1,1,130,108,0.012000," ","int(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{-d a \left(\frac{1}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{19 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}-\frac{76 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3675}-\frac{152 \sqrt{-c^{2} x^{2}+1}}{3675}\right)}{c^{5}}"," ",0,"1/c^5*(-d*a*(1/7*c^7*x^7-1/5*c^5*x^5)-d*b*(1/7*arcsin(c*x)*c^7*x^7-1/5*arcsin(c*x)*c^5*x^5+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-19/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)-76/3675*c^2*x^2*(-c^2*x^2+1)^(1/2)-152/3675*(-c^2*x^2+1)^(1/2)))","A"
2,1,118,105,0.010000," ","int(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{-d a \left(\frac{1}{6} c^{6} x^{6}-\frac{1}{4} c^{4} x^{4}\right)-d b \left(\frac{\arcsin \left(c x \right) c^{6} x^{6}}{6}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{c x \sqrt{-c^{2} x^{2}+1}}{24}+\frac{\arcsin \left(c x \right)}{24}\right)}{c^{4}}"," ",0,"1/c^4*(-d*a*(1/6*c^6*x^6-1/4*c^4*x^4)-d*b*(1/6*arcsin(c*x)*c^6*x^6-1/4*c^4*x^4*arcsin(c*x)+1/36*c^5*x^5*(-c^2*x^2+1)^(1/2)-1/36*c^3*x^3*(-c^2*x^2+1)^(1/2)-1/24*c*x*(-c^2*x^2+1)^(1/2)+1/24*arcsin(c*x)))","A"
3,1,110,89,0.008000," ","int(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{-d a \left(\frac{1}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d b \left(\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{13 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{225}-\frac{26 \sqrt{-c^{2} x^{2}+1}}{225}\right)}{c^{3}}"," ",0,"1/c^3*(-d*a*(1/5*c^5*x^5-1/3*c^3*x^3)-d*b*(1/5*arcsin(c*x)*c^5*x^5-1/3*c^3*x^3*arcsin(c*x)+1/25*c^4*x^4*(-c^2*x^2+1)^(1/2)-13/225*c^2*x^2*(-c^2*x^2+1)^(1/2)-26/225*(-c^2*x^2+1)^(1/2)))","A"
4,1,98,78,0.009000," ","int(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{-d a \left(\frac{1}{4} c^{4} x^{4}-\frac{1}{2} c^{2} x^{2}\right)-d b \left(\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}-\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{16}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{32}+\frac{5 \arcsin \left(c x \right)}{32}\right)}{c^{2}}"," ",0,"1/c^2*(-d*a*(1/4*c^4*x^4-1/2*c^2*x^2)-d*b*(1/4*c^4*x^4*arcsin(c*x)-1/2*c^2*x^2*arcsin(c*x)+1/16*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/32*c*x*(-c^2*x^2+1)^(1/2)+5/32*arcsin(c*x)))","A"
5,1,82,67,0.006000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{-d a \left(\frac{1}{3} c^{3} x^{3}-c x \right)-d b \left(\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}-c x \arcsin \left(c x \right)+\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{7 \sqrt{-c^{2} x^{2}+1}}{9}\right)}{c}"," ",0,"1/c*(-d*a*(1/3*c^3*x^3-c*x)-d*b*(1/3*c^3*x^3*arcsin(c*x)-c*x*arcsin(c*x)+1/9*c^2*x^2*(-c^2*x^2+1)^(1/2)-7/9*(-c^2*x^2+1)^(1/2)))","A"
6,1,164,127,0.235000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x,x)","-\frac{d a \,c^{2} x^{2}}{2}+d a \ln \left(c x \right)-\frac{i b d \arcsin \left(c x \right)^{2}}{2}+d b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+\frac{d b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{4}-\frac{d b \sin \left(2 \arcsin \left(c x \right)\right)}{8}"," ",0,"-1/2*d*a*c^2*x^2+d*a*ln(c*x)-1/2*I*b*d*arcsin(c*x)^2+d*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*d*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-I*d*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+1/4*d*b*cos(2*arcsin(c*x))*arcsin(c*x)-1/8*d*b*sin(2*arcsin(c*x))","A"
7,1,67,65,0.009000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^2,x)","c \left(-d a \left(c x +\frac{1}{c x}\right)-d b \left(c x \arcsin \left(c x \right)+\frac{\arcsin \left(c x \right)}{c x}+\sqrt{-c^{2} x^{2}+1}+\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(-d*a*(c*x+1/c/x)-d*b*(c*x*arcsin(c*x)+1/c/x*arcsin(c*x)+(-c^2*x^2+1)^(1/2)+arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
8,1,195,145,0.411000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^3,x)","-c^{2} d a \ln \left(c x \right)-\frac{d a}{2 x^{2}}+\frac{i c^{2} d b \arcsin \left(c x \right)^{2}}{2}+\frac{i c^{2} d b}{2}-\frac{b c d \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{d b \arcsin \left(c x \right)}{2 x^{2}}-c^{2} d b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-c^{2} d b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+i c^{2} d b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+i c^{2} d b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"-c^2*d*a*ln(c*x)-1/2*d*a/x^2+1/2*I*c^2*d*b*arcsin(c*x)^2+1/2*I*c^2*d*b-1/2*b*c*d*(-c^2*x^2+1)^(1/2)/x-1/2*d*b*arcsin(c*x)/x^2-c^2*d*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-c^2*d*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+I*c^2*d*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+I*c^2*d*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
9,1,91,71,0.014000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(-d a \left(\frac{1}{3 c^{3} x^{3}}-\frac{1}{c x}\right)-d b \left(\frac{\arcsin \left(c x \right)}{3 c^{3} x^{3}}-\frac{\arcsin \left(c x \right)}{c x}-\frac{5 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{6}+\frac{\sqrt{-c^{2} x^{2}+1}}{6 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(-d*a*(1/3/c^3/x^3-1/c/x)-d*b*(1/3*arcsin(c*x)/c^3/x^3-1/c/x*arcsin(c*x)-5/6*arctanh(1/(-c^2*x^2+1)^(1/2))+1/6/c^2/x^2*(-c^2*x^2+1)^(1/2)))","A"
10,1,172,160,0.014000," ","int(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{d^{2} a \left(\frac{1}{9} c^{9} x^{9}-\frac{2}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{2} b \left(\frac{\arcsin \left(c x \right) c^{9} x^{9}}{9}-\frac{2 \arcsin \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{106 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{3969}+\frac{263 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{33075}+\frac{1052 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{99225}+\frac{2104 \sqrt{-c^{2} x^{2}+1}}{99225}\right)}{c^{5}}"," ",0,"1/c^5*(d^2*a*(1/9*c^9*x^9-2/7*c^7*x^7+1/5*c^5*x^5)+d^2*b*(1/9*arcsin(c*x)*c^9*x^9-2/7*arcsin(c*x)*c^7*x^7+1/5*arcsin(c*x)*c^5*x^5+1/81*c^8*x^8*(-c^2*x^2+1)^(1/2)-106/3969*c^6*x^6*(-c^2*x^2+1)^(1/2)+263/33075*c^4*x^4*(-c^2*x^2+1)^(1/2)+1052/99225*c^2*x^2*(-c^2*x^2+1)^(1/2)+2104/99225*(-c^2*x^2+1)^(1/2)))","A"
11,1,160,160,0.010000," ","int(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{d^{2} a \left(\frac{1}{8} c^{8} x^{8}-\frac{1}{3} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{2} b \left(\frac{\arcsin \left(c x \right) c^{8} x^{8}}{8}-\frac{\arcsin \left(c x \right) c^{6} x^{6}}{3}+\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{64}-\frac{43 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{1152}+\frac{73 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4608}+\frac{73 c x \sqrt{-c^{2} x^{2}+1}}{3072}-\frac{73 \arcsin \left(c x \right)}{3072}\right)}{c^{4}}"," ",0,"1/c^4*(d^2*a*(1/8*c^8*x^8-1/3*c^6*x^6+1/4*c^4*x^4)+d^2*b*(1/8*arcsin(c*x)*c^8*x^8-1/3*arcsin(c*x)*c^6*x^6+1/4*c^4*x^4*arcsin(c*x)+1/64*c^7*x^7*(-c^2*x^2+1)^(1/2)-43/1152*c^5*x^5*(-c^2*x^2+1)^(1/2)+73/4608*c^3*x^3*(-c^2*x^2+1)^(1/2)+73/3072*c*x*(-c^2*x^2+1)^(1/2)-73/3072*arcsin(c*x)))","A"
12,1,152,139,0.007000," ","int(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{d^{2} a \left(\frac{1}{7} c^{7} x^{7}-\frac{2}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{2} b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{2 \arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{68 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}+\frac{409 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{11025}+\frac{818 \sqrt{-c^{2} x^{2}+1}}{11025}\right)}{c^{3}}"," ",0,"1/c^3*(d^2*a*(1/7*c^7*x^7-2/5*c^5*x^5+1/3*c^3*x^3)+d^2*b*(1/7*arcsin(c*x)*c^7*x^7-2/5*arcsin(c*x)*c^5*x^5+1/3*c^3*x^3*arcsin(c*x)+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-68/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)+409/11025*c^2*x^2*(-c^2*x^2+1)^(1/2)+818/11025*(-c^2*x^2+1)^(1/2)))","A"
13,1,140,108,0.007000," ","int(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{d^{2} a \left(\frac{1}{6} c^{6} x^{6}-\frac{1}{2} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{2} b \left(\frac{\arcsin \left(c x \right) c^{6} x^{6}}{6}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{2}+\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{13 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{144}+\frac{11 c x \sqrt{-c^{2} x^{2}+1}}{96}-\frac{11 \arcsin \left(c x \right)}{96}\right)}{c^{2}}"," ",0,"1/c^2*(d^2*a*(1/6*c^6*x^6-1/2*c^4*x^4+1/2*c^2*x^2)+d^2*b*(1/6*arcsin(c*x)*c^6*x^6-1/2*c^4*x^4*arcsin(c*x)+1/2*c^2*x^2*arcsin(c*x)+1/36*c^5*x^5*(-c^2*x^2+1)^(1/2)-13/144*c^3*x^3*(-c^2*x^2+1)^(1/2)+11/96*c*x*(-c^2*x^2+1)^(1/2)-11/96*arcsin(c*x)))","A"
14,1,122,115,0.005000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{d^{2} a \left(\frac{1}{5} c^{5} x^{5}-\frac{2}{3} c^{3} x^{3}+c x \right)+d^{2} b \left(\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{2 c^{3} x^{3} \arcsin \left(c x \right)}{3}+c x \arcsin \left(c x \right)+\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{38 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{225}+\frac{149 \sqrt{-c^{2} x^{2}+1}}{225}\right)}{c}"," ",0,"1/c*(d^2*a*(1/5*c^5*x^5-2/3*c^3*x^3+c*x)+d^2*b*(1/5*arcsin(c*x)*c^5*x^5-2/3*c^3*x^3*arcsin(c*x)+c*x*arcsin(c*x)+1/25*c^4*x^4*(-c^2*x^2+1)^(1/2)-38/225*c^2*x^2*(-c^2*x^2+1)^(1/2)+149/225*(-c^2*x^2+1)^(1/2)))","A"
15,1,224,184,0.301000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x,x)","\frac{d^{2} a \,c^{4} x^{4}}{4}-d^{2} a \,c^{2} x^{2}+d^{2} a \ln \left(c x \right)-\frac{i b \,d^{2} \arcsin \left(c x \right)^{2}}{2}+d^{2} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d^{2} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d^{2} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d^{2} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+\frac{d^{2} b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{32}-\frac{d^{2} b \sin \left(4 \arcsin \left(c x \right)\right)}{128}+\frac{3 d^{2} b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{8}-\frac{3 d^{2} b \sin \left(2 \arcsin \left(c x \right)\right)}{16}"," ",0,"1/4*d^2*a*c^4*x^4-d^2*a*c^2*x^2+d^2*a*ln(c*x)-1/2*I*b*d^2*arcsin(c*x)^2+d^2*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d^2*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*d^2*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-I*d^2*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+1/32*d^2*b*arcsin(c*x)*cos(4*arcsin(c*x))-1/128*d^2*b*sin(4*arcsin(c*x))+3/8*d^2*b*cos(2*arcsin(c*x))*arcsin(c*x)-3/16*d^2*b*sin(2*arcsin(c*x))","A"
16,1,117,111,0.011000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x)","c \left(d^{2} a \left(\frac{c^{3} x^{3}}{3}-2 c x -\frac{1}{c x}\right)+d^{2} b \left(\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}-2 c x \arcsin \left(c x \right)-\frac{\arcsin \left(c x \right)}{c x}+\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{9}-\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(d^2*a*(1/3*c^3*x^3-2*c*x-1/c/x)+d^2*b*(1/3*c^3*x^3*arcsin(c*x)-2*c*x*arcsin(c*x)-1/c/x*arcsin(c*x)+1/9*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/9*(-c^2*x^2+1)^(1/2)-arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
17,1,278,207,0.566000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x)","\frac{c^{4} d^{2} a \,x^{2}}{2}-2 c^{2} d^{2} a \ln \left(c x \right)-\frac{d^{2} a}{2 x^{2}}+i c^{2} d^{2} b \arcsin \left(c x \right)^{2}+\frac{b \,c^{3} d^{2} x \sqrt{-c^{2} x^{2}+1}}{4}+\frac{c^{4} d^{2} b \arcsin \left(c x \right) x^{2}}{2}-\frac{b \,c^{2} d^{2} \arcsin \left(c x \right)}{4}+\frac{i c^{2} d^{2} b}{2}-\frac{b c \,d^{2} \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{d^{2} b \arcsin \left(c x \right)}{2 x^{2}}-2 c^{2} d^{2} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d^{2} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i c^{2} d^{2} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i c^{2} d^{2} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"1/2*c^4*d^2*a*x^2-2*c^2*d^2*a*ln(c*x)-1/2*d^2*a/x^2+I*c^2*d^2*b*arcsin(c*x)^2+1/4*b*c^3*d^2*x*(-c^2*x^2+1)^(1/2)+1/2*c^4*d^2*b*arcsin(c*x)*x^2-1/4*b*c^2*d^2*arcsin(c*x)+1/2*I*c^2*d^2*b-1/2*b*c*d^2*(-c^2*x^2+1)^(1/2)/x-1/2*d^2*b*arcsin(c*x)/x^2-2*c^2*d^2*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d^2*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*c^2*d^2*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*c^2*d^2*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
18,1,115,116,0.013000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(d^{2} a \left(c x -\frac{1}{3 c^{3} x^{3}}+\frac{2}{c x}\right)+d^{2} b \left(c x \arcsin \left(c x \right)-\frac{\arcsin \left(c x \right)}{3 c^{3} x^{3}}+\frac{2 \arcsin \left(c x \right)}{c x}+\sqrt{-c^{2} x^{2}+1}-\frac{\sqrt{-c^{2} x^{2}+1}}{6 c^{2} x^{2}}+\frac{11 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{6}\right)\right)"," ",0,"c^3*(d^2*a*(c*x-1/3/c^3/x^3+2/c/x)+d^2*b*(c*x*arcsin(c*x)-1/3*arcsin(c*x)/c^3/x^3+2/c/x*arcsin(c*x)+(-c^2*x^2+1)^(1/2)-1/6/c^2/x^2*(-c^2*x^2+1)^(1/2)+11/6*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
19,1,214,200,0.027000," ","int(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{11} c^{11} x^{11}-\frac{1}{3} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{11} x^{11}}{11}-\frac{\arcsin \left(c x \right) c^{9} x^{9}}{3}+\frac{3 \arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{10} x^{10} \sqrt{-c^{2} x^{2}+1}}{121}-\frac{91 c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{3267}+\frac{4705 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{160083}-\frac{6311 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1334025}-\frac{25244 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{4002075}-\frac{50488 \sqrt{-c^{2} x^{2}+1}}{4002075}\right)}{c^{5}}"," ",0,"1/c^5*(-d^3*a*(1/11*c^11*x^11-1/3*c^9*x^9+3/7*c^7*x^7-1/5*c^5*x^5)-d^3*b*(1/11*arcsin(c*x)*c^11*x^11-1/3*arcsin(c*x)*c^9*x^9+3/7*arcsin(c*x)*c^7*x^7-1/5*arcsin(c*x)*c^5*x^5+1/121*c^10*x^10*(-c^2*x^2+1)^(1/2)-91/3267*c^8*x^8*(-c^2*x^2+1)^(1/2)+4705/160083*c^6*x^6*(-c^2*x^2+1)^(1/2)-6311/1334025*c^4*x^4*(-c^2*x^2+1)^(1/2)-25244/4002075*c^2*x^2*(-c^2*x^2+1)^(1/2)-50488/4002075*(-c^2*x^2+1)^(1/2)))","A"
20,1,202,180,0.016000," ","int(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{10} c^{10} x^{10}-\frac{3}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}-\frac{1}{4} c^{4} x^{4}\right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{10} x^{10}}{10}-\frac{3 \arcsin \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsin \left(c x \right) c^{6} x^{6}}{2}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{9} x^{9} \sqrt{-c^{2} x^{2}+1}}{100}-\frac{57 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{1600}+\frac{401 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{9600}-\frac{79 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{7680}-\frac{79 c x \sqrt{-c^{2} x^{2}+1}}{5120}+\frac{79 \arcsin \left(c x \right)}{5120}\right)}{c^{4}}"," ",0,"1/c^4*(-d^3*a*(1/10*c^10*x^10-3/8*c^8*x^8+1/2*c^6*x^6-1/4*c^4*x^4)-d^3*b*(1/10*arcsin(c*x)*c^10*x^10-3/8*arcsin(c*x)*c^8*x^8+1/2*arcsin(c*x)*c^6*x^6-1/4*c^4*x^4*arcsin(c*x)+1/100*c^9*x^9*(-c^2*x^2+1)^(1/2)-57/1600*c^7*x^7*(-c^2*x^2+1)^(1/2)+401/9600*c^5*x^5*(-c^2*x^2+1)^(1/2)-79/7680*c^3*x^3*(-c^2*x^2+1)^(1/2)-79/5120*c*x*(-c^2*x^2+1)^(1/2)+79/5120*arcsin(c*x)))","A"
21,1,194,179,0.007000," ","int(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{9} c^{9} x^{9}-\frac{3}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{9} x^{9}}{9}-\frac{3 \arcsin \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{187 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{3969}+\frac{2099 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{33075}-\frac{2629 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{99225}-\frac{5258 \sqrt{-c^{2} x^{2}+1}}{99225}\right)}{c^{3}}"," ",0,"1/c^3*(-d^3*a*(1/9*c^9*x^9-3/7*c^7*x^7+3/5*c^5*x^5-1/3*c^3*x^3)-d^3*b*(1/9*arcsin(c*x)*c^9*x^9-3/7*arcsin(c*x)*c^7*x^7+3/5*arcsin(c*x)*c^5*x^5-1/3*c^3*x^3*arcsin(c*x)+1/81*c^8*x^8*(-c^2*x^2+1)^(1/2)-187/3969*c^6*x^6*(-c^2*x^2+1)^(1/2)+2099/33075*c^4*x^4*(-c^2*x^2+1)^(1/2)-2629/99225*c^2*x^2*(-c^2*x^2+1)^(1/2)-5258/99225*(-c^2*x^2+1)^(1/2)))","A"
22,1,182,130,0.007000," ","int(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{8} c^{8} x^{8}-\frac{1}{2} c^{6} x^{6}+\frac{3}{4} c^{4} x^{4}-\frac{1}{2} c^{2} x^{2}\right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{8} x^{8}}{8}-\frac{\arcsin \left(c x \right) c^{6} x^{6}}{2}+\frac{3 c^{4} x^{4} \arcsin \left(c x \right)}{4}-\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{64}-\frac{25 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{384}+\frac{163 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{1536}-\frac{93 c x \sqrt{-c^{2} x^{2}+1}}{1024}+\frac{93 \arcsin \left(c x \right)}{1024}\right)}{c^{2}}"," ",0,"1/c^2*(-d^3*a*(1/8*c^8*x^8-1/2*c^6*x^6+3/4*c^4*x^4-1/2*c^2*x^2)-d^3*b*(1/8*arcsin(c*x)*c^8*x^8-1/2*arcsin(c*x)*c^6*x^6+3/4*c^4*x^4*arcsin(c*x)-1/2*c^2*x^2*arcsin(c*x)+1/64*c^7*x^7*(-c^2*x^2+1)^(1/2)-25/384*c^5*x^5*(-c^2*x^2+1)^(1/2)+163/1536*c^3*x^3*(-c^2*x^2+1)^(1/2)-93/1024*c*x*(-c^2*x^2+1)^(1/2)+93/1024*arcsin(c*x)))","A"
23,1,164,155,0.005000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{-d^{3} a \left(\frac{1}{7} c^{7} x^{7}-\frac{3}{5} c^{5} x^{5}+c^{3} x^{3}-c x \right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{3 \arcsin \left(c x \right) c^{5} x^{5}}{5}+c^{3} x^{3} \arcsin \left(c x \right)-c x \arcsin \left(c x \right)+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{117 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}+\frac{757 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3675}-\frac{2161 \sqrt{-c^{2} x^{2}+1}}{3675}\right)}{c}"," ",0,"1/c*(-d^3*a*(1/7*c^7*x^7-3/5*c^5*x^5+c^3*x^3-c*x)-d^3*b*(1/7*arcsin(c*x)*c^7*x^7-3/5*arcsin(c*x)*c^5*x^5+c^3*x^3*arcsin(c*x)-c*x*arcsin(c*x)+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-117/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)+757/3675*c^2*x^2*(-c^2*x^2+1)^(1/2)-2161/3675*(-c^2*x^2+1)^(1/2)))","A"
24,1,266,229,0.352000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x,x)","-\frac{d^{3} a \,c^{6} x^{6}}{6}+\frac{3 d^{3} a \,c^{4} x^{4}}{4}-\frac{3 d^{3} a \,c^{2} x^{2}}{2}+d^{3} a \ln \left(c x \right)-\frac{i b \,d^{3} \arcsin \left(c x \right)^{2}}{2}+d^{3} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d^{3} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d^{3} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-i d^{3} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{d^{3} b \arcsin \left(c x \right) \cos \left(6 \arcsin \left(c x \right)\right)}{192}-\frac{d^{3} b \sin \left(6 \arcsin \left(c x \right)\right)}{1152}+\frac{d^{3} b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{16}-\frac{d^{3} b \sin \left(4 \arcsin \left(c x \right)\right)}{64}+\frac{29 d^{3} b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{64}-\frac{29 d^{3} b \sin \left(2 \arcsin \left(c x \right)\right)}{128}"," ",0,"-1/6*d^3*a*c^6*x^6+3/4*d^3*a*c^4*x^4-3/2*d^3*a*c^2*x^2+d^3*a*ln(c*x)-1/2*I*b*d^3*arcsin(c*x)^2+d^3*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d^3*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*d^3*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-I*d^3*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/192*d^3*b*arcsin(c*x)*cos(6*arcsin(c*x))-1/1152*d^3*b*sin(6*arcsin(c*x))+1/16*d^3*b*arcsin(c*x)*cos(4*arcsin(c*x))-1/64*d^3*b*sin(4*arcsin(c*x))+29/64*d^3*b*cos(2*arcsin(c*x))*arcsin(c*x)-29/128*d^3*b*sin(2*arcsin(c*x))","A"
25,1,155,148,0.011000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x)","c \left(-d^{3} a \left(\frac{c^{5} x^{5}}{5}-c^{3} x^{3}+3 c x +\frac{1}{c x}\right)-d^{3} b \left(\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}-c^{3} x^{3} \arcsin \left(c x \right)+3 c x \arcsin \left(c x \right)+\frac{\arcsin \left(c x \right)}{c x}+\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{7 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{25}+\frac{61 \sqrt{-c^{2} x^{2}+1}}{25}+\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)\right)"," ",0,"c*(-d^3*a*(1/5*c^5*x^5-c^3*x^3+3*c*x+1/c/x)-d^3*b*(1/5*arcsin(c*x)*c^5*x^5-c^3*x^3*arcsin(c*x)+3*c*x*arcsin(c*x)+1/c/x*arcsin(c*x)+1/25*c^4*x^4*(-c^2*x^2+1)^(1/2)-7/25*c^2*x^2*(-c^2*x^2+1)^(1/2)+61/25*(-c^2*x^2+1)^(1/2)+arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
26,1,326,257,0.681000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x)","-\frac{c^{6} d^{3} a \,x^{4}}{4}+\frac{3 c^{4} d^{3} a \,x^{2}}{2}-3 c^{2} d^{3} a \ln \left(c x \right)-\frac{d^{3} a}{2 x^{2}}+\frac{i c^{2} d^{3} b}{2}+\frac{5 b \,c^{3} d^{3} x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{5 c^{4} d^{3} b \arcsin \left(c x \right) x^{2}}{4}-\frac{5 b \,c^{2} d^{3} \arcsin \left(c x \right)}{8}+3 i c^{2} d^{3} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{b c \,d^{3} \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{d^{3} b \arcsin \left(c x \right)}{2 x^{2}}-3 c^{2} d^{3} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-3 c^{2} d^{3} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+3 i c^{2} d^{3} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{3 i c^{2} d^{3} b \arcsin \left(c x \right)^{2}}{2}-\frac{c^{2} d^{3} b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{32}+\frac{c^{2} d^{3} b \sin \left(4 \arcsin \left(c x \right)\right)}{128}"," ",0,"-1/4*c^6*d^3*a*x^4+3/2*c^4*d^3*a*x^2-3*c^2*d^3*a*ln(c*x)-1/2*d^3*a/x^2+3*I*c^2*d^3*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+5/8*b*c^3*d^3*x*(-c^2*x^2+1)^(1/2)+5/4*c^4*d^3*b*arcsin(c*x)*x^2-5/8*b*c^2*d^3*arcsin(c*x)+1/2*I*c^2*d^3*b-1/2*b*c*d^3*(-c^2*x^2+1)^(1/2)/x-1/2*d^3*b*arcsin(c*x)/x^2-3*c^2*d^3*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*c^2*d^3*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+3*I*c^2*d^3*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+3/2*I*c^2*d^3*b*arcsin(c*x)^2-1/32*c^2*d^3*b*arcsin(c*x)*cos(4*arcsin(c*x))+1/128*c^2*d^3*b*sin(4*arcsin(c*x))","A"
27,1,161,158,0.013000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(-d^{3} a \left(\frac{c^{3} x^{3}}{3}-3 c x +\frac{1}{3 c^{3} x^{3}}-\frac{3}{c x}\right)-d^{3} b \left(\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}-3 c x \arcsin \left(c x \right)+\frac{\arcsin \left(c x \right)}{3 c^{3} x^{3}}-\frac{3 \arcsin \left(c x \right)}{c x}+\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{25 \sqrt{-c^{2} x^{2}+1}}{9}+\frac{\sqrt{-c^{2} x^{2}+1}}{6 c^{2} x^{2}}-\frac{17 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{6}\right)\right)"," ",0,"c^3*(-d^3*a*(1/3*c^3*x^3-3*c*x+1/3/c^3/x^3-3/c/x)-d^3*b*(1/3*c^3*x^3*arcsin(c*x)-3*c*x*arcsin(c*x)+1/3*arcsin(c*x)/c^3/x^3-3/c/x*arcsin(c*x)+1/9*c^2*x^2*(-c^2*x^2+1)^(1/2)-25/9*(-c^2*x^2+1)^(1/2)+1/6/c^2/x^2*(-c^2*x^2+1)^(1/2)-17/6*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
28,1,270,181,0.271000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \,x^{3}}{3 c^{2} d}-\frac{a x}{c^{4} d}-\frac{a \ln \left(c x -1\right)}{2 c^{5} d}+\frac{a \ln \left(c x +1\right)}{2 c^{5} d}-\frac{b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d}+\frac{b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d}+\frac{i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d}-\frac{i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d}-\frac{11 b \sqrt{-c^{2} x^{2}+1}}{9 c^{5} d}-\frac{b \arcsin \left(c x \right) x}{c^{4} d}-\frac{b \arcsin \left(c x \right) x^{3}}{3 c^{2} d}-\frac{b \sqrt{-c^{2} x^{2}+1}\, x^{2}}{9 c^{3} d}"," ",0,"-1/3/c^2*a/d*x^3-1/c^4*a/d*x-1/2/c^5*a/d*ln(c*x-1)+1/2/c^5*a/d*ln(c*x+1)-1/c^5*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/c^5*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I/c^5*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I/c^5*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-11/9*b*(-c^2*x^2+1)^(1/2)/c^5/d-1/c^4*b/d*arcsin(c*x)*x-1/3/c^2*b/d*arcsin(c*x)*x^3-1/9/c^3*b/d*(-c^2*x^2+1)^(1/2)*x^2","A"
29,1,181,150,0.163000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \,x^{2}}{2 c^{2} d}-\frac{a \ln \left(c x -1\right)}{2 c^{4} d}-\frac{a \ln \left(c x +1\right)}{2 c^{4} d}+\frac{i b \arcsin \left(c x \right)^{2}}{2 c^{4} d}-\frac{b x \sqrt{-c^{2} x^{2}+1}}{4 c^{3} d}-\frac{b \arcsin \left(c x \right) x^{2}}{2 c^{2} d}+\frac{b \arcsin \left(c x \right)}{4 c^{4} d}-\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}+\frac{i b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d}"," ",0,"-1/2/c^2*a/d*x^2-1/2/c^4*a/d*ln(c*x-1)-1/2/c^4*a/d*ln(c*x+1)+1/2*I/c^4*b/d*arcsin(c*x)^2-1/4*b*x*(-c^2*x^2+1)^(1/2)/c^3/d-1/2/c^2*b/d*arcsin(c*x)*x^2+1/4*b*arcsin(c*x)/c^4/d-1/c^4*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*I*b*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^4/d","A"
30,1,218,141,0.109000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","-\frac{a x}{c^{2} d}-\frac{a \ln \left(c x -1\right)}{2 c^{3} d}+\frac{a \ln \left(c x +1\right)}{2 c^{3} d}-\frac{i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d}+\frac{i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d}+\frac{b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d}-\frac{b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d}-\frac{b \arcsin \left(c x \right) x}{c^{2} d}-\frac{b \sqrt{-c^{2} x^{2}+1}}{c^{3} d}"," ",0,"-1/c^2*a/d*x-1/2/c^3*a/d*ln(c*x-1)+1/2/c^3*a/d*ln(c*x+1)-I/c^3*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I/c^3*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/c^3*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/c^3*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/c^2*b/d*arcsin(c*x)*x-b*(-c^2*x^2+1)^(1/2)/c^3/d","A"
31,1,118,96,0.068000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","-\frac{a \ln \left(c x -1\right)}{2 c^{2} d}-\frac{a \ln \left(c x +1\right)}{2 c^{2} d}+\frac{i b \arcsin \left(c x \right)^{2}}{2 c^{2} d}-\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{i b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{2} d}"," ",0,"-1/2/c^2*a/d*ln(c*x-1)-1/2/c^2*a/d*ln(c*x+1)+1/2*I/c^2*b/d*arcsin(c*x)^2-1/c^2*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*I*b*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^2/d","A"
32,1,170,103,0.145000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","\frac{a \arctanh \left(c x \right)}{c d}-\frac{i b \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}+\frac{i b \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}+\frac{b \arctanh \left(c x \right) \arcsin \left(c x \right)}{c d}-\frac{i b \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}+\frac{i b \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}"," ",0,"1/c*a/d*arctanh(c*x)-I/c*b/d*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+I/c*b/d*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/c*b/d*arctanh(c*x)*arcsin(c*x)-I/c*b/d*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+I/c*b/d*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))","A"
33,1,164,95,0.089000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d),x)","-\frac{a \ln \left(c x +1\right)}{2 d}+\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c x -1\right)}{2 d}+\frac{b \arcsin \left(c x \right) \ln \left(1-\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{i b \dilog \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}-\frac{i b \dilog \left(1-\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}"," ",0,"-1/2*a/d*ln(c*x+1)+a/d*ln(c*x)-1/2*a/d*ln(c*x-1)+b/d*arcsin(c*x)*ln(1-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*I*b/d*dilog(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*I*b/d*dilog(1-(I*c*x+(-c^2*x^2+1)^(1/2))^2)","A"
34,1,236,135,0.194000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d),x)","\frac{c a \ln \left(c x +1\right)}{2 d}-\frac{a}{d x}-\frac{c a \ln \left(c x -1\right)}{2 d}-\frac{b \arcsin \left(c x \right)}{d x}-\frac{c b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{c b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{c b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{c b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d}+\frac{i c b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{i c b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}"," ",0,"1/2*c*a/d*ln(c*x+1)-a/d/x-1/2*c*a/d*ln(c*x-1)-b/d*arcsin(c*x)/x-c*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+c*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-c*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+I*c*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I*c*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
35,1,296,145,0.329000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d),x)","-\frac{c^{2} a \ln \left(c x +1\right)}{2 d}-\frac{a}{2 d \,x^{2}}+\frac{c^{2} a \ln \left(c x \right)}{d}-\frac{c^{2} a \ln \left(c x -1\right)}{2 d}+\frac{i c^{2} b}{2 d}-\frac{b c \sqrt{-c^{2} x^{2}+1}}{2 d x}-\frac{b \arcsin \left(c x \right)}{2 d \,x^{2}}+\frac{c^{2} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{i c^{2} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{c^{2} b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{i b \,c^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}+\frac{c^{2} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{i c^{2} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}"," ",0,"-1/2*c^2*a/d*ln(c*x+1)-1/2*a/d/x^2+c^2*a/d*ln(c*x)-1/2*c^2*a/d*ln(c*x-1)+1/2*I*c^2*b/d-1/2*b*c*(-c^2*x^2+1)^(1/2)/d/x-1/2*b/d*arcsin(c*x)/x^2+c^2*b/d*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*c^2*b/d*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-c^2*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*I*b*c^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d+c^2*b/d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*c^2*b/d*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
36,1,303,185,0.255000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d),x)","\frac{c^{3} a \ln \left(c x +1\right)}{2 d}-\frac{a}{3 d \,x^{3}}-\frac{c^{2} a}{d x}-\frac{c^{3} a \ln \left(c x -1\right)}{2 d}-\frac{c^{2} b \arcsin \left(c x \right)}{d x}-\frac{b c \sqrt{-c^{2} x^{2}+1}}{6 d \,x^{2}}-\frac{b \arcsin \left(c x \right)}{3 d \,x^{3}}-\frac{7 c^{3} b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{6 d}+\frac{7 c^{3} b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{6 d}-\frac{i c^{3} b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{i c^{3} b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{c^{3} b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{c^{3} b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}"," ",0,"1/2*c^3*a/d*ln(c*x+1)-1/3*a/d/x^3-c^2*a/d/x-1/2*c^3*a/d*ln(c*x-1)-c^2*b/d*arcsin(c*x)/x-1/6*b*c*(-c^2*x^2+1)^(1/2)/d/x^2-1/3*b/d*arcsin(c*x)/x^3-7/6*c^3*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+7/6*c^3*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-I*c^3*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I*c^3*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-c^3*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+c^3*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
37,1,305,192,0.405000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{a x}{c^{4} d^{2}}-\frac{a}{4 c^{5} d^{2} \left(c x +1\right)}-\frac{3 a \ln \left(c x +1\right)}{4 c^{5} d^{2}}-\frac{a}{4 c^{5} d^{2} \left(c x -1\right)}+\frac{3 a \ln \left(c x -1\right)}{4 c^{5} d^{2}}+\frac{b \sqrt{-c^{2} x^{2}+1}}{c^{5} d^{2}}+\frac{b \arcsin \left(c x \right) x}{c^{4} d^{2}}-\frac{b \arcsin \left(c x \right) x}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}-\frac{3 b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}-\frac{3 i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}+\frac{3 i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}"," ",0,"1/c^4*a/d^2*x-1/4/c^5*a/d^2/(c*x+1)-3/4/c^5*a/d^2*ln(c*x+1)-1/4/c^5*a/d^2/(c*x-1)+3/4/c^5*a/d^2*ln(c*x-1)+b*(-c^2*x^2+1)^(1/2)/c^5/d^2+1/c^4*b/d^2*arcsin(c*x)*x-1/2/c^4*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/2/c^5*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+3/2/c^5*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/2/c^5*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/2*I/c^5*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/2*I/c^5*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
