log\left(-c x + 1\right)\right)}}{c^{4} d^{\frac{3}{2}}}\right)} b^{2}}{c^{6} d^{2} x^{2} - c^{4} d^{2}}"," ",0,"-a*b*c*(2*x/(c^4*d^(3/2)) + log(c*x + 1)/(c^5*d^(3/2)) - log(c*x - 1)/(c^5*d^(3/2))) - 2*a*b*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))*arcsin(c*x) - a^2*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d)) + ((c^2*x^2 - 2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 - (c^6*d^2*x^2 - c^4*d^2)*sqrt(d)*integrate(2*(c^2*x^4 - 2*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^3*d^2*x^2 - c*d^2), x))*b^2/(c^6*d^2*x^2 - c^4*d^2)","F",0
247,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + \sqrt{d} \int \frac{{\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}"," ",0,"a^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + sqrt(d)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x)","F",0
248,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\sqrt{d} \int \frac{{\left(b^{2} x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x} + \frac{a^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"sqrt(d)*integrate((b^2*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) + a^2/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
249,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{2 \, a b x \arcsin\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}}{d}}{\sqrt{d}} + \frac{a^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{a b \log\left(x^{2} - \frac{1}{c^{2}}\right)}{c d^{\frac{3}{2}}}"," ",0,"2*a*b*x*arcsin(c*x)/(sqrt(-c^2*d*x^2 + d)*d) - b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d) + a^2*x/(sqrt(-c^2*d*x^2 + d)*d) - a*b*log(x^2 - 1/c^2)/(c*d^(3/2))","F",0
250,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d}\right)} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"-a^2*(log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 1/(sqrt(-c^2*d*x^2 + d)*d)) + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
251,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a b c {\left(\frac{\log\left(c x + 1\right)}{d^{\frac{3}{2}}} + \frac{\log\left(c x - 1\right)}{d^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{d^{\frac{3}{2}}}\right)} + 2 \, {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a b \arcsin\left(c x\right) + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a^{2} - \frac{\frac{\frac{1}{4} \, {\left(7 \, {\left(2 \, c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 4 \, {\left(c^{2} d x^{3} - d x\right)} \int \frac{9 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 14 \, {\left(2 \, c^{5} x^{5} - 3 \, c^{3} x^{3} + c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{4} d x^{6} - 2 \, c^{2} d x^{4} + d x^{2}\right)}}\,{d x}\right)} b^{2}}{4 \, {\left(c^{2} d x^{3} - d x\right)}}}{\sqrt{d}}"," ",0,"a*b*c*(log(c*x + 1)/d^(3/2) + log(c*x - 1)/d^(3/2) + 2*log(x)/d^(3/2)) + 2*(2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a*b*arcsin(c*x) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a^2 - b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*d*x^4 - d*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
252,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{3 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{2}}\right)} a^{2} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*(3*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 3*c^2/(sqrt(-c^2*d*x^2 + d)*d) + 1/(sqrt(-c^2*d*x^2 + d)*d*x^2))*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
253,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{4 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{3}}\right)} a^{2} + \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{8} - 2 \, c^{2} d^{2} x^{6} + d^{2} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(sqrt(-c^2*d*x^2 + d)*d) - 4*c^2/(sqrt(-c^2*d*x^2 + d)*d*x) - 1/(sqrt(-c^2*d*x^2 + d)*d*x^3))*a^2 + sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4), x)","F",0
254,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3 \, x^{4}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{12 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)} - \frac{{\left(3 \, b^{2} c^{4} x^{4} - 12 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(3 \, a b c^{4} x^{4} - 12 \, a b c^{2} x^{2} + 8 \, a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \sqrt{d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + \frac{1}{8} \, {\left(42 \, a b c^{3} x^{3} - 38 \, a b c x - 8 \, {\left(6 \, b^{2} c^{5} x^{5} - 11 \, b^{2} c^{3} x^{3} + 5 \, b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 16 \, {\left(c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)} \int \frac{12 \, a b c^{6} x^{6} - 48 \, a b c^{4} x^{4} + 32 \, a b c^{2} x^{2} + 11 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - 11 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right) + 2 \, {\left(6 \, b^{2} c^{5} x^{5} - 11 \, b^{2} c^{3} x^{3} + 5 \, b^{2} c x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{4 \, {\left(c^{13} d^{3} x^{8} - 3 \, c^{11} d^{3} x^{6} + 3 \, c^{9} d^{3} x^{4} - c^{7} d^{3} x^{2} + {\left(c^{11} d^{3} x^{6} - 3 \, c^{9} d^{3} x^{4} + 3 \, c^{7} d^{3} x^{2} - c^{5} d^{3}\right)} e^{\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)}\right)}}\,{d x} - {\left(45 \, a b c^{4} x^{4} - 90 \, a b c^{2} x^{2} + 45 \, a b + 44 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \log\left(c x + 1\right) + {\left(45 \, a b c^{4} x^{4} - 90 \, a b c^{2} x^{2} + 45 \, a b + 44 \, {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \log\left(-c x + 1\right)\right)} \sqrt{d}}{3 \, {\left(c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)}}"," ",0,"-1/3*a^2*(3*x^4/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 12*x^2/((-c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((-c^2*d*x^2 + d)^(3/2)*c^6*d)) - 1/3*((3*b^2*c^4*x^4 - 12*b^2*c^2*x^2 + 8*b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 3*(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3)*integrate(2/3*(3*sqrt(c*x + 1)*sqrt(-c*x + 1)*a*b*c^5*sqrt(d)*x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (3*b^2*c^6*x^6 - 15*b^2*c^4*x^4 + 20*b^2*c^2*x^2 - 8*b^2)*sqrt(d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(c^11*d^3*x^6 - 3*c^9*d^3*x^4 + 3*c^7*d^3*x^2 - c^5*d^3), x))/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3)","F",0
255,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - \frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d^{2}} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a^{2} - \sqrt{d} \int \frac{{\left(b^{2} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x}"," ",0,"1/3*(x*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - x/(sqrt(-c^2*d*x^2 + d)*c^4*d^2) + 3*arcsin(c*x)/(c^5*d^(5/2)))*a^2 - sqrt(d)*integrate((b^2*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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,-1,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\sqrt{d} \int \frac{{\left(b^{2} x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}}\,{d x} + \frac{a^{2}}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"-sqrt(d)*integrate((b^2*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 1/3*a^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
259,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{5}{2}} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1}}\,{d x}}{d^{2}}}{\sqrt{d}}"," ",0,"1/3*a*b*c*(1/(c^4*d^(5/2)*x^2 - c^2*d^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2))) + 2/3*a*b*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arcsin(c*x) + 1/3*a^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
260,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3 \, \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} - \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}\,{d x}"," ",0,"-1/3*a^2*(3*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 3/(sqrt(-c^2*d*x^2 + d)*d^2) - 1/((-c^2*d*x^2 + d)^(3/2)*d)) - sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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
261,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{8 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} - \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}}\,{d x}"," ",0,"1/3*a^2*(8*c^2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 4*c^2*x/((-c^2*d*x^2 + d)^(3/2)*d) - 3/((-c^2*d*x^2 + d)^(3/2)*d*x)) - sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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
262,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{15 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{15 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{5 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} - \sqrt{d} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}\,{d x}"," ",0,"-1/6*a^2*(15*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 15*c^2/(sqrt(-c^2*d*x^2 + d)*d^2) - 5*c^2/((-c^2*d*x^2 + d)^(3/2)*d) + 3/((-c^2*d*x^2 + d)^(3/2)*d*x^2)) - sqrt(d)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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
263,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{8 \, c^{2} \log\left(c x + 1\right)}{d^{\frac{5}{2}}} + \frac{8 \, c^{2} \log\left(c x - 1\right)}{d^{\frac{5}{2}}} + \frac{16 \, c^{2} \log\left(x\right)}{d^{\frac{5}{2}}} + \frac{1}{c^{2} d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}}\right)} + \frac{2}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a b \arcsin\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a^{2} + \frac{-\frac{\frac{1}{4} \, {\left(7 \, {\left(16 \, c^{6} x^{6} - 24 \, c^{4} x^{4} + 6 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 4 \, {\left(c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}\right)} \int \frac{27 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 14 \, {\left(16 \, c^{9} x^{9} - 40 \, c^{7} x^{7} + 30 \, c^{5} x^{5} - 5 \, c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{6} d^{2} x^{10} - 3 \, c^{4} d^{2} x^{8} + 3 \, c^{2} d^{2} x^{6} - d^{2} x^{4}\right)}}\,{d x}\right)} b^{2}}{12 \, {\left(c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}\right)}}}{\sqrt{d}}"," ",0,"1/3*a*b*c*(8*c^2*log(c*x + 1)/d^(5/2) + 8*c^2*log(c*x - 1)/d^(5/2) + 16*c^2*log(x)/d^(5/2) + 1/(c^2*d^(5/2)*x^4 - d^(5/2)*x^2)) + 2/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a*b*arcsin(c*x) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a^2 + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^4*d^2*x^8 - 2*c^2*d^2*x^6 + d^2*x^4)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/sqrt(d)","F",0
264,0,0,0,0.000000," ","integrate(x^4*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} \arcsin\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^4*arcsin(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
265,1,105,0,0.439138," ","integrate(x^3*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \arcsin\left(a x\right)^{2} + \frac{2 \, {\left(\sqrt{-a^{2} x^{2} + 1} x^{2} + \frac{20 \, \sqrt{-a^{2} x^{2} + 1}}{a^{2}}\right)}}{27 \, a^{2}} + \frac{2 \, {\left(a^{2} x^{3} + 6 \, x\right)} \arcsin\left(a x\right)}{9 \, a^{3}}"," ",0,"-1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arcsin(a*x)^2 + 2/27*(sqrt(-a^2*x^2 + 1)*x^2 + 20*sqrt(-a^2*x^2 + 1)/a^2)/a^2 + 2/9*(a^2*x^3 + 6*x)*arcsin(a*x)/a^3","A",0
266,0,0,0,0.000000," ","integrate(x^2*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arcsin\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsin(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
267,1,49,0,0.784250," ","integrate(x*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{2}}{a^{2}} + \frac{2 \, {\left(a x \arcsin\left(a x\right) + \sqrt{-a^{2} x^{2} + 1}\right)}}{a^{2}}"," ",0,"-sqrt(-a^2*x^2 + 1)*arcsin(a*x)^2/a^2 + 2*(a*x*arcsin(a*x) + sqrt(-a^2*x^2 + 1))/a^2","A",0
268,1,11,0,2.037892," ","integrate(arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{3}}{3 \, a}"," ",0,"1/3*arcsin(a*x)^3/a","A",0
269,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsin(a*x)^2/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
270,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a x + 1} \sqrt{-a x + 1} \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)^{2} - 2 \, a x \int \frac{\arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}{x}\,{d x}}{x}"," ",0,"-(sqrt(a*x + 1)*sqrt(-a*x + 1)*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^2 - 2*a*x*integrate(arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))/x, x))/x","F",0
271,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsin(a*x)^2/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
272,1,14,0,1.280095," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{3}}{3 \, a \sqrt{c}}"," ",0,"1/3*arcsin(a*x)^3/(a*sqrt(c))","A",0
273,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arcsin(a*x)^2/(-a^2*c*x^2 + c)^(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arcsin(a*x)^2/(-a^2*c*x^2 + c)^(5/2), x)","F",0
275,0,0,0,0.000000," ","integrate(arcsin(a*x)^2/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arcsin(a*x)^2/(-a^2*c*x^2 + c)^(7/2), x)","F",0
276,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{a^{2} c^{6} d^{3} x^{m + 7}}{m + 7} + \frac{3 \, a^{2} c^{4} d^{3} x^{m + 5}}{m + 5} - \frac{3 \, a^{2} c^{2} d^{3} x^{m + 3}}{m + 3} + \frac{a^{2} d^{3} x^{m + 1}}{m + 1} - \frac{{\left({\left(b^{2} c^{6} d^{3} m^{3} + 9 \, b^{2} c^{6} d^{3} m^{2} + 23 \, b^{2} c^{6} d^{3} m + 15 \, b^{2} c^{6} d^{3}\right)} x^{7} - 3 \, {\left(b^{2} c^{4} d^{3} m^{3} + 11 \, b^{2} c^{4} d^{3} m^{2} + 31 \, b^{2} c^{4} d^{3} m + 21 \, b^{2} c^{4} d^{3}\right)} x^{5} + 3 \, {\left(b^{2} c^{2} d^{3} m^{3} + 13 \, b^{2} c^{2} d^{3} m^{2} + 47 \, b^{2} c^{2} d^{3} m + 35 \, b^{2} c^{2} d^{3}\right)} x^{3} - {\left(b^{2} d^{3} m^{3} + 15 \, b^{2} d^{3} m^{2} + 71 \, b^{2} d^{3} m + 105 \, b^{2} d^{3}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left({\left(b^{2} c^{7} d^{3} m^{3} + 9 \, b^{2} c^{7} d^{3} m^{2} + 23 \, b^{2} c^{7} d^{3} m + 15 \, b^{2} c^{7} d^{3}\right)} x^{7} - 3 \, {\left(b^{2} c^{5} d^{3} m^{3} + 11 \, b^{2} c^{5} d^{3} m^{2} + 31 \, b^{2} c^{5} d^{3} m + 21 \, b^{2} c^{5} d^{3}\right)} x^{5} + 3 \, {\left(b^{2} c^{3} d^{3} m^{3} + 13 \, b^{2} c^{3} d^{3} m^{2} + 47 \, b^{2} c^{3} d^{3} m + 35 \, b^{2} c^{3} d^{3}\right)} x^{3} - {\left(b^{2} c d^{3} m^{3} + 15 \, b^{2} c d^{3} m^{2} + 71 \, b^{2} c d^{3} m + 105 \, b^{2} c d^{3}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(a b d^{3} m^{4} + {\left(a b c^{8} d^{3} m^{4} + 16 \, a b c^{8} d^{3} m^{3} + 86 \, a b c^{8} d^{3} m^{2} + 176 \, a b c^{8} d^{3} m + 105 \, a b c^{8} d^{3}\right)} x^{8} + 16 \, a b d^{3} m^{3} + 86 \, a b d^{3} m^{2} - 4 \, {\left(a b c^{6} d^{3} m^{4} + 16 \, a b c^{6} d^{3} m^{3} + 86 \, a b c^{6} d^{3} m^{2} + 176 \, a b c^{6} d^{3} m + 105 \, a b c^{6} d^{3}\right)} x^{6} + 176 \, a b d^{3} m + 105 \, a b d^{3} + 6 \, {\left(a b c^{4} d^{3} m^{4} + 16 \, a b c^{4} d^{3} m^{3} + 86 \, a b c^{4} d^{3} m^{2} + 176 \, a b c^{4} d^{3} m + 105 \, a b c^{4} d^{3}\right)} x^{4} - 4 \, {\left(a b c^{2} d^{3} m^{4} + 16 \, a b c^{2} d^{3} m^{3} + 86 \, a b c^{2} d^{3} m^{2} + 176 \, a b c^{2} d^{3} m + 105 \, a b c^{2} d^{3}\right)} x^{2}\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{m^{4} + 16 \, m^{3} - {\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"-a^2*c^6*d^3*x^(m + 7)/(m + 7) + 3*a^2*c^4*d^3*x^(m + 5)/(m + 5) - 3*a^2*c^2*d^3*x^(m + 3)/(m + 3) + a^2*d^3*x^(m + 1)/(m + 1) - (((b^2*c^6*d^3*m^3 + 9*b^2*c^6*d^3*m^2 + 23*b^2*c^6*d^3*m + 15*b^2*c^6*d^3)*x^7 - 3*(b^2*c^4*d^3*m^3 + 11*b^2*c^4*d^3*m^2 + 31*b^2*c^4*d^3*m + 21*b^2*c^4*d^3)*x^5 + 3*(b^2*c^2*d^3*m^3 + 13*b^2*c^2*d^3*m^2 + 47*b^2*c^2*d^3*m + 35*b^2*c^2*d^3)*x^3 - (b^2*d^3*m^3 + 15*b^2*d^3*m^2 + 71*b^2*d^3*m + 105*b^2*d^3)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(-2*(((b^2*c^7*d^3*m^3 + 9*b^2*c^7*d^3*m^2 + 23*b^2*c^7*d^3*m + 15*b^2*c^7*d^3)*x^7 - 3*(b^2*c^5*d^3*m^3 + 11*b^2*c^5*d^3*m^2 + 31*b^2*c^5*d^3*m + 21*b^2*c^5*d^3)*x^5 + 3*(b^2*c^3*d^3*m^3 + 13*b^2*c^3*d^3*m^2 + 47*b^2*c^3*d^3*m + 35*b^2*c^3*d^3)*x^3 - (b^2*c*d^3*m^3 + 15*b^2*c*d^3*m^2 + 71*b^2*c*d^3*m + 105*b^2*c*d^3)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (a*b*d^3*m^4 + (a*b*c^8*d^3*m^4 + 16*a*b*c^8*d^3*m^3 + 86*a*b*c^8*d^3*m^2 + 176*a*b*c^8*d^3*m + 105*a*b*c^8*d^3)*x^8 + 16*a*b*d^3*m^3 + 86*a*b*d^3*m^2 - 4*(a*b*c^6*d^3*m^4 + 16*a*b*c^6*d^3*m^3 + 86*a*b*c^6*d^3*m^2 + 176*a*b*c^6*d^3*m + 105*a*b*c^6*d^3)*x^6 + 176*a*b*d^3*m + 105*a*b*d^3 + 6*(a*b*c^4*d^3*m^4 + 16*a*b*c^4*d^3*m^3 + 86*a*b*c^4*d^3*m^2 + 176*a*b*c^4*d^3*m + 105*a*b*c^4*d^3)*x^4 - 4*(a*b*c^2*d^3*m^4 + 16*a*b*c^2*d^3*m^3 + 86*a*b*c^2*d^3*m^2 + 176*a*b*c^2*d^3*m + 105*a*b*c^2*d^3)*x^2)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(m^4 + 16*m^3 - (c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
277,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{a^{2} c^{4} d^{2} x^{m + 5}}{m + 5} - \frac{2 \, a^{2} c^{2} d^{2} x^{m + 3}}{m + 3} + \frac{a^{2} d^{2} x^{m + 1}}{m + 1} + \frac{{\left({\left(b^{2} c^{4} d^{2} m^{2} + 4 \, b^{2} c^{4} d^{2} m + 3 \, b^{2} c^{4} d^{2}\right)} x^{5} - 2 \, {\left(b^{2} c^{2} d^{2} m^{2} + 6 \, b^{2} c^{2} d^{2} m + 5 \, b^{2} c^{2} d^{2}\right)} x^{3} + {\left(b^{2} d^{2} m^{2} + 8 \, b^{2} d^{2} m + 15 \, b^{2} d^{2}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 2 \, {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left({\left(b^{2} c^{5} d^{2} m^{2} + 4 \, b^{2} c^{5} d^{2} m + 3 \, b^{2} c^{5} d^{2}\right)} x^{5} - 2 \, {\left(b^{2} c^{3} d^{2} m^{2} + 6 \, b^{2} c^{3} d^{2} m + 5 \, b^{2} c^{3} d^{2}\right)} x^{3} + {\left(b^{2} c d^{2} m^{2} + 8 \, b^{2} c d^{2} m + 15 \, b^{2} c d^{2}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(a b d^{2} m^{3} - {\left(a b c^{6} d^{2} m^{3} + 9 \, a b c^{6} d^{2} m^{2} + 23 \, a b c^{6} d^{2} m + 15 \, a b c^{6} d^{2}\right)} x^{6} + 9 \, a b d^{2} m^{2} + 23 \, a b d^{2} m + 3 \, {\left(a b c^{4} d^{2} m^{3} + 9 \, a b c^{4} d^{2} m^{2} + 23 \, a b c^{4} d^{2} m + 15 \, a b c^{4} d^{2}\right)} x^{4} + 15 \, a b d^{2} - 3 \, {\left(a b c^{2} d^{2} m^{3} + 9 \, a b c^{2} d^{2} m^{2} + 23 \, a b c^{2} d^{2} m + 15 \, a b c^{2} d^{2}\right)} x^{2}\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{m^{3} - {\left(c^{2} m^{3} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 15 \, c^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"a^2*c^4*d^2*x^(m + 5)/(m + 5) - 2*a^2*c^2*d^2*x^(m + 3)/(m + 3) + a^2*d^2*x^(m + 1)/(m + 1) + (((b^2*c^4*d^2*m^2 + 4*b^2*c^4*d^2*m + 3*b^2*c^4*d^2)*x^5 - 2*(b^2*c^2*d^2*m^2 + 6*b^2*c^2*d^2*m + 5*b^2*c^2*d^2)*x^3 + (b^2*d^2*m^2 + 8*b^2*d^2*m + 15*b^2*d^2)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + (m^3 + 9*m^2 + 23*m + 15)*integrate(-2*(((b^2*c^5*d^2*m^2 + 4*b^2*c^5*d^2*m + 3*b^2*c^5*d^2)*x^5 - 2*(b^2*c^3*d^2*m^2 + 6*b^2*c^3*d^2*m + 5*b^2*c^3*d^2)*x^3 + (b^2*c*d^2*m^2 + 8*b^2*c*d^2*m + 15*b^2*c*d^2)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) - (a*b*d^2*m^3 - (a*b*c^6*d^2*m^3 + 9*a*b*c^6*d^2*m^2 + 23*a*b*c^6*d^2*m + 15*a*b*c^6*d^2)*x^6 + 9*a*b*d^2*m^2 + 23*a*b*d^2*m + 3*(a*b*c^4*d^2*m^3 + 9*a*b*c^4*d^2*m^2 + 23*a*b*c^4*d^2*m + 15*a*b*c^4*d^2)*x^4 + 15*a*b*d^2 - 3*(a*b*c^2*d^2*m^3 + 9*a*b*c^2*d^2*m^2 + 23*a*b*c^2*d^2*m + 15*a*b*c^2*d^2)*x^2)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(m^3 - (c^2*m^3 + 9*c^2*m^2 + 23*c^2*m + 15*c^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
278,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{a^{2} c^{2} d x^{m + 3}}{m + 3} + \frac{a^{2} d x^{m + 1}}{m + 1} - \frac{{\left({\left(b^{2} c^{2} d m + b^{2} c^{2} d\right)} x^{3} - {\left(b^{2} d m + 3 \, b^{2} d\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(m^{2} + 4 \, m + 3\right)} \int \frac{{\left({\left(b^{2} c^{3} d m + b^{2} c^{3} d\right)} x^{3} - {\left(b^{2} c d m + 3 \, b^{2} c d\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(a b d m^{2} + {\left(a b c^{4} d m^{2} + 4 \, a b c^{4} d m + 3 \, a b c^{4} d\right)} x^{4} + 4 \, a b d m + 3 \, a b d - 2 \, {\left(a b c^{2} d m^{2} + 4 \, a b c^{2} d m + 3 \, a b c^{2} d\right)} x^{2}\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c^{2} m^{2} + 4 \, c^{2} m + 3 \, c^{2}\right)} x^{2} - m^{2} - 4 \, m - 3}\,{d x}}{m^{2} + 4 \, m + 3}"," ",0,"-a^2*c^2*d*x^(m + 3)/(m + 3) + a^2*d*x^(m + 1)/(m + 1) - (((b^2*c^2*d*m + b^2*c^2*d)*x^3 - (b^2*d*m + 3*b^2*d)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + (m^2 + 4*m + 3)*integrate(2*(((b^2*c^3*d*m + b^2*c^3*d)*x^3 - (b^2*c*d*m + 3*b^2*c*d)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (a*b*d*m^2 + (a*b*c^4*d*m^2 + 4*a*b*c^4*d*m + 3*a*b*c^4*d)*x^4 + 4*a*b*d*m + 3*a*b*d - 2*(a*b*c^2*d*m^2 + 4*a*b*c^2*d*m + 3*a*b*c^2*d)*x^2)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/((c^2*m^2 + 4*c^2*m + 3*c^2)*x^2 - m^2 - 4*m - 3), x))/(m^2 + 4*m + 3)","F",0
279,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-integrate((b*arcsin(c*x) + a)^2*x^m/(c^2*d*x^2 - d), x)","F",0
280,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*x^m/(c^2*d*x^2 - d)^2, x)","F",0
281,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{{\left(c^{2} d x^{2} - d\right)}^{3}}\,{d x}"," ",0,"-integrate((b*arcsin(c*x) + a)^2*x^m/(c^2*d*x^2 - d)^3, x)","F",0
282,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^2*x^m, x)","F",0
283,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^2*x^m, x)","F",0
284,0,0,0,0.000000," ","integrate(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^2*x^m, x)","F",0
285,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*x^m/sqrt(-c^2*d*x^2 + d), x)","F",0
286,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*x^m/(-c^2*d*x^2 + d)^(3/2), x)","F",0
287,0,0,0,0.000000," ","integrate(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{2} x^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^2*x^m/(-c^2*d*x^2 + d)^(5/2), x)","F",0
288,0,0,0,0.000000," ","integrate(x^m*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arcsin\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsin(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