38,1,251,161,0.449000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{a}{4 c^{4} d^{2} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{2 c^{4} d^{2}}-\frac{a}{4 c^{4} d^{2} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{2 c^{4} d^{2}}-\frac{i b \arcsin \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{i b \,x^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b x \sqrt{-c^{2} x^{2}+1}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arcsin \left(c x \right)}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}-\frac{i b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d^{2}}"," ",0,"1/4/c^4*a/d^2/(c*x+1)+1/2/c^4*a/d^2*ln(c*x+1)-1/4/c^4*a/d^2/(c*x-1)+1/2/c^4*a/d^2*ln(c*x-1)-1/2*I/c^4*b/d^2*arcsin(c*x)^2-1/2*I/c^2*b/d^2/(c^2*x^2-1)*x^2+1/2/c^3*b/d^2/(c^2*x^2-1)*x*(-c^2*x^2+1)^(1/2)-1/2/c^4*b/d^2/(c^2*x^2-1)*arcsin(c*x)+1/2*I/c^4*b/d^2/(c^2*x^2-1)+1/c^4*b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*I*b*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^4/d^2","A"
39,1,263,153,0.266000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","-\frac{a}{4 c^{3} d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{4 c^{3} d^{2}}-\frac{a}{4 c^{3} d^{2} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{4 c^{3} d^{2}}-\frac{b \arcsin \left(c x \right) x}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}-\frac{b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}-\frac{i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}+\frac{i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}"," ",0,"-1/4/c^3*a/d^2/(c*x+1)-1/4/c^3*a/d^2*ln(c*x+1)-1/4/c^3*a/d^2/(c*x-1)+1/4/c^3*a/d^2*ln(c*x-1)-1/2/c^2*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/2/c^3*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/2/c^3*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/2/c^3*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/2*I/c^3*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/2*I/c^3*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
40,1,98,51,0.012000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","\frac{-\frac{a}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \left(-\frac{\arcsin \left(c x \right)}{2 \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{4 c x +4}+\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{4 c x -4}\right)}{d^{2}}}{c^{2}}"," ",0,"1/c^2*(-1/2*a/d^2/(c^2*x^2-1)+b/d^2*(-1/2/(c^2*x^2-1)*arcsin(c*x)+1/4/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)+1/4/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)))","A"
41,1,260,150,0.109000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","-\frac{a}{4 c \,d^{2} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{4 c \,d^{2}}-\frac{a}{4 c \,d^{2} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{4 c \,d^{2}}-\frac{b \arcsin \left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}}{2 c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}+\frac{b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}+\frac{i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}-\frac{i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}"," ",0,"-1/4/c*a/d^2/(c*x+1)+1/4/c*a/d^2*ln(c*x+1)-1/4/c*a/d^2/(c*x-1)-1/4/c*a/d^2*ln(c*x-1)-1/2*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/2/c*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/2/c*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/2/c*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/2*I/c*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/2*I/c*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
42,1,335,140,0.293000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^2,x)","\frac{a}{4 d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{2 d^{2}}+\frac{a \ln \left(c x \right)}{d^{2}}-\frac{a}{4 d^{2} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{2 d^{2}}-\frac{i b \,c^{2} x^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b c x \sqrt{-c^{2} x^{2}+1}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \arcsin \left(c x \right)}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{i b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{2}}+\frac{b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}"," ",0,"1/4*a/d^2/(c*x+1)-1/2*a/d^2*ln(c*x+1)+a/d^2*ln(c*x)-1/4*a/d^2/(c*x-1)-1/2*a/d^2*ln(c*x-1)-1/2*I*b/d^2/(c^2*x^2-1)*c^2*x^2+1/2*b/d^2/(c^2*x^2-1)*c*x*(-c^2*x^2+1)^(1/2)-1/2*b/d^2/(c^2*x^2-1)*arcsin(c*x)+1/2*I*b/d^2/(c^2*x^2-1)+b/d^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*b/d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*I*b*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^2+b/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b/d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
43,1,330,195,0.266000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^2,x)","-\frac{c a}{4 d^{2} \left(c x +1\right)}+\frac{3 c a \ln \left(c x +1\right)}{4 d^{2}}-\frac{a}{d^{2} x}-\frac{c a}{4 d^{2} \left(c x -1\right)}-\frac{3 c a \ln \left(c x -1\right)}{4 d^{2}}-\frac{3 b \arcsin \left(c x \right) c^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{c b \sqrt{-c^{2} x^{2}+1}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right)}{d^{2} x \left(c^{2} x^{2}-1\right)}-\frac{c b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{c b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{2}}-\frac{3 i c b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}-\frac{3 c b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{3 c b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{3 i c b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}"," ",0,"-1/4*c*a/d^2/(c*x+1)+3/4*c*a/d^2*ln(c*x+1)-a/d^2/x-1/4*c*a/d^2/(c*x-1)-3/4*c*a/d^2*ln(c*x-1)-3/2*b/d^2/(c^2*x^2-1)*arcsin(c*x)*c^2*x+1/2*c*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+b/d^2/x/(c^2*x^2-1)*arcsin(c*x)-c*b/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c*b/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-3/2*I*c*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/2*c*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/2*c*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/2*I*c*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
44,1,367,184,0.274000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^2,x)","\frac{c^{2} a}{4 d^{2} \left(c x +1\right)}-\frac{c^{2} a \ln \left(c x +1\right)}{d^{2}}-\frac{a}{2 d^{2} x^{2}}+\frac{2 c^{2} a \ln \left(c x \right)}{d^{2}}-\frac{c^{2} a}{4 d^{2} \left(c x -1\right)}-\frac{c^{2} a \ln \left(c x -1\right)}{d^{2}}-\frac{c^{2} b \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{c b \sqrt{-c^{2} x^{2}+1}}{2 d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right)}{2 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 c^{2} b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 c^{2} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 c^{2} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 i c^{2} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 i c^{2} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b \,c^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}"," ",0,"1/4*c^2*a/d^2/(c*x+1)-c^2*a/d^2*ln(c*x+1)-1/2*a/d^2/x^2+2*c^2*a/d^2*ln(c*x)-1/4*c^2*a/d^2/(c*x-1)-c^2*a/d^2*ln(c*x-1)-c^2*b/d^2/(c^2*x^2-1)*arcsin(c*x)+1/2*c*b/d^2/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/2*b/d^2/x^2/(c^2*x^2-1)*arcsin(c*x)-2*c^2*b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*c^2*b/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c^2*b/d^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*c^2*b/d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*c^2*b/d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*b*c^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^2","A"
45,1,426,259,0.329000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^2,x)","-\frac{c^{3} a}{4 d^{2} \left(c x +1\right)}+\frac{5 c^{3} a \ln \left(c x +1\right)}{4 d^{2}}-\frac{a}{3 d^{2} x^{3}}-\frac{2 c^{2} a}{d^{2} x}-\frac{c^{3} a}{4 d^{2} \left(c x -1\right)}-\frac{5 c^{3} a \ln \left(c x -1\right)}{4 d^{2}}-\frac{5 c^{4} b \arcsin \left(c x \right) x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}}{3 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{5 c^{2} b \arcsin \left(c x \right)}{3 d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{c b \sqrt{-c^{2} x^{2}+1}}{6 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \arcsin \left(c x \right)}{3 d^{2} x^{3} \left(c^{2} x^{2}-1\right)}-\frac{13 c^{3} b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{6 d^{2}}+\frac{13 c^{3} b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{6 d^{2}}-\frac{5 c^{3} b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{5 c^{3} b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}-\frac{5 i c^{3} b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{5 i c^{3} b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}"," ",0,"-1/4*c^3*a/d^2/(c*x+1)+5/4*c^3*a/d^2*ln(c*x+1)-1/3*a/d^2/x^3-2*c^2*a/d^2/x-1/4*c^3*a/d^2/(c*x-1)-5/4*c^3*a/d^2*ln(c*x-1)-5/2*c^4*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/3*c^3*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+5/3*c^2*b/d^2/x/(c^2*x^2-1)*arcsin(c*x)+1/6*c*b/d^2/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/3*b/d^2/x^3/(c^2*x^2-1)*arcsin(c*x)-13/6*c^3*b/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+13/6*c^3*b/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-5/2*c^3*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/2*c^3*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-5/2*I*c^3*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/2*I*c^3*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
46,1,389,205,0.553000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","-\frac{a}{16 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{5 a}{16 c^{5} d^{3} \left(c x +1\right)}+\frac{3 a \ln \left(c x +1\right)}{16 c^{5} d^{3}}+\frac{a}{16 c^{5} d^{3} \left(c x -1\right)^{2}}+\frac{5 a}{16 c^{5} d^{3} \left(c x -1\right)}-\frac{3 a \ln \left(c x -1\right)}{16 c^{5} d^{3}}+\frac{5 b \arcsin \left(c x \right) x^{3}}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{5 b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{8 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b \arcsin \left(c x \right) x}{8 c^{4} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{13 b \sqrt{-c^{2} x^{2}+1}}{24 c^{5} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}+\frac{3 b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}+\frac{3 i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}-\frac{3 i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}"," ",0,"-1/16/c^5*a/d^3/(c*x+1)^2+5/16/c^5*a/d^3/(c*x+1)+3/16/c^5*a/d^3*ln(c*x+1)+1/16/c^5*a/d^3/(c*x-1)^2+5/16/c^5*a/d^3/(c*x-1)-3/16/c^5*a/d^3*ln(c*x-1)+5/8/c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3-5/8/c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)-3/8/c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x+13/24/c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-3/8/c^5*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/8/c^5*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/8*I/c^5*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/8*I/c^5*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
47,1,212,88,0.022000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{-\frac{a \left(-\frac{1}{16 \left(c x +1\right)^{2}}+\frac{3}{16 \left(c x +1\right)}-\frac{1}{16 \left(c x -1\right)^{2}}-\frac{3}{16 \left(c x -1\right)}\right)}{d^{3}}-\frac{b \left(-\frac{\arcsin \left(c x \right)}{16 \left(c x +1\right)^{2}}+\frac{3 \arcsin \left(c x \right)}{16 \left(c x +1\right)}-\frac{\arcsin \left(c x \right)}{16 \left(c x -1\right)^{2}}-\frac{3 \arcsin \left(c x \right)}{16 \left(c x -1\right)}+\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{6 c x +6}+\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{48 \left(c x -1\right)^{2}}+\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{6 c x -6}-\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{48 \left(c x +1\right)^{2}}\right)}{d^{3}}}{c^{4}}"," ",0,"1/c^4*(-a/d^3*(-1/16/(c*x+1)^2+3/16/(c*x+1)-1/16/(c*x-1)^2-3/16/(c*x-1))-b/d^3*(-1/16*arcsin(c*x)/(c*x+1)^2+3/16*arcsin(c*x)/(c*x+1)-1/16*arcsin(c*x)/(c*x-1)^2-3/16*arcsin(c*x)/(c*x-1)+1/6/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)+1/48/(c*x-1)^2*(-(c*x-1)^2-2*c*x+2)^(1/2)+1/6/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)-1/48/(c*x+1)^2*(-(c*x+1)^2+2*c*x+2)^(1/2)))","B"
48,1,386,203,0.412000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","-\frac{a}{16 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{a}{16 c^{3} d^{3} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{16 c^{3} d^{3}}+\frac{a}{16 c^{3} d^{3} \left(c x -1\right)^{2}}+\frac{a}{16 c^{3} d^{3} \left(c x -1\right)}+\frac{a \ln \left(c x -1\right)}{16 c^{3} d^{3}}+\frac{b \arcsin \left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{8 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \arcsin \left(c x \right) x}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}}{24 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}-\frac{b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}-\frac{i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}+\frac{i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}"," ",0,"-1/16/c^3*a/d^3/(c*x+1)^2+1/16/c^3*a/d^3/(c*x+1)-1/16/c^3*a/d^3*ln(c*x+1)+1/16/c^3*a/d^3/(c*x-1)^2+1/16/c^3*a/d^3/(c*x-1)+1/16/c^3*a/d^3*ln(c*x-1)+1/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3-1/8/c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+1/8/c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x+1/24/c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)+1/8/c^3*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/8/c^3*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/8*I/c^3*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/8*I/c^3*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
49,1,151,73,0.010000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","\frac{\frac{a}{4 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b \left(-\frac{\arcsin \left(c x \right)}{4 \left(c^{2} x^{2}-1\right)^{2}}-\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{12 \left(c x +1\right)}+\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{48 \left(c x -1\right)^{2}}-\frac{\sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{12 \left(c x -1\right)}-\frac{\sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{48 \left(c x +1\right)^{2}}\right)}{d^{3}}}{c^{2}}"," ",0,"1/c^2*(1/4*a/d^3/(c^2*x^2-1)^2-b/d^3*(-1/4/(c^2*x^2-1)^2*arcsin(c*x)-1/12/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)+1/48/(c*x-1)^2*(-(c*x-1)^2-2*c*x+2)^(1/2)-1/12/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)-1/48/(c*x+1)^2*(-(c*x+1)^2+2*c*x+2)^(1/2)))","B"
50,1,384,197,0.187000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","-\frac{a}{16 c \,d^{3} \left(c x +1\right)^{2}}-\frac{3 a}{16 c \,d^{3} \left(c x +1\right)}+\frac{3 a \ln \left(c x +1\right)}{16 c \,d^{3}}+\frac{a}{16 c \,d^{3} \left(c x -1\right)^{2}}-\frac{3 a}{16 c \,d^{3} \left(c x -1\right)}-\frac{3 a \ln \left(c x -1\right)}{16 c \,d^{3}}-\frac{3 c^{2} b \arcsin \left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 c b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{5 b \arcsin \left(c x \right) x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{11 b \sqrt{-c^{2} x^{2}+1}}{24 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}+\frac{3 b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}+\frac{3 i b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}-\frac{3 i b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}"," ",0,"-1/16/c*a/d^3/(c*x+1)^2-3/16/c*a/d^3/(c*x+1)+3/16/c*a/d^3*ln(c*x+1)+1/16/c*a/d^3/(c*x-1)^2-3/16/c*a/d^3/(c*x-1)-3/16/c*a/d^3*ln(c*x-1)-3/8*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3+3/8*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+5/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x-11/24/c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-3/8/c*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/8/c*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/8*I/c*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/8*I/c*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
51,1,503,185,0.306000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^3,x)","\frac{a}{16 d^{3} \left(c x +1\right)^{2}}+\frac{5 a}{16 d^{3} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{2 d^{3}}+\frac{a \ln \left(c x \right)}{d^{3}}+\frac{a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{5 a}{16 d^{3} \left(c x -1\right)}-\frac{a \ln \left(c x -1\right)}{2 d^{3}}-\frac{2 i b \,c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 b \,c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \arcsin \left(c x \right) c^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{2 i b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b c x \sqrt{-c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b \arcsin \left(c x \right)}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{4 i b \,c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{i b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}-\frac{b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{i b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{i b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"1/16*a/d^3/(c*x+1)^2+5/16*a/d^3/(c*x+1)-1/2*a/d^3*ln(c*x+1)+a/d^3*ln(c*x)+1/16*a/d^3/(c*x-1)^2-5/16*a/d^3/(c*x-1)-1/2*a/d^3*ln(c*x-1)-I*b/d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^3*x^3*(-c^2*x^2+1)^(1/2)-1/2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2*x^2-2/3*I*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^4*x^4-3/4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c*x*(-c^2*x^2+1)^(1/2)+3/4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)+1/2*I*b*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^3+b/d^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2/3*I*b/d^3/(c^4*x^4-2*c^2*x^2+1)-b/d^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+4/3*I*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2*x^2+b/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b/d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
52,1,461,243,0.327000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^3,x)","-\frac{c a}{16 d^{3} \left(c x +1\right)^{2}}-\frac{7 c a}{16 d^{3} \left(c x +1\right)}+\frac{15 c a \ln \left(c x +1\right)}{16 d^{3}}-\frac{a}{d^{3} x}+\frac{c a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{7 c a}{16 d^{3} \left(c x -1\right)}-\frac{15 c a \ln \left(c x -1\right)}{16 d^{3}}-\frac{15 b \arcsin \left(c x \right) c^{4} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{7 b \,c^{3} x^{2} \sqrt{-c^{2} x^{2}+1}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{25 b \arcsin \left(c x \right) c^{2} x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{23 c b \sqrt{-c^{2} x^{2}+1}}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \arcsin \left(c x \right)}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{c b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{c b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{15 i c b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{15 i c b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{15 c b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}+\frac{15 c b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}"," ",0,"-1/16*c*a/d^3/(c*x+1)^2-7/16*c*a/d^3/(c*x+1)+15/16*c*a/d^3*ln(c*x+1)-a/d^3/x+1/16*c*a/d^3/(c*x-1)^2-7/16*c*a/d^3/(c*x-1)-15/16*c*a/d^3*ln(c*x-1)-15/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^4*x^3+7/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^3*x^2*(-c^2*x^2+1)^(1/2)+25/8*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2*x-23/24*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)-c*b/d^3*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c*b/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+15/8*I*c*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-15/8*I*c*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-15/8*c*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+15/8*c*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
53,1,635,257,0.412000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^3,x)","\frac{c^{2} a}{16 d^{3} \left(c x +1\right)^{2}}+\frac{9 c^{2} a}{16 d^{3} \left(c x +1\right)}-\frac{3 c^{2} a \ln \left(c x +1\right)}{2 d^{3}}-\frac{a}{2 d^{3} x^{2}}+\frac{3 c^{2} a \ln \left(c x \right)}{d^{3}}+\frac{c^{2} a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{9 c^{2} a}{16 d^{3} \left(c x -1\right)}-\frac{3 c^{2} a \ln \left(c x -1\right)}{2 d^{3}}+\frac{3 i b \,c^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}+\frac{2 c^{5} b \,x^{3} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} b \arcsin \left(c x \right) x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{2 i c^{6} b \,x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c^{3} b x \sqrt{-c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{9 c^{2} b \arcsin \left(c x \right)}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{2 i c^{2} b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c b \sqrt{-c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{b \arcsin \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}+\frac{3 c^{2} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 i c^{2} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 c^{2} b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{4 i c^{4} b \,x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 c^{2} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 i c^{2} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"1/16*c^2*a/d^3/(c*x+1)^2+9/16*c^2*a/d^3/(c*x+1)-3/2*c^2*a/d^3*ln(c*x+1)-1/2*a/d^3/x^2+3*c^2*a/d^3*ln(c*x)+1/16*c^2*a/d^3/(c*x-1)^2-9/16*c^2*a/d^3/(c*x-1)-3/2*c^2*a/d^3*ln(c*x-1)-2/3*I*c^6*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^4+2/3*c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3*(-c^2*x^2+1)^(1/2)-3/2*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^2-3*I*c^2*b/d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/4*c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x*(-c^2*x^2+1)^(1/2)+9/4*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)-2/3*I*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)-1/2*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)-1/2*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)+3*c^2*b/d^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+4/3*I*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2-3*c^2*b/d^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-3*I*c^2*b/d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+3*c^2*b/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+3/2*I*b*c^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^3","B"
54,1,576,309,0.420000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^3,x)","-\frac{c^{3} a}{16 d^{3} \left(c x +1\right)^{2}}-\frac{11 c^{3} a}{16 d^{3} \left(c x +1\right)}+\frac{35 c^{3} a \ln \left(c x +1\right)}{16 d^{3}}-\frac{a}{3 d^{3} x^{3}}-\frac{3 c^{2} a}{d^{3} x}+\frac{c^{3} a}{16 d^{3} \left(c x -1\right)^{2}}-\frac{11 c^{3} a}{16 d^{3} \left(c x -1\right)}-\frac{35 c^{3} a \ln \left(c x -1\right)}{16 d^{3}}-\frac{35 c^{6} b \arcsin \left(c x \right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{29 c^{5} b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{175 c^{4} b \arcsin \left(c x \right) x}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{9 c^{3} b \sqrt{-c^{2} x^{2}+1}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{7 c^{2} b \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{c b \sqrt{-c^{2} x^{2}+1}}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{b \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{3}}-\frac{19 c^{3} b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{6 d^{3}}+\frac{19 c^{3} b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{6 d^{3}}+\frac{35 c^{3} b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}+\frac{35 i c^{3} b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{35 c^{3} b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{35 i c^{3} b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}"," ",0,"-1/16*c^3*a/d^3/(c*x+1)^2-11/16*c^3*a/d^3/(c*x+1)+35/16*c^3*a/d^3*ln(c*x+1)-1/3*a/d^3/x^3-3*c^2*a/d^3/x+1/16*c^3*a/d^3/(c*x-1)^2-11/16*c^3*a/d^3/(c*x-1)-35/16*c^3*a/d^3*ln(c*x-1)-35/8*c^6*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3+29/24*c^5*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+175/24*c^4*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x-9/8*c^3*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-7/3*c^2*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)-1/6*c*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*(-c^2*x^2+1)^(1/2)-1/3*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^3*arcsin(c*x)-19/6*c^3*b/d^3*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+19/6*c^3*b/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+35/8*c^3*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-35/8*I*c^3*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-35/8*c^3*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+35/8*I*c^3*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
55,1,1690,226,0.714000," ","int(x^4*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{192 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{64 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{5}}{6 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{512 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{288 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right)}{4608 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{a \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6 c^{2} d}-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8 c^{4} d}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 c^{4} \sqrt{c^{2} d}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5}}{36 \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{96 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{96 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) x^{2}}{4608 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) x^{2}}{512 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{4}}+\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right)}{4608 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right)}{512 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{12 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{192 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) x^{2}}{512 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{64 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{32 c^{5} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{4}}{48 c \left(c^{2} x^{2}-1\right)}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) x^{2}}{4608 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{288 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{96 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{7}}{72 c^{2} x^{2}-72}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{7}}{12 c^{2} x^{2}-12}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{6}}{72 c^{2} x^{2}-72}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) x^{2}}{192 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) x^{2}}{64 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, x}{4608 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, x}{512 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{16 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) x^{2}}{96 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, x}{4608 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, x}{512 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{6}}{12 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{96 c^{4} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/192*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/6*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x^5+3/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))/c^5/(c^2*x^2-1)+1/288*b*(-d*(c^2*x^2-1))^(1/2)/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+7/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^5/(c^2*x^2-1)-1/36*I*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*x^5-1/6*a*x^3*(-c^2*d*x^2+d)^(3/2)/c^2/d-1/8*a/c^4*x*(-c^2*d*x^2+d)^(3/2)/d+1/16*a/c^4*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/16*a/c^4*x*(-c^2*d*x^2+d)^(1/2)+1/12*b*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/192*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^5/(c^2*x^2-1)*arcsin(c*x)-3/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))/c^3/(c^2*x^2-1)*x^2+1/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^5/(c^2*x^2-1)*arcsin(c*x)-1/32*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/(c^2*x^2-1)*arcsin(c*x)^2+1/12*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)*x^7+1/72*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6-1/48*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-7/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^3/(c^2*x^2-1)*x^2+7/288*I*b*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*x^3-1/96*I*b*(-d*(c^2*x^2-1))^(1/2)/c^4/(c^2*x^2-1)*x+11/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^5/(c^2*x^2-1)+1/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^5/(c^2*x^2-1)+1/72*I*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*x^7-1/192*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-1/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+11/4608*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/512*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/96*I*b*(-d*(c^2*x^2-1))^(1/2)/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/96*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^5/(c^2*x^2-1)*arcsin(c*x)-11/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))/c^3/(c^2*x^2-1)*x^2-1/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))/c^3/(c^2*x^2-1)*x^2-1/96*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-3/512*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/12*I*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-1/16*I*b*(-d*(c^2*x^2-1))^(1/2)/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+1/96*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-7/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x","C"
56,1,373,163,0.293000," ","int(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{16 c^{2} x^{2}-16}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{2}}{16 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{16 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{128 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{5}}{4 c^{2} x^{2}-4}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/16*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-1/16*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2+1/128*b*(-d*(c^2*x^2-1))^(1/2)/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*arcsin(c*x)*x+1/4*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5-3/8*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x^3","B"
57,1,260,100,0.144000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{4 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{3}}{2 c^{2} x^{2}-2}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{2} x^{2}-4}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{8 c \left(c^{2} x^{2}-1\right)}"," ",0,"1/2*a*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/4*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x-1/8*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)","B"
58,1,308,98,0.280000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^2,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}-a \,c^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{a \,c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} c}{2 c^{2} x^{2}-2}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c}{c^{2} x^{2}-1}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(3/2)-a*c^2*x*(-c^2*d*x^2+d)^(1/2)-a*c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*c+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)*x*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/x-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c","C"
59,1,1117,95,0.398000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^4,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 d \,x^{3}}-\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{3}}{3 c^{2} x^{2}-3}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{8}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{4}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, c^{5}}{2 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{2 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 \left(3 c^{4} x^{4}-3 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 c^{2} x^{2}-3}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(3/2)-2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*c^3/(3*c^2*x^2-3)+I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7+b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*c^4-3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6+1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5-I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+10/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-5/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)+1/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3","C"
60,1,1902,161,0.481000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^6,x)","\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{5}}{15 \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{11}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{9}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{7}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{10}}{6 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{8}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{6}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{10}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \sqrt{-c^{2} x^{2}+1}\, c^{9}}{2 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{8}}{3 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{7} \sqrt{-c^{2} x^{2}+1}}{12 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{98 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{6}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{4}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x \left(c^{2} x^{2}-1\right)}-\frac{21 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{20 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{2} \left(c^{2} x^{2}-1\right)}-\frac{27 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{3} \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{20 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{4} \left(c^{2} x^{2}-1\right)}-\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{15 c^{2} x^{2}-15}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{14}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{12}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \arcsin \left(c x \right) c^{12}}{\left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 d \,x^{5}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5} \sqrt{-c^{2} x^{2}+1}}{4 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) x^{5} \left(c^{2} x^{2}-1\right)}+\frac{6 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{5}}{5 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{6}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(-c^{2} x^{2}+1\right) c^{12}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right) c^{10}}{15 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{8}}{10 \left(15 c^{6} x^{6}-5 c^{4} x^{4}-15 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,x^{3}}"," ",0,"2*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^6/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^11-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^4/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^9-2*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^7-5/3*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^10-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^9-17/3*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^8+11/12*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^2/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)+98/15*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x/(c^2*x^2-1)*arcsin(c*x)*c^6+12/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x/(c^2*x^2-1)*arcsin(c*x)*c^4-21/20*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^2/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-27/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^2+9/20*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-4*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5/(15*c^2*x^2-15)+2/15*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^9/(c^2*x^2-1)*c^14-4/15*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7/(c^2*x^2-1)*c^12-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5/(c^2*x^2-1)*c^10+3/5*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3/(c^2*x^2-1)*c^8-3/10*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x/(c^2*x^2-1)*c^6+2*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^12-1/5*a/d/x^5*(-c^2*d*x^2+d)^(3/2)+1/4*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)+2/15*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^5+9/5*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/x^5/(c^2*x^2-1)*arcsin(c*x)+2/15*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^12-2/15*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^10-3/10*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^8+3/10*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+6/5*I*b*(-d*(c^2*x^2-1))^(1/2)/(15*c^6*x^6-5*c^4*x^4-15*c^2*x^2+9)/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^5-2/15*a*c^2/d/x^3*(-c^2*d*x^2+d)^(3/2)","C"
61,1,2748,227,0.564000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^8,x)","\frac{225 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{7} \left(c^{2} x^{2}-1\right)}+\frac{73 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{7} \sqrt{-c^{2} x^{2}+1}}{20 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{7}}{105 \left(c^{2} x^{2}-1\right)}-\frac{71 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5} \sqrt{-c^{2} x^{2}+1}}{28 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{2} \left(c^{2} x^{2}-1\right)}+\frac{342 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{4}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{3} \left(c^{2} x^{2}-1\right)}-\frac{255 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{28 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{4} \left(c^{2} x^{2}-1\right)}+\frac{64 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{8} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{15}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{13}}{\left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{11}}{5 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{24 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{9}}{\left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{8 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{105 d \,x^{3}}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{7 d \,x^{7}}-\frac{214 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{14}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{152 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{12}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{30 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{10}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{20 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{8}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{105 c^{2} x^{2}-105}+\frac{128 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{13} c^{20}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{585 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{5} \left(c^{2} x^{2}-1\right)}+\frac{75 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{14 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x^{6} \left(c^{2} x^{2}-1\right)}+\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} \arcsin \left(c x \right) c^{16}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \arcsin \left(c x \right) c^{14}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{16 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \sqrt{-c^{2} x^{2}+1}\, c^{13}}{3 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{12}}{15 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{351 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{10}}{5 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{469 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{9} \sqrt{-c^{2} x^{2}+1}}{60 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{3057 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{8}}{35 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{594 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{6}}{35 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) x \left(c^{2} x^{2}-1\right)}-\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} c^{18}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{40 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{16}}{21 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{128 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} \left(-c^{2} x^{2}+1\right) c^{18}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} \left(-c^{2} x^{2}+1\right) c^{16}}{15 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{88 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(-c^{2} x^{2}+1\right) c^{14}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{302 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right) c^{12}}{105 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{10 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{10}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{20 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{8}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}+\frac{120 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{7 \left(280 c^{8} x^{8}-105 c^{6} x^{6}-21 c^{4} x^{4}-315 c^{2} x^{2}+225\right) \left(c^{2} x^{2}-1\right)}-\frac{4 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{35 d \,x^{5}}"," ",0,"225/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^7/(c^2*x^2-1)*arcsin(c*x)+8/105*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^7+73/20*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)-16/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^11/(c^2*x^2-1)*c^18-40/21*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9/(c^2*x^2-1)*c^16-214/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7/(c^2*x^2-1)*c^14+152/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5/(c^2*x^2-1)*c^12+30/7*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3/(c^2*x^2-1)*c^10-20/7*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x/(c^2*x^2-1)*c^8-71/28*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^2/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)+342/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^4-255/28*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^4/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)+64/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^15-8*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^13-8/5*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^11-24*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^9-8/105*a*c^4/d/x^3*(-c^2*d*x^2+d)^(3/2)-1/7*a/d/x^7*(-c^2*d*x^2+d)^(3/2)-585/7*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^5/(c^2*x^2-1)*arcsin(c*x)*c^2+75/14*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+64/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^16-56/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^14-16/3*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^13-4/15*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^12-351/5*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^10+469/60*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^2/(c^2*x^2-1)*c^9*(-c^2*x^2+1)^(1/2)+3057/35*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x/(c^2*x^2-1)*arcsin(c*x)*c^8-594/35*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/x/(c^2*x^2-1)*arcsin(c*x)*c^6-16*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7/(105*c^2*x^2-105)+128/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^13/(c^2*x^2-1)*c^20+128/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^11/(c^2*x^2-1)*(-c^2*x^2+1)*c^18+16/15*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^9/(c^2*x^2-1)*(-c^2*x^2+1)*c^16-88/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^14-302/105*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^12-10/7*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^10+20/7*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^8+120/7*I*b*(-d*(c^2*x^2-1))^(1/2)/(280*c^8*x^8-105*c^6*x^6-21*c^4*x^4-315*c^2*x^2+225)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-4/35*a*c^2/d/x^5*(-c^2*d*x^2+d)^(3/2)","C"
62,1,880,220,0.518000," ","int(x^5*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{7 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{35 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{105 d \,c^{4}}}{c^{2}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right)}{6272 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right)}{3200 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{128 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{128 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{1152 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-i+7 \arcsin \left(c x \right)\right)}{6272 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(-13 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right)}{7200 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(-i+105 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right)}{14400 c^{6} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/7*x^4*(-c^2*d*x^2+d)^(3/2)/c^2/d+4/7/c^2*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2)))+b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))/c^6/(c^2*x^2-1)+3/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))/c^6/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^6/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^6/(c^2*x^2-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))/c^6/(c^2*x^2-1)+1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-I+7*arcsin(c*x))/c^6/(c^2*x^2-1)+1/7200*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(-13*I+15*arcsin(c*x))*cos(4*arcsin(c*x))/c^6/(c^2*x^2-1)-1/14400*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(-I+105*arcsin(c*x))*sin(4*arcsin(c*x))/c^6/(c^2*x^2-1))","C"
63,1,544,157,0.291000," ","int(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(17 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right)}{3600 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(2 i+15 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right)}{900 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2))+b*(1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^4/(c^2*x^2-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))/c^4/(c^2*x^2-1)-1/3600*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(17*I+15*arcsin(c*x))*cos(4*arcsin(c*x))/c^4/(c^2*x^2-1)-1/900*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(2*I+15*arcsin(c*x))*sin(4*arcsin(c*x))/c^4/(c^2*x^2-1))","C"
64,1,343,94,0.181000," ","int(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/3*a/c^2/d*(-c^2*d*x^2+d)^(3/2)+b*(1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^2/(c^2*x^2-1)+1/72*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))/c^2/(c^2*x^2-1))","C"
65,1,413,207,0.236000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x,x)","-\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) a +\sqrt{-c^{2} d \,x^{2}+d}\, a +\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x c}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2}}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}"," ",0,"-d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*a+(-c^2*d*x^2+d)^(1/2)*a+b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c+b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2-b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
66,1,462,221,0.358000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2 d \,x^{2}}+\frac{a \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) c^{2}}{2}-\frac{a \sqrt{-c^{2} d \,x^{2}+d}\, c^{2}}{2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{2 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 \left(c^{2} x^{2}-1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 \left(c^{2} x^{2}-1\right) x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(3/2)+1/2*a*d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*c^2-1/2*a*(-c^2*d*x^2+d)^(1/2)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x*(-c^2*x^2+1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x^2*arcsin(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(2*c^2*x^2-2)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(2*c^2*x^2-2)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
67,1,571,285,0.454000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 d \,x^{4}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8 d \,x^{2}}+\frac{a \,c^{4} \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}-\frac{a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{4}}{8 c^{2} x^{2}-8}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{3}}{8 \left(c^{2} x^{2}-1\right) x}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{8 \left(c^{2} x^{2}-1\right) x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{12 \left(c^{2} x^{2}-1\right) x^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{4 \left(c^{2} x^{2}-1\right) x^{4}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{4} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{8 c^{2} x^{2}-8}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{4} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{8 c^{2} x^{2}-8}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{4} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{4} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(3/2)-1/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(3/2)+1/8*a*c^4*d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/8*a*c^4*(-c^2*d*x^2+d)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c^4-1/8*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x*(-c^2*x^2+1)^(1/2)*c^3-3/8*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x^2*arcsin(c*x)*c^2+1/12*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x^3*(-c^2*x^2+1)^(1/2)*c+1/4*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/x^4*arcsin(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^4/(8*c^2*x^2-8)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^4/(8*c^2*x^2-8)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^4/(8*c^2*x^2-8)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^4/(8*c^2*x^2-8)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
68,1,600,294,0.683000," ","int(x^4*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","-\frac{a \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8 c^{2} d}-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{16 c^{4} d}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{64 c^{4}}+\frac{3 a d x \sqrt{-c^{2} d \,x^{2}+d}}{128 c^{4}}+\frac{3 a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{128 c^{4} \sqrt{c^{2} d}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d}{256 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right) x^{7}}{16 \left(c^{2} x^{2}-1\right)}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{5}}{64 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{3}}{128 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}}{8192 c^{5} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x}{128 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right) x^{9}}{8 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{8}}{64 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, x^{6}}{32 c^{2} x^{2}-32}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x^{4}}{256 c \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x^{2}}{256 c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/8*a*x^3*(-c^2*d*x^2+d)^(5/2)/c^2/d-1/16*a/c^4*x*(-c^2*d*x^2+d)^(5/2)/d+1/64*a/c^4*x*(-c^2*d*x^2+d)^(3/2)+3/128*a/c^4*d*x*(-c^2*d*x^2+d)^(1/2)+3/128*a/c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/256*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/(c^2*x^2-1)*arcsin(c*x)^2*d+5/16*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^7-13/64*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^5-1/128*b*(-d*(c^2*x^2-1))^(1/2)*d/c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+15/8192*b*(-d*(c^2*x^2-1))^(1/2)*d/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+3/128*b*(-d*(c^2*x^2-1))^(1/2)*d/c^4/(c^2*x^2-1)*arcsin(c*x)*x-1/8*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^9-1/64*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^8+1/32*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6-1/256*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-3/256*b*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2","B"
69,1,1725,229,0.352000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{192 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x}{96 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d}{4608 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d}{512 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3}}{288 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{64 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) x^{2}}{64 c \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{512 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4}}{8 \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{16 c \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) x^{2}}{192 c \left(c^{2} x^{2}-1\right)}-\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{4608 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{3}}{12 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}}{288 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d}{4608 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d}{512 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 c^{2} \sqrt{c^{2} d}}-\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6 c^{2} d}+\frac{a d x \sqrt{-c^{2} d \,x^{2}+d}}{16 c^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right) x^{5}}{6 c^{2} x^{2}-6}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{48 c^{2} x^{2}-48}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x^{5}}{36 c^{2} x^{2}-36}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{96 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{192 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d \,x^{2}}{4608 c \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{64 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d \,x^{2}}{512 c \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{96 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{4608 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) x^{2}}{96 c \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{512 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right) x^{7}}{12 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{96 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d}{32 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{6}}{72 \left(c^{2} x^{2}-1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d \,x^{2}}{4608 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \,x^{2}}{512 c \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{7}}{72 \left(c^{2} x^{2}-1\right)}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24 c^{2}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{6}}{12 c^{2} x^{2}-12}"," ",0,"-1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/512*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/12*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+1/16*I*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-1/192*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/64*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/192*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-11/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/12*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^3-1/288*b*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+11/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-1/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)-7/288*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x^3+1/16*a/c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/6*a*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/16*a/c^2*d*x*(-c^2*d*x^2+d)^(1/2)-1/96*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+7/4608*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/96*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-3/512*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/96*I*b*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/192*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-7/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)+3/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2-1/12*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^7+1/6*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+1/96*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-1/32*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*d-1/72*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6+1/48*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-11/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2-1/72*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^7+1/36*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^5+1/96*I*b*(-d*(c^2*x^2-1))^(1/2)*d/c^2/(c^2*x^2-1)*x+7/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-3/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)+1/24*a/c^2*x*(-c^2*d*x^2+d)^(3/2)","C"
70,1,1167,162,0.167000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x}{64 \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d}{256 c \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x}{16 \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}}{256 c \left(c^{2} x^{2}-1\right)}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d}{256 c \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{32 \left(c^{2} x^{2}-1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d c \,x^{2}}{256 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right) x^{5}}{8 \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right) x^{3}}{16 \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d}{16 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{4}}{32 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{5}}{32 \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x^{3}}{64 \left(c^{2} x^{2}-1\right)}+\frac{9 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{64 \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d c \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}+\frac{3 a d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{3 a \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 c^{2} x^{2}-8}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 c^{2} x^{2}-8}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d c \,x^{2}}{256 \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{64 c \left(c^{2} x^{2}-1\right)}+\frac{17 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}+\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{64 \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d c \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}"," ",0,"-17/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x-5/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x-17/256*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+5/32*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-15/256*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+17/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^5-5/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^3-15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)-1/8*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5+7/16*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*d-1/32*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+9/64*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4+3/8*a*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/4*a*x*(-c^2*d*x^2+d)^(3/2)+15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+17/256*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)+7/64*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2","C"
71,1,464,163,0.308000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^2,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}-a \,c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}-\frac{3 a \,c^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{2}-\frac{3 a \,c^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d c}{4 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right) x^{3}}{2 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}}{8 c^{2} x^{2}-8}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) d c}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d}{\left(c^{2} x^{2}-1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d c}{c^{2} x^{2}-1}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(5/2)-a*c^2*x*(-c^2*d*x^2+d)^(3/2)-3/2*a*c^2*d*x*(-c^2*d*x^2+d)^(1/2)-3/2*a*c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d*c-1/4*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^3+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*d*c-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d/(c^2*x^2-1)/x-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c","C"
72,1,1289,167,0.410000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^4,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d \,x^{3}}+\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3 d x}+\frac{2 a \,c^{4} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}+a \,c^{4} d x \sqrt{-c^{2} d \,x^{2}+d}+\frac{a \,c^{4} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d \,c^{3}}{2 \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} c^{8}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{32 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} \arcsin \left(c x \right) c^{8}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \left(-c^{2} x^{2}+1\right) c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{12 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) d \,c^{3}}{3 c^{2} x^{2}-3}-\frac{52 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \arcsin \left(c x \right) c^{6}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} \sqrt{-c^{2} x^{2}+1}\, c^{5}}{\left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{10 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{6}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{73 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \arcsin \left(c x \right) c^{4}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}}{2 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) c^{2}}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)}{3 \left(24 c^{4} x^{4}-9 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d \,c^{3}}{3 \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(5/2)+2/3*a*c^2/d/x*(-c^2*d*x^2+d)^(5/2)+2/3*a*c^4*x*(-c^2*d*x^2+d)^(3/2)+a*c^4*d*x*(-c^2*d*x^2+d)^(1/2)+a*c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d*c^3-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+32*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+32*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4-12*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5-8*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d*c^3/(3*c^2*x^2-3)-52*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+4*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5+10/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+73/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-3/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-14/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)+4/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c^3","C"