289,1,284,0,0.452402," ","integrate((-a^2*c*x^2+c)^3*arcsin(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{1225} \, {\left(75 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{3} x^{6} - 351 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{4} + 757 \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{2} - \frac{2161 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2}}\right)} a \arcsin\left(a x\right)^{2} - \frac{1}{35} \, {\left(5 \, a^{6} c^{3} x^{7} - 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} - 35 \, c^{3} x\right)} \arcsin\left(a x\right)^{3} + \frac{2}{13505625} \, {\left(16875 \, \sqrt{-a^{2} x^{2} + 1} a^{4} c^{3} x^{6} - 134541 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{3} x^{4} + 747937 \, \sqrt{-a^{2} x^{2} + 1} c^{3} x^{2} - \frac{22329151 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2}} + \frac{105 \, {\left(1125 \, a^{6} c^{3} x^{7} - 7371 \, a^{4} c^{3} x^{5} + 26495 \, a^{2} c^{3} x^{3} - 226905 \, c^{3} x\right)} \arcsin\left(a x\right)}{a}\right)} a"," ",0,"-1/1225*(75*sqrt(-a^2*x^2 + 1)*a^4*c^3*x^6 - 351*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^4 + 757*sqrt(-a^2*x^2 + 1)*c^3*x^2 - 2161*sqrt(-a^2*x^2 + 1)*c^3/a^2)*a*arcsin(a*x)^2 - 1/35*(5*a^6*c^3*x^7 - 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 - 35*c^3*x)*arcsin(a*x)^3 + 2/13505625*(16875*sqrt(-a^2*x^2 + 1)*a^4*c^3*x^6 - 134541*sqrt(-a^2*x^2 + 1)*a^2*c^3*x^4 + 747937*sqrt(-a^2*x^2 + 1)*c^3*x^2 - 22329151*sqrt(-a^2*x^2 + 1)*c^3/a^2 + 105*(1125*a^6*c^3*x^7 - 7371*a^4*c^3*x^5 + 26495*a^2*c^3*x^3 - 226905*c^3*x)*arcsin(a*x)/a)*a","A",0
290,1,216,0,0.505855," ","integrate((-a^2*c*x^2+c)^2*arcsin(a*x)^3,x, algorithm=""maxima"")","\frac{1}{75} \, {\left(9 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2} x^{4} - 38 \, \sqrt{-a^{2} x^{2} + 1} c^{2} x^{2} + \frac{149 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2}}\right)} a \arcsin\left(a x\right)^{2} + \frac{1}{15} \, {\left(3 \, a^{4} c^{2} x^{5} - 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \arcsin\left(a x\right)^{3} - \frac{2}{16875} \, {\left(81 \, \sqrt{-a^{2} x^{2} + 1} a^{2} c^{2} x^{4} - 842 \, \sqrt{-a^{2} x^{2} + 1} c^{2} x^{2} + \frac{15 \, {\left(27 \, a^{4} c^{2} x^{5} - 190 \, a^{2} c^{2} x^{3} + 2235 \, c^{2} x\right)} \arcsin\left(a x\right)}{a} + \frac{31841 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2}}\right)} a"," ",0,"1/75*(9*sqrt(-a^2*x^2 + 1)*a^2*c^2*x^4 - 38*sqrt(-a^2*x^2 + 1)*c^2*x^2 + 149*sqrt(-a^2*x^2 + 1)*c^2/a^2)*a*arcsin(a*x)^2 + 1/15*(3*a^4*c^2*x^5 - 10*a^2*c^2*x^3 + 15*c^2*x)*arcsin(a*x)^3 - 2/16875*(81*sqrt(-a^2*x^2 + 1)*a^2*c^2*x^4 - 842*sqrt(-a^2*x^2 + 1)*c^2*x^2 + 15*(27*a^4*c^2*x^5 - 190*a^2*c^2*x^3 + 2235*c^2*x)*arcsin(a*x)/a + 31841*sqrt(-a^2*x^2 + 1)*c^2/a^2)*a","A",0
291,1,128,0,0.487283," ","integrate((-a^2*c*x^2+c)*arcsin(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\sqrt{-a^{2} x^{2} + 1} c x^{2} - \frac{7 \, \sqrt{-a^{2} x^{2} + 1} c}{a^{2}}\right)} a \arcsin\left(a x\right)^{2} - \frac{1}{3} \, {\left(a^{2} c x^{3} - 3 \, c x\right)} \arcsin\left(a x\right)^{3} + \frac{2}{27} \, {\left(\sqrt{-a^{2} x^{2} + 1} c x^{2} + \frac{3 \, {\left(a^{2} c x^{3} - 21 \, c x\right)} \arcsin\left(a x\right)}{a} - \frac{61 \, \sqrt{-a^{2} x^{2} + 1} c}{a^{2}}\right)} a"," ",0,"-1/3*(sqrt(-a^2*x^2 + 1)*c*x^2 - 7*sqrt(-a^2*x^2 + 1)*c/a^2)*a*arcsin(a*x)^2 - 1/3*(a^2*c*x^3 - 3*c*x)*arcsin(a*x)^3 + 2/27*(sqrt(-a^2*x^2 + 1)*c*x^2 + 3*(a^2*c*x^3 - 21*c*x)*arcsin(a*x)/a - 61*sqrt(-a^2*x^2 + 1)*c/a^2)*a","A",0
292,1,36,0,0.618225," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{\log\left(a x + 1\right)}{a c} - \frac{\log\left(a x - 1\right)}{a c}\right)} \arcsin\left(a x\right)^{3}"," ",0,"1/2*(log(a*x + 1)/(a*c) - log(a*x - 1)/(a*c))*arcsin(a*x)^3","A",0
293,1,57,0,0.842711," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{a^{2} c^{2} x^{2} - c^{2}} - \frac{\log\left(a x + 1\right)}{a c^{2}} + \frac{\log\left(a x - 1\right)}{a c^{2}}\right)} \arcsin\left(a x\right)^{3}"," ",0,"-1/4*(2*x/(a^2*c^2*x^2 - c^2) - log(a*x + 1)/(a*c^2) + log(a*x - 1)/(a*c^2))*arcsin(a*x)^3","A",0
294,1,78,0,1.035750," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{2} x^{3} - 5 \, x\right)}}{a^{4} c^{3} x^{4} - 2 \, a^{2} c^{3} x^{2} + c^{3}} - \frac{3 \, \log\left(a x + 1\right)}{a c^{3}} + \frac{3 \, \log\left(a x - 1\right)}{a c^{3}}\right)} \arcsin\left(a x\right)^{3}"," ",0,"-1/16*(2*(3*a^2*x^3 - 5*x)/(a^4*c^3*x^4 - 2*a^2*c^3*x^2 + c^3) - 3*log(a*x + 1)/(a*c^3) + 3*log(a*x - 1)/(a*c^3))*arcsin(a*x)^3","A",0
295,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)*arcsin(a*x)^3,x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \arcsin\left(a x\right)^{3}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)*arcsin(a*x)^3, x)","F",0
296,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^3,x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \arcsin\left(a x\right)^{3}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*arcsin(a*x)^3, x)","F",0
297,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^3,x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \arcsin\left(a x\right)^{3}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*arcsin(a*x)^3, x)","F",0
298,1,14,0,0.483638," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{4}}{4 \, a \sqrt{c}}"," ",0,"1/4*arcsin(a*x)^4/(a*sqrt(c))","A",0
299,1,49,0,1.401211," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{x \arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} c x^{2} + c} c} - \frac{3 \, \arcsin\left(a x\right)^{2} \log\left(x^{2} - \frac{1}{a^{2}}\right)}{2 \, a c^{\frac{3}{2}}}"," ",0,"x*arcsin(a*x)^3/(sqrt(-a^2*c*x^2 + c)*c) - 3/2*arcsin(a*x)^2*log(x^2 - 1/a^2)/(a*c^(3/2))","A",0
300,1,106,0,0.842736," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{a^{4} c^{\frac{5}{2}} x^{2} - a^{2} c^{\frac{5}{2}}} + \frac{2 \, \log\left(a x + 1\right)}{a^{2} c^{\frac{5}{2}}} + \frac{2 \, \log\left(a x - 1\right)}{a^{2} c^{\frac{5}{2}}}\right)} \arcsin\left(a x\right)^{2} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a^{2} c x^{2} + c} c^{2}} + \frac{x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \arcsin\left(a x\right)^{3}"," ",0,"1/2*a*(1/(a^4*c^(5/2)*x^2 - a^2*c^(5/2)) + 2*log(a*x + 1)/(a^2*c^(5/2)) + 2*log(a*x - 1)/(a^2*c^(5/2)))*arcsin(a*x)^2 + 1/3*(2*x/(sqrt(-a^2*c*x^2 + c)*c^2) + x/((-a^2*c*x^2 + c)^(3/2)*c))*arcsin(a*x)^3","A",0
301,0,0,0,0.000000," ","integrate(arcsin(a*x)^3/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arcsin(a*x)^3/(-a^2*c*x^2 + c)^(7/2), x)","F",0
302,0,0,0,0.000000," ","integrate(x^m*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m} \arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^m*arcsin(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
303,0,0,0,0.000000," ","integrate(x^4*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4} \arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^4*arcsin(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
304,1,131,0,0.515533," ","integrate(x^3*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \arcsin\left(a x\right)^{3} + \frac{2}{27} \, a {\left(\frac{3 \, {\left(\sqrt{-a^{2} x^{2} + 1} x^{2} + \frac{20 \, \sqrt{-a^{2} x^{2} + 1}}{a^{2}}\right)} \arcsin\left(a x\right)}{a^{3}} - \frac{a^{2} x^{3} + 60 \, x}{a^{4}}\right)} + \frac{{\left(a^{2} x^{3} + 6 \, x\right)} \arcsin\left(a x\right)^{2}}{3 \, a^{3}}"," ",0,"-1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arcsin(a*x)^3 + 2/27*a*(3*(sqrt(-a^2*x^2 + 1)*x^2 + 20*sqrt(-a^2*x^2 + 1)/a^2)*arcsin(a*x)/a^3 - (a^2*x^3 + 60*x)/a^4) + 1/3*(a^2*x^3 + 6*x)*arcsin(a*x)^2/a^3","A",0
305,0,0,0,0.000000," ","integrate(x^2*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2} \arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(x^2*arcsin(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
306,1,64,0,0.433141," ","integrate(x*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{3 \, x \arcsin\left(a x\right)^{2}}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)^{3}}{a^{2}} - \frac{6 \, {\left(x - \frac{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}{a}\right)}}{a}"," ",0,"3*x*arcsin(a*x)^2/a - sqrt(-a^2*x^2 + 1)*arcsin(a*x)^3/a^2 - 6*(x - sqrt(-a^2*x^2 + 1)*arcsin(a*x)/a)/a","A",0
307,1,11,0,0.419136," ","integrate(arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{4}}{4 \, a}"," ",0,"1/4*arcsin(a*x)^4/a","A",0
308,0,0,0,0.000000," ","integrate(arcsin(a*x)^3/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arcsin(a*x)^3/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
309,0,0,0,0.000000," ","integrate(arcsin(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\frac{3}{8} \, {\left(x^{2} \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)^{2} + 8 \, \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1} a x^{2} \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right) + 3 \, {\left(a^{2} x^{3} - x\right)} \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)^{2}}{4 \, {\left(a^{2} x^{2} - 1\right)}}\,{d x}\right)} a^{3} x - \sqrt{a x + 1} \sqrt{-a x + 1} \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)^{3}}{x}"," ",0,"(3*a^3*x*integrate(x*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^2, x) - sqrt(a*x + 1)*sqrt(-a*x + 1)*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))^3)/x","F",0
310,0,0,0,0.000000," ","integrate(arcsin(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arcsin\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arcsin(a*x)^3/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
311,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^3/arcsin(a*x),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} c x^{2} - c\right)}^{3}}{\arcsin\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)^3/arcsin(a*x), x)","F",0
312,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^2/arcsin(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} - c\right)}^{2}}{\arcsin\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2/arcsin(a*x), x)","F",0
313,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)/arcsin(a*x),x, algorithm=""maxima"")","-\int \frac{a^{2} c x^{2} - c}{\arcsin\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)/arcsin(a*x), x)","F",0
314,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)/arcsin(a*x),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} c x^{2} - c\right)} \arcsin\left(a x\right)}\,{d x}"," ",0,"-integrate(1/((a^2*c*x^2 - c)*arcsin(a*x)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^2/arcsin(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} - c\right)}^{2} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 - c)^2*arcsin(a*x)), x)","F",0
316,0,0,0,0.000000," ","integrate(x^4*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{4}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^4/(b*arcsin(c*x) + a), x)","F",0
317,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^3/(b*arcsin(c*x) + a), x)","F",0
318,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^2/(b*arcsin(c*x) + a), x)","F",0
319,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x/(b*arcsin(c*x) + a), x)","F",0
320,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/(b*arcsin(c*x) + a), x)","F",0
321,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arcsin(c*x) + a)*x), x)","F",0
322,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arcsin(c*x) + a)*x^2), x)","F",0
323,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arcsin(c*x) + a)*x^3), x)","F",0
324,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arcsin(c*x) + a)*x^4), x)","F",0
325,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^3/(b*arcsin(c*x) + a), x)","F",0
326,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^2/(b*arcsin(c*x) + a), x)","F",0
327,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x/(b*arcsin(c*x) + a), x)","F",0
328,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/(b*arcsin(c*x) + a), x)","F",0
329,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arcsin(c*x) + a)*x), x)","F",0
330,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arcsin(c*x) + a)*x^2), x)","F",0
331,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arcsin(c*x) + a)*x^3), x)","F",0
332,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arcsin(c*x) + a)*x^4), x)","F",0
333,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{3}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x^3/(b*arcsin(c*x) + a), x)","F",0
334,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{2}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x^2/(b*arcsin(c*x) + a), x)","F",0
335,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x/(b*arcsin(c*x) + a), x)","F",0
336,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/(b*arcsin(c*x) + a), x)","F",0
337,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arcsin(c*x) + a)*x), x)","F",0
338,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arcsin(c*x) + a)*x^2), x)","F",0
339,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arcsin(c*x) + a)*x^3), x)","F",0
340,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \arcsin\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arcsin(c*x) + a)*x^4), x)","F",0
341,0,0,0,0.000000," ","integrate(x^4/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
342,0,0,0,0.000000," ","integrate(x^3/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
343,0,0,0,0.000000," ","integrate(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
344,0,0,0,0.000000," ","integrate(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
345,0,0,0,0.000000," ","integrate(x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
346,1,9,0,0.428758," ","integrate(1/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\arcsin\left(a x\right)\right)}{a}"," ",0,"log(arcsin(a*x))/a","A",0
347,0,0,0,0.000000," ","integrate(1/x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} x \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*x*arcsin(a*x)), x)","F",0
348,0,0,0,0.000000," ","integrate(1/x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*x^2*arcsin(a*x)), x)","F",0
349,0,0,0,0.000000," ","integrate(x^5/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{5}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^5/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
350,0,0,0,0.000000," ","integrate(x^4/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^4/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
351,0,0,0,0.000000," ","integrate(x^3/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^3/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
352,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
353,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
354,1,16,0,0.412612," ","integrate(1/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(b \arcsin\left(c x\right) + a\right)}{b c}"," ",0,"log(b*arcsin(c*x) + a)/(b*c)","A",0
355,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)*x), x)","F",0
356,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)*x^2), x)","F",0
357,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)), x)","F",0
358,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)), x)","F",0
359,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)), x)","F",0
360,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)*x), x)","F",0
361,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)*x^2), x)","F",0
362,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)), x)","F",0
363,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)), x)","F",0
364,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)), x)","F",0
365,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)*x), x)","F",0
366,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)*x^2), x)","F",0
367,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{m}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x^m/(b*arcsin(c*x) + a), x)","F",0
368,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^m/(b*arcsin(c*x) + a), x)","F",0
369,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^m/(b*arcsin(c*x) + a), x)","F",0
370,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/(sqrt(-c^2*x^2 + 1)*(b*arcsin(c*x) + a)), x)","F",0
371,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/((-c^2*x^2 + 1)^(3/2)*(b*arcsin(c*x) + a)), x)","F",0
372,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/((-c^2*x^2 + 1)^(5/2)*(b*arcsin(c*x) + a)), x)","F",0
373,0,0,0,0.000000," ","integrate(x^m/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{-a^{2} x^{2} + 1} \arcsin\left(a x\right)}\,{d x}"," ",0,"integrate(x^m/(sqrt(-a^2*x^2 + 1)*arcsin(a*x)), x)","F",0
374,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^3/arcsin(a*x)^2,x, algorithm=""maxima"")","-\frac{7 \, a \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right) \int \frac{{\left(a^{5} c^{3} x^{5} - 2 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{\arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}\,{d x} - {\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}"," ",0,"-(a*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))*integrate(7*(a^5*c^3*x^5 - 2*a^3*c^3*x^3 + a*c^3*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)), x) - (a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(-a*x + 1))/(a*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)))","F",0
375,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^2/arcsin(a*x)^2,x, algorithm=""maxima"")","\frac{5 \, a \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right) \int \frac{{\left(a^{3} c^{2} x^{3} - a c^{2} x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{\arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}\,{d x} - {\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}"," ",0,"(a*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))*integrate(5*(a^3*c^2*x^3 - a*c^2*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)), x) - (a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(-a*x + 1))/(a*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)))","F",0
376,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)/arcsin(a*x)^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} c \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right) \int \frac{\sqrt{a x + 1} \sqrt{-a x + 1} x}{\arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}\,{d x} - {\left(a^{2} c x^{2} - c\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{a \arctan\left(a x, \sqrt{a x + 1} \sqrt{-a x + 1}\right)}"," ",0,"-(3*a^2*c*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1))*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)*x/arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)), x) - (a^2*c*x^2 - c)*sqrt(a*x + 1)*sqrt(-a*x + 1))/(a*arctan2(a*x, sqrt(a*x + 1)*sqrt(-a*x + 1)))","F",0
377,-1,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)/arcsin(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^2/arcsin(a*x)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,1,37,0,1.707406," ","integrate(1/(-x^2+1)/arcsin(x)^2-x/(-x^2+1)^(3/2)/arcsin(x),x, algorithm=""maxima"")","\frac{\sqrt{x + 1} \sqrt{-x + 1}}{{\left(x^{2} - 1\right)} \arctan\left(x, \sqrt{x + 1} \sqrt{-x + 1}\right)}"," ",0,"sqrt(x + 1)*sqrt(-x + 1)/((x^2 - 1)*arctan2(x, sqrt(x + 1)*sqrt(-x + 1)))","B",0
380,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{{\left(c^{2} x^{2} - 1\right)} x^{m} - \frac{{\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} {\left(c^{2} m \int \frac{x^{m + 2}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} + 2 \, c^{2} \int \frac{x^{m + 2}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} - m \int \frac{x^{m}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x}\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"((c^2*x^2 - 1)*x^m - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(((c^2*m + 2*c^2)*x^2 - m)*x^m/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
381,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{5} - x^{3} - \frac{{\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} {\left(5 \, c^{2} \int \frac{x^{4}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - 3 \, \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^2*x^5 - x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate((5*c^2*x^4 - 3*x^2)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
382,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{4} - x^{2} - 2 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{2 \, c^{2} x^{3} - x}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}\,{d x}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^2*x^4 - x^2 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(2*(2*c^2*x^3 - x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
383,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{3} - x - \frac{{\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} {\left(3 \, c^{2} \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - \int \frac{1}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^2*x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate((3*c^2*x^2 - 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x) - x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
384,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{2} - \frac{2 \, {\left(b^{2} c^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c^{2}\right)} \int \frac{x}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b} - 1}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^2*x^2 - 2*(b^2*c^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c^2)*integrate(x/(b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b), x) - 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
385,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{2} - \frac{{\left(b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x\right)} {\left(c^{2} \int \frac{x^{2}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} + \int \frac{1}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x^{2}}\,{d x}\right)}}{b c} - 1}{b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x}"," ",0,"(c^2*x^2 - (b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)*integrate((c^2*x^2 + 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2), x) - 1)/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)","F",0
386,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{2} - \frac{2 \, {\left(b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}\right)} \int \frac{1}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x^{3}}\,{d x}}{b c} - 1}{b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}}"," ",0,"(c^2*x^2 - 2*(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)*integrate(1/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3), x) - 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)","F",0
387,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{2} + \frac{{\left(b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}\right)} {\left(c^{2} \int \frac{x^{2}}{b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{4}}\,{d x} - 3 \, \int \frac{1}{b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{4}}\,{d x}\right)}}{b c} - 1}{b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}}"," ",0,"(c^2*x^2 + (b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)*integrate((c^2*x^2 - 3)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4), x) - 1)/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)","F",0
388,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{2} x^{2} + 2 \, {\left(b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}\right)} \int \frac{c^{2} x^{2} - 2}{b^{2} c x^{5} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{5}}\,{d x} - 1}{b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}}"," ",0,"(c^2*x^2 + (b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)*integrate(2*(c^2*x^2 - 2)/(b^2*c*x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^5), x) - 1)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)","F",0
389,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} x^{m} - \frac{{\left(c^{4} m \int \frac{x^{m + 4}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} + 4 \, c^{4} \int \frac{x^{m + 4}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} - 2 \, c^{2} m \int \frac{x^{m + 2}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} - 4 \, c^{2} \int \frac{x^{m + 2}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x} + m \int \frac{x^{m}}{b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x}\,{d x}\right)} {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-((c^4*x^4 - 2*c^2*x^2 + 1)*x^m - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(((c^4*m + 4*c^4)*x^4 - 2*(c^2*m + 2*c^2)*x^2 + m)*x^m/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
390,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{7} - 2 \, c^{2} x^{5} + x^{3} - \frac{{\left(7 \, c^{4} \int \frac{x^{6}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - 10 \, c^{2} \int \frac{x^{4}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} + 3 \, \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)} {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(c^4*x^7 - 2*c^2*x^5 + x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate((7*c^4*x^6 - 10*c^2*x^4 + 3*x^2)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
391,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{6} - 2 \, c^{2} x^{4} + x^{2} - 2 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{3 \, c^{4} x^{5} - 4 \, c^{2} x^{3} + x}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}\,{d x}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(c^4*x^6 - 2*c^2*x^4 + x^2 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(2*(3*c^4*x^5 - 4*c^2*x^3 + x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
392,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{5} - 2 \, c^{2} x^{3} + x - \frac{{\left(5 \, c^{4} \int \frac{x^{4}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - 6 \, c^{2} \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} + \int \frac{1}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)} {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(c^4*x^5 - 2*c^2*x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate((5*c^4*x^4 - 6*c^2*x^2 + 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x) + x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
393,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - 4 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{c^{3} x^{3} - c x}{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b}\,{d x} + 1}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(c^4*x^4 - 2*c^2*x^2 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(4*(c^3*x^3 - c*x)/(b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b), x) + 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
394,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - \frac{{\left(b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x\right)} {\left(3 \, c^{4} \int \frac{x^{4}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} - 2 \, c^{2} \int \frac{x^{2}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} - \int \frac{1}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x}\right)}}{b c} + 1}{b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x}"," ",0,"-(c^4*x^4 - 2*c^2*x^2 - (b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)*integrate((3*c^4*x^4 - 2*c^2*x^2 - 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2), x) + 1)/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)","F",0
395,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - 2 \, {\left(b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}\right)} \int \frac{c^{4} x^{4} - 1}{b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}}\,{d x} + 1}{b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}}"," ",0,"-(c^4*x^4 - 2*c^2*x^2 - (b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)*integrate(2*(c^4*x^4 - 1)/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3), x) + 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)","F",0
396,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - \frac{{\left(b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}\right)} {\left(c^{4} \int \frac{x^{4}}{b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{4}}\,{d x} + 2 \, c^{2} \int \frac{x^{2}}{b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{4}}\,{d x} - 3 \, \int \frac{1}{b x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{4}}\,{d x}\right)}}{b c} + 1}{b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}}"," ",0,"-(c^4*x^4 - 2*c^2*x^2 - (b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)*integrate((c^4*x^4 + 2*c^2*x^2 - 3)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4), x) + 1)/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)","F",0
397,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{4} x^{4} - 2 \, c^{2} x^{2} - 4 \, {\left(b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}\right)} \int \frac{c^{2} x^{2} - 1}{b^{2} c x^{5} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{5}}\,{d x} + 1}{b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}}"," ",0,"-(c^4*x^4 - 2*c^2*x^2 - (b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)*integrate(4*(c^2*x^2 - 1)/(b^2*c*x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^5), x) + 1)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)","F",0
398,-1,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{9} - 3 \, c^{4} x^{7} + 3 \, c^{2} x^{5} - x^{3} - 3 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{3 \, c^{6} x^{8} - 7 \, c^{4} x^{6} + 5 \, c^{2} x^{4} - x^{2}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}\,{d x}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^6*x^9 - 3*c^4*x^7 + 3*c^2*x^5 - x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(3*(3*c^6*x^8 - 7*c^4*x^6 + 5*c^2*x^4 - x^2)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
400,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{8} - 3 \, c^{4} x^{6} + 3 \, c^{2} x^{4} - x^{2} - 2 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{4 \, c^{6} x^{7} - 9 \, c^{4} x^{5} + 6 \, c^{2} x^{3} - x}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}\,{d x}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^6*x^8 - 3*c^4*x^6 + 3*c^2*x^4 - x^2 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(2*(4*c^6*x^7 - 9*c^4*x^5 + 6*c^2*x^3 - x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
401,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{7} - 3 \, c^{4} x^{5} + 3 \, c^{2} x^{3} - x - \frac{{\left(7 \, c^{6} \int \frac{x^{6}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - 15 \, c^{4} \int \frac{x^{4}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} + 9 \, c^{2} \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - \int \frac{1}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)} {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^6*x^7 - 3*c^4*x^5 + 3*c^2*x^3 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate((7*c^6*x^6 - 15*c^4*x^4 + 9*c^2*x^2 - 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x) - x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
402,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 6 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{c^{5} x^{5} - 2 \, c^{3} x^{3} + c x}{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b}\,{d x} - 1}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - (b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(6*(c^5*x^5 - 2*c^3*x^3 + c*x)/(b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b), x) - 1)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
403,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - \frac{{\left(5 \, c^{6} \int \frac{x^{6}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} - 9 \, c^{4} \int \frac{x^{4}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} + 3 \, c^{2} \int \frac{x^{2}}{b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} + \int \frac{1}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x^{2}}\,{d x}\right)} {\left(b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x\right)}}{b c} - 1}{b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x}"," ",0,"(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - (b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)*integrate((5*c^6*x^6 - 9*c^4*x^4 + 3*c^2*x^2 + 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2), x) - 1)/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)","F",0
404,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 2 \, {\left(b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}\right)} \int \frac{2 \, c^{6} x^{6} - 3 \, c^{4} x^{4} + 1}{b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}}\,{d x} - 1}{b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}}"," ",0,"(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - (b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)*integrate(2*(2*c^6*x^6 - 3*c^4*x^4 + 1)/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3), x) - 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)","F",0
405,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 3 \, {\left(b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}\right)} \int \frac{c^{6} x^{6} - c^{4} x^{4} - c^{2} x^{2} + 1}{b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}}\,{d x} - 1}{b^{2} c x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{3}}"," ",0,"(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - (b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)*integrate(3*(c^6*x^6 - c^4*x^4 - c^2*x^2 + 1)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4), x) - 1)/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3)","F",0
406,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 2 \, {\left(b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}\right)} \int \frac{c^{6} x^{6} - 3 \, c^{2} x^{2} + 2}{b^{2} c x^{5} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{5}}\,{d x} - 1}{b^{2} c x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{4}}"," ",0,"(c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - (b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)*integrate(2*(c^6*x^6 - 3*c^2*x^2 + 2)/(b^2*c*x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^5), x) - 1)/(b^2*c*x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^4)","F",0
407,0,0,0,0.000000," ","integrate(x^m/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{-x^{m} + \frac{{\left(b^{2} c m \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c m\right)} \int \frac{x^{m}}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"((b^2*c*m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*m)*integrate(x^m/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x), x) - x^m)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
408,0,0,0,0.000000," ","integrate(x^5/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x^{5} - \frac{5 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{x^{4}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(x^5 - 5*(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(x^4/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
409,0,0,0,0.000000," ","integrate(x^4/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x^{4} - \frac{4 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{x^{3}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(x^4 - 4*(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(x^3/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
410,0,0,0,0.000000," ","integrate(x^3/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x^{3} - \frac{3 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{x^{2}}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(x^3 - 3*(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(x^2/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
411,0,0,0,0.000000," ","integrate(x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{x^{2} - \frac{2 \, {\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{x}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"-(x^2 - 2*(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(x/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
412,0,0,0,0.000000," ","integrate(x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{-x + \frac{{\left(b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c\right)} \int \frac{1}{b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}}{b c}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"((b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)*integrate(1/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c), x) - x)/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
413,1,18,0,0.519791," ","integrate(1/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{{\left(b \arcsin\left(c x\right) + a\right)} b c}"," ",0,"-1/((b*arcsin(c*x) + a)*b*c)","A",0
414,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{{\left(b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x\right)} \int \frac{1}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x^{2}}\,{d x}}{b c} + 1}{b^{2} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x}"," ",0,"-((b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)*integrate(1/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2), x) + 1)/(b^2*c*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x)","F",0
415,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}\right)} \int \frac{1}{{\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)} x^{3}}\,{d x}}{b c} + 1}{b^{2} c x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c x^{2}}"," ",0,"-(2*(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)*integrate(1/(b^2*c*x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^3), x) + 1)/(b^2*c*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c*x^2)","F",0
416,-1,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,0,0,0,0.000000," ","integrate(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{x^{3} - \frac{{\left(a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} {\left(c^{2} \int \frac{x^{4}}{b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a c^{4} x^{4} - 2 \, b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 2 \, a c^{2} x^{2} + b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} - 3 \, \int \frac{x^{2}}{b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a c^{4} x^{4} - 2 \, b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 2 \, a c^{2} x^{2} + b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x}\right)}}{b c}}{a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"(x^3 - (a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate((c^2*x^4 - 3*x^2)/(a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x))/(a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
418,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{x^{2} + \frac{2 \, {\left(a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{x}{{\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}}{b c}}{a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"(x^2 + 2*(a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(x/(a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x))/(a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
419,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{x + \frac{{\left(a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} {\left(c^{2} \int \frac{x^{2}}{b c^{4} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a c^{4} x^{4} - 2 \, b c^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 2 \, a c^{2} x^{2} + b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a}\,{d x} + \int \frac{1}{{\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}\right)}}{b c}}{a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"((a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate((c^2*x^2 + 1)/(a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + x)/(a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
420,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a b c^{4} x^{2} - a b c^{2} + {\left(b^{2} c^{4} x^{2} - b^{2} c^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{x}{{\left(c x + 1\right)}^{2} {\left(c x - 1\right)}^{2} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}}{b} + 1}{a b c^{3} x^{2} - a b c + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"(2*(a*b*c^4*x^2 - a*b*c^2 + (b^2*c^4*x^2 - b^2*c^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(x/(a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + 1)/(a*b*c^3*x^2 - a*b*c + (b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
421,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(a b c^{3} x^{3} - a b c x + {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} {\left(3 \, c^{2} \int \frac{x^{2}}{b c^{4} x^{6} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a c^{4} x^{6} - 2 \, b c^{2} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 2 \, a c^{2} x^{4} + b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x} - \int \frac{1}{b c^{4} x^{6} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a c^{4} x^{6} - 2 \, b c^{2} x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - 2 \, a c^{2} x^{4} + b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a x^{2}}\,{d x}\right)}}{b c} + 1}{a b c^{3} x^{3} - a b c x + {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"((a*b*c^3*x^3 - a*b*c*x + (b^2*c^3*x^3 - b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate((3*c^2*x^2 - 1)/(a*b*c^5*x^6 - 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 - 2*b^2*c^3*x^4 + b^2*c*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + 1)/(a*b*c^3*x^3 - a*b*c*x + (b^2*c^3*x^3 - b^2*c*x)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
422,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(a b c^{3} x^{4} - a b c x^{2} + {\left(b^{2} c^{3} x^{4} - b^{2} c x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{2 \, c^{2} x^{2} - 1}{a b c^{5} x^{7} - 2 \, a b c^{3} x^{5} + a b c x^{3} + {\left(b^{2} c^{5} x^{7} - 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}\,{d x} + 1}{a b c^{3} x^{4} - a b c x^{2} + {\left(b^{2} c^{3} x^{4} - b^{2} c x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"((a*b*c^3*x^4 - a*b*c*x^2 + (b^2*c^3*x^4 - b^2*c*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(2*(2*c^2*x^2 - 1)/(a*b*c^5*x^7 - 2*a*b*c^3*x^5 + a*b*c*x^3 + (b^2*c^5*x^7 - 2*b^2*c^3*x^5 + b^2*c*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + 1)/(a*b*c^3*x^4 - a*b*c*x^2 + (b^2*c^3*x^4 - b^2*c*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
423,-1,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{x^{2} + 2 \, {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{c^{2} x^{3} + x}{a b c^{7} x^{6} - 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} - a b c + {\left(b^{2} c^{7} x^{6} - 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} - b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}\,{d x}}{a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"-(x^2 + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(2*(c^2*x^3 + x)/(a*b*c^7*x^6 - 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 - a*b*c + (b^2*c^7*x^6 - 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 - b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x))/(a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
426,-1,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(a b c^{6} x^{4} - 2 \, a b c^{4} x^{2} + a b c^{2} + {\left(b^{2} c^{6} x^{4} - 2 \, b^{2} c^{4} x^{2} + b^{2} c^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{x}{{\left(c x + 1\right)}^{3} {\left(c x - 1\right)}^{3} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}}{b} + 1}{a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"-(4*(a*b*c^6*x^4 - 2*a*b*c^4*x^2 + a*b*c^2 + (b^2*c^6*x^4 - 2*b^2*c^4*x^2 + b^2*c^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(x/(a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + 1)/(a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
428,-1,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(a b c^{5} x^{6} - 2 \, a b c^{3} x^{4} + a b c x^{2} + {\left(b^{2} c^{5} x^{6} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \int \frac{3 \, c^{2} x^{2} - 1}{a b c^{7} x^{9} - 3 \, a b c^{5} x^{7} + 3 \, a b c^{3} x^{5} - a b c x^{3} + {\left(b^{2} c^{7} x^{9} - 3 \, b^{2} c^{5} x^{7} + 3 \, b^{2} c^{3} x^{5} - b^{2} c x^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}\,{d x} + 1}{a b c^{5} x^{6} - 2 \, a b c^{3} x^{4} + a b c x^{2} + {\left(b^{2} c^{5} x^{6} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}"," ",0,"-((a*b*c^5*x^6 - 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 - 2*b^2*c^3*x^4 + b^2*c*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*integrate(2*(3*c^2*x^2 - 1)/(a*b*c^7*x^9 - 3*a*b*c^5*x^7 + 3*a*b*c^3*x^5 - a*b*c*x^3 + (b^2*c^7*x^9 - 3*b^2*c^5*x^7 + 3*b^2*c^3*x^5 - b^2*c*x^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) + 1)/(a*b*c^5*x^6 - 2*a*b*c^3*x^4 + a*b*c*x^2 + (b^2*c^5*x^6 - 2*b^2*c^3*x^4 + b^2*c*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))","F",0
430,1,11,0,0.428315," ","integrate(1/arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2 \, a \arcsin\left(a x\right)^{2}}"," ",0,"-1/2/(a*arcsin(a*x)^2)","A",0
431,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x^{3}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x^3/(b*arcsin(c*x) + a)^(3/2), x)","F",0
432,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x^{2}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x^2/(b*arcsin(c*x) + a)^(3/2), x)","F",0