73,1,2350,132,0.470000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^6,x)","-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} \left(-c^{2} x^{2}+1\right) c^{12}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{9 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} \left(-c^{2} x^{2}+1\right) c^{10}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \left(-c^{2} x^{2}+1\right) c^{8}}{10 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \left(-c^{2} x^{2}+1\right) c^{6}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 d \,x^{5}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{8} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{13}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{6} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{11}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{9}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{5} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{5} \sqrt{-c^{2} x^{2}+1}}{2 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d \,c^{5}}{5 \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} c^{8}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \,c^{6}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) d \,c^{5}}{5 c^{2} x^{2}-5}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{9} c^{14}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{13 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} c^{12}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} c^{10}}{4 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{4} \sqrt{-c^{2} x^{2}+1}\, c^{9}}{4 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{3} \arcsin \left(c x \right) c^{8}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{2} c^{7} \sqrt{-c^{2} x^{2}+1}}{2 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d x \arcsin \left(c x \right) c^{6}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{28 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) c^{4}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{6} \sqrt{-c^{2} x^{2}+1}\, c^{11}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{9} \arcsin \left(c x \right) c^{14}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{7} \arcsin \left(c x \right) c^{12}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,x^{5} \arcsin \left(c x \right) c^{10}}{\left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{2} \left(c^{2} x^{2}-1\right)}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) c^{2}}{5 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, c}{20 \left(5 c^{8} x^{8}-10 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) x^{4} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+1/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^12-9/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^10+3/10*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^8-1/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^6-1/5*a/d/x^5*(-c^2*d*x^2+d)^(5/2)+I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^13+2*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^11-2*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^9+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^5/(c^2*x^2-1)*arcsin(c*x)-1/5*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c^5+3/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)-7/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^8+1/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x/(c^2*x^2-1)*c^6+9/4*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^9+14*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^8-5/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^2/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)-56/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^6+28/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^4-b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^11-b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^14+5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^12-11*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^10-9/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^2/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-8/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^2+1/20*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+2*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d*c^5/(5*c^2*x^2-5)+1/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^9/(c^2*x^2-1)*c^14-13/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^7/(c^2*x^2-1)*c^12+3/4*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(5*c^8*x^8-10*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^10","C"
74,1,3383,199,0.569000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^8,x)","\text{output too large to display}"," ",0,"-2/35*a*c^2/d/x^5*(-c^2*d*x^2+d)^(5/2)-359/30*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)+25/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^7/(c^2*x^2-1)*arcsin(c*x)-2/35*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c^7-44/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^4/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^11+6*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^9+2*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^8/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^15+4*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^6/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^13-2*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^10/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^17-1/7*a/d/x^7*(-c^2*d*x^2+d)^(5/2)-10/7*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^7-2/35*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11/(c^2*x^2-1)*(-c^2*x^2+1)*c^18+1/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9/(c^2*x^2-1)*(-c^2*x^2+1)*c^16+26/105*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^14-116/105*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^12+20/21*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^10-5/21*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^8-2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11/(c^2*x^2-1)*arcsin(c*x)*c^18+25/42*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+421/42*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^2/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)+472/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^4-55/14*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^4/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-170/7*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x^5/(c^2*x^2-1)*arcsin(c*x)*c^2+3*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^16+12*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^14-5/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^13-164/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^12+11/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^11+52/5*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^10-25/21*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^3/(c^2*x^2-1)*c^10+5/21*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x/(c^2*x^2-1)*c^8+4*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d*c^7/(35*c^2*x^2-35)-2/35*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^13/(c^2*x^2-1)*c^20+9/35*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^11/(c^2*x^2-1)*c^18+1/21*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^9/(c^2*x^2-1)*c^16-142/105*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^7/(c^2*x^2-1)*c^14+72/35*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^5/(c^2*x^2-1)*c^12+1/2*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^15+161/30*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x^2/(c^2*x^2-1)*c^9*(-c^2*x^2+1)^(1/2)+1966/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)*x/(c^2*x^2-1)*arcsin(c*x)*c^8-3272/35*b*(-d*(c^2*x^2-1))^(1/2)*d/(35*c^10*x^10-35*c^8*x^8-70*c^6*x^6+154*c^4*x^4-105*c^2*x^2+25)/x/(c^2*x^2-1)*arcsin(c*x)*c^6","C"
75,1,4560,266,0.691000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^10,x)","\text{output too large to display}"," ",0,"-8/315*a*c^4/d/x^5*(-c^2*d*x^2+d)^(5/2)+1225/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^9/(c^2*x^2-1)*arcsin(c*x)+30055/504*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/(c^2*x^2-1)*c^9*(-c^2*x^2+1)^(1/2)-8/315*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c^9-1/9*a/d/x^9*(-c^2*d*x^2+d)^(5/2)+350/27*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^12-35/9*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^10-40/63*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^16-2189/189*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^14+2306/945*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9/(c^2*x^2-1)*(-c^2*x^2+1)*c^18+1384/945*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11/(c^2*x^2-1)*(-c^2*x^2+1)*c^20-128/315*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^15/(c^2*x^2-1)*(-c^2*x^2+1)*c^24-16/45*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13/(c^2*x^2-1)*(-c^2*x^2+1)*c^22-280/9*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^9-60632/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^14+1187/60*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^13+59884/105*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^12+829/56*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^11-4*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^17+3151/15*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^16-4189/180*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^15-212/15*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^18-7700/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^7/(c^2*x^2-1)*arcsin(c*x)*c^2+1225/72*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-21175/216*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^6/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)+16/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^10/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^19-128/315*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^17/(c^2*x^2-1)*c^26-455/27*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^3/(c^2*x^2-1)*c^12+35/9*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x/(c^2*x^2-1)*c^10+16*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d*c^9/(315*c^2*x^2-315)+104/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11/(c^2*x^2-1)*arcsin(c*x)*c^20-2906/945*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^9/(c^2*x^2-1)*c^18-2069/189*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^7/(c^2*x^2-1)*c^16+4639/189*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^5/(c^2*x^2-1)*c^14-64/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13/(c^2*x^2-1)*arcsin(c*x)*c^22+19540/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^5/(c^2*x^2-1)*arcsin(c*x)*c^4+16/315*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^15/(c^2*x^2-1)*c^24+344/189*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^13/(c^2*x^2-1)*c^22+922/945*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^11/(c^2*x^2-1)*c^20-43264/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x/(c^2*x^2-1)*arcsin(c*x)*c^10+113594/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x/(c^2*x^2-1)*arcsin(c*x)*c^8-25915/126*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^2/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)-174520/63*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+1285/6*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)/x^4/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)+24*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^10/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^19-24/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^17+208/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^15-1104/7*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^13+120*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^11-64/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(840*c^12*x^12-945*c^10*x^10+189*c^8*x^8-2730*c^6*x^6+6210*c^4*x^4-4725*c^2*x^2+1225)*x^12/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^21-4/63*a*c^2/d/x^7*(-c^2*d*x^2+d)^(5/2)","C"
76,1,5881,333,0.868000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^12,x)","\text{output too large to display}"," ",0,"result too large to display","C"
77,1,1781,323,0.817000," ","int(x^7*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{6} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{11 c^{2} d}+\frac{-\frac{2 x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{33 c^{2} d}+\frac{6 \left(-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{63 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{315 d \,c^{4}}\right)}{11 c^{2}}}{c^{2}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1+1024 x^{12} c^{12}-220 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+1232 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-1024 i \sqrt{-c^{2} x^{2}+1}\, x^{11} c^{11}+2816 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}-3328 c^{10} x^{10}+11 i \sqrt{-c^{2} x^{2}+1}\, x c -61 c^{2} x^{2}+620 c^{4} x^{4}-2352 c^{6} x^{6}-2816 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+4096 c^{8} x^{8}\right) \left(i+11 \arcsin \left(c x \right)\right) d}{247808 c^{8} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+9 \arcsin \left(c x \right)\right) d}{55296 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d}{100352 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right) d}{51200 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right) d}{3072 c^{8} \left(c^{2} x^{2}-1\right)}-\frac{7 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{1024 c^{8} \left(c^{2} x^{2}-1\right)}-\frac{7 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{1024 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{3072 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+16 c^{6} x^{6}-20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-28 c^{4} x^{4}+5 i \sqrt{-c^{2} x^{2}+1}\, x c +13 c^{2} x^{2}-1\right) \left(-i+5 \arcsin \left(c x \right)\right) d}{51200 c^{8} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-i+7 \arcsin \left(c x \right)\right) d}{100352 c^{8} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-i+9 \arcsin \left(c x \right)\right) d}{55296 c^{8} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1024 i \sqrt{-c^{2} x^{2}+1}\, x^{11} c^{11}+1024 x^{12} c^{12}-2816 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}-3328 c^{10} x^{10}+2816 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+4096 c^{8} x^{8}-1232 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-2352 c^{6} x^{6}+220 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+620 c^{4} x^{4}-11 i \sqrt{-c^{2} x^{2}+1}\, x c -61 c^{2} x^{2}+1\right) \left(-i+11 \arcsin \left(c x \right)\right) d}{247808 c^{8} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/11*x^6*(-c^2*d*x^2+d)^(5/2)/c^2/d+6/11/c^2*(-1/9*x^4*(-c^2*d*x^2+d)^(5/2)/c^2/d+4/9/c^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))))+b*(-1/247808*(-d*(c^2*x^2-1))^(1/2)*(1+1024*x^12*c^12-220*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+1232*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-1024*I*(-c^2*x^2+1)^(1/2)*x^11*c^11+2816*I*(-c^2*x^2+1)^(1/2)*x^9*c^9-3328*c^10*x^10+11*I*(-c^2*x^2+1)^(1/2)*x*c-61*c^2*x^2+620*c^4*x^4-2352*c^6*x^6-2816*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+4096*c^8*x^8)*(I+11*arcsin(c*x))*d/c^8/(c^2*x^2-1)-1/55296*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+9*arcsin(c*x))*d/c^8/(c^2*x^2-1)+1/100352*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d/c^8/(c^2*x^2-1)+11/51200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))*d/c^8/(c^2*x^2-1)+1/3072*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))*d/c^8/(c^2*x^2-1)-7/1024*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^8/(c^2*x^2-1)-7/1024*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^8/(c^2*x^2-1)+1/3072*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^8/(c^2*x^2-1)+11/51200*(-d*(c^2*x^2-1))^(1/2)*(16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+16*c^6*x^6-20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-28*c^4*x^4+5*I*(-c^2*x^2+1)^(1/2)*x*c+13*c^2*x^2-1)*(-I+5*arcsin(c*x))*d/c^8/(c^2*x^2-1)+1/100352*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-I+7*arcsin(c*x))*d/c^8/(c^2*x^2-1)-1/55296*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-I+9*arcsin(c*x))*d/c^8/(c^2*x^2-1)-1/247808*(-d*(c^2*x^2-1))^(1/2)*(1024*I*(-c^2*x^2+1)^(1/2)*x^11*c^11+1024*x^12*c^12-2816*I*(-c^2*x^2+1)^(1/2)*x^9*c^9-3328*c^10*x^10+2816*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+4096*c^8*x^8-1232*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-2352*c^6*x^6+220*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+620*c^4*x^4-11*I*(-c^2*x^2+1)^(1/2)*x*c-61*c^2*x^2+1)*(-I+11*arcsin(c*x))*d/c^8/(c^2*x^2-1))","C"
78,1,1254,259,0.542000," ","int(x^5*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{9 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{63 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{315 d \,c^{4}}}{c^{2}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+9 \arcsin \left(c x \right)\right) d}{41472 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d}{25088 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right) d}{3200 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{256 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{256 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{1152 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-i+7 \arcsin \left(c x \right)\right) d}{25088 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-i+9 \arcsin \left(c x \right)\right) d}{41472 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(17 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d}{14400 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(2 i+15 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d}{3600 c^{6} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/9*x^4*(-c^2*d*x^2+d)^(5/2)/c^2/d+4/9/c^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2)))+b*(-1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+9*arcsin(c*x))*d/c^6/(c^2*x^2-1)-1/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d/c^6/(c^2*x^2-1)+1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))*d/c^6/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^6/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^6/(c^2*x^2-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^6/(c^2*x^2-1)-1/25088*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-I+7*arcsin(c*x))*d/c^6/(c^2*x^2-1)-1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-I+9*arcsin(c*x))*d/c^6/(c^2*x^2-1)-1/14400*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(17*I+15*arcsin(c*x))*cos(4*arcsin(c*x))*d/c^6/(c^2*x^2-1)-1/3600*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(2*I+15*arcsin(c*x))*sin(4*arcsin(c*x))*d/c^6/(c^2*x^2-1))","C"
79,1,727,195,0.296000," ","int(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(2 i+35 \arcsin \left(c x \right)\right) \cos \left(6 \arcsin \left(c x \right)\right) d}{39200 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(37 i+35 \arcsin \left(c x \right)\right) \sin \left(6 \arcsin \left(c x \right)\right) d}{78400 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(7 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d}{2400 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(11 i+45 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d}{4800 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))+b*(-1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^4/(c^2*x^2-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^4/(c^2*x^2-1)+3/39200*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(2*I+35*arcsin(c*x))*cos(6*arcsin(c*x))*d/c^4/(c^2*x^2-1)+1/78400*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(37*I+35*arcsin(c*x))*sin(6*arcsin(c*x))*d/c^4/(c^2*x^2-1)-1/2400*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(7*I+15*arcsin(c*x))*cos(4*arcsin(c*x))*d/c^4/(c^2*x^2-1)-1/4800*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(11*I+45*arcsin(c*x))*sin(4*arcsin(c*x))*d/c^4/(c^2*x^2-1))","C"
80,1,524,131,0.188000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(11 i+45 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d}{1200 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(7 i+15 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d}{600 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/5*a/c^2/d*(-c^2*d*x^2+d)^(5/2)+b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^2/(c^2*x^2-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/1200*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(11*I+45*arcsin(c*x))*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/600*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(7*I+15*arcsin(c*x))*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1))","C"
81,1,525,270,0.281000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x,x)","\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a}{3}-a \,d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{-c^{2} d \,x^{2}+d}\, d -\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{4} c^{4}}{3 \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{2} c^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)}{3 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{9 \left(c^{2} x^{2}-1\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x c}{3 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}"," ",0,"1/3*(-c^2*d*x^2+d)^(3/2)*a-a*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a*(-c^2*d*x^2+d)^(1/2)*d-1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^4*c^4+5/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-1/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*c^3+4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)","A"
82,1,574,285,0.351000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 d \,x^{2}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2}+\frac{3 a \,c^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{3 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d}{2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \sqrt{-c^{2} x^{2}+1}\, x}{c^{2} x^{2}-1}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \arcsin \left(c x \right) x^{2}}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}+\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 x \left(c^{2} x^{2}-1\right)}+\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 x^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(5/2)-1/2*a*c^2*(-c^2*d*x^2+d)^(3/2)+3/2*a*c^2*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-3/2*a*c^2*(-c^2*d*x^2+d)^(1/2)*d-b*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-b*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c^2*x^2-1)*arcsin(c*x)*x^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c^2*x^2-1)*arcsin(c*x)+1/2*b*d*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/2*b*d*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)*arcsin(c*x)+3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(2*c^2*x^2-2)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(2*c^2*x^2-2)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
83,1,601,291,0.438000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{4 d \,x^{4}}+\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8 d \,x^{2}}+\frac{a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8}-\frac{3 a \,c^{4} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}+\frac{3 a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}\, d}{8}+\frac{5 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{4}}{8 \left(c^{2} x^{2}-1\right)}-\frac{5 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{3}}{8 x \left(c^{2} x^{2}-1\right)}-\frac{7 b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{8 x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{12 x^{3} \left(c^{2} x^{2}-1\right)}+\frac{b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{4 x^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \,c^{4} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{8 c^{2} x^{2}-8}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \,c^{4} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{8 c^{2} x^{2}-8}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \,c^{4} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \,c^{4} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(5/2)+1/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(5/2)+1/8*a*c^4*(-c^2*d*x^2+d)^(3/2)-3/8*a*c^4*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+3/8*a*c^4*(-c^2*d*x^2+d)^(1/2)*d+5/8*b*d*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c^4-5/8*b*d*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3-7/8*b*d*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)*arcsin(c*x)*c^2+1/12*b*d*(-d*(c^2*x^2-1))^(1/2)/x^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/4*b*d*(-d*(c^2*x^2-1))^(1/2)/x^4/(c^2*x^2-1)*arcsin(c*x)-3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d*c^4/(8*c^2*x^2-8)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)+3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d*c^4/(8*c^2*x^2-8)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d*c^4/(8*c^2*x^2-8)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d*c^4/(8*c^2*x^2-8)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
84,1,3481,374,0.748000," ","int(x^4*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"-5/98304*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2-7/12288*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2+1/200*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^10+19/1024*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/160*a/c^4*x*(-c^2*d*x^2+d)^(5/2)-5/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+7/20480*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-7/12288*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-3/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*cos(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2-1/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^10+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^8-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6+3/20480*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-3/4096*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-3/2048*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/1024*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*cos(3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+5/128*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-3/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-3/20480*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+33/819200*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+3/4096*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-5/98304*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/128*a/c^4*d*x*(-c^2*d*x^2+d)^(3/2)+3/256*a/c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)+3/256*a/c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/1024*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^4/(c^2*x^2-1)*arcsin(c*x)*x-7/20480*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)+1/4096*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)+5/12288*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)-1/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)+1/200*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^11-3/200*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^9+53/3200*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x^7+7/10240*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^2/(c^2*x^2-1)*x^3+9/10240*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^4/(c^2*x^2-1)*x-17/819200*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)+11/98304*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)+5/2048*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)+1/1024*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)+1/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^11-3/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^9+53/320*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^7-3/512*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/(c^2*x^2-1)*arcsin(c*x)^2*d^2-1/80*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^8+7/640*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6-1/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+3/2048*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+33/819200*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2+5/98304*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)-13/1600*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*x^5-1/4096*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-13/160*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^5+7/12288*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)-51/102400*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-33/819200*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)+1/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2+3/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*cos(3*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)-9/10240*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+3/20480*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(9*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)-1/1024*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+17/819200*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2-3/4096*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)-11/98304*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2-3/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^5/(c^2*x^2-1)*arcsin(c*x)-5/12288*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*x^2-1/1024*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-17/819200*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+11/98304*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+5/12288*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+7/20480*b*(-d*(c^2*x^2-1))^(1/2)*sin(9*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-1/4096*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-5/2048*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-1/10*a*x^3*(-c^2*d*x^2+d)^(7/2)/c^2/d-3/80*a/c^4*x*(-c^2*d*x^2+d)^(7/2)/d","C"
85,1,2828,305,0.380000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"-7/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^3+73/147456*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)+13/9216*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)-3/1024*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)-63/16384*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-27/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*x^3+5/768*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)-1/256*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)+1/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^9-5/32*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^7+17/128*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5-3/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x-5/256*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*d^2+3/1024*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2+1/128*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^8-1/64*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6+5/512*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+3/512*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-73/147456*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2-13/9216*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2+1/48*a/c^2*x*(-c^2*d*x^2+d)^(5/2)+5/128*a/c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+55/147456*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)+5/9216*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)-5/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)+1/128*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^9-5/256*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^7+17/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x^5+17/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^2/(c^2*x^2-1)*x+19/6144*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)+5/128*a/c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+5/192*a/c^2*d*x*(-c^2*d*x^2+d)^(3/2)-1/8*a*x*(-c^2*d*x^2+d)^(7/2)/c^2/d-1/768*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)-5/9216*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2+5/9216*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-5/1024*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+55/147456*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/256*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2-19/6144*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2-5/768*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2+3/256*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)+5/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2-17/2048*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-13/6144*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^3/(c^2*x^2-1)*arcsin(c*x)-55/147456*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c/(c^2*x^2-1)*x^2-1/768*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-13/6144*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-13/9216*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-3/256*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2+3/1024*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/16*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^8+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6-5/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+13/6144*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2-73/147456*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/768*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)*x^2-19/6144*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-5/768*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x","C"
86,1,1985,229,0.194000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\frac{a x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{6}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{48 c^{2} x^{2}-48}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{5}}{36 \left(c^{2} x^{2}-1\right)}-\frac{29 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x^{3}}{288 \left(c^{2} x^{2}-1\right)}-\frac{25 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2}}{4608 c \left(c^{2} x^{2}-1\right)}-\frac{27 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2}}{512 c \left(c^{2} x^{2}-1\right)}+\frac{5 a d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{24}+\frac{5 a \,d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{16}+\frac{5 a \,d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{16 \sqrt{c^{2} d}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right)}{192 c \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}-\frac{25 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2} \sqrt{-c^{2} x^{2}+1}\, x}{4608 \left(c^{2} x^{2}-1\right)}-\frac{27 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} \sqrt{-c^{2} x^{2}+1}\, x}{512 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{4}}{48 \left(c^{2} x^{2}-1\right)}+\frac{29 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2} c \,x^{2}}{4608 \left(c^{2} x^{2}-1\right)}+\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c \,x^{2}}{512 \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d^{2}}{32 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right) x^{5}}{6 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right) x^{7}}{12 c^{2} x^{2}-12}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \arcsin \left(c x \right) x^{3}}{3 c^{2} x^{2}-3}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, x^{6}}{72 c^{2} x^{2}-72}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 c^{2} x^{2}-8}+\frac{33 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} \sqrt{-c^{2} x^{2}+1}\, x}{512 \left(c^{2} x^{2}-1\right)}-\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{96 c \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right)}{48 c \left(c^{2} x^{2}-1\right)}+\frac{25 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2} c \,x^{2}}{4608 \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right)}{32 c \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{7}}{72 c^{2} x^{2}-72}+\frac{29 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2} \sqrt{-c^{2} x^{2}+1}\, x}{4608 \left(c^{2} x^{2}-1\right)}+\frac{27 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c \,x^{2}}{512 \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{32 \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right) x^{2}}{192 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{6}}{12 \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{16 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right) x^{2}}{48 \left(c^{2} x^{2}-1\right)}+\frac{9 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{64 \left(c^{2} x^{2}-1\right)}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{192 \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right) x^{2}}{32 \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 c^{2} x^{2}-8}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}}{288 c \left(c^{2} x^{2}-1\right)}-\frac{29 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right) d^{2}}{4608 c \left(c^{2} x^{2}-1\right)}-\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2}}{512 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x}{4 \left(c^{2} x^{2}-1\right)}+\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x}{96 \left(c^{2} x^{2}-1\right)}"," ",0,"1/6*a*x*(-c^2*d*x^2+d)^(5/2)+5/24*a*d*x*(-c^2*d*x^2+d)^(3/2)+5/16*a*d^2*x*(-c^2*d*x^2+d)^(1/2)+5/16*a*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/192*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)-9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)-25/4608*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-27/512*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/72*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6-1/48*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+29/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+33/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+1/72*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^7-1/36*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^5-29/288*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x^3-25/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)-27/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)-5/32*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*d^2+1/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^7-1/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4+3/16*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-1/48*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2+9/64*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+5/192*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-3/32*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2-1/12*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^6+27/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+29/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+33/512*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-11/96*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+1/48*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)+25/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+3/32*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)+9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/48*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+3/32*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+5/192*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2-17/288*b*(-d*(c^2*x^2-1))^(1/2)*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-29/4608*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)-33/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)-1/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x+11/96*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*x","C"
87,1,1391,236,0.348000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^2,x)","\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d^{2}}{\left(c^{2} x^{2}-1\right) x}+\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c \sqrt{-c^{2} x^{2}+1}}{256 \left(c^{2} x^{2}-1\right)}+\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c}{256 \left(c^{2} x^{2}-1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{64 \left(c^{2} x^{2}-1\right)}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c^{3} \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}-\frac{33 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c^{2} \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 \left(c^{2} x^{2}-1\right)}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 \left(c^{2} x^{2}-1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{d x}-a \,c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}-\frac{5 a \,c^{2} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}-\frac{15 a \,c^{2} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right)}{64 \left(c^{2} x^{2}-1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right) x^{3}}{16 \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{32 \left(c^{2} x^{2}-1\right)}-\frac{33 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c^{3} x^{2}}{256 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c}{c^{2} x^{2}-1}+\frac{31 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c}{256 \left(c^{2} x^{2}-1\right)}+\frac{13 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{3}}{64 \left(c^{2} x^{2}-1\right)}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x}{64 \left(c^{2} x^{2}-1\right)}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d^{2} c}{16 \left(c^{2} x^{2}-1\right)}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \arcsin \left(c x \right) x}{16 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, x^{4}}{32 c^{2} x^{2}-32}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{5}}{32 c^{2} x^{2}-32}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right) x^{5}}{8 c^{2} x^{2}-8}-\frac{31 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c^{3} x^{2}}{256 \left(c^{2} x^{2}-1\right)}+\frac{79 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d^{2} c}{64 \left(c^{2} x^{2}-1\right)}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right) d^{2} c \arcsin \left(c x \right)}{64 \left(c^{2} x^{2}-1\right)}+\frac{31 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c^{2} \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c^{3} \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}-\frac{17 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) d^{2} c^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{64 \left(c^{2} x^{2}-1\right)}-\frac{15 a \,c^{2} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}"," ",0,"b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d^2/(c^2*x^2-1)/x+33/256*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+33/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)-15/64*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+15/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-33/256*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4-3/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-a/d/x*(-c^2*d*x^2+d)^(7/2)-a*c^2*x*(-c^2*d*x^2+d)^(5/2)-5/4*a*c^2*d*x*(-c^2*d*x^2+d)^(3/2)-15/8*a*c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c+17/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^5-11/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^3-9/32*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-33/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2+1/32*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+31/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)+1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^5+13/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^3-15/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x+15/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d^2*c-7/16*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x-31/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2+79/64*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*d^2*c+31/256*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-17/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-15/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)-17/64*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-15/8*a*c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))","C"
88,1,1527,241,0.476000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^4,x)","\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c^{3}}{3 \left(c^{2} x^{2}-1\right)}+\frac{5 a \,c^{4} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{4 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d x}+\frac{5 a \,c^{4} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d^{2} c^{3}}{4 \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}}{2 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x^{3} \left(c^{2} x^{2}-1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{3 d \,x^{3}}+\frac{4 a \,c^{4} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{3}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{49 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \left(-c^{2} x^{2}+1\right) c^{4}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{35 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{147 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{7}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}}{8 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{2} x^{2}-4}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right) x^{3}}{2 c^{2} x^{2}-2}+\frac{28 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{6}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{4}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{14 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d^{2} c^{3}}{3 c^{2} x^{2}-3}-\frac{49 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{8}}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{21 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} \sqrt{-c^{2} x^{2}+1}\, c^{5}}{2 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{190 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \arcsin \left(c x \right) c^{4}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) c^{2}}{3 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) x^{2} \left(c^{2} x^{2}-1\right)}+\frac{147 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} \arcsin \left(c x \right) c^{8}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}-\frac{203 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \arcsin \left(c x \right) c^{6}}{\left(63 c^{4} x^{4}-15 c^{2} x^{2}+1\right) \left(c^{2} x^{2}-1\right)}+\frac{5 a \,c^{4} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}"," ",0,"5/2*a*c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+4/3*a*c^2/d/x*(-c^2*d*x^2+d)^(7/2)+5/3*a*c^4*d*x*(-c^2*d*x^2+d)^(3/2)-5/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d^2*c^3-5/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)+1/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^3+7/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c^3+1/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/3*a/d/x^3*(-c^2*d*x^2+d)^(7/2)+4/3*a*c^4*x*(-c^2*d*x^2+d)^(5/2)+7/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-49/6*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+7/6*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4-35*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+147*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+21/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5+190/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-23/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-14*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d^2*c^3/(3*c^2*x^2-3)-49/6*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+28/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-7/6*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+147*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-203*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+5/2*a*c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)","C"
89,1,2615,243,0.506000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^6,x)","-\frac{69 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{5}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{7153 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} \left(-c^{2} x^{2}+1\right) c^{10}}{60 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{759 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \left(-c^{2} x^{2}+1\right) c^{8}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{69 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \left(-c^{2} x^{2}+1\right) c^{6}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{5} \left(c^{2} x^{2}-1\right)}+\frac{175 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}}{4 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{5 d \,x^{5}}-\frac{8 a \,c^{6} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{15}-\frac{8 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{15 d x}-\frac{2 a \,c^{6} d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a \,c^{6} d^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d^{2} c^{5}}{15 \left(c^{2} x^{2}-1\right)}+\frac{5819 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} \left(-c^{2} x^{2}+1\right) c^{12}}{30 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{207 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} c^{8}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{69 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \,c^{6}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d^{2} c^{5}}{2 c^{2} x^{2}-2}+\frac{46 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d^{2} c^{5}}{15 c^{2} x^{2}-15}+\frac{5819 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{9} c^{14}}{30 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{18791 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} c^{12}}{60 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{943 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} c^{10}}{6 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{1587 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{9} \arcsin \left(c x \right) c^{14}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{759 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{6} \sqrt{-c^{2} x^{2}+1}\, c^{11}}{2 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{777 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) c^{4}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x \left(c^{2} x^{2}-1\right)}-\frac{141 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{2} \left(c^{2} x^{2}-1\right)}-\frac{117 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) c^{2}}{5 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{3} \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, c}{20 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) x^{4} \left(c^{2} x^{2}-1\right)}+\frac{3519 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{7} \arcsin \left(c x \right) c^{12}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{9595 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{5} \arcsin \left(c x \right) c^{10}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{1329 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} \sqrt{-c^{2} x^{2}+1}\, c^{9}}{4 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{5318 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{3} \arcsin \left(c x \right) c^{8}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{1889 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} c^{7} \sqrt{-c^{2} x^{2}+1}}{12 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{9602 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x \arcsin \left(c x \right) c^{6}}{15 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{115 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{7}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{1173 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{6} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{11}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{1495 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{4} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{9}}{3 \left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}-\frac{1587 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} x^{8} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{13}}{\left(1035 c^{8} x^{8}-765 c^{6} x^{6}+325 c^{4} x^{4}-75 c^{2} x^{2}+9\right) \left(c^{2} x^{2}-1\right)}+\frac{2 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{15 d \,x^{3}}-\frac{a \,c^{6} d^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}"," ",0,"-69/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^5-7153/60*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^10+759/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^8-69/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+5819/30*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^12+9/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^5/(c^2*x^2-1)*arcsin(c*x)-23/15*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c^5+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d^2*c^5+175/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)-1/5*a/d/x^5*(-c^2*d*x^2+d)^(7/2)-8/15*a*c^6*x*(-c^2*d*x^2+d)^(5/2)-8/15*a*c^4/d/x*(-c^2*d*x^2+d)^(7/2)-2/3*a*c^6*d*x*(-c^2*d*x^2+d)^(3/2)-a*c^6*d^2*x*(-c^2*d*x^2+d)^(1/2)-1587*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^14+46*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d^2*c^5/(15*c^2*x^2-15)+5819/30*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^9/(c^2*x^2-1)*c^14-18791/60*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7/(c^2*x^2-1)*c^12+943/6*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5/(c^2*x^2-1)*c^10-207/5*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3/(c^2*x^2-1)*c^8-759/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^11+777/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x/(c^2*x^2-1)*arcsin(c*x)*c^4-141/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^2/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-117/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^2+9/20*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)/x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+69/20*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x/(c^2*x^2-1)*c^6+3519*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^12-9595/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^10+1329/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^9+5318/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^8-1889/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^2/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)-9602/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x/(c^2*x^2-1)*arcsin(c*x)*c^6+115*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^7+1173*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^6/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^11-1495/3*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^4/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^9-1587*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(1035*c^8*x^8-765*c^6*x^6+325*c^4*x^4-75*c^2*x^2+9)*x^8/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^13+2/15*a*c^2/d/x^3*(-c^2*d*x^2+d)^(7/2)-a*c^6*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))","C"
90,1,4031,175,0.576000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^8,x)","\text{output too large to display}"," ",0,"17/28*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5/(c^2*x^2-1)*(-c^2*x^2+1)*c^12+1/7*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-5/28*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^10+1/42*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^8-3/14*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11/(c^2*x^2-1)*(-c^2*x^2+1)*c^18+3/4*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9/(c^2*x^2-1)*(-c^2*x^2+1)*c^16-83/84*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7/(c^2*x^2-1)*(-c^2*x^2+1)*c^14-55/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/(c^2*x^2-1)*c^7*(-c^2*x^2+1)^(1/2)+1/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^7/(c^2*x^2-1)*arcsin(c*x)+1/7*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c^7-1/7*a/d/x^7*(-c^2*d*x^2+d)^(7/2)-1/42*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x/(c^2*x^2-1)*c^8-2*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d^2*c^7/(7*c^2*x^2-7)-3/14*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^13/(c^2*x^2-1)*c^20+3/2*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^10/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^17-21/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^15-23/84*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^4/(c^2*x^2-1)*c^3*(-c^2*x^2+1)^(1/2)-11/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^5/(c^2*x^2-1)*arcsin(c*x)*c^2+1/42*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+41/28*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^2/(c^2*x^2-1)*c^5*(-c^2*x^2+1)^(1/2)+55/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)*c^4-165/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^6+27/28*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11/(c^2*x^2-1)*c^18-73/42*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9/(c^2*x^2-1)*c^16+67/42*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7/(c^2*x^2-1)*c^14-11/14*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^12+17/84*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^10+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^13/(c^2*x^2-1)*arcsin(c*x)*c^20-7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^11/(c^2*x^2-1)*arcsin(c*x)*c^18+23*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^9/(c^2*x^2-1)*arcsin(c*x)*c^16-47*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^7/(c^2*x^2-1)*arcsin(c*x)*c^14+119/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^13+66*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^12-47/4*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^11-66*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^10+109/12*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^2/(c^2*x^2-1)*c^9*(-c^2*x^2+1)^(1/2)+330/7*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^8+I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^12/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^19-3*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^10/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^17+5*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^8/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^15-5*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^6/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^13+3*I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^11-I*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(7*c^12*x^12-21*c^10*x^10+35*c^8*x^8-35*c^6*x^6+21*c^4*x^4-7*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^9","C"
91,1,5323,244,0.730000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^10,x)","\text{output too large to display}"," ",0,"result too large to display","C"
92,1,6758,313,0.934000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^12,x)","\text{output too large to display}"," ",0,"result too large to display","C"
93,1,1644,306,0.641000," ","int(x^5*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{11 c^{2} d}+\frac{-\frac{4 x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{99 c^{2} d}-\frac{8 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{693 d \,c^{4}}}{c^{2}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1+1024 x^{12} c^{12}-220 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+1232 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-1024 i \sqrt{-c^{2} x^{2}+1}\, x^{11} c^{11}+2816 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}-3328 c^{10} x^{10}+11 i \sqrt{-c^{2} x^{2}+1}\, x c -61 c^{2} x^{2}+620 c^{4} x^{4}-2352 c^{6} x^{6}-2816 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+4096 c^{8} x^{8}\right) \left(i+11 \arcsin \left(c x \right)\right) d^{2}}{247808 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+9 \arcsin \left(c x \right)\right) d^{2}}{165888 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d^{2}}{100352 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right) d^{2}}{9216 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d^{2}}{1024 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d^{2}}{1024 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d^{2}}{9216 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+16 c^{6} x^{6}-20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-28 c^{4} x^{4}+5 i \sqrt{-c^{2} x^{2}+1}\, x c +13 c^{2} x^{2}-1\right) \left(-i+5 \arcsin \left(c x \right)\right) d^{2}}{10240 c^{6} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-i+9 \arcsin \left(c x \right)\right) d^{2}}{165888 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(1024 i \sqrt{-c^{2} x^{2}+1}\, x^{11} c^{11}+1024 x^{12} c^{12}-2816 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}-3328 c^{10} x^{10}+2816 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+4096 c^{8} x^{8}-1232 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-2352 c^{6} x^{6}+220 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+620 c^{4} x^{4}-11 i \sqrt{-c^{2} x^{2}+1}\, x c -61 c^{2} x^{2}+1\right) \left(-i+11 \arcsin \left(c x \right)\right) d^{2}}{247808 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(2 i+35 \arcsin \left(c x \right)\right) \cos \left(6 \arcsin \left(c x \right)\right) d^{2}}{125440 c^{6} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(37 i+35 \arcsin \left(c x \right)\right) \sin \left(6 \arcsin \left(c x \right)\right) d^{2}}{250880 c^{6} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/11*x^4*(-c^2*d*x^2+d)^(7/2)/c^2/d+4/11/c^2*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2)))+b*(1/247808*(-d*(c^2*x^2-1))^(1/2)*(1+1024*x^12*c^12-220*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+1232*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-1024*I*(-c^2*x^2+1)^(1/2)*x^11*c^11+2816*I*(-c^2*x^2+1)^(1/2)*x^9*c^9-3328*c^10*x^10+11*I*(-c^2*x^2+1)^(1/2)*x*c-61*c^2*x^2+620*c^4*x^4-2352*c^6*x^6-2816*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+4096*c^8*x^8)*(I+11*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)-1/165888*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+9*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)-5/100352*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)+5/9216*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)-5/1024*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d^2/c^6/(c^2*x^2-1)-5/1024*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d^2/c^6/(c^2*x^2-1)+5/9216*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)+1/10240*(-d*(c^2*x^2-1))^(1/2)*(16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+16*c^6*x^6-20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-28*c^4*x^4+5*I*(-c^2*x^2+1)^(1/2)*x*c+13*c^2*x^2-1)*(-I+5*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)-1/165888*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-I+9*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)+1/247808*(-d*(c^2*x^2-1))^(1/2)*(1024*I*(-c^2*x^2+1)^(1/2)*x^11*c^11+1024*x^12*c^12-2816*I*(-c^2*x^2+1)^(1/2)*x^9*c^9-3328*c^10*x^10+2816*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+4096*c^8*x^8-1232*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-2352*c^6*x^6+220*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+620*c^4*x^4-11*I*(-c^2*x^2+1)^(1/2)*x*c-61*c^2*x^2+1)*(-I+11*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)+3/125440*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(2*I+35*arcsin(c*x))*cos(6*arcsin(c*x))*d^2/c^6/(c^2*x^2-1)+1/250880*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(37*I+35*arcsin(c*x))*sin(6*arcsin(c*x))*d^2/c^6/(c^2*x^2-1))","C"
94,1,1063,240,0.378000," ","int(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","a \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+9 \arcsin \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-i+7 \arcsin \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-i+9 \arcsin \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2))+b*(1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d^2/c^4/(c^2*x^2-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-I+7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)+1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-I+9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1))","C"
95,1,717,174,0.226000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(11 i+70 \arcsin \left(c x \right)\right) \cos \left(6 \arcsin \left(c x \right)\right) d^{2}}{7840 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(9 i+35 \arcsin \left(c x \right)\right) \sin \left(6 \arcsin \left(c x \right)\right) d^{2}}{15680 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(i+5 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d^{2}}{160 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(3 i+5 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d^{2}}{320 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/7*a/c^2/d*(-c^2*d*x^2+d)^(7/2)+b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d^2/c^2/(c^2*x^2-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/7840*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(11*I+70*arcsin(c*x))*cos(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-3/15680*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(9*I+35*arcsin(c*x))*sin(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/160*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(I+5*arcsin(c*x))*cos(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/320*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(3*I+5*arcsin(c*x))*sin(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1))","C"