433,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x/(b*arcsin(c*x) + a)^(3/2), x)","F",0
434,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{c^{2} d x^{2} - d}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)/(b*arcsin(c*x) + a)^(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/x/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{c^{2} d x^{2} - d}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)/((b*arcsin(c*x) + a)^(3/2)*x), x)","F",0
436,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x^{3}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x^3/(b*arcsin(c*x) + a)^(3/2), x)","F",0
437,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x^{2}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x^2/(b*arcsin(c*x) + a)^(3/2), x)","F",0
438,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x/(b*arcsin(c*x) + a)^(3/2), x)","F",0
439,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2/(b*arcsin(c*x) + a)^(3/2), x)","F",0
440,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/x/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2}}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2/((b*arcsin(c*x) + a)^(3/2)*x), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
455,-2,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arcsin(x/a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
456,-2,0,0,0.000000," ","integrate((a^2-x^2)^(1/2)*arcsin(x/a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
457,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
458,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
459,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(1/2)/(a^2-x^2)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
460,-2,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arcsin(x/a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
461,-2,0,0,0.000000," ","integrate((a^2-x^2)^(1/2)*arcsin(x/a)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
462,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
463,-2,0,0,0.000000," ","integrate(arcsin(x/a)^(3/2)/(a^2-x^2)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
464,-2,0,0,0.000000," ","integrate(x/(-x^2+1)^(1/2)/arcsin(x)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
474,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
475,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
479,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
480,-2,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
482,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n*x^2, x)","F",0
483,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n*x, x)","F",0
484,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n, x)","F",0
485,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x, x)","F",0
486,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
487,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n*x^2, x)","F",0
488,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n*x, x)","F",0
489,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n, x)","F",0
490,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n/x, x)","F",0
491,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
492,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^n*x^2, x)","F",0
493,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^n*x, x)","F",0
494,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^n, x)","F",0
495,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^n/x, x)","F",0
496,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)^n/x^2, x)","F",0
497,-2,0,0,0.000000," ","integrate(x^m*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
498,-2,0,0,0.000000," ","integrate(x^3*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
499,-2,0,0,0.000000," ","integrate(x^2*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
500,-2,0,0,0.000000," ","integrate(x*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
501,1,17,0,0.451685," ","integrate(arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\arcsin\left(a x\right)^{n + 1}}{a {\left(n + 1\right)}}"," ",0,"arcsin(a*x)^(n + 1)/(a*(n + 1))","A",0
502,-2,0,0,0.000000," ","integrate(arcsin(a*x)^n/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
503,-2,0,0,0.000000," ","integrate(arcsin(a*x)^n/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
504,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int {\left(c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{24} \, {\left(15 \, \sqrt{-c^{2} d f x^{2} + d f} d^{2} x + \frac{15 \, d^{3} f \arcsin\left(c x\right)}{\sqrt{d f} c} - \frac{6 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d x}{f} - \frac{16 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d}{c f}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c^2*d^2*x^2 + 2*c*d^2*x + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/24*(15*sqrt(-c^2*d*f*x^2 + d*f)*d^2*x + 15*d^3*f*arcsin(c*x)/(sqrt(d*f)*c) - 6*(-c^2*d*f*x^2 + d*f)^(3/2)*d*x/f - 16*(-c^2*d*f*x^2 + d*f)^(3/2)*d/(c*f))*a","F",0
505,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int {\left(c d x + d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{6} \, {\left(3 \, \sqrt{-c^{2} d f x^{2} + d f} d x + \frac{3 \, d^{2} f \arcsin\left(c x\right)}{\sqrt{d f} c} - \frac{2 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c f}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c*d*x + d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/6*(3*sqrt(-c^2*d*f*x^2 + d*f)*d*x + 3*d^2*f*arcsin(c*x)/(sqrt(d*f)*c) - 2*(-c^2*d*f*x^2 + d*f)^(3/2)/(c*f))*a","F",0
506,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{2} \, {\left(\sqrt{-c^{2} d f x^{2} + d f} x + \frac{d f \arcsin\left(c x\right)}{\sqrt{d f} c}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/2*(sqrt(-c^2*d*f*x^2 + d*f)*x + d*f*arcsin(c*x)/(sqrt(d*f)*c))*a","F",0
507,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","a {\left(\frac{f \arcsin\left(c x\right)}{c d \sqrt{\frac{f}{d}}} + \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c d}\right)} + \frac{-\frac{1}{2} \, b \sqrt{f} {\left(2 \, x - \frac{2 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{c} - \frac{2}{c}\right)}}{\sqrt{d}}"," ",0,"a*(f*arcsin(c*x)/(c*d*sqrt(f/d)) + sqrt(-c^2*d*f*x^2 + d*f)/(c*d)) + b*sqrt(f)*integrate(sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(c*x + 1), x)/sqrt(d)","F",0
508,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d^{2} x + c d^{2}} + \frac{f \arcsin\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)} + \frac{\frac{b \sqrt{f} \int \frac{\sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{3}{2}}}\,{d x}}{d}}{\sqrt{d}}"," ",0,"-a*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d^2*x + c*d^2) + f*arcsin(c*x)/(c*d^2*sqrt(f/d))) + b*sqrt(f)*integrate(sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c*d*x + d)*sqrt(c*x + 1)), x)/sqrt(d)","F",0
509,1,215,0,0.487229," ","integrate((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b c {\left(\frac{2 \, \sqrt{f}}{c^{3} d^{\frac{5}{2}} x + c^{2} d^{\frac{5}{2}}} + \frac{\sqrt{f} \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d^{3} x + c d^{3}}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d^{3} x + c d^{3}}\right)}"," ",0,"-1/3*b*c*(2*sqrt(f)/(c^3*d^(5/2)*x + c^2*d^(5/2)) + sqrt(f)*log(c*x + 1)/(c^2*d^(5/2))) - 1/3*b*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d^3*x + c*d^3))*arcsin(c*x) - 1/3*a*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d^3*x + c*d^3))","A",0
510,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int -{\left(c^{3} d^{2} f x^{3} + c^{2} d^{2} f x^{2} - c d^{2} f x - d^{2} f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{40} \, {\left(15 \, \sqrt{-c^{2} d f x^{2} + d f} d^{2} f x + \frac{15 \, d^{3} f^{2} \arcsin\left(c x\right)}{\sqrt{d f} c} + 10 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d x - \frac{8 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{5}{2}}}{c f}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate(-(c^3*d^2*f*x^3 + c^2*d^2*f*x^2 - c*d^2*f*x - d^2*f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/40*(15*sqrt(-c^2*d*f*x^2 + d*f)*d^2*f*x + 15*d^3*f^2*arcsin(c*x)/(sqrt(d*f)*c) + 10*(-c^2*d*f*x^2 + d*f)^(3/2)*d*x - 8*(-c^2*d*f*x^2 + d*f)^(5/2)/(c*f))*a","F",0
511,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int -{\left(c^{2} d f x^{2} - d f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{8} \, {\left(3 \, \sqrt{-c^{2} d f x^{2} + d f} d f x + \frac{3 \, d^{2} f^{2} \arcsin\left(c x\right)}{\sqrt{d f} c} + 2 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} x\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate(-(c^2*d*f*x^2 - d*f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/8*(3*sqrt(-c^2*d*f*x^2 + d*f)*d*f*x + 3*d^2*f^2*arcsin(c*x)/(sqrt(d*f)*c) + 2*(-c^2*d*f*x^2 + d*f)^(3/2)*x)*a","F",0
512,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int -{\left(c f x - f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{6} \, {\left(3 \, \sqrt{-c^{2} d f x^{2} + d f} f x + \frac{3 \, d f^{2} \arcsin\left(c x\right)}{\sqrt{d f} c} + \frac{2 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c d}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate(-(c*f*x - f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/6*(3*sqrt(-c^2*d*f*x^2 + d*f)*f*x + 3*d*f^2*arcsin(c*x)/(sqrt(d*f)*c) + 2*(-c^2*d*f*x^2 + d*f)^(3/2)/(c*d))*a","F",0
513,0,0,0,0.000000," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f} f x}{d} - \frac{3 \, f^{2} \arcsin\left(c x\right)}{\sqrt{d f} c} - \frac{4 \, \sqrt{-c^{2} d f x^{2} + d f} f}{c d}\right)} a - \frac{-\frac{1}{4} \, {\left(\frac{2 \, \sqrt{c x + 1} {\left(-c x + 1\right)}^{\frac{3}{2}} f \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{{\left(c x - 1\right)}^{2} f}{c} - 6 \, f x - \frac{12 \, f \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{-c x + 1}\right)^{2}}{c} + \frac{6 \, \sqrt{c x + 1} \sqrt{-c x + 1} f \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{12 \, f \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{-c x + 1}\right) \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{6 \, f}{c}\right)} b \sqrt{f}}{\sqrt{d}}"," ",0,"-1/2*(sqrt(-c^2*d*f*x^2 + d*f)*f*x/d - 3*f^2*arcsin(c*x)/(sqrt(d*f)*c) - 4*sqrt(-c^2*d*f*x^2 + d*f)*f/(c*d))*a - b*sqrt(f)*integrate((c*f*x - f)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(c*x + 1), x)/sqrt(d)","F",0
514,0,0,0,0.000000," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","-b \sqrt{d} \sqrt{f} \int \frac{{\left(c f x - f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}\,{d x} + a {\left(\frac{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{6 \, \sqrt{-c^{2} d f x^{2} + d f} f}{c^{2} d^{2} x + c d^{2}} - \frac{3 \, f^{2} \arcsin\left(c x\right)}{c d^{2} \sqrt{\frac{f}{d}}}\right)}"," ",0,"-b*sqrt(d)*sqrt(f)*integrate((c*f*x - f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x) + a*((-c^2*d*f*x^2 + d*f)^(3/2)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - 6*sqrt(-c^2*d*f*x^2 + d*f)*f/(c^2*d^2*x + c*d^2) - 3*f^2*arcsin(c*x)/(c*d^2*sqrt(f/d)))","F",0
515,0,0,0,0.000000," ","integrate((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","-b \sqrt{d} \sqrt{f} \int \frac{{\left(c f x - f\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}\,{d x} - \frac{1}{3} \, a {\left(\frac{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{4} d^{4} x^{3} + 3 \, c^{3} d^{4} x^{2} + 3 \, c^{2} d^{4} x + c d^{4}} + \frac{2 \, \sqrt{-c^{2} d f x^{2} + d f} f}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{7 \, \sqrt{-c^{2} d f x^{2} + d f} f}{c^{2} d^{3} x + c d^{3}} - \frac{3 \, f^{2} \arcsin\left(c x\right)}{c d^{3} \sqrt{\frac{f}{d}}}\right)}"," ",0,"-b*sqrt(d)*sqrt(f)*integrate((c*f*x - f)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x) - 1/3*a*((-c^2*d*f*x^2 + d*f)^(3/2)/(c^4*d^4*x^3 + 3*c^3*d^4*x^2 + 3*c^2*d^4*x + c*d^4) + 2*sqrt(-c^2*d*f*x^2 + d*f)*f/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - 7*sqrt(-c^2*d*f*x^2 + d*f)*f/(c^2*d^3*x + c*d^3) - 3*f^2*arcsin(c*x)/(c*d^3*sqrt(f/d)))","F",0
516,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int {\left(c^{4} d^{2} f^{2} x^{4} - 2 \, c^{2} d^{2} f^{2} x^{2} + d^{2} f^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{48} \, {\left(15 \, \sqrt{-c^{2} d f x^{2} + d f} d^{2} f^{2} x + \frac{15 \, d^{3} f^{3} \arcsin\left(c x\right)}{\sqrt{d f} c} + 10 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f x + 8 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{5}{2}} x\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c^4*d^2*f^2*x^4 - 2*c^2*d^2*f^2*x^2 + d^2*f^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/48*(15*sqrt(-c^2*d*f*x^2 + d*f)*d^2*f^2*x + 15*d^3*f^3*arcsin(c*x)/(sqrt(d*f)*c) + 10*(-c^2*d*f*x^2 + d*f)^(3/2)*d*f*x + 8*(-c^2*d*f*x^2 + d*f)^(5/2)*x)*a","F",0
517,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int {\left(c^{3} d f^{2} x^{3} - c^{2} d f^{2} x^{2} - c d f^{2} x + d f^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{40} \, {\left(15 \, \sqrt{-c^{2} d f x^{2} + d f} d f^{2} x + \frac{15 \, d^{2} f^{3} \arcsin\left(c x\right)}{\sqrt{d f} c} + 10 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} f x + \frac{8 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{5}{2}}}{c d}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c^3*d*f^2*x^3 - c^2*d*f^2*x^2 - c*d*f^2*x + d*f^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/40*(15*sqrt(-c^2*d*f*x^2 + d*f)*d*f^2*x + 15*d^2*f^3*arcsin(c*x)/(sqrt(d*f)*c) + 10*(-c^2*d*f*x^2 + d*f)^(3/2)*f*x + 8*(-c^2*d*f*x^2 + d*f)^(5/2)/(c*d))*a","F",0
518,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int {\left(c^{2} f^{2} x^{2} - 2 \, c f^{2} x + f^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x} + \frac{1}{24} \, {\left(15 \, \sqrt{-c^{2} d f x^{2} + d f} f^{2} x + \frac{15 \, d f^{3} \arcsin\left(c x\right)}{\sqrt{d f} c} - \frac{6 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} f x}{d} + \frac{16 \, {\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} f}{c d}\right)} a"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c^2*f^2*x^2 - 2*c*f^2*x + f^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1/24*(15*sqrt(-c^2*d*f*x^2 + d*f)*f^2*x + 15*d*f^3*arcsin(c*x)/(sqrt(d*f)*c) - 6*(-c^2*d*f*x^2 + d*f)^(3/2)*f*x/d + 16*(-c^2*d*f*x^2 + d*f)^(3/2)*f/(c*d))*a","F",0
519,0,0,0,0.000000," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f} c f^{2} x^{2}}{d} - \frac{9 \, \sqrt{-c^{2} d f x^{2} + d f} f^{2} x}{d} + \frac{15 \, f^{3} \arcsin\left(c x\right)}{\sqrt{d f} c} + \frac{22 \, \sqrt{-c^{2} d f x^{2} + d f} f^{2}}{c d}\right)} a + \frac{\frac{1}{36} \, {\left(\frac{12 \, \sqrt{c x + 1} {\left(-c x + 1\right)}^{\frac{5}{2}} f^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{4 \, {\left(c x - 1\right)}^{3} f^{2}}{c} + \frac{30 \, \sqrt{c x + 1} {\left(-c x + 1\right)}^{\frac{3}{2}} f^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{15 \, {\left(c x - 1\right)}^{2} f^{2}}{c} - 90 \, f^{2} x - \frac{180 \, f^{2} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{-c x + 1}\right)^{2}}{c} + \frac{90 \, \sqrt{c x + 1} \sqrt{-c x + 1} f^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{180 \, f^{2} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{-c x + 1}\right) \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{90 \, f^{2}}{c}\right)} b \sqrt{f}}{\sqrt{d}}"," ",0,"1/6*(2*sqrt(-c^2*d*f*x^2 + d*f)*c*f^2*x^2/d - 9*sqrt(-c^2*d*f*x^2 + d*f)*f^2*x/d + 15*f^3*arcsin(c*x)/(sqrt(d*f)*c) + 22*sqrt(-c^2*d*f*x^2 + d*f)*f^2/(c*d))*a + b*sqrt(f)*integrate((c^2*f^2*x^2 - 2*c*f^2*x + f^2)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(c*x + 1), x)/sqrt(d)","F",0
520,0,0,0,0.000000," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} f^{3} x^{3}}{\sqrt{-c^{2} d f x^{2} + d f} d} - \frac{8 \, c f^{3} x^{2}}{\sqrt{-c^{2} d f x^{2} + d f} d} - \frac{17 \, f^{3} x}{\sqrt{-c^{2} d f x^{2} + d f} d} + \frac{15 \, f^{3} \arcsin\left(c x\right)}{\sqrt{d f} c d} + \frac{24 \, f^{3}}{\sqrt{-c^{2} d f x^{2} + d f} c d}\right)} a + \frac{\frac{{\left(c^{2} \int \frac{\sqrt{-c x + 1} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} c x + \sqrt{c x + 1}}\,{d x} - 2 \, c \int \frac{\sqrt{-c x + 1} x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{c x + 1} c x + \sqrt{c x + 1}}\,{d x} + \int \frac{\sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x + 1\right)}^{\frac{3}{2}}}\,{d x}\right)} b f^{\frac{5}{2}}}{d}}{\sqrt{d}}"," ",0,"-1/2*(c^2*f^3*x^3/(sqrt(-c^2*d*f*x^2 + d*f)*d) - 8*c*f^3*x^2/(sqrt(-c^2*d*f*x^2 + d*f)*d) - 17*f^3*x/(sqrt(-c^2*d*f*x^2 + d*f)*d) + 15*f^3*arcsin(c*x)/(sqrt(d*f)*c*d) + 24*f^3/(sqrt(-c^2*d*f*x^2 + d*f)*c*d))*a + b*sqrt(f)*integrate((c^2*f^2*x^2 - 2*c*f^2*x + f^2)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c*d*x + d)*sqrt(c*x + 1)), x)/sqrt(d)","F",0
521,-1,0,0,0.000000," ","integrate((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f} c d^{2} x^{2}}{f} + \frac{9 \, \sqrt{-c^{2} d f x^{2} + d f} d^{2} x}{f} - \frac{15 \, d^{3} \arcsin\left(c x\right)}{\sqrt{d f} c} + \frac{22 \, \sqrt{-c^{2} d f x^{2} + d f} d^{2}}{c f}\right)} a + \frac{-\frac{1}{36} \, {\left(\frac{12 \, {\left(c x + 1\right)}^{\frac{5}{2}} \sqrt{-c x + 1} d^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{4 \, {\left(c x + 1\right)}^{3} d^{2}}{c} + \frac{30 \, {\left(c x + 1\right)}^{\frac{3}{2}} \sqrt{-c x + 1} d^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{15 \, {\left(c x + 1\right)}^{2} d^{2}}{c} - 90 \, d^{2} x + \frac{180 \, d^{2} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{c x + 1}\right)^{2}}{c} + \frac{90 \, \sqrt{c x + 1} \sqrt{-c x + 1} d^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{180 \, d^{2} \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{c x + 1}\right) \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} - \frac{90 \, d^{2}}{c}\right)} b \sqrt{d}}{\sqrt{f}}"," ",0,"-1/6*(2*sqrt(-c^2*d*f*x^2 + d*f)*c*d^2*x^2/f + 9*sqrt(-c^2*d*f*x^2 + d*f)*d^2*x/f - 15*d^3*arcsin(c*x)/(sqrt(d*f)*c) + 22*sqrt(-c^2*d*f*x^2 + d*f)*d^2/(c*f))*a + b*sqrt(d)*integrate((c^2*d^2*x^2 + 2*c*d^2*x + d^2)*sqrt(c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(-c*x + 1), x)/sqrt(f)","F",0
523,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f} d x}{f} - \frac{3 \, d^{2} \arcsin\left(c x\right)}{\sqrt{d f} c} + \frac{4 \, \sqrt{-c^{2} d f x^{2} + d f} d}{c f}\right)} a - \frac{b d^{\frac{3}{2}} {\left(\int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} c x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c x - 1}\,{d x} + \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c x - 1}\,{d x}\right)}}{\sqrt{f}}"," ",0,"-1/2*(sqrt(-c^2*d*f*x^2 + d*f)*d*x/f - 3*d^2*arcsin(c*x)/(sqrt(d*f)*c) + 4*sqrt(-c^2*d*f*x^2 + d*f)*d/(c*f))*a - b*sqrt(d)*integrate((c*d*x + d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c*x - 1), x)/sqrt(f)","F",0
524,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","a {\left(\frac{d \arcsin\left(c x\right)}{c f \sqrt{\frac{d}{f}}} - \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c f}\right)} + \frac{b \sqrt{d} {\left(x - \frac{2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{c x + 1}\right)^{2}}{c} - \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{2 \, \arcsin\left(\frac{1}{2} \, \sqrt{2} \sqrt{c x + 1}\right) \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c} + \frac{1}{c}\right)}}{\sqrt{f}}"," ",0,"a*(d*arcsin(c*x)/(c*f*sqrt(d/f)) - sqrt(-c^2*d*f*x^2 + d*f)/(c*f)) + b*sqrt(d)*integrate(sqrt(c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(-c*x + 1), x)/sqrt(f)","F",0
525,1,32,0,0.467134," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","\frac{b \arcsin\left(c x\right)^{2}}{2 \, \sqrt{d f} c} + \frac{a \arcsin\left(c x\right)}{\sqrt{d f} c}"," ",0,"1/2*b*arcsin(c*x)^2/(sqrt(d*f)*c) + a*arcsin(c*x)/(sqrt(d*f)*c)","A",0
526,1,96,0,0.482391," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-c^{2} d f x^{2} + d f} b \arcsin\left(c x\right)}{c^{2} d^{2} f x + c d^{2} f} - \frac{\sqrt{-c^{2} d f x^{2} + d f} a}{c^{2} d^{2} f x + c d^{2} f} + \frac{b \log\left(c x + 1\right)}{c d^{\frac{3}{2}} \sqrt{f}}"," ",0,"-sqrt(-c^2*d*f*x^2 + d*f)*b*arcsin(c*x)/(c^2*d^2*f*x + c*d^2*f) - sqrt(-c^2*d*f*x^2 + d*f)*a/(c^2*d^2*f*x + c*d^2*f) + b*log(c*x + 1)/(c*d^(3/2)*sqrt(f))","A",0
527,1,223,0,0.489865," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b c {\left(\frac{1}{c^{3} d^{\frac{5}{2}} \sqrt{f} x + c^{2} d^{\frac{5}{2}} \sqrt{f}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} \sqrt{f}}\right)} - \frac{1}{3} \, b {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d^{3} f x^{2} + 2 \, c^{2} d^{3} f x + c d^{3} f} + \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d^{3} f x + c d^{3} f}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d^{3} f x^{2} + 2 \, c^{2} d^{3} f x + c d^{3} f} + \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d^{3} f x + c d^{3} f}\right)}"," ",0,"-1/3*b*c*(1/(c^3*d^(5/2)*sqrt(f)*x + c^2*d^(5/2)*sqrt(f)) - log(c*x + 1)/(c^2*d^(5/2)*sqrt(f))) - 1/3*b*(sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d^3*f*x^2 + 2*c^2*d^3*f*x + c*d^3*f) + sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d^3*f*x + c*d^3*f))*arcsin(c*x) - 1/3*a*(sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d^3*f*x^2 + 2*c^2*d^3*f*x + c*d^3*f) + sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d^3*f*x + c*d^3*f))","A",0
528,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} d^{3} x^{3}}{\sqrt{-c^{2} d f x^{2} + d f} f} + \frac{8 \, c d^{3} x^{2}}{\sqrt{-c^{2} d f x^{2} + d f} f} - \frac{17 \, d^{3} x}{\sqrt{-c^{2} d f x^{2} + d f} f} + \frac{15 \, d^{3} \arcsin\left(c x\right)}{\sqrt{d f} c f} - \frac{24 \, d^{3}}{\sqrt{-c^{2} d f x^{2} + d f} c f}\right)} a - \frac{\frac{{\left(c^{2} \int \frac{\sqrt{c x + 1} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{-c x + 1} c x - \sqrt{-c x + 1}}\,{d x} + 2 \, c \int \frac{\sqrt{c x + 1} x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{-c x + 1} c x - \sqrt{-c x + 1}}\,{d x} + \int \frac{\sqrt{c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}\right)} b d^{\frac{5}{2}}}{f}}{\sqrt{f}}"," ",0,"-1/2*(c^2*d^3*x^3/(sqrt(-c^2*d*f*x^2 + d*f)*f) + 8*c*d^3*x^2/(sqrt(-c^2*d*f*x^2 + d*f)*f) - 17*d^3*x/(sqrt(-c^2*d*f*x^2 + d*f)*f) + 15*d^3*arcsin(c*x)/(sqrt(d*f)*c*f) - 24*d^3/(sqrt(-c^2*d*f*x^2 + d*f)*c*f))*a - b*sqrt(d)*integrate((c^2*d^2*x^2 + 2*c*d^2*x + d^2)*sqrt(c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c*f*x - f)*sqrt(-c*x + 1)), x)/sqrt(f)","F",0