96,1,652,343,0.337000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x,x)","\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a}{5}+\frac{a d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a \,d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)}{15 \left(c^{2} x^{2}-1\right)}+\frac{34 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{2} c^{2}}{15 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{6} c^{6}}{5 c^{2} x^{2}-5}-\frac{14 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{4} c^{4}}{15 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}}{25 c^{2} x^{2}-25}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{45 \left(c^{2} x^{2}-1\right)}+\frac{23 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x c}{15 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}"," ",0,"1/5*(-c^2*d*x^2+d)^(5/2)*a+1/3*a*d*(-c^2*d*x^2+d)^(3/2)-a*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a*(-c^2*d*x^2+d)^(1/2)*d^2+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)+34/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^6*c^6-14/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^4*c^4+1/25*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5*c^5-11/45*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*c^3+23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))","A"
97,1,704,362,0.418000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^3,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{2 d \,x^{2}}-\frac{a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2}-\frac{5 a \,c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6}+\frac{5 a \,c^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{5 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}}{2}+\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 x \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} d^{2} \arcsin \left(c x \right) x^{4}}{3 c^{2} x^{2}-3}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d^{2} \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{5} d^{2} \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 c^{2} x^{2}-9}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d^{2} \sqrt{-c^{2} x^{2}+1}\, x}{3 \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d^{2} \arcsin \left(c x \right)}{6 \left(c^{2} x^{2}-1\right)}+\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 x^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(7/2)-1/2*a*c^2*(-c^2*d*x^2+d)^(5/2)-5/6*a*c^2*d*(-c^2*d*x^2+d)^(3/2)+5/2*a*c^2*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-5/2*a*c^2*(-c^2*d*x^2+d)^(1/2)*d^2+1/2*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)*c^6*d^2/(c^2*x^2-1)*arcsin(c*x)*x^4-8/3*b*(-d*(c^2*x^2-1))^(1/2)*c^4*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2+1/9*b*(-d*(c^2*x^2-1))^(1/2)*c^5*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-7/3*b*(-d*(c^2*x^2-1))^(1/2)*c^3*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-5*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d^2/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+5*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d^2/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+11/6*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d^2/(c^2*x^2-1)*arcsin(c*x)+1/2*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)*arcsin(c*x)-5*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d^2/(2*c^2*x^2-2)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+5*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d^2/(2*c^2*x^2-2)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)","A"
98,1,727,365,0.479000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/x^5,x)","-\frac{a \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{4 d \,x^{4}}+\frac{3 a \,c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{8 d \,x^{2}}+\frac{3 a \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{8}+\frac{5 a \,c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{8}-\frac{15 a \,c^{4} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{8}+\frac{15 a \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}}{8}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, x}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right) x^{2}}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right)}{8 c^{2} x^{2}-8}-\frac{9 b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{3}}{8 x \left(c^{2} x^{2}-1\right)}-\frac{11 b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{8 x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{12 x^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{4 x^{4} \left(c^{2} x^{2}-1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{4} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{4} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{4} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{4} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{8 c^{2} x^{2}-8}"," ",0,"-1/4*a/d/x^4*(-c^2*d*x^2+d)^(7/2)+3/8*a*c^2/d/x^2*(-c^2*d*x^2+d)^(7/2)+3/8*a*c^4*(-c^2*d*x^2+d)^(5/2)+5/8*a*c^4*d*(-c^2*d*x^2+d)^(3/2)-15/8*a*c^4*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+15/8*a*c^4*(-c^2*d*x^2+d)^(1/2)*d^2+b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^2+1/8*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)-9/8*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3-11/8*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)*arcsin(c*x)*c^2+1/12*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/4*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x^4/(c^2*x^2-1)*arcsin(c*x)-15*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^4/(8*c^2*x^2-8)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+15*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^4/(8*c^2*x^2-8)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-15*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^4/(8*c^2*x^2-8)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+15*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^4/(8*c^2*x^2-8)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
99,1,31,26,0.080000," ","int(arcsin(x)*(-x^2+1)^(1/2),x)","\frac{\arcsin \left(x \right) \left(x \sqrt{-x^{2}+1}+\arcsin \left(x \right)\right)}{2}-\frac{\arcsin \left(x \right)^{2}}{4}-\frac{x^{2}}{4}"," ",0,"1/2*arcsin(x)*(x*(-x^2+1)^(1/2)+arcsin(x))-1/4*arcsin(x)^2-1/4*x^2","A"
100,1,101,56,0.061000," ","int((a+b*arcsin(c*x))*(-Pi*c^2*x^2+Pi)^(1/2),x)","\frac{a x \sqrt{-\pi  \,c^{2} x^{2}+\pi}}{2}+\frac{a \pi  \arctan \left(\frac{\sqrt{\pi  \,c^{2}}\, x}{\sqrt{-\pi  \,c^{2} x^{2}+\pi}}\right)}{2 \sqrt{\pi  \,c^{2}}}+\frac{b \sqrt{\pi}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{2}-\frac{b c \,x^{2} \sqrt{\pi}}{4}+\frac{b \sqrt{\pi}\, \arcsin \left(c x \right)^{2}}{4 c}"," ",0,"1/2*a*x*(-Pi*c^2*x^2+Pi)^(1/2)+1/2*a*Pi/(Pi*c^2)^(1/2)*arctan((Pi*c^2)^(1/2)*x/(-Pi*c^2*x^2+Pi)^(1/2))+1/2*b*Pi^(1/2)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-1/4*b*c*x^2*Pi^(1/2)+1/4*b*Pi^(1/2)/c*arcsin(c*x)^2","A"
101,1,74,74,0.103000," ","int(x^4*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{-4 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+a^{4} x^{4}-6 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a +3 a^{2} x^{2}+3 \arcsin \left(a x \right)^{2}}{16 a^{5}}"," ",0,"1/16*(-4*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3+a^4*x^4-6*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a+3*a^2*x^2+3*arcsin(a*x)^2)/a^5","A"
102,1,95,60,0.088000," ","int(x^3*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\left(3 a^{4} x^{4} \arcsin \left(a x \right)+3 a^{2} x^{2} \arcsin \left(a x \right)+a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}-6 \arcsin \left(a x \right)+6 a x \sqrt{-a^{2} x^{2}+1}\right) \sqrt{-a^{2} x^{2}+1}}{9 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/9/a^4*(3*a^4*x^4*arcsin(a*x)+3*a^2*x^2*arcsin(a*x)+a^3*x^3*(-a^2*x^2+1)^(1/2)-6*arcsin(a*x)+6*a*x*(-a^2*x^2+1)^(1/2))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
103,1,40,42,0.086000," ","int(x^2*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{-2 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a +a^{2} x^{2}+\arcsin \left(a x \right)^{2}}{4 a^{3}}"," ",0,"1/4*(-2*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a+a^2*x^2+arcsin(a*x)^2)/a^3","A"
104,1,62,27,0.075000," ","int(x*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2} \arcsin \left(a x \right)-\arcsin \left(a x \right)+a x \sqrt{-a^{2} x^{2}+1}\right)}{a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a^2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)*(a^2*x^2*arcsin(a*x)-arcsin(a*x)+a*x*(-a^2*x^2+1)^(1/2))","B"
105,1,12,11,0.009000," ","int(arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\arcsin \left(a x \right)^{2}}{2 a}"," ",0,"1/2*arcsin(a*x)^2/a","A"
106,1,103,74,0.077000," ","int(arcsin(a*x)/x/(-a^2*x^2+1)^(1/2),x)","\arcsin \left(a x \right) \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)-\arcsin \left(a x \right) \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)+i \dilog \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)-i \dilog \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)"," ",0,"arcsin(a*x)*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-arcsin(a*x)*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+I*dilog(1+I*a*x+(-a^2*x^2+1)^(1/2))-I*dilog(1-I*a*x-(-a^2*x^2+1)^(1/2))","A"
107,1,32,26,0.089000," ","int(arcsin(a*x)/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{-\ln \left(a x \right) a x +\arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}}{x}"," ",0,"-(-ln(a*x)*a*x+arcsin(a*x)*(-a^2*x^2+1)^(1/2))/x","A"
108,1,178,110,0.352000," ","int(arcsin(a*x)/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a^{2} x^{2} \arcsin \left(a x \right)-a x \sqrt{-a^{2} x^{2}+1}-\arcsin \left(a x \right)\right)}{2 \left(a^{2} x^{2}-1\right) x^{2}}-\frac{a^{2} \arcsin \left(a x \right) \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)}{2}+\frac{a^{2} \arcsin \left(a x \right) \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)}{2}+\frac{i a^{2} \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)}{2}-\frac{i a^{2} \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)}{2}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)/x^2*(a^2*x^2*arcsin(a*x)-a*x*(-a^2*x^2+1)^(1/2)-arcsin(a*x))-1/2*a^2*arcsin(a*x)*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+1/2*a^2*arcsin(a*x)*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))+1/2*I*a^2*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))-1/2*I*a^2*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))","A"
109,1,521,194,0.496000," ","int(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{4} \sqrt{-c^{2} d \,x^{2}+d}}{5 c^{2} d}+\frac{-\frac{4 x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{15 c^{2} d}-\frac{8 \sqrt{-c^{2} d \,x^{2}+d}}{15 d \,c^{4}}}{c^{2}}\right)+b \left(\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+3 \arcsin \left(c x \right)\right)}{576 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{576 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(6 \arcsin \left(c x \right)\right)}{160 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(6 \arcsin \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{240 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{29 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{1800 c^{6} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/5*x^4/c^2/d*(-c^2*d*x^2+d)^(1/2)+4/5/c^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2)))+b*(5/576*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+3*arcsin(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^6/d/(c^2*x^2-1)+5/576*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-I+3*arcsin(c*x))/c^6/d/(c^2*x^2-1)+1/160*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*cos(6*arcsin(c*x))-1/800*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*sin(6*arcsin(c*x))-11/240*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))+29/1800*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*sin(4*arcsin(c*x)))","C"
110,1,381,174,0.605000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,x^{3} \sqrt{-c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{4} \sqrt{c^{2} d}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{16 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}}{16 c^{5} \sqrt{-d \left(c^{2} x^{2}-1\right)}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right)}{256 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(5 \arcsin \left(c x \right)\right)}{64 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{256 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{64 c^{5} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a*x^3/c^2/d*(-c^2*d*x^2+d)^(1/2)-3/8*a/c^4*x/d*(-c^2*d*x^2+d)^(1/2)+3/8*a/c^4/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)^2-1/16*b/c^5/(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*x-1/256*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*cos(5*arcsin(c*x))-1/64*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*sin(5*arcsin(c*x))+15/256*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*cos(3*arcsin(c*x))+7/64*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","B"
111,1,407,128,0.287000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","a \left(-\frac{x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+3 \arcsin \left(c x \right)\right)}{144 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{144 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{24 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2))+b*(1/144*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+3*arcsin(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^4/d/(c^2*x^2-1)+1/144*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-I+3*arcsin(c*x))/c^4/d/(c^2*x^2-1)-1/24*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))+1/72*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*sin(4*arcsin(c*x)))","C"
112,1,270,108,0.283000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{4 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}}{16 c^{3} \sqrt{-d \left(c^{2} x^{2}-1\right)}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{8 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2-1/16*b/c^3/(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*arcsin(c*x)*x+1/16*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*cos(3*arcsin(c*x))+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","B"
113,1,159,61,0.133000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-a/c^2/d*(-c^2*d*x^2+d)^(1/2)+b*(-1/2*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^2/d/(c^2*x^2-1))","C"
114,1,86,43,0.058000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 c d \left(c^{2} x^{2}-1\right)}"," ",0,"a/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2","A"
115,1,180,155,0.184000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{\sqrt{d}}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-i \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+\polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(I*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-polylog(2,I*c*x+(-c^2*x^2+1)^(1/2)))/d/(c^2*x^2-1)","A"
116,1,216,60,0.258000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{d x}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c}{d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d x \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d/x*(-c^2*d*x^2+d)^(1/2)+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d*x/(c^2*x^2-1)*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/x/(c^2*x^2-1)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c","C"
117,1,461,225,0.374000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{2 d \,x^{2}}-\frac{a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 \sqrt{d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 x d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 x^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a/d/x^2*(-c^2*d*x^2+d)^(1/2)-1/2*a*c^2/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/x/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/x^2/d/(c^2*x^2-1)*arcsin(c*x)+1/2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","B"
118,1,849,127,0.487000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,x^{3}}-\frac{2 a \,c^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d x}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{2 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a/d/x^3*(-c^2*d*x^2+d)^(1/2)-2/3*a*c^2/d/x*(-c^2*d*x^2+d)^(1/2)-1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*(-c^2*x^2+1)*c^4-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^5*c^8-2*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c^3-2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*arcsin(c*x)*c^6+1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*c^6-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*c^4+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*arcsin(c*x)*c^4-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*(-c^2*x^2+1)*c^6+1/2*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*c^3*(-c^2*x^2+1)^(1/2)+4/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^2*(-c^2*x^2+1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^3*arcsin(c*x)-2/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3","C"
119,1,419,197,0.503000," ","int(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{4}}{3 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a \,x^{2}}{3 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a}{3 c^{6} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{24 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{3 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{31 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{18 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}-\frac{65 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{24 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{72 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a*x^4/c^2/d/(-c^2*d*x^2+d)^(1/2)-4/3*a/c^4*x^2/d/(-c^2*d*x^2+d)^(1/2)+8/3*a/c^6/d/(-c^2*d*x^2+d)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^6/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+1/24*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))+5/3*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arcsin(c*x)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^6/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+31/18*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-65/24*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)-1/72*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*sin(4*arcsin(c*x))","C"
120,1,432,190,0.597000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{3}}{2 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a x}{2 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{4} d \sqrt{c^{2} d}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{4 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{16 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{8 d^{2} \left(c^{2} x^{2}-1\right) c^{4}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{16 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a*x^3/c^2/d/(-c^2*d*x^2+d)^(1/2)+3/2*a/c^4*x/d/(-c^2*d*x^2+d)^(1/2)-3/2*a/c^4/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)^2+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)-9/8*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/c^4*arcsin(c*x)*x-1/16*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*cos(3*arcsin(c*x))-1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","C"
121,1,306,130,0.268000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a/d/c^4/(-c^2*d*x^2+d)^(1/2)+b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x^2-2*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)","C"
122,1,274,121,0.275000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)^2+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/c^2/(c^2*x^2-1)*x-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","C"
123,1,194,67,0.127000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a/c^2/d/(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)","C"
124,1,177,72,0.109000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a*x/d/(-c^2*d*x^2+d)^(1/2)+I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","C"
125,1,344,224,0.225000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(3/2),x)","\frac{a}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{3}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a/d/(-c^2*d*x^2+d)^(1/2)-a/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)-2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))","A"
126,1,239,138,0.259000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a \,c^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) d^{2} x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{4}-1\right) c}{d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a/d/x/(-c^2*d*x^2+d)^(1/2)+2*a*c^2/d*x/(-c^2*d*x^2+d)^(1/2)+2*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*c-2*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/d^2*x*c^2+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/d^2/x-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^4-1)*c","C"
127,1,474,307,0.378000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{2 d \,x^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a \,c^{2}}{2 d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{3}{2}}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 d^{2} \left(c^{2} x^{2}-1\right) x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 d^{2} \left(c^{2} x^{2}-1\right) x^{2}}-\frac{2 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right) d^{2}}"," ",0,"-1/2*a/d/x^2/(-c^2*d*x^2+d)^(1/2)+3/2*a*c^2/d/(-c^2*d*x^2+d)^(1/2)-3/2*a*c^2/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-3/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*c^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x*(-c^2*x^2+1)^(1/2)*c+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x^2*arcsin(c*x)-2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-3/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)/d^2*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+3/2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)/d^2*dilog(I*c*x+(-c^2*x^2+1)^(1/2))","A"
128,1,1045,211,0.499000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a}{3 d \,x^{3} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a \,c^{2}}{3 d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a \,c^{4} x}{3 d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{\left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}-\frac{64 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{10}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}-\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{4}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}-\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{\left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}-\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{\left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{\left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2} x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2} x^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 \left(8 c^{4} x^{4}-7 c^{2} x^{2}-1\right) d^{2} x^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right) c^{3}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a/d/x^3/(-c^2*d*x^2+d)^(1/2)-4/3*a*c^2/d/x/(-c^2*d*x^2+d)^(1/2)+8/3*a*c^4/d*x/(-c^2*d*x^2+d)^(1/2)+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*c^4+4*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*c^6+16/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*c^3-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-64/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^7*c^10+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*(-c^2*x^2+1)*c^8-64/3*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*arcsin(c*x)*c^6-4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*(-c^2*x^2+1)*c^4-16*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*c^8-16/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*(-c^2*x^2+1)*c^6+8*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*arcsin(c*x)*c^4+4/3*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*c^3*(-c^2*x^2+1)^(1/2)+4*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^2*(-c^2*x^2+1)^(1/2)*c+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^3*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)*c^3-5/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3","C"
129,1,2245,257,0.690000," ","int(x^6*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","-\frac{14 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 c^{7} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{7}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x^{5}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}+\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{6}}+\frac{19 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}+\frac{135 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{3}}+\frac{245 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{6 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{5}}-\frac{185 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{2 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{7} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{6}}+\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}-\frac{65 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5}}{4 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{2}}-\frac{14 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{3 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{4}}+\frac{49 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{12 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{6}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{16 c^{7} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{48 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{7}}-\frac{629 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \arcsin \left(c x \right)}{8 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{17 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7}}{2 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{2}}{48 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{37 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \sqrt{-c^{2} x^{2}+1}}{2 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c}+\frac{19 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}+\frac{1177 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right)}{8 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{2}}-\frac{301 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right)}{24 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{4}}-\frac{343 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right)}{24 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{6}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{4 c^{7} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{2 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{8 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{29 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{6}}+\frac{27 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \sqrt{-c^{2} x^{2}+1}}{d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{3}}+\frac{49 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}}{6 d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{5}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 a x}{2 c^{6} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{5 a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{6} d^{2} \sqrt{c^{2} d}}-\frac{a \,x^{5}}{2 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a \,x^{3}}{6 c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{10 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right)}{d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{2}}+\frac{10 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right)}{d^{3} \left(111 c^{8} x^{8}-384 c^{6} x^{6}+386 c^{4} x^{4}-64 c^{2} x^{2}-49\right) c^{4}}"," ",0,"-14/3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^7/d^3/(c^2*x^2-1)*arcsin(c*x)-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^7*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/4*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*(-c^2*x^2+1)*x^5+3/8*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*(-c^2*x^2+1)*x^3-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^6*(-c^2*x^2+1)*x-10*I*b*(-d*(c^2*x^2-1))^(1/2)*x^5/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^2*(-c^2*x^2+1)+10*I*b*(-d*(c^2*x^2-1))^(1/2)*x^3/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^4*(-c^2*x^2+1)-185/2*I*b*(-d*(c^2*x^2-1))^(1/2)*x^6/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+19/6*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+135*I*b*(-d*(c^2*x^2-1))^(1/2)*x^4/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+245/6*I*b*(-d*(c^2*x^2-1))^(1/2)*x^2/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^5*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+1/16*b*(-d*(c^2*x^2-1))^(1/2)/c^7/d^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-11/48*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^7*(-c^2*x^2+1)^(1/2)-629/8*b*(-d*(c^2*x^2-1))^(1/2)*x^7/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)*arcsin(c*x)-1/4*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^7+17/2*I*b*(-d*(c^2*x^2-1))^(1/2)*x^7/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)+11/48*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*(-c^2*x^2+1)^(1/2)*x^2-37/2*b*(-d*(c^2*x^2-1))^(1/2)*x^6/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c*(-c^2*x^2+1)^(1/2)+19/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*arcsin(c*x)*x^3+7/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^7/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1177/8*b*(-d*(c^2*x^2-1))^(1/2)*x^5/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^2*arcsin(c*x)-301/24*b*(-d*(c^2*x^2-1))^(1/2)*x^3/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^4*arcsin(c*x)-343/24*b*(-d*(c^2*x^2-1))^(1/2)*x/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^6*arcsin(c*x)-5/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^7/d^3/(c^2*x^2-1)*arcsin(c*x)^2+5/24*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^6*x+5/8*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*x^5-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*x^3-65/4*I*b*(-d*(c^2*x^2-1))^(1/2)*x^5/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^2-14/3*I*b*(-d*(c^2*x^2-1))^(1/2)*x^3/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^4+49/12*I*b*(-d*(c^2*x^2-1))^(1/2)*x/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^6-1/2*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)*x^3+3/8*b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)*x-29/12*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^6*arcsin(c*x)*x+27*b*(-d*(c^2*x^2-1))^(1/2)*x^4/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^3*(-c^2*x^2+1)^(1/2)+49/6*b*(-d*(c^2*x^2-1))^(1/2)*x^2/d^3/(111*c^8*x^8-384*c^6*x^6+386*c^4*x^4-64*c^2*x^2-49)/c^5*(-c^2*x^2+1)^(1/2)-1/4*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-5/2*a/c^6/d^2*x/(-c^2*d*x^2+d)^(1/2)+5/2*a/c^6/d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*a*x^5/c^2/d/(-c^2*d*x^2+d)^(3/2)+5/6*a/c^4*x^3/d/(-c^2*d*x^2+d)^(3/2)","C"
130,1,459,195,0.500000," ","int(x^5*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a \,x^{4}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a \,x^{2}}{c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{8 a}{3 c^{6} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{c^{4} \left(c^{2} x^{2}-1\right)^{2} d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{6 c^{5} \left(c^{2} x^{2}-1\right)^{2} d^{3}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 c^{6} \left(c^{2} x^{2}-1\right)^{2} d^{3}}-\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{6 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{6 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*x^4/c^2/d/(-c^2*d*x^2+d)^(3/2)+4*a/c^4*x^2/d/(-c^2*d*x^2+d)^(3/2)-8/3*a/c^6/d/(-c^2*d*x^2+d)^(3/2)-b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)+2*b*(-d*(c^2*x^2-1))^(1/2)/c^4/(c^2*x^2-1)^2/d^3*arcsin(c*x)*x^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/c^5/(c^2*x^2-1)^2/d^3*(-c^2*x^2+1)^(1/2)*x-5/3*b*(-d*(c^2*x^2-1))^(1/2)/c^6/(c^2*x^2-1)^2/d^3*arcsin(c*x)-11/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+11/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)","C"
131,1,531,188,0.605000," ","int(x^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{3}}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a x}{c^{4} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{4} d^{2} \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{3}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}"," ",0,"1/3*a*x^3/c^2/d/(-c^2*d*x^2+d)^(3/2)-a/c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)+a/c^4/d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)^2-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*(-c^2*x^2+1)^(1/2)-4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*arcsin(c*x)*x+4/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)*x^3","C"
132,1,307,134,0.276000," ","int(x^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a \,x^{2}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a}{3 d \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{6 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{6 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a*x^2/c^2/d/(-c^2*d*x^2+d)^(3/2)-2/3*a/d/c^4/(-c^2*d*x^2+d)^(3/2)+b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arcsin(c*x)*x^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*(-c^2*x^2+1)^(1/2)*x-2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arcsin(c*x)-5/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+5/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)","C"
133,1,1219,109,0.328000," ","int(x^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a x}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a x}{3 c^{2} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{5}}{3 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x^{3}}{6 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(-c^{2} x^{2}+1\right) x^{5}}{6 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \arcsin \left(c x \right) x^{7}}{d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4}}{d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{2 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{3 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 c^{3} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{5}}{d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{6 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c^{3}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{6}}{d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{3 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{6 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right) c^{3}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{7}}{6 d^{3} \left(3 c^{8} x^{8}-9 c^{6} x^{6}+10 c^{4} x^{4}-5 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{3} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/c^2*x/d/(-c^2*d*x^2+d)^(3/2)-1/3*a/c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*x^5+1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*(-c^2*x^2+1)*x^3-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*(-c^2*x^2+1)*x^5+b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*arcsin(c*x)*x^7-2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*x^4+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-2/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^3/(c^2*x^2-1)*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*arcsin(c*x)*x^5-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*x^2-1/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*arcsin(c*x)*x^3-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)-1/6*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*x^7+1/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","C"
134,1,259,103,0.184000," ","int(x*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{6 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{6 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{6 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/c^2/d/(-c^2*d*x^2+d)^(3/2)-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*x+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)-1/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+1/6*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)","C"
135,1,1071,134,0.164000," ","int((a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\frac{a x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 a x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}+\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{3}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{14 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{4}}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \arcsin \left(c x \right) x^{5}}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(-c^{2} x^{2}+1\right) x^{3}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \left(-c^{2} x^{2}+1\right) x^{5}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{3}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{5}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} x^{7}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a*x/d/(-c^2*d*x^2+d)^(3/2)+2/3*a/d^2*x/(-c^2*d*x^2+d)^(1/2)+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^3/(c^2*x^2-1)*arcsin(c*x)+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^3+14/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x-2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^5+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^2-5/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^3+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^5+17/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^3-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^5+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^7-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x-2/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","C"
136,1,449,283,0.251000," ","int((a+b*arcsin(c*x))/x/(-c^2*d*x^2+d)^(5/2),x)","\frac{a}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{a}{d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{5}{2}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x c}{6 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a/d/(-c^2*d*x^2+d)^(3/2)+a/d^2/(-c^2*d*x^2+d)^(1/2)-a/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)*x^2*c^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)*x*c+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))","A"
137,1,1346,200,0.334000," ","int((a+b*arcsin(c*x))/x^2/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a}{d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 a \,c^{2} x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{8 a \,c^{2} x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{2}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{80 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3} x}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{6}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{56 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{4}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{3} \sqrt{-c^{2} x^{2}+1}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right) c}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{44 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{2}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{64 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{5}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{140 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{6}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{24 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{112 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{8}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(-c^{2} x^{2}+1\right) c^{8}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{136 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{20 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{4}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{24 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{4}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}-\frac{4 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{2}}{\left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{10}}{3 \left(8 c^{6} x^{6}-25 c^{4} x^{4}+26 c^{2} x^{2}-9\right) d^{3}}"," ",0,"-a/d/x/(-c^2*d*x^2+d)^(3/2)+4/3*a*c^2*x/d/(-c^2*d*x^2+d)^(3/2)+8/3*a*c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+4*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*c^2-80/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*(-c^2*x^2+1)*c^6+9*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3/x*arcsin(c*x)+3/2*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*(-c^2*x^2+1)^(1/2)*c-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c-64/3*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*arcsin(c*x)*c^6+56*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*arcsin(c*x)*c^4-4/3*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*c^3*(-c^2*x^2+1)^(1/2)-5/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)*c-44*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*arcsin(c*x)*c^2-64/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^5+140/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*c^6-24*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c-112/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*c^8+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*(-c^2*x^2+1)*c^8+136/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3+16/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*c+20*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*(-c^2*x^2+1)*c^4-24*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*c^4-4*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*(-c^2*x^2+1)*c^2+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^9*c^10","C"
138,1,624,406,0.451000," ","int((a+b*arcsin(c*x))/x^3/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a}{2 d \,x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a \,c^{2}}{6 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a \,c^{2}}{2 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{5 a \,c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{5}{2}}}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right) c^{4}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{3} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{10 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{13 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a/d/x^2/(-c^2*d*x^2+d)^(3/2)+5/6*a*c^2/d/(-c^2*d*x^2+d)^(3/2)+5/2*a*c^2/d^2/(-c^2*d*x^2+d)^(1/2)-5/2*a*c^2/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-5/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*arcsin(c*x)*c^4+1/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x*c^3*(-c^2*x^2+1)^(1/2)+10/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)*c-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)-13/3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-5/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+5/2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-5/2*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))","A"
139,1,1875,275,0.525000," ","int((a+b*arcsin(c*x))/x^4/(-c^2*d*x^2+d)^(5/2),x)","\frac{6 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3} x}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{6 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3} x^{2}}-\frac{64 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \arcsin \left(c x \right) c^{10}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{160 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{8}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{344 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{5} \sqrt{-c^{2} x^{2}+1}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{12 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{4}-1\right) c^{3}}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{128 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{11} c^{14}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{448 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} c^{12}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{560 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} c^{10}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{280 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{128 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{4} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{7}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{176 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{5}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{64 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{6} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{9}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{a}{3 d \,x^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{32 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{16 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{40 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{128 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{9} \left(-c^{2} x^{2}+1\right) c^{12}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{320 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{7} \left(-c^{2} x^{2}+1\right) c^{10}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{80 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \left(-c^{2} x^{2}+1\right) c^{8}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{4}}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{\left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 \left(12 c^{8} x^{8}-36 c^{6} x^{6}+35 c^{4} x^{4}-10 c^{2} x^{2}-1\right) d^{3} x^{3}}+\frac{8 a \,c^{4} x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{16 a \,c^{4} x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{2 a \,c^{2}}{d x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}"," ",0,"6*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3/x*arcsin(c*x)*c^2+1/6*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3/x^2*(-c^2*x^2+1)^(1/2)*c-64*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^7*arcsin(c*x)*c^10+160*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^5*arcsin(c*x)*c^8-8/3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^4-1)*c^3-344/3*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^3*arcsin(c*x)*c^6-2*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^2*c^5*(-c^2*x^2+1)^(1/2)+12*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x*arcsin(c*x)*c^4+128/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^11*c^14-448/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^9*c^12+128*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^7-176/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^5-64*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^9+560/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^7*c^10-280/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^5*c^8+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^3*c^6+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x*c^4-1/3*a/d/x^3/(-c^2*d*x^2+d)^(3/2)+128/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^9*(-c^2*x^2+1)*c^12-320/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^7*(-c^2*x^2+1)*c^10+80*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^5*(-c^2*x^2+1)*c^8-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x*(-c^2*x^2+1)*c^4+32/3*I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*c^3-16/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3-40/3*I*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*x^3*(-c^2*x^2+1)*c^6+2*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3*c^3*(-c^2*x^2+1)^(1/2)+1/3*b*(-d*(c^2*x^2-1))^(1/2)/(12*c^8*x^8-36*c^6*x^6+35*c^4*x^4-10*c^2*x^2-1)/d^3/x^3*arcsin(c*x)+8/3*a*c^4*x/d/(-c^2*d*x^2+d)^(3/2)+16/3*a*c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)-2*a*c^2/d/x/(-c^2*d*x^2+d)^(3/2)","C"
140,1,409,180,0.334000," ","int(arcsin(a*x)/(-a^2*c*x^2+c)^(7/2),x)","\frac{16 i \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)}{15 a \,c^{4} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{5} x^{5}-20 a^{3} x^{3}+8 i \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+15 a x -16 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+8 i \sqrt{-a^{2} x^{2}+1}\right) \left(64 i x^{8} a^{8}+64 \sqrt{-a^{2} x^{2}+1}\, x^{7} a^{7}-280 i x^{6} a^{6}-248 \sqrt{-a^{2} x^{2}+1}\, a^{5} x^{5}+160 a^{4} x^{4} \arcsin \left(a x \right)+456 i x^{4} a^{4}+340 a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}-380 a^{2} x^{2} \arcsin \left(a x \right)-328 i x^{2} a^{2}-165 a x \sqrt{-a^{2} x^{2}+1}+256 \arcsin \left(a x \right)+88 i\right)}{60 c^{4} \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 a^{6} x^{6}-517 a^{4} x^{4}+287 a^{2} x^{2}-64\right) a}-\frac{8 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{15 a \,c^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"16/15*I*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*arcsin(a*x)-1/60*(-c*(a^2*x^2-1))^(1/2)*(8*a^5*x^5-20*a^3*x^3+8*I*(-a^2*x^2+1)^(1/2)*x^4*a^4+15*a*x-16*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+8*I*(-a^2*x^2+1)^(1/2))*(64*I*x^8*a^8+64*(-a^2*x^2+1)^(1/2)*x^7*a^7-280*I*x^6*a^6-248*(-a^2*x^2+1)^(1/2)*a^5*x^5+160*a^4*x^4*arcsin(a*x)+456*I*x^4*a^4+340*a^3*x^3*(-a^2*x^2+1)^(1/2)-380*a^2*x^2*arcsin(a*x)-328*I*x^2*a^2-165*a*x*(-a^2*x^2+1)^(1/2)+256*arcsin(a*x)+88*I)/c^4/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a-8/15*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)","C"
141,0,0,59,0.380000," ","int((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
142,0,0,109,0.829000," ","int((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((f*x)^(3/2)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","F"
143,0,0,305,12.572000," ","int(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{3} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x)),x)","F"
144,0,0,209,7.351000," ","int(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x)),x)","F"
145,0,0,123,4.431000," ","int(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x)),x)","F"
146,0,0,27,0.652000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d),x)","F"
147,0,0,106,0.719000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^2,x)","F"
148,0,0,189,0.819000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^3,x)","F"
149,0,0,583,6.795000," ","int(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","F"
150,0,0,361,3.922000," ","int(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","F"
151,0,0,217,2.609000," ","int(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","\int x^{m} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","F"
152,0,0,141,1.236000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","F"
153,0,0,242,0.787000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","F"
154,0,0,358,0.813000," ","int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","F"
155,0,0,86,0.682000," ","int(x^m*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsin \left(a x \right)}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
156,1,276,254,0.198000," ","int(x^4*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{-d \,a^{2} \left(\frac{1}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d \,b^{2} \left(-\frac{\arcsin \left(c x \right)^{2} c^{5} x^{5}}{5}-\frac{2 \arcsin \left(c x \right) \left(3 c^{4} x^{4}+4 c^{2} x^{2}+8\right) \sqrt{-c^{2} x^{2}+1}}{75}+\frac{38 c^{5} x^{5}}{6125}+\frac{152 c^{3} x^{3}}{11025}+\frac{304 c x}{3675}+\frac{\arcsin \left(c x \right)^{2} c^{7} x^{7}}{7}+\frac{2 \arcsin \left(c x \right) \left(5 c^{6} x^{6}+6 c^{4} x^{4}+8 c^{2} x^{2}+16\right) \sqrt{-c^{2} x^{2}+1}}{245}-\frac{2 c^{7} x^{7}}{343}\right)-2 d a b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{19 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}-\frac{76 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3675}-\frac{152 \sqrt{-c^{2} x^{2}+1}}{3675}\right)}{c^{5}}"," ",0,"1/c^5*(-d*a^2*(1/7*c^7*x^7-1/5*c^5*x^5)-d*b^2*(-1/5*arcsin(c*x)^2*c^5*x^5-2/75*arcsin(c*x)*(3*c^4*x^4+4*c^2*x^2+8)*(-c^2*x^2+1)^(1/2)+38/6125*c^5*x^5+152/11025*c^3*x^3+304/3675*c*x+1/7*arcsin(c*x)^2*c^7*x^7+2/245*arcsin(c*x)*(5*c^6*x^6+6*c^4*x^4+8*c^2*x^2+16)*(-c^2*x^2+1)^(1/2)-2/343*c^7*x^7)-2*d*a*b*(1/7*arcsin(c*x)*c^7*x^7-1/5*arcsin(c*x)*c^5*x^5+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-19/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)-76/3675*c^2*x^2*(-c^2*x^2+1)^(1/2)-152/3675*(-c^2*x^2+1)^(1/2)))","A"
157,1,306,178,0.057000," ","int(x^3*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{-d \,a^{2} \left(\frac{1}{6} c^{6} x^{6}-\frac{1}{4} c^{4} x^{4}\right)-d \,b^{2} \left(-\frac{\arcsin \left(c x \right)^{2} c^{4} x^{4}}{4}+\frac{\arcsin \left(c x \right) \left(-2 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-3 c x \sqrt{-c^{2} x^{2}+1}+3 \arcsin \left(c x \right)\right)}{16}-\frac{\arcsin \left(c x \right)^{2}}{24}+\frac{c^{4} x^{4}}{72}+\frac{c^{2} x^{2}}{24}+\frac{\arcsin \left(c x \right)^{2} c^{6} x^{6}}{6}-\frac{\arcsin \left(c x \right) \left(-8 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-10 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-15 c x \sqrt{-c^{2} x^{2}+1}+15 \arcsin \left(c x \right)\right)}{144}-\frac{c^{6} x^{6}}{108}\right)-2 d a b \left(\frac{\arcsin \left(c x \right) c^{6} x^{6}}{6}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{c x \sqrt{-c^{2} x^{2}+1}}{24}+\frac{\arcsin \left(c x \right)}{24}\right)}{c^{4}}"," ",0,"1/c^4*(-d*a^2*(1/6*c^6*x^6-1/4*c^4*x^4)-d*b^2*(-1/4*arcsin(c*x)^2*c^4*x^4+1/16*arcsin(c*x)*(-2*c^3*x^3*(-c^2*x^2+1)^(1/2)-3*c*x*(-c^2*x^2+1)^(1/2)+3*arcsin(c*x))-1/24*arcsin(c*x)^2+1/72*c^4*x^4+1/24*c^2*x^2+1/6*arcsin(c*x)^2*c^6*x^6-1/144*arcsin(c*x)*(-8*c^5*x^5*(-c^2*x^2+1)^(1/2)-10*c^3*x^3*(-c^2*x^2+1)^(1/2)-15*c*x*(-c^2*x^2+1)^(1/2)+15*arcsin(c*x))-1/108*c^6*x^6)-2*d*a*b*(1/6*arcsin(c*x)*c^6*x^6-1/4*c^4*x^4*arcsin(c*x)+1/36*c^5*x^5*(-c^2*x^2+1)^(1/2)-1/36*c^3*x^3*(-c^2*x^2+1)^(1/2)-1/24*c*x*(-c^2*x^2+1)^(1/2)+1/24*arcsin(c*x)))","A"
158,1,280,185,0.142000," ","int(x^2*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{-d \,a^{2} \left(\frac{1}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d \,b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-3\right) c x}{3}+\frac{4 c x}{15}-\frac{4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{15}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{45}-\frac{2 \left(c^{2} x^{2}-3\right) c x}{135}+\frac{\arcsin \left(c x \right)^{2} \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{15}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{2 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{375}\right)-2 d a b \left(\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{13 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{225}-\frac{26 \sqrt{-c^{2} x^{2}+1}}{225}\right)}{c^{3}}"," ",0,"1/c^3*(-d*a^2*(1/5*c^5*x^5-1/3*c^3*x^3)-d*b^2*(1/3*arcsin(c*x)^2*(c^2*x^2-3)*c*x+4/15*c*x-4/15*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/45*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-2/135*(c^2*x^2-3)*c*x+1/15*arcsin(c*x)^2*(3*c^4*x^4-10*c^2*x^2+15)*c*x+2/25*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)-2/375*(3*c^4*x^4-10*c^2*x^2+15)*c*x)-2*d*a*b*(1/5*arcsin(c*x)*c^5*x^5-1/3*c^3*x^3*arcsin(c*x)+1/25*c^4*x^4*(-c^2*x^2+1)^(1/2)-13/225*c^2*x^2*(-c^2*x^2+1)^(1/2)-26/225*(-c^2*x^2+1)^(1/2)))","A"
159,1,206,122,0.141000," ","int(x*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{-d \,a^{2} \left(\frac{1}{4} c^{4} x^{4}-\frac{1}{2} c^{2} x^{2}\right)-d \,b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{2}}{4}-\frac{\arcsin \left(c x \right) \left(-2 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+5 c x \sqrt{-c^{2} x^{2}+1}+3 \arcsin \left(c x \right)\right)}{16}+\frac{3 \arcsin \left(c x \right)^{2}}{32}-\frac{\left(c^{2} x^{2}-1\right)^{2}}{32}+\frac{3 c^{2} x^{2}}{32}-\frac{3}{32}\right)-2 d a b \left(\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}-\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{16}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{32}+\frac{5 \arcsin \left(c x \right)}{32}\right)}{c^{2}}"," ",0,"1/c^2*(-d*a^2*(1/4*c^4*x^4-1/2*c^2*x^2)-d*b^2*(1/4*arcsin(c*x)^2*(c^2*x^2-1)^2-1/16*arcsin(c*x)*(-2*c^3*x^3*(-c^2*x^2+1)^(1/2)+5*c*x*(-c^2*x^2+1)^(1/2)+3*arcsin(c*x))+3/32*arcsin(c*x)^2-1/32*(c^2*x^2-1)^2+3/32*c^2*x^2-3/32)-2*d*a*b*(1/4*c^4*x^4*arcsin(c*x)-1/2*c^2*x^2*arcsin(c*x)+1/16*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/32*c*x*(-c^2*x^2+1)^(1/2)+5/32*arcsin(c*x)))","A"
160,1,173,112,0.056000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{-d \,a^{2} \left(\frac{1}{3} c^{3} x^{3}-c x \right)-d \,b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-3\right) c x}{3}+\frac{4 c x}{3}-\frac{4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{9}-\frac{2 \left(c^{2} x^{2}-3\right) c x}{27}\right)-2 d a b \left(\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}-c x \arcsin \left(c x \right)+\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{7 \sqrt{-c^{2} x^{2}+1}}{9}\right)}{c}"," ",0,"1/c*(-d*a^2*(1/3*c^3*x^3-c*x)-d*b^2*(1/3*arcsin(c*x)^2*(c^2*x^2-3)*c*x+4/3*c*x-4/3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/9*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-2/27*(c^2*x^2-3)*c*x)-2*d*a*b*(1/3*c^3*x^3*arcsin(c*x)-c*x*arcsin(c*x)+1/9*c^2*x^2*(-c^2*x^2+1)^(1/2)-7/9*(-c^2*x^2+1)^(1/2)))","A"
161,1,421,192,0.346000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x,x)","-\frac{d \,a^{2} c^{2} x^{2}}{2}+d \,a^{2} \ln \left(c x \right)-2 i d a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+d \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 i d a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 d \,b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+d \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i d \,b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 d \,b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)+\frac{d \,b^{2} \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{4}-\frac{d \,b^{2} \cos \left(2 \arcsin \left(c x \right)\right)}{8}-\frac{d \,b^{2} \arcsin \left(c x \right) \sin \left(2 \arcsin \left(c x \right)\right)}{4}-2 i d \,b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 d a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 d a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{i d \,b^{2} \arcsin \left(c x \right)^{3}}{3}-i d a b \arcsin \left(c x \right)^{2}+\frac{d a b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{2}-\frac{d a b \sin \left(2 \arcsin \left(c x \right)\right)}{4}"," ",0,"-1/2*d*a^2*c^2*x^2+d*a^2*ln(c*x)-2*I*d*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+d*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*d*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*d*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+d*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*d*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*d*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+1/4*d*b^2*cos(2*arcsin(c*x))*arcsin(c*x)^2-1/8*d*b^2*cos(2*arcsin(c*x))-1/4*d*b^2*arcsin(c*x)*sin(2*arcsin(c*x))-2*I*d*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*d*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*d*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/3*I*d*b^2*arcsin(c*x)^3-I*d*a*b*arcsin(c*x)^2+1/2*d*a*b*cos(2*arcsin(c*x))*arcsin(c*x)-1/4*d*a*b*sin(2*arcsin(c*x))","B"
162,1,269,169,0.401000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^2,x)","-d \,a^{2} c^{2} x -\frac{d \,a^{2}}{x}-2 c d \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)-d \,b^{2} \arcsin \left(c x \right)^{2} c^{2} x +2 b^{2} c^{2} d x -\frac{d \,b^{2} \arcsin \left(c x \right)^{2}}{x}-2 c d \,b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 c d \,b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i b^{2} c d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i b^{2} c d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 d a b \arcsin \left(c x \right) c^{2} x -\frac{2 d a b \arcsin \left(c x \right)}{x}-2 c d a b \sqrt{-c^{2} x^{2}+1}-2 c d a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)"," ",0,"-d*a^2*c^2*x-d*a^2/x-2*c*d*b^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-d*b^2*arcsin(c*x)^2*c^2*x+2*b^2*c^2*d*x-d*b^2/x*arcsin(c*x)^2-2*c*d*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*d*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*c*d*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2*c*d*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*d*a*b*arcsin(c*x)*c^2*x-2*d*a*b*arcsin(c*x)/x-2*c*d*a*b*(-c^2*x^2+1)^(1/2)-2*c*d*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))","A"
163,1,564,211,0.591000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^3,x)","-c^{2} d \,a^{2} \ln \left(c x \right)-\frac{d \,a^{2}}{2 x^{2}}+\frac{i c^{2} d \,b^{2} \arcsin \left(c x \right)^{3}}{3}+2 i c^{2} d \,b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{c d \,b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{x}-\frac{d \,b^{2} \arcsin \left(c x \right)^{2}}{2 x^{2}}-c^{2} d \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+i c^{2} d a b -2 c^{2} d \,b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-c^{2} d \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+i c^{2} d \,b^{2} \arcsin \left(c x \right)-2 c^{2} d \,b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)+c^{2} d \,b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d \,b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)+c^{2} d \,b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)+2 i c^{2} d a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i c^{2} d a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{c d a b \sqrt{-c^{2} x^{2}+1}}{x}-\frac{d a b \arcsin \left(c x \right)}{x^{2}}-2 c^{2} d a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i c^{2} d \,b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+i c^{2} d a b \arcsin \left(c x \right)^{2}"," ",0,"-c^2*d*a^2*ln(c*x)-1/2*d*a^2/x^2+1/3*I*c^2*d*b^2*arcsin(c*x)^3+I*c^2*d*a*b-c*d*b^2*arcsin(c*x)/x*(-c^2*x^2+1)^(1/2)-1/2*d*b^2*arcsin(c*x)^2/x^2-c^2*d*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*c^2*d*b^2*arcsin(c*x)-2*c^2*d*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-c^2*d*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*c^2*d*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+c^2*d*b^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))+c^2*d*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+I*c^2*d*a*b*arcsin(c*x)^2+2*I*c^2*d*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-c*d*a*b/x*(-c^2*x^2+1)^(1/2)-d*a*b*arcsin(c*x)/x^2-2*c^2*d*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*c^2*d*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c^2*d*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
164,1,291,182,0.619000," ","int((-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2/x^4,x)","-\frac{d \,a^{2}}{3 x^{3}}+\frac{c^{2} d \,a^{2}}{x}+\frac{c^{2} d \,b^{2} \arcsin \left(c x \right)^{2}}{x}-\frac{c d \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 x^{2}}-\frac{d \,b^{2} \arcsin \left(c x \right)^{2}}{3 x^{3}}-\frac{b^{2} c^{2} d}{3 x}+\frac{5 c^{3} d \,b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{5 i b^{2} c^{3} d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{5 c^{3} d \,b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}+\frac{5 i b^{2} c^{3} d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{2 d a b \arcsin \left(c x \right)}{3 x^{3}}+\frac{2 c^{2} d a b \arcsin \left(c x \right)}{x}+\frac{5 c^{3} d a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-\frac{c d a b \sqrt{-c^{2} x^{2}+1}}{3 x^{2}}"," ",0,"-1/3*d*a^2/x^3+c^2*d*a^2/x+c^2*d*b^2/x*arcsin(c*x)^2-1/3*c*d*b^2/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/3*d*b^2/x^3*arcsin(c*x)^2-1/3*b^2*c^2*d/x+5/3*c^3*d*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-5/3*I*b^2*c^3*d*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-5/3*c^3*d*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+5/3*I*b^2*c^3*d*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2/3*d*a*b*arcsin(c*x)/x^3+2*c^2*d*a*b*arcsin(c*x)/x+5/3*c^3*d*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))-1/3*c*d*a*b/x^2*(-c^2*x^2+1)^(1/2)","A"