529,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","b \sqrt{d} \sqrt{f} \int \frac{{\left(c d x + d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{2} f^{2} x^{2} - 2 \, c f^{2} x + f^{2}}\,{d x} - a {\left(\frac{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{3} f^{3} x^{2} - 2 \, c^{2} f^{3} x + c f^{3}} + \frac{6 \, \sqrt{-c^{2} d f x^{2} + d f} d}{c^{2} f^{2} x - c f^{2}} + \frac{3 \, d^{2} \arcsin\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)}"," ",0,"b*sqrt(d)*sqrt(f)*integrate((c*d*x + d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^2*f^2*x^2 - 2*c*f^2*x + f^2), x) - a*((-c^2*d*f*x^2 + d*f)^(3/2)/(c^3*f^3*x^2 - 2*c^2*f^3*x + c*f^3) + 6*sqrt(-c^2*d*f*x^2 + d*f)*d/(c^2*f^2*x - c*f^2) + 3*d^2*arcsin(c*x)/(c*f^2*sqrt(d/f)))","F",0
530,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{2} f^{2} x - c f^{2}} + \frac{d \arcsin\left(c x\right)}{c f^{2} \sqrt{\frac{d}{f}}}\right)} - \frac{\frac{b \sqrt{d} \int \frac{\sqrt{c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}}{f}}{\sqrt{f}}"," ",0,"-a*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^2*f^2*x - c*f^2) + d*arcsin(c*x)/(c*f^2*sqrt(d/f))) - b*sqrt(d)*integrate(sqrt(c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((c*f*x - f)*sqrt(-c*x + 1)), x)/sqrt(f)","F",0
531,1,98,0,0.484477," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{-c^{2} d f x^{2} + d f} b \arcsin\left(c x\right)}{c^{2} d f^{2} x - c d f^{2}} - \frac{\sqrt{-c^{2} d f x^{2} + d f} a}{c^{2} d f^{2} x - c d f^{2}} + \frac{b \log\left(c x - 1\right)}{c \sqrt{d} f^{\frac{3}{2}}}"," ",0,"-sqrt(-c^2*d*f*x^2 + d*f)*b*arcsin(c*x)/(c^2*d*f^2*x - c*d*f^2) - sqrt(-c^2*d*f*x^2 + d*f)*a/(c^2*d*f^2*x - c*d*f^2) + b*log(c*x - 1)/(c*sqrt(d)*f^(3/2))","A",0
532,1,86,0,0.458935," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","\frac{b x \arcsin\left(c x\right)}{\sqrt{-c^{2} d f x^{2} + d f} d f} + \frac{a x}{\sqrt{-c^{2} d f x^{2} + d f} d f} - \frac{b \sqrt{\frac{1}{d f}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, c d f}"," ",0,"b*x*arcsin(c*x)/(sqrt(-c^2*d*f*x^2 + d*f)*d*f) + a*x/(sqrt(-c^2*d*f*x^2 + d*f)*d*f) - 1/2*b*sqrt(1/(d*f))*log(x^2 - 1/c^2)/(c*d*f)","A",0
533,1,234,0,0.479615," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(3/2),x, algorithm=""maxima"")","-\frac{1}{12} \, b c {\left(\frac{2 \, \sqrt{d} \sqrt{f}}{c^{3} d^{3} f^{2} x + c^{2} d^{3} f^{2}} - \frac{5 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{3}{2}}} - \frac{3 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{3}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{1}{\sqrt{-c^{2} d f x^{2} + d f} c^{2} d^{2} f x + \sqrt{-c^{2} d f x^{2} + d f} c d^{2} f} - \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d^{2} f}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{1}{\sqrt{-c^{2} d f x^{2} + d f} c^{2} d^{2} f x + \sqrt{-c^{2} d f x^{2} + d f} c d^{2} f} - \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d^{2} f}\right)}"," ",0,"-1/12*b*c*(2*sqrt(d)*sqrt(f)/(c^3*d^3*f^2*x + c^2*d^3*f^2) - 5*log(c*x + 1)/(c^2*d^(5/2)*f^(3/2)) - 3*log(c*x - 1)/(c^2*d^(5/2)*f^(3/2))) - 1/3*b*(1/(sqrt(-c^2*d*f*x^2 + d*f)*c^2*d^2*f*x + sqrt(-c^2*d*f*x^2 + d*f)*c*d^2*f) - 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d^2*f))*arcsin(c*x) - 1/3*a*(1/(sqrt(-c^2*d*f*x^2 + d*f)*c^2*d^2*f*x + sqrt(-c^2*d*f*x^2 + d*f)*c*d^2*f) - 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d^2*f))","A",0
534,-1,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","-b \sqrt{d} \sqrt{f} \int \frac{{\left(c d x + d\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{c^{3} f^{3} x^{3} - 3 \, c^{2} f^{3} x^{2} + 3 \, c f^{3} x - f^{3}}\,{d x} - \frac{1}{3} \, a {\left(\frac{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}}}{c^{4} f^{4} x^{3} - 3 \, c^{3} f^{4} x^{2} + 3 \, c^{2} f^{4} x - c f^{4}} - \frac{2 \, \sqrt{-c^{2} d f x^{2} + d f} d}{c^{3} f^{3} x^{2} - 2 \, c^{2} f^{3} x + c f^{3}} - \frac{7 \, \sqrt{-c^{2} d f x^{2} + d f} d}{c^{2} f^{3} x - c f^{3}} - \frac{3 \, d^{2} \arcsin\left(c x\right)}{c f^{3} \sqrt{\frac{d}{f}}}\right)}"," ",0,"-b*sqrt(d)*sqrt(f)*integrate((c*d*x + d)*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(c^3*f^3*x^3 - 3*c^2*f^3*x^2 + 3*c*f^3*x - f^3), x) - 1/3*a*((-c^2*d*f*x^2 + d*f)^(3/2)/(c^4*f^4*x^3 - 3*c^3*f^4*x^2 + 3*c^2*f^4*x - c*f^4) - 2*sqrt(-c^2*d*f*x^2 + d*f)*d/(c^3*f^3*x^2 - 2*c^2*f^3*x + c*f^3) - 7*sqrt(-c^2*d*f*x^2 + d*f)*d/(c^2*f^3*x - c*f^3) - 3*d^2*arcsin(c*x)/(c*f^3*sqrt(d/f)))","F",0
536,1,217,0,0.495933," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, b c {\left(\frac{2 \, \sqrt{d}}{c^{3} f^{\frac{5}{2}} x - c^{2} f^{\frac{5}{2}}} - \frac{\sqrt{d} \log\left(c x - 1\right)}{c^{2} f^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{3} f^{3} x^{2} - 2 \, c^{2} f^{3} x + c f^{3}} + \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} f^{3} x - c f^{3}}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{-c^{2} d f x^{2} + d f}}{c^{3} f^{3} x^{2} - 2 \, c^{2} f^{3} x + c f^{3}} + \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} f^{3} x - c f^{3}}\right)}"," ",0,"1/3*b*c*(2*sqrt(d)/(c^3*f^(5/2)*x - c^2*f^(5/2)) - sqrt(d)*log(c*x - 1)/(c^2*f^(5/2))) + 1/3*b*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^3*f^3*x^2 - 2*c^2*f^3*x + c*f^3) + sqrt(-c^2*d*f*x^2 + d*f)/(c^2*f^3*x - c*f^3))*arcsin(c*x) + 1/3*a*(2*sqrt(-c^2*d*f*x^2 + d*f)/(c^3*f^3*x^2 - 2*c^2*f^3*x + c*f^3) + sqrt(-c^2*d*f*x^2 + d*f)/(c^2*f^3*x - c*f^3))","A",0
537,1,227,0,0.490263," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, b c {\left(\frac{1}{c^{3} \sqrt{d} f^{\frac{5}{2}} x - c^{2} \sqrt{d} f^{\frac{5}{2}}} + \frac{\log\left(c x - 1\right)}{c^{2} \sqrt{d} f^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d f^{3} x^{2} - 2 \, c^{2} d f^{3} x + c d f^{3}} - \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d f^{3} x - c d f^{3}}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a {\left(\frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{3} d f^{3} x^{2} - 2 \, c^{2} d f^{3} x + c d f^{3}} - \frac{\sqrt{-c^{2} d f x^{2} + d f}}{c^{2} d f^{3} x - c d f^{3}}\right)}"," ",0,"1/3*b*c*(1/(c^3*sqrt(d)*f^(5/2)*x - c^2*sqrt(d)*f^(5/2)) + log(c*x - 1)/(c^2*sqrt(d)*f^(5/2))) + 1/3*b*(sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d*f^3*x^2 - 2*c^2*d*f^3*x + c*d*f^3) - sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d*f^3*x - c*d*f^3))*arcsin(c*x) + 1/3*a*(sqrt(-c^2*d*f*x^2 + d*f)/(c^3*d*f^3*x^2 - 2*c^2*d*f^3*x + c*d*f^3) - sqrt(-c^2*d*f*x^2 + d*f)/(c^2*d*f^3*x - c*d*f^3))","A",0
538,1,237,0,0.546128," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","\frac{1}{12} \, b c {\left(\frac{2 \, \sqrt{d} \sqrt{f}}{c^{3} d^{2} f^{3} x - c^{2} d^{2} f^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{3}{2}} f^{\frac{5}{2}}} + \frac{5 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{3}{2}} f^{\frac{5}{2}}}\right)} - \frac{1}{3} \, b {\left(\frac{1}{\sqrt{-c^{2} d f x^{2} + d f} c^{2} d f^{2} x - \sqrt{-c^{2} d f x^{2} + d f} c d f^{2}} - \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d f^{2}}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a {\left(\frac{1}{\sqrt{-c^{2} d f x^{2} + d f} c^{2} d f^{2} x - \sqrt{-c^{2} d f x^{2} + d f} c d f^{2}} - \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d f^{2}}\right)}"," ",0,"1/12*b*c*(2*sqrt(d)*sqrt(f)/(c^3*d^2*f^3*x - c^2*d^2*f^3) + 3*log(c*x + 1)/(c^2*d^(3/2)*f^(5/2)) + 5*log(c*x - 1)/(c^2*d^(3/2)*f^(5/2))) - 1/3*b*(1/(sqrt(-c^2*d*f*x^2 + d*f)*c^2*d*f^2*x - sqrt(-c^2*d*f*x^2 + d*f)*c*d*f^2) - 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d*f^2))*arcsin(c*x) - 1/3*a*(1/(sqrt(-c^2*d*f*x^2 + d*f)*c^2*d*f^2*x - sqrt(-c^2*d*f*x^2 + d*f)*c*d*f^2) - 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d*f^2))","A",0
539,1,177,0,0.523070," ","integrate((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} f^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}} f^{\frac{5}{2}}}\right)} + \frac{1}{3} \, b {\left(\frac{x}{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a {\left(\frac{x}{{\left(-c^{2} d f x^{2} + d f\right)}^{\frac{3}{2}} d f} + \frac{2 \, x}{\sqrt{-c^{2} d f x^{2} + d f} d^{2} f^{2}}\right)}"," ",0,"1/6*b*c*(1/(c^4*d^(5/2)*f^(5/2)*x^2 - c^2*d^(5/2)*f^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)*f^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2)*f^(5/2))) + 1/3*b*(x/((-c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d^2*f^2))*arcsin(c*x) + 1/3*a*(x/((-c^2*d*f*x^2 + d*f)^(3/2)*d*f) + 2*x/(sqrt(-c^2*d*f*x^2 + d*f)*d^2*f^2))","A",0
540,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(15 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2} x + \frac{15 \, d^{3} e \arcsin\left(c x\right)}{\sqrt{d e} c} - \frac{6 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d x}{e} - \frac{16 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d}{c e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left({\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/24*(15*sqrt(-c^2*d*e*x^2 + d*e)*d^2*x + 15*d^3*e*arcsin(c*x)/(sqrt(d*e)*c) - 6*(-c^2*d*e*x^2 + d*e)^(3/2)*d*x/e - 16*(-c^2*d*e*x^2 + d*e)^(3/2)*d/(c*e))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
541,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(3 \, \sqrt{-c^{2} d e x^{2} + d e} d x + \frac{3 \, d^{2} e \arcsin\left(c x\right)}{\sqrt{d e} c} - \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left({\left(b^{2} c d x + b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/6*(3*sqrt(-c^2*d*e*x^2 + d*e)*d*x + 3*d^2*e*arcsin(c*x)/(sqrt(d*e)*c) - 2*(-c^2*d*e*x^2 + d*e)^(3/2)/(c*e))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c*d*x + b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*d*x + a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
542,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d e x^{2} + d e} x + \frac{d e \arcsin\left(c x\right)}{\sqrt{d e} c}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*e*x^2 + d*e)*x + d*e*arcsin(c*x)/(sqrt(d*e)*c))*a^2 + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
543,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{e \arcsin\left(c x\right)}{c d \sqrt{\frac{e}{d}}} + \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c d}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c d x + d}\,{d x}"," ",0,"a^2*(e*arcsin(c*x)/(c*d*sqrt(e/d)) + sqrt(-c^2*d*e*x^2 + d*e)/(c*d)) + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*d*x + d), x)","F",0
544,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e}}{c^{2} d^{2} x + c d^{2}} + \frac{e \arcsin\left(c x\right)}{c d^{2} \sqrt{\frac{e}{d}}}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}\,{d x}"," ",0,"-a^2*(2*sqrt(-c^2*d*e*x^2 + d*e)/(c^2*d^2*x + c*d^2) + e*arcsin(c*x)/(c*d^2*sqrt(e/d))) + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
545,-1,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{40} \, {\left(15 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2} e x + \frac{15 \, d^{3} e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} + 10 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d x - \frac{8 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}}}{c e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int -{\left({\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/40*(15*sqrt(-c^2*d*e*x^2 + d*e)*d^2*e*x + 15*d^3*e^2*arcsin(c*x)/(sqrt(d*e)*c) + 10*(-c^2*d*e*x^2 + d*e)^(3/2)*d*x - 8*(-c^2*d*e*x^2 + d*e)^(5/2)/(c*e))*a^2 + sqrt(d)*sqrt(e)*integrate(-((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
547,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(3 \, \sqrt{-c^{2} d e x^{2} + d e} d e x + \frac{3 \, d^{2} e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} + 2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} x\right)} a^{2} + \sqrt{d} \sqrt{e} \int -{\left({\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/8*(3*sqrt(-c^2*d*e*x^2 + d*e)*d*e*x + 3*d^2*e^2*arcsin(c*x)/(sqrt(d*e)*c) + 2*(-c^2*d*e*x^2 + d*e)^(3/2)*x)*a^2 + sqrt(d)*sqrt(e)*integrate(-((b^2*c^2*d*e*x^2 - b^2*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
548,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(3 \, \sqrt{-c^{2} d e x^{2} + d e} e x + \frac{3 \, d e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} + \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c d}\right)} a^{2} + \sqrt{d} \sqrt{e} \int -{\left({\left(b^{2} c e x - b^{2} e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/6*(3*sqrt(-c^2*d*e*x^2 + d*e)*e*x + 3*d*e^2*arcsin(c*x)/(sqrt(d*e)*c) + 2*(-c^2*d*e*x^2 + d*e)^(3/2)/(c*d))*a^2 + sqrt(d)*sqrt(e)*integrate(-((b^2*c*e*x - b^2*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*e*x - a*b*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
549,0,0,0,0.000000," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e} e x}{d} - \frac{3 \, e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} - \frac{4 \, \sqrt{-c^{2} d e x^{2} + d e} e}{c d}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c e x - b^{2} e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c d x + d}\,{d x}"," ",0,"-1/2*(sqrt(-c^2*d*e*x^2 + d*e)*e*x/d - 3*e^2*arcsin(c*x)/(sqrt(d*e)*c) - 4*sqrt(-c^2*d*e*x^2 + d*e)*e/(c*d))*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c*e*x - b^2*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*e*x - a*b*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*d*x + d), x)","F",0
550,0,0,0,0.000000," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{6 \, \sqrt{-c^{2} d e x^{2} + d e} e}{c^{2} d^{2} x + c d^{2}} - \frac{3 \, e^{2} \arcsin\left(c x\right)}{c d^{2} \sqrt{\frac{e}{d}}}\right)} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c e x - b^{2} e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}\,{d x}"," ",0,"a^2*((-c^2*d*e*x^2 + d*e)^(3/2)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - 6*sqrt(-c^2*d*e*x^2 + d*e)*e/(c^2*d^2*x + c*d^2) - 3*e^2*arcsin(c*x)/(c*d^2*sqrt(e/d))) - sqrt(d)*sqrt(e)*integrate(((b^2*c*e*x - b^2*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*e*x - a*b*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
551,0,0,0,0.000000," ","integrate((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c^{4} d^{4} x^{3} + 3 \, c^{3} d^{4} x^{2} + 3 \, c^{2} d^{4} x + c d^{4}} + \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} e}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} - \frac{7 \, \sqrt{-c^{2} d e x^{2} + d e} e}{c^{2} d^{3} x + c d^{3}} - \frac{3 \, e^{2} \arcsin\left(c x\right)}{c d^{3} \sqrt{\frac{e}{d}}}\right)} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c e x - b^{2} e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c e x - a b e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}\,{d x}"," ",0,"-1/3*a^2*((-c^2*d*e*x^2 + d*e)^(3/2)/(c^4*d^4*x^3 + 3*c^3*d^4*x^2 + 3*c^2*d^4*x + c*d^4) + 2*sqrt(-c^2*d*e*x^2 + d*e)*e/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) - 7*sqrt(-c^2*d*e*x^2 + d*e)*e/(c^2*d^3*x + c*d^3) - 3*e^2*arcsin(c*x)/(c*d^3*sqrt(e/d))) - sqrt(d)*sqrt(e)*integrate(((b^2*c*e*x - b^2*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*e*x - a*b*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
552,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(15 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2} e^{2} x + \frac{15 \, d^{3} e^{3} \arcsin\left(c x\right)}{\sqrt{d e} c} + 10 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d e x + 8 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}} x\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left({\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/48*(15*sqrt(-c^2*d*e*x^2 + d*e)*d^2*e^2*x + 15*d^3*e^3*arcsin(c*x)/(sqrt(d*e)*c) + 10*(-c^2*d*e*x^2 + d*e)^(3/2)*d*e*x + 8*(-c^2*d*e*x^2 + d*e)^(5/2)*x)*a^2 + sqrt(d)*sqrt(e)*integrate(((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
553,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{40} \, {\left(15 \, \sqrt{-c^{2} d e x^{2} + d e} d e^{2} x + \frac{15 \, d^{2} e^{3} \arcsin\left(c x\right)}{\sqrt{d e} c} + 10 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} e x + \frac{8 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}}}{c d}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left({\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\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)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/40*(15*sqrt(-c^2*d*e*x^2 + d*e)*d*e^2*x + 15*d^2*e^3*arcsin(c*x)/(sqrt(d*e)*c) + 10*(-c^2*d*e*x^2 + d*e)^(3/2)*e*x + 8*(-c^2*d*e*x^2 + d*e)^(5/2)/(c*d))*a^2 + sqrt(d)*sqrt(e)*integrate(((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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^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)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
554,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(15 \, \sqrt{-c^{2} d e x^{2} + d e} e^{2} x + \frac{15 \, d e^{3} \arcsin\left(c x\right)}{\sqrt{d e} c} - \frac{6 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} e x}{d} + \frac{16 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} e}{c d}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left({\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/24*(15*sqrt(-c^2*d*e*x^2 + d*e)*e^2*x + 15*d*e^3*arcsin(c*x)/(sqrt(d*e)*c) - 6*(-c^2*d*e*x^2 + d*e)^(3/2)*e*x/d + 16*(-c^2*d*e*x^2 + d*e)^(3/2)*e/(c*d))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
555,0,0,0,0.000000," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} c e^{2} x^{2}}{d} - \frac{9 \, \sqrt{-c^{2} d e x^{2} + d e} e^{2} x}{d} + \frac{15 \, e^{3} \arcsin\left(c x\right)}{\sqrt{d e} c} + \frac{22 \, \sqrt{-c^{2} d e x^{2} + d e} e^{2}}{c d}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c d x + d}\,{d x}"," ",0,"1/6*(2*sqrt(-c^2*d*e*x^2 + d*e)*c*e^2*x^2/d - 9*sqrt(-c^2*d*e*x^2 + d*e)*e^2*x/d + 15*e^3*arcsin(c*x)/(sqrt(d*e)*c) + 22*sqrt(-c^2*d*e*x^2 + d*e)*e^2/(c*d))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*d*x + d), x)","F",0
556,0,0,0,0.000000," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} e^{3} x^{3}}{\sqrt{-c^{2} d e x^{2} + d e} d} - \frac{8 \, c e^{3} x^{2}}{\sqrt{-c^{2} d e x^{2} + d e} d} - \frac{17 \, e^{3} x}{\sqrt{-c^{2} d e x^{2} + d e} d} + \frac{15 \, e^{3} \arcsin\left(c x\right)}{\sqrt{d e} c d} + \frac{24 \, e^{3}}{\sqrt{-c^{2} d e x^{2} + d e} c d}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}\,{d x}"," ",0,"-1/2*(c^2*e^3*x^3/(sqrt(-c^2*d*e*x^2 + d*e)*d) - 8*c*e^3*x^2/(sqrt(-c^2*d*e*x^2 + d*e)*d) - 17*e^3*x/(sqrt(-c^2*d*e*x^2 + d*e)*d) + 15*e^3*arcsin(c*x)/(sqrt(d*e)*c*d) + 24*e^3/(sqrt(-c^2*d*e*x^2 + d*e)*c*d))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
557,0,0,0,0.000000," ","integrate((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}}}{c^{5} d^{5} x^{4} + 4 \, c^{4} d^{5} x^{3} + 6 \, c^{3} d^{5} x^{2} + 4 \, c^{2} d^{5} x + c d^{5}} - \frac{5 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} e}{c^{4} d^{4} x^{3} + 3 \, c^{3} d^{4} x^{2} + 3 \, c^{2} d^{4} x + c d^{4}} - \frac{10 \, \sqrt{-c^{2} d e x^{2} + d e} e^{2}}{c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}} + \frac{35 \, \sqrt{-c^{2} d e x^{2} + d e} e^{2}}{c^{2} d^{3} x + c d^{3}} + \frac{15 \, e^{3} \arcsin\left(c x\right)}{c d^{3} \sqrt{\frac{e}{d}}}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} e^{2} x^{2} - 2 \, b^{2} c e^{2} x + b^{2} e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} e^{2} x^{2} - 2 \, a b c e^{2} x + a b e^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}\,{d x}"," ",0,"1/3*(3*(-c^2*d*e*x^2 + d*e)^(5/2)/(c^5*d^5*x^4 + 4*c^4*d^5*x^3 + 6*c^3*d^5*x^2 + 4*c^2*d^5*x + c*d^5) - 5*(-c^2*d*e*x^2 + d*e)^(3/2)*e/(c^4*d^4*x^3 + 3*c^3*d^4*x^2 + 3*c^2*d^4*x + c*d^4) - 10*sqrt(-c^2*d*e*x^2 + d*e)*e^2/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3) + 35*sqrt(-c^2*d*e*x^2 + d*e)*e^2/(c^2*d^3*x + c*d^3) + 15*e^3*arcsin(c*x)/(c*d^3*sqrt(e/d)))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*e^2*x^2 - 2*b^2*c*e^2*x + b^2*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*e^2*x^2 - 2*a*b*c*e^2*x + a*b*e^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
558,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} c d^{2} x^{2}}{e} + \frac{9 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2} x}{e} - \frac{15 \, d^{3} \arcsin\left(c x\right)}{\sqrt{d e} c} + \frac{22 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2}}{c e}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c e x - e}\,{d x}"," ",0,"-1/6*(2*sqrt(-c^2*d*e*x^2 + d*e)*c*d^2*x^2/e + 9*sqrt(-c^2*d*e*x^2 + d*e)*d^2*x/e - 15*d^3*arcsin(c*x)/(sqrt(d*e)*c) + 22*sqrt(-c^2*d*e*x^2 + d*e)*d^2/(c*e))*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*e*x - e), x)","F",0
559,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e} d x}{e} - \frac{3 \, d^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} + \frac{4 \, \sqrt{-c^{2} d e x^{2} + d e} d}{c e}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c d x + b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c e x - e}\,{d x}"," ",0,"-1/2*(sqrt(-c^2*d*e*x^2 + d*e)*d*x/e - 3*d^2*arcsin(c*x)/(sqrt(d*e)*c) + 4*sqrt(-c^2*d*e*x^2 + d*e)*d/(c*e))*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c*d*x + b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*d*x + a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*e*x - e), x)","F",0
560,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{d \arcsin\left(c x\right)}{c e \sqrt{\frac{d}{e}}} - \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c e}\right)} - \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c e x - e}\,{d x}"," ",0,"a^2*(d*arcsin(c*x)/(c*e*sqrt(d/e)) - sqrt(-c^2*d*e*x^2 + d*e)/(c*e)) - sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c*e*x - e), x)","F",0
561,1,53,0,0.471890," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \arcsin\left(c x\right)^{3}}{3 \, \sqrt{d e} c} + \frac{a b \arcsin\left(c x\right)^{2}}{\sqrt{d e} c} + \frac{a^{2} \arcsin\left(c x\right)}{\sqrt{d e} c}"," ",0,"1/3*b^2*arcsin(c*x)^3/(sqrt(d*e)*c) + a*b*arcsin(c*x)^2/(sqrt(d*e)*c) + a^2*arcsin(c*x)/(sqrt(d*e)*c)","A",0
562,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} a b \arcsin\left(c x\right)}{c^{2} d^{2} e x + c d^{2} e} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{3}{2}} \sqrt{-c x + 1}}\,{d x}}{d}}{\sqrt{d} \sqrt{e}} - \frac{\sqrt{-c^{2} d e x^{2} + d e} a^{2}}{c^{2} d^{2} e x + c d^{2} e} + \frac{2 \, a b \log\left(c x + 1\right)}{c d^{\frac{3}{2}} \sqrt{e}}"," ",0,"-2*sqrt(-c^2*d*e*x^2 + d*e)*a*b*arcsin(c*x)/(c^2*d^2*e*x + c*d^2*e) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c*d*x + d)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e)) - sqrt(-c^2*d*e*x^2 + d*e)*a^2/(c^2*d^2*e*x + c*d^2*e) + 2*a*b*log(c*x + 1)/(c*d^(3/2)*sqrt(e))","F",0
563,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{2}{3} \, a b c {\left(\frac{1}{c^{3} d^{\frac{5}{2}} \sqrt{e} x + c^{2} d^{\frac{5}{2}} \sqrt{e}} - \frac{\log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} \sqrt{e}}\right)} - \frac{2}{3} \, a b {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{3} d^{3} e x^{2} + 2 \, c^{2} d^{3} e x + c d^{3} e} + \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{2} d^{3} e x + c d^{3} e}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{3} d^{3} e x^{2} + 2 \, c^{2} d^{3} e x + c d^{3} e} + \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{2} d^{3} e x + c d^{3} e}\right)} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{5}{2}} \sqrt{-c x + 1}}\,{d x}}{d^{2}}}{\sqrt{d} \sqrt{e}}"," ",0,"-2/3*a*b*c*(1/(c^3*d^(5/2)*sqrt(e)*x + c^2*d^(5/2)*sqrt(e)) - log(c*x + 1)/(c^2*d^(5/2)*sqrt(e))) - 2/3*a*b*(sqrt(-c^2*d*e*x^2 + d*e)/(c^3*d^3*e*x^2 + 2*c^2*d^3*e*x + c*d^3*e) + sqrt(-c^2*d*e*x^2 + d*e)/(c^2*d^3*e*x + c*d^3*e))*arcsin(c*x) - 1/3*a^2*(sqrt(-c^2*d*e*x^2 + d*e)/(c^3*d^3*e*x^2 + 2*c^2*d^3*e*x + c*d^3*e) + sqrt(-c^2*d*e*x^2 + d*e)/(c^2*d^3*e*x + c*d^3*e)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*d^2*x^2 + 2*c*d^2*x + d^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
564,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} d^{3} x^{3}}{\sqrt{-c^{2} d e x^{2} + d e} e} + \frac{8 \, c d^{3} x^{2}}{\sqrt{-c^{2} d e x^{2} + d e} e} - \frac{17 \, d^{3} x}{\sqrt{-c^{2} d e x^{2} + d e} e} + \frac{15 \, d^{3} \arcsin\left(c x\right)}{\sqrt{d e} c e} - \frac{24 \, d^{3}}{\sqrt{-c^{2} d e x^{2} + d e} c e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}\,{d x}"," ",0,"-1/2*(c^2*d^3*x^3/(sqrt(-c^2*d*e*x^2 + d*e)*e) + 8*c*d^3*x^2/(sqrt(-c^2*d*e*x^2 + d*e)*e) - 17*d^3*x/(sqrt(-c^2*d*e*x^2 + d*e)*e) + 15*d^3*arcsin(c*x)/(sqrt(d*e)*c*e) - 24*d^3/(sqrt(-c^2*d*e*x^2 + d*e)*c*e))*a^2 + sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
565,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c^{3} e^{3} x^{2} - 2 \, c^{2} e^{3} x + c e^{3}} + \frac{6 \, \sqrt{-c^{2} d e x^{2} + d e} d}{c^{2} e^{2} x - c e^{2}} + \frac{3 \, d^{2} \arcsin\left(c x\right)}{c e^{2} \sqrt{\frac{d}{e}}}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c d x + b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}\,{d x}"," ",0,"-a^2*((-c^2*d*e*x^2 + d*e)^(3/2)/(c^3*e^3*x^2 - 2*c^2*e^3*x + c*e^3) + 6*sqrt(-c^2*d*e*x^2 + d*e)*d/(c^2*e^2*x - c*e^2) + 3*d^2*arcsin(c*x)/(c*e^2*sqrt(d/e))) + sqrt(d)*sqrt(e)*integrate(((b^2*c*d*x + b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*d*x + a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
566,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e}}{c^{2} e^{2} x - c e^{2}} + \frac{d \arcsin\left(c x\right)}{c e^{2} \sqrt{\frac{d}{e}}}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} e^{2} x^{2} - 2 \, c e^{2} x + e^{2}}\,{d x}"," ",0,"-a^2*(2*sqrt(-c^2*d*e*x^2 + d*e)/(c^2*e^2*x - c*e^2) + d*arcsin(c*x)/(c*e^2*sqrt(d/e))) + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*e^2*x^2 - 2*c*e^2*x + e^2), x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} a b \arcsin\left(c x\right)}{c^{2} d e^{2} x - c d e^{2}} - \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{\sqrt{c x + 1} {\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}}{e}}{\sqrt{d} \sqrt{e}} - \frac{\sqrt{-c^{2} d e x^{2} + d e} a^{2}}{c^{2} d e^{2} x - c d e^{2}} + \frac{2 \, a b \log\left(c x - 1\right)}{c \sqrt{d} e^{\frac{3}{2}}}"," ",0,"-2*sqrt(-c^2*d*e*x^2 + d*e)*a*b*arcsin(c*x)/(c^2*d*e^2*x - c*d*e^2) - b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c*e*x - e)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e)) - sqrt(-c^2*d*e*x^2 + d*e)*a^2/(c^2*d*e^2*x - c*d*e^2) + 2*a*b*log(c*x - 1)/(c*sqrt(d)*e^(3/2))","F",0
568,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-\frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}}{d e}}{\sqrt{d} \sqrt{e}} + \frac{2 \, a b x \arcsin\left(c x\right)}{\sqrt{-c^{2} d e x^{2} + d e} d e} + \frac{a^{2} x}{\sqrt{-c^{2} d e x^{2} + d e} d e} - \frac{a b \sqrt{\frac{1}{d e}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{c d e}"," ",0,"-b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*d*e*x^2 - d*e)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e)) + 2*a*b*x*arcsin(c*x)/(sqrt(-c^2*d*e*x^2 + d*e)*d*e) + a^2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d*e) - a*b*sqrt(1/(d*e))*log(x^2 - 1/c^2)/(c*d*e)","F",0
569,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a b c {\left(\frac{2 \, \sqrt{d} \sqrt{e}}{c^{3} d^{3} e^{2} x + c^{2} d^{3} e^{2}} - \frac{5 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} e^{\frac{3}{2}}} - \frac{3 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}} e^{\frac{3}{2}}}\right)} - \frac{2}{3} \, a b {\left(\frac{1}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d^{2} e x + \sqrt{-c^{2} d e x^{2} + d e} c d^{2} e} - \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d^{2} e}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{1}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d^{2} e x + \sqrt{-c^{2} d e x^{2} + d e} c d^{2} e} - \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d^{2} e}\right)} - \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{5}{2}} {\left(c x - 1\right)} \sqrt{-c x + 1}}\,{d x}}{d^{2} e}}{\sqrt{d} \sqrt{e}}"," ",0,"-1/6*a*b*c*(2*sqrt(d)*sqrt(e)/(c^3*d^3*e^2*x + c^2*d^3*e^2) - 5*log(c*x + 1)/(c^2*d^(5/2)*e^(3/2)) - 3*log(c*x - 1)/(c^2*d^(5/2)*e^(3/2))) - 2/3*a*b*(1/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d^2*e*x + sqrt(-c^2*d*e*x^2 + d*e)*c*d^2*e) - 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d^2*e))*arcsin(c*x) - 1/3*a^2*(1/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d^2*e*x + sqrt(-c^2*d*e*x^2 + d*e)*c*d^2*e) - 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d^2*e)) - b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^3*d^2*e*x^3 + c^2*d^2*e*x^2 - c*d^2*e*x - d^2*e)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
570,0,0,0,0.000000," ","integrate((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{3 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}}}{c^{5} e^{5} x^{4} - 4 \, c^{4} e^{5} x^{3} + 6 \, c^{3} e^{5} x^{2} - 4 \, c^{2} e^{5} x + c e^{5}} + \frac{5 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d}{c^{4} e^{4} x^{3} - 3 \, c^{3} e^{4} x^{2} + 3 \, c^{2} e^{4} x - c e^{4}} - \frac{10 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2}}{c^{3} e^{3} x^{2} - 2 \, c^{2} e^{3} x + c e^{3}} - \frac{35 \, \sqrt{-c^{2} d e x^{2} + d e} d^{2}}{c^{2} e^{3} x - c e^{3}} - \frac{15 \, d^{3} \arcsin\left(c x\right)}{c e^{3} \sqrt{\frac{d}{e}}}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} e^{3} x^{3} - 3 \, c^{2} e^{3} x^{2} + 3 \, c e^{3} x - e^{3}}\,{d x}"," ",0,"-1/3*(3*(-c^2*d*e*x^2 + d*e)^(5/2)/(c^5*e^5*x^4 - 4*c^4*e^5*x^3 + 6*c^3*e^5*x^2 - 4*c^2*e^5*x + c*e^5) + 5*(-c^2*d*e*x^2 + d*e)^(3/2)*d/(c^4*e^4*x^3 - 3*c^3*e^4*x^2 + 3*c^2*e^4*x - c*e^4) - 10*sqrt(-c^2*d*e*x^2 + d*e)*d^2/(c^3*e^3*x^2 - 2*c^2*e^3*x + c*e^3) - 35*sqrt(-c^2*d*e*x^2 + d*e)*d^2/(c^2*e^3*x - c*e^3) - 15*d^3*arcsin(c*x)/(c*e^3*sqrt(d/e)))*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*e^3*x^3 - 3*c^2*e^3*x^2 + 3*c*e^3*x - e^3), x)","F",0
571,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{c^{4} e^{4} x^{3} - 3 \, c^{3} e^{4} x^{2} + 3 \, c^{2} e^{4} x - c e^{4}} - \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} d}{c^{3} e^{3} x^{2} - 2 \, c^{2} e^{3} x + c e^{3}} - \frac{7 \, \sqrt{-c^{2} d e x^{2} + d e} d}{c^{2} e^{3} x - c e^{3}} - \frac{3 \, d^{2} \arcsin\left(c x\right)}{c e^{3} \sqrt{\frac{d}{e}}}\right)} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c d x + b^{2} d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} e^{3} x^{3} - 3 \, c^{2} e^{3} x^{2} + 3 \, c e^{3} x - e^{3}}\,{d x}"," ",0,"-1/3*a^2*((-c^2*d*e*x^2 + d*e)^(3/2)/(c^4*e^4*x^3 - 3*c^3*e^4*x^2 + 3*c^2*e^4*x - c*e^4) - 2*sqrt(-c^2*d*e*x^2 + d*e)*d/(c^3*e^3*x^2 - 2*c^2*e^3*x + c*e^3) - 7*sqrt(-c^2*d*e*x^2 + d*e)*d/(c^2*e^3*x - c*e^3) - 3*d^2*arcsin(c*x)/(c*e^3*sqrt(d/e))) - sqrt(d)*sqrt(e)*integrate(((b^2*c*d*x + b^2*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c*d*x + a*b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*e^3*x^3 - 3*c^2*e^3*x^2 + 3*c*e^3*x - e^3), x)","F",0
572,-1,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","\frac{2}{3} \, a b c {\left(\frac{1}{c^{3} \sqrt{d} e^{\frac{5}{2}} x - c^{2} \sqrt{d} e^{\frac{5}{2}}} + \frac{\log\left(c x - 1\right)}{c^{2} \sqrt{d} e^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{3} d e^{3} x^{2} - 2 \, c^{2} d e^{3} x + c d e^{3}} - \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{2} d e^{3} x - c d e^{3}}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{3} d e^{3} x^{2} - 2 \, c^{2} d e^{3} x + c d e^{3}} - \frac{\sqrt{-c^{2} d e x^{2} + d e}}{c^{2} d e^{3} x - c d e^{3}}\right)} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{\sqrt{c x + 1} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1}}\,{d x}}{e^{2}}}{\sqrt{d} \sqrt{e}}"," ",0,"2/3*a*b*c*(1/(c^3*sqrt(d)*e^(5/2)*x - c^2*sqrt(d)*e^(5/2)) + log(c*x - 1)/(c^2*sqrt(d)*e^(5/2))) + 2/3*a*b*(sqrt(-c^2*d*e*x^2 + d*e)/(c^3*d*e^3*x^2 - 2*c^2*d*e^3*x + c*d*e^3) - sqrt(-c^2*d*e*x^2 + d*e)/(c^2*d*e^3*x - c*d*e^3))*arcsin(c*x) + 1/3*a^2*(sqrt(-c^2*d*e*x^2 + d*e)/(c^3*d*e^3*x^2 - 2*c^2*d*e^3*x + c*d*e^3) - sqrt(-c^2*d*e*x^2 + d*e)/(c^2*d*e^3*x - c*d*e^3)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*e^2*x^2 - 2*c*e^2*x + e^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
574,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a b c {\left(\frac{2 \, \sqrt{d} \sqrt{e}}{c^{3} d^{2} e^{3} x - c^{2} d^{2} e^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{3}{2}} e^{\frac{5}{2}}} + \frac{5 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{3}{2}} e^{\frac{5}{2}}}\right)} - \frac{2}{3} \, a b {\left(\frac{1}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d e^{2} x - \sqrt{-c^{2} d e x^{2} + d e} c d e^{2}} - \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d e^{2}}\right)} \arcsin\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{1}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d e^{2} x - \sqrt{-c^{2} d e x^{2} + d e} c d e^{2}} - \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d e^{2}}\right)} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1}}\,{d x}}{d e^{2}}}{\sqrt{d} \sqrt{e}}"," ",0,"1/6*a*b*c*(2*sqrt(d)*sqrt(e)/(c^3*d^2*e^3*x - c^2*d^2*e^3) + 3*log(c*x + 1)/(c^2*d^(3/2)*e^(5/2)) + 5*log(c*x - 1)/(c^2*d^(3/2)*e^(5/2))) - 2/3*a*b*(1/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d*e^2*x - sqrt(-c^2*d*e*x^2 + d*e)*c*d*e^2) - 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d*e^2))*arcsin(c*x) - 1/3*a^2*(1/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d*e^2*x - sqrt(-c^2*d*e*x^2 + d*e)*c*d*e^2) - 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d*e^2)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^3*d*e^2*x^3 - c^2*d*e^2*x^2 - c*d*e^2*x + d*e^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
575,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{1}{c^{4} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{2} - c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}}} + \frac{2 \, \log\left(c x + 1\right)}{c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}}} + \frac{2 \, \log\left(c x - 1\right)}{c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}}}\right)} + \frac{2}{3} \, a b {\left(\frac{x}{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d e} + \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d^{2} e^{2}}\right)} \arcsin\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{x}{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} d e} + \frac{2 \, x}{\sqrt{-c^{2} d e x^{2} + d e} d^{2} e^{2}}\right)} + \frac{\frac{b^{2} \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2}}{{\left(c x + 1\right)}^{\frac{5}{2}} {\left(c x - 1\right)}^{2} \sqrt{-c x + 1}}\,{d x}}{d^{2} e^{2}}}{\sqrt{d} \sqrt{e}}"," ",0,"1/3*a*b*c*(1/(c^4*d^(5/2)*e^(5/2)*x^2 - c^2*d^(5/2)*e^(5/2)) + 2*log(c*x + 1)/(c^2*d^(5/2)*e^(5/2)) + 2*log(c*x - 1)/(c^2*d^(5/2)*e^(5/2))) + 2/3*a*b*(x/((-c^2*d*e*x^2 + d*e)^(3/2)*d*e) + 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d^2*e^2))*arcsin(c*x) + 1/3*a^2*(x/((-c^2*d*e*x^2 + d*e)^(3/2)*d*e) + 2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d^2*e^2)) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
576,0,0,0,0.000000," ","integrate(x^2*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e} x}{c^{2}} + \frac{d e \arcsin\left(c x\right)}{\sqrt{d e} c^{3}} - \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} x}{c^{2} d e}\right)} + \sqrt{d} \sqrt{e} \int {\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/8*a^2*(sqrt(-c^2*d*e*x^2 + d*e)*x/c^2 + d*e*arcsin(c*x)/(sqrt(d*e)*c^3) - 2*(-c^2*d*e*x^2 + d*e)^(3/2)*x/(c^2*d*e)) + sqrt(d)*sqrt(e)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
577,1,233,0,1.350199," ","integrate(x*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","-\frac{2}{27} \, b^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}} e^{\frac{3}{2}} x^{2} - \frac{7 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{3}{2}} e^{\frac{3}{2}}}{c^{2}}}{d e} + \frac{3 \, {\left(c^{2} d^{\frac{3}{2}} e^{\frac{3}{2}} x^{3} - 3 \, d^{\frac{3}{2}} e^{\frac{3}{2}} x\right)} \arcsin\left(c x\right)}{c d e}\right)} - \frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} b^{2} \arcsin\left(c x\right)^{2}}{3 \, c^{2} d e} - \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} a b \arcsin\left(c x\right)}{3 \, c^{2} d e} - \frac{2 \, {\left(c^{2} d^{\frac{3}{2}} e^{\frac{3}{2}} x^{3} - 3 \, d^{\frac{3}{2}} e^{\frac{3}{2}} x\right)} a b}{9 \, c d e} - \frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} a^{2}}{3 \, c^{2} d e}"," ",0,"-2/27*b^2*((sqrt(-c^2*x^2 + 1)*d^(3/2)*e^(3/2)*x^2 - 7*sqrt(-c^2*x^2 + 1)*d^(3/2)*e^(3/2)/c^2)/(d*e) + 3*(c^2*d^(3/2)*e^(3/2)*x^3 - 3*d^(3/2)*e^(3/2)*x)*arcsin(c*x)/(c*d*e)) - 1/3*(-c^2*d*e*x^2 + d*e)^(3/2)*b^2*arcsin(c*x)^2/(c^2*d*e) - 2/3*(-c^2*d*e*x^2 + d*e)^(3/2)*a*b*arcsin(c*x)/(c^2*d*e) - 2/9*(c^2*d^(3/2)*e^(3/2)*x^3 - 3*d^(3/2)*e^(3/2)*x)*a*b/(c*d*e) - 1/3*(-c^2*d*e*x^2 + d*e)^(3/2)*a^2/(c^2*d*e)","A",0
578,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d e x^{2} + d e} x + \frac{d e \arcsin\left(c x\right)}{\sqrt{d e} c}\right)} a^{2} + \sqrt{d} \sqrt{e} \int {\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*e*x^2 + d*e)*x + d*e*arcsin(c*x)/(sqrt(d*e)*c))*a^2 + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
579,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-{\left(\frac{d e \log\left(\frac{2 \, d e}{{\left| x \right|}} + \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} \sqrt{d e}}{{\left| x \right|}}\right)}{\sqrt{d e}} - \sqrt{-c^{2} d e x^{2} + d e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x}\,{d x}"," ",0,"-(d*e*log(2*d*e/abs(x) + 2*sqrt(-c^2*d*e*x^2 + d*e)*sqrt(d*e)/abs(x))/sqrt(d*e) - sqrt(-c^2*d*e*x^2 + d*e))*a^2 + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x, x)","F",0
580,0,0,0,0.000000," ","integrate((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-{\left(\frac{c d e \arcsin\left(c x\right)}{\sqrt{d e}} + \frac{\sqrt{-c^{2} d e x^{2} + d e}}{x}\right)} a^{2} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{2}}\,{d x}"," ",0,"-(c*d*e*arcsin(c*x)/sqrt(d*e) + sqrt(-c^2*d*e*x^2 + d*e)/x)*a^2 + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^2, x)","F",0
581,0,0,0,0.000000," ","integrate(x^2*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(\frac{3 \, \sqrt{-c^{2} d e x^{2} + d e} d e x}{c^{2}} + \frac{3 \, d^{2} e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c^{3}} + \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}} x}{c^{2} d e}\right)} a^{2} + \sqrt{d} \sqrt{e} \int -{\left({\left(b^{2} c^{2} d e x^{4} - b^{2} d e x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d e x^{4} - a b d e x^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/48*(3*sqrt(-c^2*d*e*x^2 + d*e)*d*e*x/c^2 + 3*d^2*e^2*arcsin(c*x)/(sqrt(d*e)*c^3) + 2*(-c^2*d*e*x^2 + d*e)^(3/2)*x/c^2 - 8*(-c^2*d*e*x^2 + d*e)^(5/2)*x/(c^2*d*e))*a^2 + sqrt(d)*sqrt(e)*integrate(-((b^2*c^2*d*e*x^4 - b^2*d*e*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*e*x^4 - a*b*d*e*x^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
582,1,290,0,1.541632," ","integrate(x*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{2}{1125} \, b^{2} {\left(\frac{9 \, \sqrt{-c^{2} x^{2} + 1} c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{4} - 38 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{2} + \frac{149 \, \sqrt{-c^{2} x^{2} + 1} d^{\frac{5}{2}} e^{\frac{5}{2}}}{c^{2}}}{d e} + \frac{15 \, {\left(3 \, c^{4} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{5} - 10 \, c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} e^{\frac{5}{2}} x\right)} \arcsin\left(c x\right)}{c d e}\right)} - \frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}} b^{2} \arcsin\left(c x\right)^{2}}{5 \, c^{2} d e} - \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}} a b \arcsin\left(c x\right)}{5 \, c^{2} d e} - \frac{{\left(-c^{2} d e x^{2} + d e\right)}^{\frac{5}{2}} a^{2}}{5 \, c^{2} d e} + \frac{2 \, {\left(3 \, c^{4} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{5} - 10 \, c^{2} d^{\frac{5}{2}} e^{\frac{5}{2}} x^{3} + 15 \, d^{\frac{5}{2}} e^{\frac{5}{2}} x\right)} a b}{75 \, c d e}"," ",0,"2/1125*b^2*((9*sqrt(-c^2*x^2 + 1)*c^2*d^(5/2)*e^(5/2)*x^4 - 38*sqrt(-c^2*x^2 + 1)*d^(5/2)*e^(5/2)*x^2 + 149*sqrt(-c^2*x^2 + 1)*d^(5/2)*e^(5/2)/c^2)/(d*e) + 15*(3*c^4*d^(5/2)*e^(5/2)*x^5 - 10*c^2*d^(5/2)*e^(5/2)*x^3 + 15*d^(5/2)*e^(5/2)*x)*arcsin(c*x)/(c*d*e)) - 1/5*(-c^2*d*e*x^2 + d*e)^(5/2)*b^2*arcsin(c*x)^2/(c^2*d*e) - 2/5*(-c^2*d*e*x^2 + d*e)^(5/2)*a*b*arcsin(c*x)/(c^2*d*e) - 1/5*(-c^2*d*e*x^2 + d*e)^(5/2)*a^2/(c^2*d*e) + 2/75*(3*c^4*d^(5/2)*e^(5/2)*x^5 - 10*c^2*d^(5/2)*e^(5/2)*x^3 + 15*d^(5/2)*e^(5/2)*x)*a*b/(c*d*e)","A",0
583,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(3 \, \sqrt{-c^{2} d e x^{2} + d e} d e x + \frac{3 \, d^{2} e^{2} \arcsin\left(c x\right)}{\sqrt{d e} c} + 2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}} x\right)} a^{2} + \sqrt{d} \sqrt{e} \int -{\left({\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}\,{d x}"," ",0,"1/8*(3*sqrt(-c^2*d*e*x^2 + d*e)*d*e*x + 3*d^2*e^2*arcsin(c*x)/(sqrt(d*e)*c) + 2*(-c^2*d*e*x^2 + d*e)^(3/2)*x)*a^2 + sqrt(d)*sqrt(e)*integrate(-((b^2*c^2*d*e*x^2 - b^2*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1), x)","F",0
584,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{3 \, d^{2} e^{2} \log\left(\frac{2 \, d e}{{\left| x \right|}} + \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} \sqrt{d e}}{{\left| x \right|}}\right)}{\sqrt{d e}} - 3 \, \sqrt{-c^{2} d e x^{2} + d e} d e - {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x}\,{d x}"," ",0,"-1/3*(3*d^2*e^2*log(2*d*e/abs(x) + 2*sqrt(-c^2*d*e*x^2 + d*e)*sqrt(d*e)/abs(x))/sqrt(d*e) - 3*sqrt(-c^2*d*e*x^2 + d*e)*d*e - (-c^2*d*e*x^2 + d*e)^(3/2))*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d*e*x^2 - b^2*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x, x)","F",0
585,0,0,0,0.000000," ","integrate((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{-c^{2} d e x^{2} + d e} c^{2} d e x + \frac{3 \, c d^{2} e^{2} \arcsin\left(c x\right)}{\sqrt{d e}} + \frac{2 \, {\left(-c^{2} d e x^{2} + d e\right)}^{\frac{3}{2}}}{x}\right)} a^{2} - \sqrt{d} \sqrt{e} \int \frac{{\left({\left(b^{2} c^{2} d e x^{2} - b^{2} d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, {\left(a b c^{2} d e x^{2} - a b d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{x^{2}}\,{d x}"," ",0,"-1/2*(3*sqrt(-c^2*d*e*x^2 + d*e)*c^2*d*e*x + 3*c*d^2*e^2*arcsin(c*x)/sqrt(d*e) + 2*(-c^2*d*e*x^2 + d*e)^(3/2)/x)*a^2 - sqrt(d)*sqrt(e)*integrate(((b^2*c^2*d*e*x^2 - b^2*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*(a*b*c^2*d*e*x^2 - a*b*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/x^2, x)","F",0
586,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\sqrt{-c^{2} d e x^{2} + d e} x}{c^{2} d e} - \frac{\arcsin\left(c x\right)}{\sqrt{d e} c^{3}}\right)} - \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d e x^{2} - d e}\,{d x}"," ",0,"-1/2*a^2*(sqrt(-c^2*d*e*x^2 + d*e)*x/(c^2*d*e) - arcsin(c*x)/(sqrt(d*e)*c^3)) - sqrt(d)*sqrt(e)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*e*x^2 - d*e), x)","F",0
587,1,157,0,0.609983," ","integrate(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","2 \, b^{2} {\left(\frac{x \arcsin\left(c x\right)}{c \sqrt{d} \sqrt{e}} + \frac{\sqrt{-c^{2} x^{2} + 1}}{c^{2} \sqrt{d} \sqrt{e}}\right)} + \frac{2 \, a b x}{c \sqrt{d} \sqrt{e}} - \frac{\sqrt{-c^{2} d e x^{2} + d e} b^{2} \arcsin\left(c x\right)^{2}}{c^{2} d e} - \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} a b \arcsin\left(c x\right)}{c^{2} d e} - \frac{\sqrt{-c^{2} d e x^{2} + d e} a^{2}}{c^{2} d e}"," ",0,"2*b^2*(x*arcsin(c*x)/(c*sqrt(d)*sqrt(e)) + sqrt(-c^2*x^2 + 1)/(c^2*sqrt(d)*sqrt(e))) + 2*a*b*x/(c*sqrt(d)*sqrt(e)) - sqrt(-c^2*d*e*x^2 + d*e)*b^2*arcsin(c*x)^2/(c^2*d*e) - 2*sqrt(-c^2*d*e*x^2 + d*e)*a*b*arcsin(c*x)/(c^2*d*e) - sqrt(-c^2*d*e*x^2 + d*e)*a^2/(c^2*d*e)","A",0
588,1,53,0,0.496236," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","\frac{b^{2} \arcsin\left(c x\right)^{3}}{3 \, \sqrt{d e} c} + \frac{a b \arcsin\left(c x\right)^{2}}{\sqrt{d e} c} + \frac{a^{2} \arcsin\left(c x\right)}{\sqrt{d e} c}"," ",0,"1/3*b^2*arcsin(c*x)^3/(sqrt(d*e)*c) + a*b*arcsin(c*x)^2/(sqrt(d*e)*c) + a^2*arcsin(c*x)/(sqrt(d*e)*c)","A",0
589,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{2 \, d e}{{\left| x \right|}} + \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} \sqrt{d e}}{{\left| x \right|}}\right)}{\sqrt{d e}} - \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d e x^{3} - d e x}\,{d x}"," ",0,"-a^2*log(2*d*e/abs(x) + 2*sqrt(-c^2*d*e*x^2 + d*e)*sqrt(d*e)/abs(x))/sqrt(d*e) - sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*e*x^3 - d*e*x), x)","F",0
590,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(\frac{\left(-1\right)^{-2 \, c^{2} d e x^{2} + 2 \, d e} d e \log\left(-2 \, c^{2} d e + \frac{2 \, d e}{x^{2}}\right)}{\sqrt{d e}} + d e \sqrt{\frac{1}{d e}} \log\left(x^{2} - \frac{1}{c^{2}}\right)\right)} a b c}{d e} + \frac{-\frac{\frac{1}{4} \, {\left(7 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 4 \, x \int \frac{9 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 14 \, {\left(c^{3} x^{3} - c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{2} x^{4} - x^{2}\right)}}\,{d x}\right)} b^{2}}{4 \, x}}{\sqrt{d} \sqrt{e}} - \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} a b \arcsin\left(c x\right)}{d e x} - \frac{\sqrt{-c^{2} d e x^{2} + d e} a^{2}}{d e x}"," ",0,"-((-1)^(-2*c^2*d*e*x^2 + 2*d*e)*d*e*log(-2*c^2*d*e + 2*d*e/x^2)/sqrt(d*e) + d*e*sqrt(1/(d*e))*log(x^2 - 1/c^2))*a*b*c/(d*e) + b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2), x)/(sqrt(d)*sqrt(e)) - 2*sqrt(-c^2*d*e*x^2 + d*e)*a*b*arcsin(c*x)/(d*e*x) - sqrt(-c^2*d*e*x^2 + d*e)*a^2/(d*e*x)","F",0
591,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d e} - \frac{\arcsin\left(c x\right)}{\sqrt{d e} c^{3} d e}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}\,{d x}"," ",0,"a^2*(x/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d*e) - arcsin(c*x)/(sqrt(d*e)*c^3*d*e)) + sqrt(d)*sqrt(e)*integrate((b^2*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x)","F",0
592,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","\sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} e^{2} x^{4} - 2 \, c^{2} d^{2} e^{2} x^{2} + d^{2} e^{2}}\,{d x} + \frac{a^{2}}{\sqrt{-c^{2} d e x^{2} + d e} c^{2} d e}"," ",0,"sqrt(d)*sqrt(e)*integrate((b^2*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*e^2*x^4 - 2*c^2*d^2*e^2*x^2 + d^2*e^2), x) + a^2/(sqrt(-c^2*d*e*x^2 + d*e)*c^2*d*e)","F",0
593,-1,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(\frac{2 \, d e}{{\left| x \right|}} + \frac{2 \, \sqrt{-c^{2} d e x^{2} + d e} \sqrt{d e}}{{\left| x \right|}}\right)}{\sqrt{d e} d e} - \frac{1}{\sqrt{-c^{2} d e x^{2} + d e} d e}\right)} + \sqrt{d} \sqrt{e} \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} e^{2} x^{5} - 2 \, c^{2} d^{2} e^{2} x^{3} + d^{2} e^{2} x}\,{d x}"," ",0,"-a^2*(log(2*d*e/abs(x) + 2*sqrt(-c^2*d*e*x^2 + d*e)*sqrt(d*e)/abs(x))/(sqrt(d*e)*d*e) - 1/(sqrt(-c^2*d*e*x^2 + d*e)*d*e)) + sqrt(d)*sqrt(e)*integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(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
595,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x, algorithm=""maxima"")","a b c {\left(\frac{\log\left(c x + 1\right)}{d^{\frac{3}{2}} e^{\frac{3}{2}}} + \frac{\log\left(c x - 1\right)}{d^{\frac{3}{2}} e^{\frac{3}{2}}} + \frac{2 \, \log\left(x\right)}{d^{\frac{3}{2}} e^{\frac{3}{2}}}\right)} + 2 \, a b {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d e x^{2} + d e} d e} - \frac{1}{\sqrt{-c^{2} d e x^{2} + d e} d e x}\right)} \arcsin\left(c x\right) + a^{2} {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d e x^{2} + d e} d e} - \frac{1}{\sqrt{-c^{2} d e x^{2} + d e} d e x}\right)} - \frac{\frac{\frac{1}{4} \, {\left(7 \, {\left(2 \, c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} - 4 \, {\left(c^{2} d e x^{3} - d e x\right)} \int \frac{9 \, \sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 14 \, {\left(2 \, c^{5} x^{5} - 3 \, c^{3} x^{3} + c x\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{4 \, {\left(c^{4} d e x^{6} - 2 \, c^{2} d e x^{4} + d e x^{2}\right)}}\,{d x}\right)} b^{2}}{4 \, {\left(c^{2} d e x^{3} - d e x\right)}}}{\sqrt{d} \sqrt{e}}"," ",0,"a*b*c*(log(c*x + 1)/(d^(3/2)*e^(3/2)) + log(c*x - 1)/(d^(3/2)*e^(3/2)) + 2*log(x)/(d^(3/2)*e^(3/2))) + 2*a*b*(2*c^2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d*e) - 1/(sqrt(-c^2*d*e*x^2 + d*e)*d*e*x))*arcsin(c*x) + a^2*(2*c^2*x/(sqrt(-c^2*d*e*x^2 + d*e)*d*e) - 1/(sqrt(-c^2*d*e*x^2 + d*e)*d*e*x)) - b^2*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2/((c^2*d*e*x^4 - d*e*x^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)/(sqrt(d)*sqrt(e))","F",0
596,1,183,0,1.080264," ","integrate(x^4*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d + \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b e"," ",0,"1/7*a*e*x^7 + 1/5*a*d*x^5 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d + 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*e","A",0
597,1,163,0,0.513836," ","integrate(x^3*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*x^4 + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e","A",0
598,1,142,0,0.593570," ","integrate(x^2*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e","A",0
599,1,122,0,1.238636," ","integrate(x*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e","A",0
600,1,91,0,0.491828," ","integrate((e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b e + a d x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d}{c}"," ",0,"1/3*a*e*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e + a*d*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d/c","A",0
601,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) + \int \frac{{\left(b e x^{2} + b d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/2*a*e*x^2 + a*d*log(x) + integrate((b*e*x^2 + b*d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
602,1,79,0,0.526817," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","-{\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d + a e x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b e}{c} - \frac{a d}{x}"," ",0,"-(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d + a*e*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*e/c - a*d/x","A",0
603,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, b d {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} + b e \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"-1/2*b*d*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) + b*e*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x) + a*e*log(x) - 1/2*a*d/x^2","F",0
604,1,119,0,1.213366," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b e - \frac{a e}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"-1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*e - a*e/x - 1/3*a*d/x^3","A",0
605,1,314,0,1.848728," ","integrate(x^4*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{2} x^{9} + \frac{2}{7} \, a d e x^{7} + \frac{1}{5} \, a d^{2} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2} + \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b d e + \frac{1}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b e^{2}"," ",0,"1/9*a*e^2*x^9 + 2/7*a*d*e*x^7 + 1/5*a*d^2*x^5 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^2 + 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*d*e + 1/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*e^2","A",0
606,1,284,0,0.676180," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{2} x^{8} + \frac{1}{3} \, a d e x^{6} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2} + \frac{1}{144} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b d e + \frac{1}{3072} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b e^{2}"," ",0,"1/8*a*e^2*x^8 + 1/3*a*d*e*x^6 + 1/4*a*d^2*x^4 + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2 + 1/144*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*d*e + 1/3072*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*e^2","A",0
607,1,253,0,1.088056," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{2} x^{7} + \frac{2}{5} \, a d e x^{5} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e + \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b e^{2}"," ",0,"1/7*a*e^2*x^7 + 2/5*a*d*e*x^5 + 1/3*a*d^2*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2 + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d*e + 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*e^2","A",0
608,1,223,0,0.615769," ","integrate(x*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} x^{6} + \frac{1}{2} \, a d e x^{4} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d e + \frac{1}{288} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e^{2}"," ",0,"1/6*a*e^2*x^6 + 1/2*a*d*e*x^4 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^2 + 1/16*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d*e + 1/288*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e^2","A",0
609,1,182,0,0.479857," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d e + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{2} + a d^{2} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d*e + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^2 + a*d^2*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2/c","A",0
610,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} x^{4} + a d e x^{2} + a d^{2} \log\left(x\right) + \int \frac{{\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/4*a*e^2*x^4 + a*d*e*x^2 + a*d^2*log(x) + integrate((b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
611,1,151,0,1.497314," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d^{2} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b e^{2} + 2 \, a d e x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d e}{c} - \frac{a d^{2}}{x}"," ",0,"1/3*a*e^2*x^3 - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d^2 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e^2 + 2*a*d*e*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d*e/c - a*d^2/x","A",0
612,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{2} x^{2} - \frac{1}{2} \, b d^{2} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} + 2 \, a d e \log\left(x\right) - \frac{a d^{2}}{2 \, x^{2}} + \int \frac{{\left(b e^{2} x^{2} + 2 \, b d e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/2*a*e^2*x^2 - 1/2*b*d^2*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) + 2*a*d*e*log(x) - 1/2*a*d^2/x^2 + integrate((b*e^2*x^2 + 2*b*d*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
613,1,159,0,1.073457," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d^{2} - 2 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d e + a e^{2} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b e^{2}}{c} - \frac{2 \, a d e}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"-1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d^2 - 2*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d*e + a*e^2*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*e^2/c - 2*a*d*e/x - 1/3*a*d^2/x^3","A",0
614,1,465,0,0.751642," ","integrate(x^4*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{11} \, a e^{3} x^{11} + \frac{1}{3} \, a d e^{2} x^{9} + \frac{3}{7} \, a d^{2} e x^{7} + \frac{1}{5} \, a d^{3} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{3} + \frac{3}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b d^{2} e + \frac{1}{945} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b d e^{2} + \frac{1}{7623} \, {\left(693 \, x^{11} \arcsin\left(c x\right) + {\left(\frac{63 \, \sqrt{-c^{2} x^{2} + 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{-c^{2} x^{2} + 1}}{c^{12}}\right)} c\right)} b e^{3}"," ",0,"1/11*a*e^3*x^11 + 1/3*a*d*e^2*x^9 + 3/7*a*d^2*e*x^7 + 1/5*a*d^3*x^5 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^3 + 3/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*d^2*e + 1/945*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*d*e^2 + 1/7623*(693*x^11*arcsin(c*x) + (63*sqrt(-c^2*x^2 + 1)*x^10/c^2 + 70*sqrt(-c^2*x^2 + 1)*x^8/c^4 + 80*sqrt(-c^2*x^2 + 1)*x^6/c^6 + 96*sqrt(-c^2*x^2 + 1)*x^4/c^8 + 128*sqrt(-c^2*x^2 + 1)*x^2/c^10 + 256*sqrt(-c^2*x^2 + 1)/c^12)*c)*b*e^3","A",0
615,1,425,0,1.135323," ","integrate(x^3*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{10} \, a e^{3} x^{10} + \frac{3}{8} \, a d e^{2} x^{8} + \frac{1}{2} \, a d^{2} e x^{6} + \frac{1}{4} \, a d^{3} x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{3} + \frac{1}{96} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b d^{2} e + \frac{1}{1024} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b d e^{2} + \frac{1}{12800} \, {\left(1280 \, x^{10} \arcsin\left(c x\right) + {\left(\frac{128 \, \sqrt{-c^{2} x^{2} + 1} x^{9}}{c^{2}} + \frac{144 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{6}} + \frac{210 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{10}} - \frac{315 \, \arcsin\left(c x\right)}{c^{11}}\right)} c\right)} b e^{3}"," ",0,"1/10*a*e^3*x^10 + 3/8*a*d*e^2*x^8 + 1/2*a*d^2*e*x^6 + 1/4*a*d^3*x^4 + 1/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^3 + 1/96*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*d^2*e + 1/1024*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*d*e^2 + 1/12800*(1280*x^10*arcsin(c*x) + (128*sqrt(-c^2*x^2 + 1)*x^9/c^2 + 144*sqrt(-c^2*x^2 + 1)*x^7/c^4 + 168*sqrt(-c^2*x^2 + 1)*x^5/c^6 + 210*sqrt(-c^2*x^2 + 1)*x^3/c^8 + 315*sqrt(-c^2*x^2 + 1)*x/c^10 - 315*arcsin(c*x)/c^11)*c)*b*e^3","A",0
616,1,384,0,0.561546," ","integrate(x^2*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{3} x^{9} + \frac{3}{7} \, a d e^{2} x^{7} + \frac{3}{5} \, a d^{2} e x^{5} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2} e + \frac{3}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b d e^{2} + \frac{1}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b e^{3}"," ",0,"1/9*a*e^3*x^9 + 3/7*a*d*e^2*x^7 + 3/5*a*d^2*e*x^5 + 1/3*a*d^3*x^3 + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^3 + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^2*e + 3/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*d*e^2 + 1/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*e^3","A",0
617,1,344,0,0.964128," ","integrate(x*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{3} x^{8} + \frac{1}{2} \, a d e^{2} x^{6} + \frac{3}{4} \, a d^{2} e x^{4} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d^{3} + \frac{3}{32} \, {\left(8 \, x^{4} \arcsin\left(c x\right) + {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d^{2} e + \frac{1}{96} \, {\left(48 \, x^{6} \arcsin\left(c x\right) + {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b d e^{2} + \frac{1}{3072} \, {\left(384 \, x^{8} \arcsin\left(c x\right) + {\left(\frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{8}} - \frac{105 \, \arcsin\left(c x\right)}{c^{9}}\right)} c\right)} b e^{3}"," ",0,"1/8*a*e^3*x^8 + 1/2*a*d*e^2*x^6 + 3/4*a*d^2*e*x^4 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d^3 + 3/32*(8*x^4*arcsin(c*x) + (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d^2*e + 1/96*(48*x^6*arcsin(c*x) + (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*d*e^2 + 1/3072*(384*x^8*arcsin(c*x) + (48*sqrt(-c^2*x^2 + 1)*x^7/c^2 + 56*sqrt(-c^2*x^2 + 1)*x^5/c^4 + 70*sqrt(-c^2*x^2 + 1)*x^3/c^6 + 105*sqrt(-c^2*x^2 + 1)*x/c^8 - 105*arcsin(c*x)/c^9)*c)*b*e^3","A",0
618,1,292,0,1.204288," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{3} x^{7} + \frac{3}{5} \, a d e^{2} x^{5} + a d^{2} e x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{2} e + \frac{1}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d e^{2} + \frac{1}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{3}}{c}"," ",0,"1/7*a*e^3*x^7 + 3/5*a*d*e^2*x^5 + a*d^2*e*x^3 + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^2*e + 1/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d*e^2 + 1/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*e^3 + a*d^3*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^3/c","A",0
619,0,0,0,0.000000," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x,x, algorithm=""maxima"")","\frac{1}{6} \, a e^{3} x^{6} + \frac{3}{4} \, a d e^{2} x^{4} + \frac{3}{2} \, a d^{2} e x^{2} + a d^{3} \log\left(x\right) + \int \frac{{\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/6*a*e^3*x^6 + 3/4*a*d*e^2*x^4 + 3/2*a*d^2*e*x^2 + a*d^3*log(x) + integrate((b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
620,1,241,0,1.095334," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a e^{3} x^{5} + a d e^{2} x^{3} - {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d e^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e^{3} + 3 \, a d^{2} e x + \frac{3 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{2} e}{c} - \frac{a d^{3}}{x}"," ",0,"1/5*a*e^3*x^5 + a*d*e^2*x^3 - (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d^3 + 1/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d*e^2 + 1/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e^3 + 3*a*d^2*e*x + 3*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^2*e/c - a*d^3/x","A",0
621,0,0,0,0.000000," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + \frac{3}{2} \, a d e^{2} x^{2} - \frac{1}{2} \, b d^{3} {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} + \frac{\arcsin\left(c x\right)}{x^{2}}\right)} + 3 \, a d^{2} e \log\left(x\right) - \frac{a d^{3}}{2 \, x^{2}} + \int \frac{{\left(b e^{3} x^{4} + 3 \, b d e^{2} x^{2} + 3 \, b d^{2} e\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{x}\,{d x}"," ",0,"1/4*a*e^3*x^4 + 3/2*a*d*e^2*x^2 - 1/2*b*d^3*(sqrt(-c^2*x^2 + 1)*c/x + arcsin(c*x)/x^2) + 3*a*d^2*e*log(x) - 1/2*a*d^3/x^2 + integrate((b*e^3*x^4 + 3*b*d*e^2*x^2 + 3*b*d^2*e)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/x, x)","F",0
622,1,231,0,0.657741," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{3} x^{3} - \frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c + \frac{2 \, \arcsin\left(c x\right)}{x^{3}}\right)} b d^{3} - 3 \, {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\arcsin\left(c x\right)}{x}\right)} b d^{2} e + \frac{1}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b e^{3} + 3 \, a d e^{2} x + \frac{3 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d e^{2}}{c} - \frac{3 \, a d^{2} e}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"1/3*a*e^3*x^3 - 1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c + 2*arcsin(c*x)/x^3)*b*d^3 - 3*(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + arcsin(c*x)/x)*b*d^2*e + 1/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e^3 + 3*a*d*e^2*x + 3*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d*e^2/c - 3*a*d^2*e/x - 1/3*a*d^3/x^3","A",0
623,1,424,0,0.785838," ","integrate((e*x^2+d)^4*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{4} x^{9} + \frac{4}{7} \, a d e^{3} x^{7} + \frac{6}{5} \, a d^{2} e^{2} x^{5} + \frac{4}{3} \, a d^{3} e x^{3} + \frac{4}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d^{3} e + \frac{2}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b d^{2} e^{2} + \frac{4}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} b d e^{3} + \frac{1}{2835} \, {\left(315 \, x^{9} \arcsin\left(c x\right) + {\left(\frac{35 \, \sqrt{-c^{2} x^{2} + 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{-c^{2} x^{2} + 1}}{c^{10}}\right)} c\right)} b e^{4} + a d^{4} x + \frac{{\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} b d^{4}}{c}"," ",0,"1/9*a*e^4*x^9 + 4/7*a*d*e^3*x^7 + 6/5*a*d^2*e^2*x^5 + 4/3*a*d^3*e*x^3 + 4/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d^3*e + 2/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*d^2*e^2 + 4/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*b*d*e^3 + 1/2835*(315*x^9*arcsin(c*x) + (35*sqrt(-c^2*x^2 + 1)*x^8/c^2 + 40*sqrt(-c^2*x^2 + 1)*x^6/c^4 + 48*sqrt(-c^2*x^2 + 1)*x^4/c^6 + 64*sqrt(-c^2*x^2 + 1)*x^2/c^8 + 128*sqrt(-c^2*x^2 + 1)/c^10)*c)*b*e^4 + a*d^4*x + (c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*b*d^4/c","A",0
624,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, d^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{e x^{3} - 3 \, d x}{e^{2}}\right)} + b \int \frac{x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"1/3*a*(3*d^2*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) + (e*x^3 - 3*d*x)/e^2) + b*integrate(x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^2 + d), x)","F",0
625,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{2}}{e} - \frac{d \log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"1/2*a*(x^2/e - d*log(e*x^2 + d)/e^2) + b*integrate(x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^2 + d), x)","F",0
626,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + b \int \frac{x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"-a*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + b*integrate(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^2 + d), x)","F",0
627,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{x \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"b*integrate(x*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^2 + d), x) + 1/2*a*log(e*x^2 + d)/e","F",0
628,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
629,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{3} + d x}\,{d x}"," ",0,"-1/2*a*(log(e*x^2 + d)/d - 2*log(x)/d) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^3 + d*x), x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{4} + d x^{2}}\,{d x}"," ",0,"-a*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^4 + d*x^2), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \log\left(e x^{2} + d\right)}{d^{2}} - \frac{2 \, e \log\left(x\right)}{d^{2}} - \frac{1}{d x^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{5} + d x^{3}}\,{d x}"," ",0,"1/2*a*(e*log(e*x^2 + d)/d^2 - 2*e*log(x)/d^2 - 1/(d*x^2)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^5 + d*x^3), x)","F",0
632,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^4/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, e^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}} + \frac{3 \, e x^{2} - d}{d^{2} x^{3}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{6} + d x^{4}}\,{d x}"," ",0,"1/3*a*(3*e^2*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2) + (3*e*x^2 - d)/(d^2*x^3)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e*x^6 + d*x^4), x)","F",0
633,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + b*integrate(x^3*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
634,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c e^{2} x^{2} + c d e\right)} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{2} x^{6} - c^{2} d e x^{2} + {\left(c^{4} d e - c^{2} e^{2}\right)} x^{4} - {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{2 \, {\left(e^{2} x^{2} + d e\right)}} - \frac{a}{2 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"-1/2*(2*(c*e^2*x^2 + c*d*e)*integrate(1/2*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^2*x^6 - c^2*d*e*x^2 + (c^4*d*e - c^2*e^2)*x^4 + (c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(e^2*x^2 + d*e) - 1/2*a/(e^2*x^2 + d*e)","F",0
635,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{d e x^{2} + d^{2}} - \frac{\log\left(e x^{2} + d\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a*(1/(d*e*x^2 + d^2) - log(e*x^2 + d)/d^2 + 2*log(x)/d^2) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e x^{2} + d}{d^{2} e x^{4} + d^{3} x^{2}} - \frac{2 \, e \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, e \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*((2*e*x^2 + d)/(d^2*e*x^4 + d^3*x^2) - 2*e*log(e*x^2 + d)/d^3 + 4*e*log(x)/d^3) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
637,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d x}{e^{3} x^{2} + d e^{2}} - \frac{3 \, d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{2 \, x}{e^{2}}\right)} + b \int \frac{x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d*x/(e^3*x^2 + d*e^2) - 3*d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) + 2*x/e^2) + b*integrate(x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
638,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x}{e^{2} x^{2} + d e} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} + b \int \frac{x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(x/(e^2*x^2 + d*e) - arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) + b*integrate(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
639,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{d e x^{2} + d^{2}} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(x/(d*e*x^2 + d^2) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
640,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{3 \, e x^{2} + 2 \, d}{d^{2} e x^{3} + d^{3} x} + \frac{3 \, e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}\,{d x}"," ",0,"-1/2*a*((3*e*x^2 + 2*d)/(d^2*e*x^3 + d^3*x) + 3*e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
641,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{4 \, d e x^{2} + 3 \, d^{2}}{e^{5} x^{4} + 2 \, d e^{4} x^{2} + d^{2} e^{3}} + \frac{2 \, \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/4*a*((4*d*e*x^2 + 3*d^2)/(e^5*x^4 + 2*d*e^4*x^2 + d^2*e^3) + 2*log(e*x^2 + d)/e^3) + b*integrate(x^5*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
642,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, e x^{2} + d\right)} a}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}} - \frac{{\left({\left(2 \, e x^{2} + d\right)} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)} \int \frac{{\left(2 \, c e x^{2} + c d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{4} x^{8} - c^{2} d^{2} e^{2} x^{2} + {\left(2 \, c^{4} d e^{3} - c^{2} e^{4}\right)} x^{6} + {\left(c^{4} d^{2} e^{2} - 2 \, c^{2} d e^{3}\right)} x^{4} - {\left(c^{2} e^{4} x^{6} + {\left(2 \, c^{2} d e^{3} - e^{4}\right)} x^{4} - d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, d e^{3}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} b}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}}"," ",0,"-1/4*(2*e*x^2 + d)*a/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2) - 1/4*((2*e*x^2 + d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + 4*(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)*integrate(1/4*(2*c*e*x^2 + c*d)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^4*x^8 - c^2*d^2*e^2*x^2 + (2*c^4*d*e^3 - c^2*e^4)*x^6 + (c^4*d^2*e^2 - 2*c^2*d*e^3)*x^4 + (c^2*e^4*x^6 + (2*c^2*d*e^3 - e^4)*x^4 - d^2*e^2 + (c^2*d^2*e^2 - 2*d*e^3)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))*b/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)","F",0
643,0,0,0,0.000000," ","integrate(x*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{{\left({\left(c e^{3} x^{4} + 2 \, c d e^{2} x^{2} + c d^{2} e\right)} \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{4} e^{3} x^{8} - c^{2} d^{2} e x^{2} + {\left(2 \, c^{4} d e^{2} - c^{2} e^{3}\right)} x^{6} + {\left(c^{4} d^{2} e - 2 \, c^{2} d e^{2}\right)} x^{4} - {\left(c^{2} e^{3} x^{6} + {\left(2 \, c^{2} d e^{2} - e^{3}\right)} x^{4} - d^{2} e + {\left(c^{2} d^{2} e - 2 \, d e^{2}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} + \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} b}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}} - \frac{a}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}}"," ",0,"-1/4*(4*(c*e^3*x^4 + 2*c*d*e^2*x^2 + c*d^2*e)*integrate(1/4*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))/(c^4*e^3*x^8 - c^2*d^2*e*x^2 + (2*c^4*d*e^2 - c^2*e^3)*x^6 + (c^4*d^2*e - 2*c^2*d*e^2)*x^4 + (c^2*e^3*x^6 + (2*c^2*d*e^2 - e^3)*x^4 - d^2*e + (c^2*d^2*e - 2*d*e^2)*x^2)*e^(log(c*x + 1) + log(-c*x + 1))), x) + arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*b/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e) - 1/4*a/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e)","F",0
644,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, e x^{2} + 3 \, d}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} - \frac{2 \, \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a*((2*e*x^2 + 3*d)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) - 2*log(e*x^2 + d)/d^3 + 4*log(x)/d^3) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/x^3/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, e^{2} x^{4} + 9 \, d e x^{2} + 2 \, d^{2}}{d^{3} e^{2} x^{6} + 2 \, d^{4} e x^{4} + d^{5} x^{2}} - \frac{6 \, e \log\left(e x^{2} + d\right)}{d^{4}} + \frac{12 \, e \log\left(x\right)}{d^{4}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}\,{d x}"," ",0,"-1/4*a*((6*e^2*x^4 + 9*d*e*x^2 + 2*d^2)/(d^3*e^2*x^6 + 2*d^4*e*x^4 + d^5*x^2) - 6*e*log(e*x^2 + d)/d^4 + 12*e*log(x)/d^4) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
646,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{5 \, e x^{3} + 3 \, d x}{e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}} - \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}}\right)} + b \int \frac{x^{4} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"-1/8*a*((5*e*x^3 + 3*d*x)/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2) - 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2)) + b*integrate(x^4*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
647,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{e x^{3} - d x}{d e^{3} x^{4} + 2 \, d^{2} e^{2} x^{2} + d^{3} e} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d e}\right)} + b \int \frac{x^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((e*x^3 - d*x)/(d*e^3*x^4 + 2*d^2*e^2*x^2 + d^3*e) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d*e)) + b*integrate(x^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
648,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{3 \, e x^{3} + 5 \, d x}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} + \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((3*e*x^3 + 5*d*x)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) + 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
649,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int \sqrt{e x^{2} + d} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate(sqrt(e*x^2 + d)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
650,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
651,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
652,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
653,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))/(e*x^2+d)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{8 \, x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} + \frac{3 \, x}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} d}\right)} + b \int \frac{\arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{{\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/15*a*(8*x/(sqrt(e*x^2 + d)*d^3) + 4*x/((e*x^2 + d)^(3/2)*d^2) + 3*x/((e*x^2 + d)^(5/2)*d)) + b*integrate(arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))/((e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)*sqrt(e*x^2 + d)), x)","F",0
654,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{a e^{3} f^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a d e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a d^{2} e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{3}}{f {\left(m + 1\right)}} + \frac{{\left({\left(b e^{3} f^{m} m^{3} + 9 \, b e^{3} f^{m} m^{2} + 23 \, b e^{3} f^{m} m + 15 \, b e^{3} f^{m}\right)} x^{7} + 3 \, {\left(b d e^{2} f^{m} m^{3} + 11 \, b d e^{2} f^{m} m^{2} + 31 \, b d e^{2} f^{m} m + 21 \, b d e^{2} f^{m}\right)} x^{5} + 3 \, {\left(b d^{2} e f^{m} m^{3} + 13 \, b d^{2} e f^{m} m^{2} + 47 \, b d^{2} e f^{m} m + 35 \, b d^{2} e f^{m}\right)} x^{3} + {\left(b d^{3} f^{m} m^{3} + 15 \, b d^{3} f^{m} m^{2} + 71 \, b d^{3} f^{m} m + 105 \, b d^{3} f^{m}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left({\left(b c e^{3} f^{m} m^{3} + 9 \, b c e^{3} f^{m} m^{2} + 23 \, b c e^{3} f^{m} m + 15 \, b c e^{3} f^{m}\right)} x^{7} + 3 \, {\left(b c d e^{2} f^{m} m^{3} + 11 \, b c d e^{2} f^{m} m^{2} + 31 \, b c d e^{2} f^{m} m + 21 \, b c d e^{2} f^{m}\right)} x^{5} + 3 \, {\left(b c d^{2} e f^{m} m^{3} + 13 \, b c d^{2} e f^{m} m^{2} + 47 \, b c d^{2} e f^{m} m + 35 \, b c d^{2} e f^{m}\right)} x^{3} + {\left(b c d^{3} f^{m} m^{3} + 15 \, b c d^{3} f^{m} m^{2} + 71 \, b c d^{3} f^{m} m + 105 \, b c d^{3} f^{m}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m}}{m^{4} + 16 \, m^{3} - {\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"a*e^3*f^m*x^7*x^m/(m + 7) + 3*a*d*e^2*f^m*x^5*x^m/(m + 5) + 3*a*d^2*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^3/(f*(m + 1)) + (((b*e^3*f^m*m^3 + 9*b*e^3*f^m*m^2 + 23*b*e^3*f^m*m + 15*b*e^3*f^m)*x^7 + 3*(b*d*e^2*f^m*m^3 + 11*b*d*e^2*f^m*m^2 + 31*b*d*e^2*f^m*m + 21*b*d*e^2*f^m)*x^5 + 3*(b*d^2*e*f^m*m^3 + 13*b*d^2*e*f^m*m^2 + 47*b*d^2*e*f^m*m + 35*b*d^2*e*f^m)*x^3 + (b*d^3*f^m*m^3 + 15*b*d^3*f^m*m^2 + 71*b*d^3*f^m*m + 105*b*d^3*f^m)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(-((b*c*e^3*f^m*m^3 + 9*b*c*e^3*f^m*m^2 + 23*b*c*e^3*f^m*m + 15*b*c*e^3*f^m)*x^7 + 3*(b*c*d*e^2*f^m*m^3 + 11*b*c*d*e^2*f^m*m^2 + 31*b*c*d*e^2*f^m*m + 21*b*c*d*e^2*f^m)*x^5 + 3*(b*c*d^2*e*f^m*m^3 + 13*b*c*d^2*e*f^m*m^2 + 47*b*c*d^2*e*f^m*m + 35*b*c*d^2*e*f^m)*x^3 + (b*c*d^3*f^m*m^3 + 15*b*c*d^3*f^m*m^2 + 71*b*c*d^3*f^m*m + 105*b*c*d^3*f^m)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m/(m^4 + 16*m^3 - (c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
655,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\frac{a e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a d e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{2}}{f {\left(m + 1\right)}} + \frac{{\left({\left(b e^{2} f^{m} m^{2} + 4 \, b e^{2} f^{m} m + 3 \, b e^{2} f^{m}\right)} x^{5} + 2 \, {\left(b d e f^{m} m^{2} + 6 \, b d e f^{m} m + 5 \, b d e f^{m}\right)} x^{3} + {\left(b d^{2} f^{m} m^{2} + 8 \, b d^{2} f^{m} m + 15 \, b d^{2} f^{m}\right)} x\right)} x^{m} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left({\left(b c e^{2} f^{m} m^{2} + 4 \, b c e^{2} f^{m} m + 3 \, b c e^{2} f^{m}\right)} x^{5} + 2 \, {\left(b c d e f^{m} m^{2} + 6 \, b c d e f^{m} m + 5 \, b c d e f^{m}\right)} x^{3} + {\left(b c d^{2} f^{m} m^{2} + 8 \, b c d^{2} f^{m} m + 15 \, b c d^{2} f^{m}\right)} x\right)} \sqrt{c x + 1} \sqrt{-c x + 1} x^{m}}{m^{3} - {\left(c^{2} m^{3} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 15 \, c^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"a*e^2*f^m*x^5*x^m/(m + 5) + 2*a*d*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^2/(f*(m + 1)) + (((b*e^2*f^m*m^2 + 4*b*e^2*f^m*m + 3*b*e^2*f^m)*x^5 + 2*(b*d*e*f^m*m^2 + 6*b*d*e*f^m*m + 5*b*d*e*f^m)*x^3 + (b*d^2*f^m*m^2 + 8*b*d^2*f^m*m + 15*b*d^2*f^m)*x)*x^m*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + (m^3 + 9*m^2 + 23*m + 15)*integrate(-((b*c*e^2*f^m*m^2 + 4*b*c*e^2*f^m*m + 3*b*c*e^2*f^m)*x^5 + 2*(b*c*d*e*f^m*m^2 + 6*b*c*d*e*f^m*m + 5*b*c*d*e*f^m)*x^3 + (b*c*d^2*f^m*m^2 + 8*b*c*d^2*f^m*m + 15*b*c*d^2*f^m)*x)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m/(m^3 - (c^2*m^3 + 9*c^2*m^2 + 23*c^2*m + 15*c^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
656,-1,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
658,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
659,1,699,0,0.471557," ","integrate((e*x^2+d)^3*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} e^{3} x^{7} \arcsin\left(c x\right)^{2} + \frac{1}{7} \, a^{2} e^{3} x^{7} + \frac{3}{5} \, b^{2} d e^{2} x^{5} \arcsin\left(c x\right)^{2} + \frac{3}{5} \, a^{2} d e^{2} x^{5} + b^{2} d^{2} e x^{3} \arcsin\left(c x\right)^{2} + a^{2} d^{2} e x^{3} + b^{2} d^{3} x \arcsin\left(c x\right)^{2} + \frac{2}{3} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d^{2} e + \frac{2}{9} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d^{2} e + \frac{2}{25} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b d e^{2} + \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d e^{2} + \frac{2}{245} \, {\left(35 \, x^{7} \arcsin\left(c x\right) + {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c\right)} a b e^{3} + \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{-c^{2} x^{2} + 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{-c^{2} x^{2} + 1}}{c^{8}}\right)} c \arcsin\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} e^{3} - 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d^{3}}{c}"," ",0,"1/7*b^2*e^3*x^7*arcsin(c*x)^2 + 1/7*a^2*e^3*x^7 + 3/5*b^2*d*e^2*x^5*arcsin(c*x)^2 + 3/5*a^2*d*e^2*x^5 + b^2*d^2*e*x^3*arcsin(c*x)^2 + a^2*d^2*e*x^3 + b^2*d^3*x*arcsin(c*x)^2 + 2/3*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*d^2*e + 2/9*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d^2*e + 2/25*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*d*e^2 + 2/375*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*d*e^2 + 2/245*(35*x^7*arcsin(c*x) + (5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c)*a*b*e^3 + 2/25725*(105*(5*sqrt(-c^2*x^2 + 1)*x^6/c^2 + 6*sqrt(-c^2*x^2 + 1)*x^4/c^4 + 8*sqrt(-c^2*x^2 + 1)*x^2/c^6 + 16*sqrt(-c^2*x^2 + 1)/c^8)*c*arcsin(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*e^3 - 2*b^2*d^3*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d^3*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d^3/c","A",0
660,1,437,0,0.448478," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} e^{2} x^{5} \arcsin\left(c x\right)^{2} + \frac{1}{5} \, a^{2} e^{2} x^{5} + \frac{2}{3} \, b^{2} d e x^{3} \arcsin\left(c x\right)^{2} + \frac{2}{3} \, a^{2} d e x^{3} + b^{2} d^{2} x \arcsin\left(c x\right)^{2} + \frac{4}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b d e + \frac{4}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d e + \frac{2}{75} \, {\left(15 \, x^{5} \arcsin\left(c x\right) + {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} a b e^{2} + \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c \arcsin\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} e^{2} - 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d^{2}}{c}"," ",0,"1/5*b^2*e^2*x^5*arcsin(c*x)^2 + 1/5*a^2*e^2*x^5 + 2/3*b^2*d*e*x^3*arcsin(c*x)^2 + 2/3*a^2*d*e*x^3 + b^2*d^2*x*arcsin(c*x)^2 + 4/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*d*e + 4/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d*e + 2/75*(15*x^5*arcsin(c*x) + (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*a*b*e^2 + 2/1125*(15*(3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c*arcsin(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*e^2 - 2*b^2*d^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d^2/c","A",0
661,1,221,0,0.436445," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} e x^{3} \arcsin\left(c x\right)^{2} + \frac{1}{3} \, a^{2} e x^{3} + b^{2} d x \arcsin\left(c x\right)^{2} + \frac{2}{9} \, {\left(3 \, x^{3} \arcsin\left(c x\right) + c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} a b e + \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)} \arcsin\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} e - 2 \, b^{2} d {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b d}{c}"," ",0,"1/3*b^2*e*x^3*arcsin(c*x)^2 + 1/3*a^2*e*x^3 + b^2*d*x*arcsin(c*x)^2 + 2/9*(3*x^3*arcsin(c*x) + c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*a*b*e + 2/27*(3*c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4)*arcsin(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*e - 2*b^2*d*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*d*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b*d/c","A",0
662,1,72,0,0.416752," ","integrate((a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","b^{2} x \arcsin\left(c x\right)^{2} - 2 \, b^{2} {\left(x - \frac{\sqrt{-c^{2} x^{2} + 1} \arcsin\left(c x\right)}{c}\right)} + a^{2} x + \frac{2 \, {\left(c x \arcsin\left(c x\right) + \sqrt{-c^{2} x^{2} + 1}\right)} a b}{c}"," ",0,"b^2*x*arcsin(c*x)^2 - 2*b^2*(x - sqrt(-c^2*x^2 + 1)*arcsin(c*x)/c) + a^2*x + 2*(c*x*arcsin(c*x) + sqrt(-c^2*x^2 + 1))*a*b/c","A",0
663,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}} + \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"a^2*arctan(e*x/sqrt(d*e))/sqrt(d*e) + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/(e*x^2 + d), x)","F",0
664,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a^{2} + \int {\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{e x^{2} + d}\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a^2 + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*sqrt(e*x^2 + d), x)","F",0
665,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}} + \int \frac{b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"a^2*arcsinh(e*x/sqrt(d*e))/sqrt(e) + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))/sqrt(e*x^2 + d), x)","F",0
666,-2,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
667,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^2/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \int \frac{{\left(b^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)^{2} + 2 \, a b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right)\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/3*a^2*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + integrate((b^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))^2 + 2*a*b*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)))*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
668,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/(b*arcsin(c*x) + a), x)","F",0
669,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arcsin(c*x) + a), x)","F",0
670,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsin(c*x) + a), x)","F",0
671,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arcsin(c*x) + a)), x)","F",0
672,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arcsin(c*x) + a)), x)","F",0
673,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{e x^{2} + d}}{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)/(b*arcsin(c*x) + a), x)","F",0
674,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e x^{2} + d} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*x^2 + d)*(b*arcsin(c*x) + a)), x)","F",0
675,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(3/2)*(b*arcsin(c*x) + a)), x)","F",0
676,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} {\left(b \arcsin\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(5/2)*(b*arcsin(c*x) + a)), x)","F",0
677,-1,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\frac{-\sqrt{c x + 1} \sqrt{-c x + 1} + \frac{{\left(b^{2} c^{2} \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c^{2}\right)} \int \frac{\sqrt{-c x + 1} x}{\sqrt{c x + 1} {\left(c x - 1\right)} {\left(b \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a\right)}}\,{d x}}{b}}{b^{2} c \arctan\left(c x, \sqrt{c x + 1} \sqrt{-c x + 1}\right) + a b c}"," ",0,"((b^2*c^2*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c^2)*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x/(a*b*c^2*x^2 - a*b + (b^2*c^2*x^2 - b^2)*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1))), x) - sqrt(c*x + 1)*sqrt(-c*x + 1))/(b^2*c*arctan2(c*x, sqrt(c*x + 1)*sqrt(-c*x + 1)) + a*b*c)","F",0
680,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
681,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
682,-1,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
684,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
685,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{2} \sqrt{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*sqrt(b*arcsin(c*x) + a), x)","F",0
687,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} \sqrt{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)*sqrt(b*arcsin(c*x) + a), x)","F",0
688,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \arcsin\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(c*x) + a), x)","F",0
689,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{\sqrt{b \arcsin\left(c x\right) + a}}{e x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(c*x) + a)/(e*x^2 + d), x)","F",0
690,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(1/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{b \arcsin\left(c x\right) + a}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(b*arcsin(c*x) + a)/(e*x^2 + d)^2, x)","F",0
691,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arcsin(c*x) + a)^(3/2), x)","F",0
692,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^(3/2), x)","F",0
693,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^(3/2)/(e*x^2 + d), x)","F",0
694,0,0,0,0.000000," ","integrate((a+b*arcsin(c*x))^(3/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^(3/2)/(e*x^2 + d)^2, x)","F",0
695,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{b \arcsin\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(b*arcsin(c*x) + a), x)","F",0
696,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{\sqrt{b \arcsin\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(b*arcsin(c*x) + a), x)","F",0
697,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \arcsin\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arcsin(c*x) + a), x)","F",0
698,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} \sqrt{b \arcsin\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*sqrt(b*arcsin(c*x) + a)), x)","F",0
699,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} \sqrt{b \arcsin\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*sqrt(b*arcsin(c*x) + a)), x)","F",0
700,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arcsin(c*x) + a)^(3/2), x)","F",0
701,0,0,0,0.000000," ","integrate(1/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsin(c*x) + a)^(-3/2), x)","F",0
702,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arcsin(c*x) + a)^(3/2)), x)","F",0
703,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \arcsin\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arcsin(c*x) + a)^(3/2)), x)","F",0