165,1,531,351,0.222000," ","int(x^4*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{9} c^{9} x^{9}-\frac{2}{7} c^{7} x^{7}+\frac{1}{5} c^{5} x^{5}\right)+d^{2} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{15}-\frac{16 c x}{315}+\frac{16 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{315}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{525}-\frac{2 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{7875}-\frac{8 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{945}+\frac{8 \left(c^{2} x^{2}-3\right) c x}{2835}+\frac{2 \arcsin \left(c x \right)^{2} \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{35}+\frac{20 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{3} \sqrt{-c^{2} x^{2}+1}}{441}-\frac{4 \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{3087}+\frac{\arcsin \left(c x \right)^{2} \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{315}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{4} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{2 \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{25515}\right)+2 d^{2} a b \left(\frac{\arcsin \left(c x \right) c^{9} x^{9}}{9}-\frac{2 \arcsin \left(c x \right) c^{7} x^{7}}{7}+\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{106 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{3969}+\frac{263 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{33075}+\frac{1052 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{99225}+\frac{2104 \sqrt{-c^{2} x^{2}+1}}{99225}\right)}{c^{5}}"," ",0,"1/c^5*(d^2*a^2*(1/9*c^9*x^9-2/7*c^7*x^7+1/5*c^5*x^5)+d^2*b^2*(1/15*arcsin(c*x)^2*(3*c^4*x^4-10*c^2*x^2+15)*c*x-16/315*c*x+16/315*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/525*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)-2/7875*(3*c^4*x^4-10*c^2*x^2+15)*c*x-8/945*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+8/2835*(c^2*x^2-3)*c*x+2/35*arcsin(c*x)^2*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+20/441*arcsin(c*x)*(c^2*x^2-1)^3*(-c^2*x^2+1)^(1/2)-4/3087*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+1/315*arcsin(c*x)^2*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x+2/81*arcsin(c*x)*(c^2*x^2-1)^4*(-c^2*x^2+1)^(1/2)-2/25515*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x)+2*d^2*a*b*(1/9*arcsin(c*x)*c^9*x^9-2/7*arcsin(c*x)*c^7*x^7+1/5*arcsin(c*x)*c^5*x^5+1/81*c^8*x^8*(-c^2*x^2+1)^(1/2)-106/3969*c^6*x^6*(-c^2*x^2+1)^(1/2)+263/33075*c^4*x^4*(-c^2*x^2+1)^(1/2)+1052/99225*c^2*x^2*(-c^2*x^2+1)^(1/2)+2104/99225*(-c^2*x^2+1)^(1/2)))","A"
166,1,424,270,0.199000," ","int(x^3*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{8} c^{8} x^{8}-\frac{1}{3} c^{6} x^{6}+\frac{1}{4} c^{4} x^{4}\right)+d^{2} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{3}}{6}+\frac{\arcsin \left(c x \right) \left(8 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-26 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+33 c x \sqrt{-c^{2} x^{2}+1}+15 \arcsin \left(c x \right)\right)}{144}-\frac{55 \arcsin \left(c x \right)^{2}}{3072}-\frac{11 \left(c^{2} x^{2}-1\right)^{3}}{3456}+\frac{55 \left(c^{2} x^{2}-1\right)^{2}}{9216}-\frac{55 c^{2} x^{2}}{3072}+\frac{55}{3072}+\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{4}}{8}-\frac{\arcsin \left(c x \right) \left(-48 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}+200 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-326 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+279 c x \sqrt{-c^{2} x^{2}+1}+105 \arcsin \left(c x \right)\right)}{1536}-\frac{\left(c^{2} x^{2}-1\right)^{4}}{256}\right)+2 d^{2} a b \left(\frac{\arcsin \left(c x \right) c^{8} x^{8}}{8}-\frac{\arcsin \left(c x \right) c^{6} x^{6}}{3}+\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{64}-\frac{43 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{1152}+\frac{73 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4608}+\frac{73 c x \sqrt{-c^{2} x^{2}+1}}{3072}-\frac{73 \arcsin \left(c x \right)}{3072}\right)}{c^{4}}"," ",0,"1/c^4*(d^2*a^2*(1/8*c^8*x^8-1/3*c^6*x^6+1/4*c^4*x^4)+d^2*b^2*(1/6*arcsin(c*x)^2*(c^2*x^2-1)^3+1/144*arcsin(c*x)*(8*c^5*x^5*(-c^2*x^2+1)^(1/2)-26*c^3*x^3*(-c^2*x^2+1)^(1/2)+33*c*x*(-c^2*x^2+1)^(1/2)+15*arcsin(c*x))-55/3072*arcsin(c*x)^2-11/3456*(c^2*x^2-1)^3+55/9216*(c^2*x^2-1)^2-55/3072*c^2*x^2+55/3072+1/8*arcsin(c*x)^2*(c^2*x^2-1)^4-1/1536*arcsin(c*x)*(-48*c^7*x^7*(-c^2*x^2+1)^(1/2)+200*c^5*x^5*(-c^2*x^2+1)^(1/2)-326*c^3*x^3*(-c^2*x^2+1)^(1/2)+279*c*x*(-c^2*x^2+1)^(1/2)+105*arcsin(c*x))-1/256*(c^2*x^2-1)^4)+2*d^2*a*b*(1/8*arcsin(c*x)*c^8*x^8-1/3*arcsin(c*x)*c^6*x^6+1/4*c^4*x^4*arcsin(c*x)+1/64*c^7*x^7*(-c^2*x^2+1)^(1/2)-43/1152*c^5*x^5*(-c^2*x^2+1)^(1/2)+73/4608*c^3*x^3*(-c^2*x^2+1)^(1/2)+73/3072*c*x*(-c^2*x^2+1)^(1/2)-73/3072*arcsin(c*x)))","A"
167,1,400,276,0.053000," ","int(x^2*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{7} c^{7} x^{7}-\frac{2}{5} c^{5} x^{5}+\frac{1}{3} c^{3} x^{3}\right)+d^{2} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{15}-\frac{16 c x}{105}+\frac{16 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{105}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{175}-\frac{2 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{2625}-\frac{8 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{315}+\frac{8 \left(c^{2} x^{2}-3\right) c x}{945}+\frac{\arcsin \left(c x \right)^{2} \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{35}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{3} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{2 \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{1715}\right)+2 d^{2} a b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{2 \arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{68 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}+\frac{409 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{11025}+\frac{818 \sqrt{-c^{2} x^{2}+1}}{11025}\right)}{c^{3}}"," ",0,"1/c^3*(d^2*a^2*(1/7*c^7*x^7-2/5*c^5*x^5+1/3*c^3*x^3)+d^2*b^2*(1/15*arcsin(c*x)^2*(3*c^4*x^4-10*c^2*x^2+15)*c*x-16/105*c*x+16/105*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/175*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)-2/2625*(3*c^4*x^4-10*c^2*x^2+15)*c*x-8/315*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+8/945*(c^2*x^2-3)*c*x+1/35*arcsin(c*x)^2*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+2/49*arcsin(c*x)*(c^2*x^2-1)^3*(-c^2*x^2+1)^(1/2)-2/1715*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x)+2*d^2*a*b*(1/7*arcsin(c*x)*c^7*x^7-2/5*arcsin(c*x)*c^5*x^5+1/3*c^3*x^3*arcsin(c*x)+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-68/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)+409/11025*c^2*x^2*(-c^2*x^2+1)^(1/2)+818/11025*(-c^2*x^2+1)^(1/2)))","A"
168,1,283,187,0.052000," ","int(x*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{6} c^{6} x^{6}-\frac{1}{2} c^{4} x^{4}+\frac{1}{2} c^{2} x^{2}\right)+d^{2} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{3}}{6}+\frac{\arcsin \left(c x \right) \left(8 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-26 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+33 c x \sqrt{-c^{2} x^{2}+1}+15 \arcsin \left(c x \right)\right)}{144}-\frac{5 \arcsin \left(c x \right)^{2}}{96}-\frac{\left(c^{2} x^{2}-1\right)^{3}}{108}+\frac{5 \left(c^{2} x^{2}-1\right)^{2}}{288}-\frac{5 c^{2} x^{2}}{96}+\frac{5}{96}\right)+2 d^{2} a b \left(\frac{\arcsin \left(c x \right) c^{6} x^{6}}{6}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{2}+\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{36}-\frac{13 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{144}+\frac{11 c x \sqrt{-c^{2} x^{2}+1}}{96}-\frac{11 \arcsin \left(c x \right)}{96}\right)}{c^{2}}"," ",0,"1/c^2*(d^2*a^2*(1/6*c^6*x^6-1/2*c^4*x^4+1/2*c^2*x^2)+d^2*b^2*(1/6*arcsin(c*x)^2*(c^2*x^2-1)^3+1/144*arcsin(c*x)*(8*c^5*x^5*(-c^2*x^2+1)^(1/2)-26*c^3*x^3*(-c^2*x^2+1)^(1/2)+33*c*x*(-c^2*x^2+1)^(1/2)+15*arcsin(c*x))-5/96*arcsin(c*x)^2-1/108*(c^2*x^2-1)^3+5/288*(c^2*x^2-1)^2-5/96*c^2*x^2+5/96)+2*d^2*a*b*(1/6*arcsin(c*x)*c^6*x^6-1/2*c^4*x^4*arcsin(c*x)+1/2*c^2*x^2*arcsin(c*x)+1/36*c^5*x^5*(-c^2*x^2+1)^(1/2)-13/144*c^3*x^3*(-c^2*x^2+1)^(1/2)+11/96*c*x*(-c^2*x^2+1)^(1/2)-11/96*arcsin(c*x)))","A"
169,1,275,195,0.057000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{d^{2} a^{2} \left(\frac{1}{5} c^{5} x^{5}-\frac{2}{3} c^{3} x^{3}+c x \right)+d^{2} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{15}-\frac{16 c x}{15}+\frac{16 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{15}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{2 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{375}-\frac{8 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{45}+\frac{8 \left(c^{2} x^{2}-3\right) c x}{135}\right)+2 d^{2} a b \left(\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{2 c^{3} x^{3} \arcsin \left(c x \right)}{3}+c x \arcsin \left(c x \right)+\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}-\frac{38 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{225}+\frac{149 \sqrt{-c^{2} x^{2}+1}}{225}\right)}{c}"," ",0,"1/c*(d^2*a^2*(1/5*c^5*x^5-2/3*c^3*x^3+c*x)+d^2*b^2*(1/15*arcsin(c*x)^2*(3*c^4*x^4-10*c^2*x^2+15)*c*x-16/15*c*x+16/15*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/25*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)-2/375*(3*c^4*x^4-10*c^2*x^2+15)*c*x-8/45*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+8/135*(c^2*x^2-3)*c*x)+2*d^2*a*b*(1/5*arcsin(c*x)*c^5*x^5-2/3*c^3*x^3*arcsin(c*x)+c*x*arcsin(c*x)+1/25*c^4*x^4*(-c^2*x^2+1)^(1/2)-38/225*c^2*x^2*(-c^2*x^2+1)^(1/2)+149/225*(-c^2*x^2+1)^(1/2)))","A"
170,1,560,277,0.428000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x,x)","d^{2} a^{2} \ln \left(c x \right)-\frac{d^{2} b^{2} \cos \left(4 \arcsin \left(c x \right)\right)}{256}-\frac{3 d^{2} b^{2} \cos \left(2 \arcsin \left(c x \right)\right)}{16}+2 d^{2} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 d^{2} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{2} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{2} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-i d^{2} a b \arcsin \left(c x \right)^{2}+2 d^{2} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 d^{2} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{i d^{2} b^{2} \arcsin \left(c x \right)^{3}}{3}+d^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{3 d^{2} b^{2} \arcsin \left(c x \right) \sin \left(2 \arcsin \left(c x \right)\right)}{8}+\frac{d^{2} a^{2} c^{4} x^{4}}{4}-d^{2} a^{2} c^{2} x^{2}-\frac{d^{2} a b \sin \left(4 \arcsin \left(c x \right)\right)}{64}-\frac{3 d^{2} a b \sin \left(2 \arcsin \left(c x \right)\right)}{8}+\frac{d^{2} b^{2} \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{32}-\frac{d^{2} b^{2} \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{64}+\frac{3 d^{2} b^{2} \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{8}+\frac{d^{2} a b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{16}+\frac{3 d^{2} a b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{4}"," ",0,"2*d^2*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*d^2*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*d^2*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+d^2*a^2*ln(c*x)-1/256*d^2*b^2*cos(4*arcsin(c*x))-3/16*d^2*b^2*cos(2*arcsin(c*x))+2*d^2*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-3/8*d^2*b^2*arcsin(c*x)*sin(2*arcsin(c*x))-1/3*I*d^2*b^2*arcsin(c*x)^3+1/4*d^2*a^2*c^4*x^4-d^2*a^2*c^2*x^2-1/64*d^2*a*b*sin(4*arcsin(c*x))-3/8*d^2*a*b*sin(2*arcsin(c*x))+d^2*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d^2*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/32*d^2*b^2*cos(4*arcsin(c*x))*arcsin(c*x)^2-1/64*d^2*b^2*arcsin(c*x)*sin(4*arcsin(c*x))+3/8*d^2*b^2*cos(2*arcsin(c*x))*arcsin(c*x)^2-I*d^2*a*b*arcsin(c*x)^2-2*I*d^2*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*d^2*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*d^2*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*d^2*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+1/16*d^2*a*b*arcsin(c*x)*cos(4*arcsin(c*x))+3/4*d^2*a*b*cos(2*arcsin(c*x))*arcsin(c*x)","B"
171,1,411,255,0.429000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^2,x)","\frac{d^{2} a^{2} c^{4} x^{3}}{3}-2 d^{2} a^{2} c^{2} x -\frac{d^{2} a^{2}}{x}-\frac{7 c \,d^{2} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{2}-\frac{7 d^{2} b^{2} \arcsin \left(c x \right)^{2} c^{2} x}{4}+\frac{7 b^{2} c^{2} d^{2} x}{2}-\frac{d^{2} b^{2} \arcsin \left(c x \right)^{2}}{x}-2 c \,d^{2} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 c \,d^{2} b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i b^{2} c \,d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 i b^{2} c \,d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{c \,d^{2} b^{2} \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{18}-\frac{c \,d^{2} b^{2} \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{12}+\frac{c \,d^{2} b^{2} \sin \left(3 \arcsin \left(c x \right)\right)}{54}+\frac{2 d^{2} a b \arcsin \left(c x \right) c^{4} x^{3}}{3}-4 d^{2} a b \arcsin \left(c x \right) c^{2} x -\frac{2 d^{2} a b \arcsin \left(c x \right)}{x}+\frac{2 d^{2} a b \,c^{3} x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{32 c \,d^{2} a b \sqrt{-c^{2} x^{2}+1}}{9}-2 c \,d^{2} a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)"," ",0,"1/3*d^2*a^2*c^4*x^3-2*d^2*a^2*c^2*x-d^2*a^2/x-7/2*c*d^2*b^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-7/4*d^2*b^2*arcsin(c*x)^2*c^2*x+7/2*b^2*c^2*d^2*x-d^2*b^2/x*arcsin(c*x)^2-2*c*d^2*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*d^2*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2*c*d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*I*b^2*c*d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/18*c*d^2*b^2*arcsin(c*x)*cos(3*arcsin(c*x))-1/12*c*d^2*b^2*sin(3*arcsin(c*x))*arcsin(c*x)^2+1/54*c*d^2*b^2*sin(3*arcsin(c*x))+2/3*d^2*a*b*arcsin(c*x)*c^4*x^3-4*d^2*a*b*arcsin(c*x)*c^2*x-2*d^2*a*b*arcsin(c*x)/x+2/9*d^2*a*b*c^3*x^2*(-c^2*x^2+1)^(1/2)-32/9*c*d^2*a*b*(-c^2*x^2+1)^(1/2)-2*c*d^2*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))","A"
172,1,767,301,0.845000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^3,x)","4 i c^{2} d^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+4 i c^{2} d^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+4 i c^{2} d^{2} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+4 i c^{2} d^{2} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 i c^{2} d^{2} a b \arcsin \left(c x \right)^{2}-4 c^{2} d^{2} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-4 c^{2} d^{2} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{c^{3} d^{2} a b \sqrt{-c^{2} x^{2}+1}\, x}{2}+c^{4} d^{2} a b \arcsin \left(c x \right) x^{2}-\frac{c \,d^{2} a b \sqrt{-c^{2} x^{2}+1}}{x}-\frac{c \,d^{2} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{x}+\frac{c^{3} d^{2} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{2}-\frac{c^{2} d^{2} a b \arcsin \left(c x \right)}{2}+\frac{c^{4} d^{2} b^{2} \arcsin \left(c x \right)^{2} x^{2}}{2}+i c^{2} d^{2} b^{2} \arcsin \left(c x \right)-2 c^{2} d^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{2 i c^{2} d^{2} b^{2} \arcsin \left(c x \right)^{3}}{3}+i c^{2} d^{2} a b -\frac{d^{2} a^{2}}{2 x^{2}}+\frac{d^{2} b^{2} c^{2}}{8}-\frac{b^{2} c^{4} d^{2} x^{2}}{4}-\frac{d^{2} a b \arcsin \left(c x \right)}{x^{2}}+\frac{c^{4} d^{2} a^{2} x^{2}}{2}-2 c^{2} d^{2} a^{2} \ln \left(c x \right)-\frac{c^{2} d^{2} b^{2} \arcsin \left(c x \right)^{2}}{4}-\frac{d^{2} b^{2} \arcsin \left(c x \right)^{2}}{2 x^{2}}+c^{2} d^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)+c^{2} d^{2} b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-4 c^{2} d^{2} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-4 c^{2} d^{2} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"1/2*c^3*d^2*a*b*(-c^2*x^2+1)^(1/2)*x+4*I*c^2*d^2*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+4*I*c^2*d^2*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*c^2*d^2*a*b*arcsin(c*x)^2+4*I*c^2*d^2*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+4*I*c^2*d^2*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+c^4*d^2*a*b*arcsin(c*x)*x^2-c*d^2*a*b/x*(-c^2*x^2+1)^(1/2)-c*d^2*b^2*arcsin(c*x)/x*(-c^2*x^2+1)^(1/2)+1/2*c^3*d^2*b^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-4*c^2*d^2*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-4*c^2*d^2*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+I*c^2*d^2*b^2*arcsin(c*x)-2*c^2*d^2*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d^2*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*c^2*d^2*a*b*arcsin(c*x)+1/2*c^4*d^2*b^2*arcsin(c*x)^2*x^2+2/3*I*c^2*d^2*b^2*arcsin(c*x)^3-1/2*d^2*a^2/x^2+1/8*d^2*b^2*c^2-1/4*b^2*c^4*d^2*x^2-d^2*a*b*arcsin(c*x)/x^2+1/2*c^4*d^2*a^2*x^2-4*c^2*d^2*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-4*c^2*d^2*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d^2*a^2*ln(c*x)+c^2*d^2*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-1/4*c^2*d^2*b^2*arcsin(c*x)^2+c^2*d^2*b^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d^2*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))-1/2*d^2*b^2*arcsin(c*x)^2/x^2+I*c^2*d^2*a*b","B"
173,1,425,268,0.727000," ","int((-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2/x^4,x)","c^{4} d^{2} a^{2} x -\frac{d^{2} a^{2}}{3 x^{3}}+\frac{2 c^{2} d^{2} a^{2}}{x}+2 c^{3} d^{2} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+c^{4} d^{2} b^{2} \arcsin \left(c x \right)^{2} x -2 b^{2} c^{4} d^{2} x +\frac{2 c^{2} d^{2} b^{2} \arcsin \left(c x \right)^{2}}{x}-\frac{c \,d^{2} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 x^{2}}-\frac{d^{2} b^{2} \arcsin \left(c x \right)^{2}}{3 x^{3}}-\frac{b^{2} c^{2} d^{2}}{3 x}+\frac{11 c^{3} d^{2} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{11 i b^{2} c^{3} d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{11 c^{3} d^{2} b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}+\frac{11 i b^{2} c^{3} d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}+2 c^{4} d^{2} a b \arcsin \left(c x \right) x -\frac{2 d^{2} a b \arcsin \left(c x \right)}{3 x^{3}}+\frac{4 c^{2} d^{2} a b \arcsin \left(c x \right)}{x}+2 c^{3} d^{2} a b \sqrt{-c^{2} x^{2}+1}-\frac{c \,d^{2} a b \sqrt{-c^{2} x^{2}+1}}{3 x^{2}}+\frac{11 c^{3} d^{2} a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}"," ",0,"c^4*d^2*a^2*x-1/3*d^2*a^2/x^3+2*c^2*d^2*a^2/x+2*c^3*d^2*b^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+c^4*d^2*b^2*arcsin(c*x)^2*x-2*b^2*c^4*d^2*x+2*c^2*d^2*b^2/x*arcsin(c*x)^2-1/3*c*d^2*b^2/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/3*d^2*b^2/x^3*arcsin(c*x)^2-1/3*b^2*c^2*d^2/x+11/3*c^3*d^2*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-11/3*I*b^2*c^3*d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-11/3*c^3*d^2*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+11/3*I*b^2*c^3*d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*c^4*d^2*a*b*arcsin(c*x)*x-2/3*d^2*a*b*arcsin(c*x)/x^3+4*c^2*d^2*a*b*arcsin(c*x)/x+2*c^3*d^2*a*b*(-c^2*x^2+1)^(1/2)-1/3*c*d^2*a*b/x^2*(-c^2*x^2+1)^(1/2)+11/3*c^3*d^2*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))","A"
174,1,672,424,0.180000," ","int(x^4*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{-d^{3} a^{2} \left(\frac{1}{11} x^{11} c^{11}-\frac{1}{3} c^{9} x^{9}+\frac{3}{7} c^{7} x^{7}-\frac{1}{5} c^{5} x^{5}\right)-d^{3} b^{2} \left(\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{5} \sqrt{-c^{2} x^{2}+1}}{121}-\frac{4 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{1925}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{3} \sqrt{-c^{2} x^{2}+1}}{1617}-\frac{2 \left(63 c^{10} x^{10}-385 c^{8} x^{8}+990 c^{6} x^{6}-1386 c^{4} x^{4}+1155 c^{2} x^{2}-693\right) c x}{83853}+\frac{4 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{28875}-\frac{2 \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{56595}+\frac{16 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{3465}+\frac{32 c x}{1155}-\frac{32 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{1155}-\frac{16 \left(c^{2} x^{2}-3\right) c x}{10395}-\frac{8 \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{93555}+\frac{8 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{4} \sqrt{-c^{2} x^{2}+1}}{297}+\frac{\arcsin \left(c x \right)^{2} \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{35}+\frac{\arcsin \left(c x \right)^{2} \left(63 c^{10} x^{10}-385 c^{8} x^{8}+990 c^{6} x^{6}-1386 c^{4} x^{4}+1155 c^{2} x^{2}-693\right) c x}{693}+\frac{2 \arcsin \left(c x \right)^{2} \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{315}\right)-2 d^{3} a b \left(\frac{\arcsin \left(c x \right) c^{11} x^{11}}{11}-\frac{\arcsin \left(c x \right) c^{9} x^{9}}{3}+\frac{3 \arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{\arcsin \left(c x \right) c^{5} x^{5}}{5}+\frac{c^{10} x^{10} \sqrt{-c^{2} x^{2}+1}}{121}-\frac{91 c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{3267}+\frac{4705 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{160083}-\frac{6311 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1334025}-\frac{25244 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{4002075}-\frac{50488 \sqrt{-c^{2} x^{2}+1}}{4002075}\right)}{c^{5}}"," ",0,"1/c^5*(-d^3*a^2*(1/11*x^11*c^11-1/3*c^9*x^9+3/7*c^7*x^7-1/5*c^5*x^5)-d^3*b^2*(2/121*arcsin(c*x)*(c^2*x^2-1)^5*(-c^2*x^2+1)^(1/2)-4/1925*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)+2/1617*arcsin(c*x)*(c^2*x^2-1)^3*(-c^2*x^2+1)^(1/2)-2/83853*(63*c^10*x^10-385*c^8*x^8+990*c^6*x^6-1386*c^4*x^4+1155*c^2*x^2-693)*c*x+4/28875*(3*c^4*x^4-10*c^2*x^2+15)*c*x-2/56595*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+16/3465*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+32/1155*c*x-32/1155*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-16/10395*(c^2*x^2-3)*c*x-8/93555*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x+8/297*arcsin(c*x)*(c^2*x^2-1)^4*(-c^2*x^2+1)^(1/2)+1/35*arcsin(c*x)^2*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+1/693*arcsin(c*x)^2*(63*c^10*x^10-385*c^8*x^8+990*c^6*x^6-1386*c^4*x^4+1155*c^2*x^2-693)*c*x+2/315*arcsin(c*x)^2*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x)-2*d^3*a*b*(1/11*arcsin(c*x)*c^11*x^11-1/3*arcsin(c*x)*c^9*x^9+3/7*arcsin(c*x)*c^7*x^7-1/5*arcsin(c*x)*c^5*x^5+1/121*c^10*x^10*(-c^2*x^2+1)^(1/2)-91/3267*c^8*x^8*(-c^2*x^2+1)^(1/2)+4705/160083*c^6*x^6*(-c^2*x^2+1)^(1/2)-6311/1334025*c^4*x^4*(-c^2*x^2+1)^(1/2)-25244/4002075*c^2*x^2*(-c^2*x^2+1)^(1/2)-50488/4002075*(-c^2*x^2+1)^(1/2)))","A"
175,1,519,344,0.167000," ","int(x^3*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{-d^{3} a^{2} \left(\frac{1}{10} c^{10} x^{10}-\frac{3}{8} c^{8} x^{8}+\frac{1}{2} c^{6} x^{6}-\frac{1}{4} c^{4} x^{4}\right)-d^{3} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{4}}{8}-\frac{\arcsin \left(c x \right) \left(-48 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}+200 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-326 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+279 c x \sqrt{-c^{2} x^{2}+1}+105 \arcsin \left(c x \right)\right)}{1536}+\frac{49 \arcsin \left(c x \right)^{2}}{5120}-\frac{7 \left(c^{2} x^{2}-1\right)^{4}}{6400}+\frac{49 \left(c^{2} x^{2}-1\right)^{3}}{28800}-\frac{49 \left(c^{2} x^{2}-1\right)^{2}}{15360}+\frac{49 c^{2} x^{2}}{5120}-\frac{49}{5120}+\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{5}}{10}+\frac{\arcsin \left(c x \right) \left(128 c^{9} x^{9} \sqrt{-c^{2} x^{2}+1}-656 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}+1368 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-1490 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+965 c x \sqrt{-c^{2} x^{2}+1}+315 \arcsin \left(c x \right)\right)}{6400}-\frac{\left(c^{2} x^{2}-1\right)^{5}}{500}\right)-2 d^{3} a b \left(\frac{\arcsin \left(c x \right) c^{10} x^{10}}{10}-\frac{3 \arcsin \left(c x \right) c^{8} x^{8}}{8}+\frac{\arcsin \left(c x \right) c^{6} x^{6}}{2}-\frac{c^{4} x^{4} \arcsin \left(c x \right)}{4}+\frac{c^{9} x^{9} \sqrt{-c^{2} x^{2}+1}}{100}-\frac{57 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{1600}+\frac{401 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{9600}-\frac{79 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{7680}-\frac{79 c x \sqrt{-c^{2} x^{2}+1}}{5120}+\frac{79 \arcsin \left(c x \right)}{5120}\right)}{c^{4}}"," ",0,"1/c^4*(-d^3*a^2*(1/10*c^10*x^10-3/8*c^8*x^8+1/2*c^6*x^6-1/4*c^4*x^4)-d^3*b^2*(1/8*arcsin(c*x)^2*(c^2*x^2-1)^4-1/1536*arcsin(c*x)*(-48*c^7*x^7*(-c^2*x^2+1)^(1/2)+200*c^5*x^5*(-c^2*x^2+1)^(1/2)-326*c^3*x^3*(-c^2*x^2+1)^(1/2)+279*c*x*(-c^2*x^2+1)^(1/2)+105*arcsin(c*x))+49/5120*arcsin(c*x)^2-7/6400*(c^2*x^2-1)^4+49/28800*(c^2*x^2-1)^3-49/15360*(c^2*x^2-1)^2+49/5120*c^2*x^2-49/5120+1/10*arcsin(c*x)^2*(c^2*x^2-1)^5+1/6400*arcsin(c*x)*(128*c^9*x^9*(-c^2*x^2+1)^(1/2)-656*c^7*x^7*(-c^2*x^2+1)^(1/2)+1368*c^5*x^5*(-c^2*x^2+1)^(1/2)-1490*c^3*x^3*(-c^2*x^2+1)^(1/2)+965*c*x*(-c^2*x^2+1)^(1/2)+315*arcsin(c*x))-1/500*(c^2*x^2-1)^5)-2*d^3*a*b*(1/10*arcsin(c*x)*c^10*x^10-3/8*arcsin(c*x)*c^8*x^8+1/2*arcsin(c*x)*c^6*x^6-1/4*c^4*x^4*arcsin(c*x)+1/100*c^9*x^9*(-c^2*x^2+1)^(1/2)-57/1600*c^7*x^7*(-c^2*x^2+1)^(1/2)+401/9600*c^5*x^5*(-c^2*x^2+1)^(1/2)-79/7680*c^3*x^3*(-c^2*x^2+1)^(1/2)-79/5120*c*x*(-c^2*x^2+1)^(1/2)+79/5120*arcsin(c*x)))","A"
176,1,525,349,0.060000," ","int(x^2*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{-d^{3} a^{2} \left(\frac{1}{9} c^{9} x^{9}-\frac{3}{7} c^{7} x^{7}+\frac{3}{5} c^{5} x^{5}-\frac{1}{3} c^{3} x^{3}\right)-d^{3} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{35}+\frac{32 c x}{315}-\frac{32 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{315}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{3} \sqrt{-c^{2} x^{2}+1}}{441}-\frac{2 \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{15435}-\frac{4 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{525}+\frac{4 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{7875}+\frac{16 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{945}-\frac{16 \left(c^{2} x^{2}-3\right) c x}{2835}+\frac{\arcsin \left(c x \right)^{2} \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{315}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{4} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{2 \left(35 c^{8} x^{8}-180 c^{6} x^{6}+378 c^{4} x^{4}-420 c^{2} x^{2}+315\right) c x}{25515}\right)-2 d^{3} a b \left(\frac{\arcsin \left(c x \right) c^{9} x^{9}}{9}-\frac{3 \arcsin \left(c x \right) c^{7} x^{7}}{7}+\frac{3 \arcsin \left(c x \right) c^{5} x^{5}}{5}-\frac{c^{3} x^{3} \arcsin \left(c x \right)}{3}+\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{81}-\frac{187 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{3969}+\frac{2099 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{33075}-\frac{2629 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{99225}-\frac{5258 \sqrt{-c^{2} x^{2}+1}}{99225}\right)}{c^{3}}"," ",0,"1/c^3*(-d^3*a^2*(1/9*c^9*x^9-3/7*c^7*x^7+3/5*c^5*x^5-1/3*c^3*x^3)-d^3*b^2*(1/35*arcsin(c*x)^2*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+32/315*c*x-32/315*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/441*arcsin(c*x)*(c^2*x^2-1)^3*(-c^2*x^2+1)^(1/2)-2/15435*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x-4/525*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)+4/7875*(3*c^4*x^4-10*c^2*x^2+15)*c*x+16/945*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-16/2835*(c^2*x^2-3)*c*x+1/315*arcsin(c*x)^2*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x+2/81*arcsin(c*x)*(c^2*x^2-1)^4*(-c^2*x^2+1)^(1/2)-2/25515*(35*c^8*x^8-180*c^6*x^6+378*c^4*x^4-420*c^2*x^2+315)*c*x)-2*d^3*a*b*(1/9*arcsin(c*x)*c^9*x^9-3/7*arcsin(c*x)*c^7*x^7+3/5*arcsin(c*x)*c^5*x^5-1/3*c^3*x^3*arcsin(c*x)+1/81*c^8*x^8*(-c^2*x^2+1)^(1/2)-187/3969*c^6*x^6*(-c^2*x^2+1)^(1/2)+2099/33075*c^4*x^4*(-c^2*x^2+1)^(1/2)-2629/99225*c^2*x^2*(-c^2*x^2+1)^(1/2)-5258/99225*(-c^2*x^2+1)^(1/2)))","A"
177,1,358,240,0.069000," ","int(x*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{-d^{3} a^{2} \left(\frac{1}{8} c^{8} x^{8}-\frac{1}{2} c^{6} x^{6}+\frac{3}{4} c^{4} x^{4}-\frac{1}{2} c^{2} x^{2}\right)-d^{3} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(c^{2} x^{2}-1\right)^{4}}{8}-\frac{\arcsin \left(c x \right) \left(-48 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}+200 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}-326 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+279 c x \sqrt{-c^{2} x^{2}+1}+105 \arcsin \left(c x \right)\right)}{1536}+\frac{35 \arcsin \left(c x \right)^{2}}{1024}-\frac{\left(c^{2} x^{2}-1\right)^{4}}{256}+\frac{7 \left(c^{2} x^{2}-1\right)^{3}}{1152}-\frac{35 \left(c^{2} x^{2}-1\right)^{2}}{3072}+\frac{35 c^{2} x^{2}}{1024}-\frac{35}{1024}\right)-2 d^{3} a b \left(\frac{\arcsin \left(c x \right) c^{8} x^{8}}{8}-\frac{\arcsin \left(c x \right) c^{6} x^{6}}{2}+\frac{3 c^{4} x^{4} \arcsin \left(c x \right)}{4}-\frac{c^{2} x^{2} \arcsin \left(c x \right)}{2}+\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{64}-\frac{25 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{384}+\frac{163 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{1536}-\frac{93 c x \sqrt{-c^{2} x^{2}+1}}{1024}+\frac{93 \arcsin \left(c x \right)}{1024}\right)}{c^{2}}"," ",0,"1/c^2*(-d^3*a^2*(1/8*c^8*x^8-1/2*c^6*x^6+3/4*c^4*x^4-1/2*c^2*x^2)-d^3*b^2*(1/8*arcsin(c*x)^2*(c^2*x^2-1)^4-1/1536*arcsin(c*x)*(-48*c^7*x^7*(-c^2*x^2+1)^(1/2)+200*c^5*x^5*(-c^2*x^2+1)^(1/2)-326*c^3*x^3*(-c^2*x^2+1)^(1/2)+279*c*x*(-c^2*x^2+1)^(1/2)+105*arcsin(c*x))+35/1024*arcsin(c*x)^2-1/256*(c^2*x^2-1)^4+7/1152*(c^2*x^2-1)^3-35/3072*(c^2*x^2-1)^2+35/1024*c^2*x^2-35/1024)-2*d^3*a*b*(1/8*arcsin(c*x)*c^8*x^8-1/2*arcsin(c*x)*c^6*x^6+3/4*c^4*x^4*arcsin(c*x)-1/2*c^2*x^2*arcsin(c*x)+1/64*c^7*x^7*(-c^2*x^2+1)^(1/2)-25/384*c^5*x^5*(-c^2*x^2+1)^(1/2)+163/1536*c^3*x^3*(-c^2*x^2+1)^(1/2)-93/1024*c*x*(-c^2*x^2+1)^(1/2)+93/1024*arcsin(c*x)))","A"
178,1,384,266,0.062000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{-d^{3} a^{2} \left(\frac{1}{7} c^{7} x^{7}-\frac{3}{5} c^{5} x^{5}+c^{3} x^{3}-c x \right)-d^{3} b^{2} \left(\frac{\arcsin \left(c x \right)^{2} \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{35}+\frac{32 c x}{35}-\frac{32 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{35}+\frac{2 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{3} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{2 \left(5 c^{6} x^{6}-21 c^{4} x^{4}+35 c^{2} x^{2}-35\right) c x}{1715}-\frac{12 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right)^{2} \sqrt{-c^{2} x^{2}+1}}{175}+\frac{4 \left(3 c^{4} x^{4}-10 c^{2} x^{2}+15\right) c x}{875}+\frac{16 \arcsin \left(c x \right) \left(c^{2} x^{2}-1\right) \sqrt{-c^{2} x^{2}+1}}{105}-\frac{16 \left(c^{2} x^{2}-3\right) c x}{315}\right)-2 d^{3} a b \left(\frac{\arcsin \left(c x \right) c^{7} x^{7}}{7}-\frac{3 \arcsin \left(c x \right) c^{5} x^{5}}{5}+c^{3} x^{3} \arcsin \left(c x \right)-c x \arcsin \left(c x \right)+\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{49}-\frac{117 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{1225}+\frac{757 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3675}-\frac{2161 \sqrt{-c^{2} x^{2}+1}}{3675}\right)}{c}"," ",0,"1/c*(-d^3*a^2*(1/7*c^7*x^7-3/5*c^5*x^5+c^3*x^3-c*x)-d^3*b^2*(1/35*arcsin(c*x)^2*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x+32/35*c*x-32/35*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/49*arcsin(c*x)*(c^2*x^2-1)^3*(-c^2*x^2+1)^(1/2)-2/1715*(5*c^6*x^6-21*c^4*x^4+35*c^2*x^2-35)*c*x-12/175*arcsin(c*x)*(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)+4/875*(3*c^4*x^4-10*c^2*x^2+15)*c*x+16/105*arcsin(c*x)*(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-16/315*(c^2*x^2-3)*c*x)-2*d^3*a*b*(1/7*arcsin(c*x)*c^7*x^7-3/5*arcsin(c*x)*c^5*x^5+c^3*x^3*arcsin(c*x)-c*x*arcsin(c*x)+1/49*c^6*x^6*(-c^2*x^2+1)^(1/2)-117/1225*c^4*x^4*(-c^2*x^2+1)^(1/2)+757/3675*c^2*x^2*(-c^2*x^2+1)^(1/2)-2161/3675*(-c^2*x^2+1)^(1/2)))","A"
179,1,661,352,0.579000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x,x)","\frac{d^{3} a b \arcsin \left(c x \right) \cos \left(6 \arcsin \left(c x \right)\right)}{96}+\frac{d^{3} a b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{8}+\frac{29 d^{3} a b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)}{32}+2 d^{3} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 d^{3} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d^{3} a b \arcsin \left(c x \right)^{2}-2 i d^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{3} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{3} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 i d^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{d^{3} a b \sin \left(6 \arcsin \left(c x \right)\right)}{576}-\frac{d^{3} a b \sin \left(4 \arcsin \left(c x \right)\right)}{32}-\frac{29 d^{3} a b \sin \left(2 \arcsin \left(c x \right)\right)}{64}+\frac{d^{3} b^{2} \cos \left(6 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{192}-\frac{d^{3} b^{2} \arcsin \left(c x \right) \sin \left(6 \arcsin \left(c x \right)\right)}{576}+\frac{d^{3} b^{2} \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{16}-\frac{d^{3} b^{2} \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{32}+\frac{29 d^{3} b^{2} \arcsin \left(c x \right)^{2} \cos \left(2 \arcsin \left(c x \right)\right)}{64}-\frac{29 d^{3} b^{2} \arcsin \left(c x \right) \sin \left(2 \arcsin \left(c x \right)\right)}{64}-\frac{3 d^{3} a^{2} c^{2} x^{2}}{2}+\frac{3 d^{3} a^{2} c^{4} x^{4}}{4}-\frac{d^{3} a^{2} c^{6} x^{6}}{6}+d^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 d^{3} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 d^{3} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{i d^{3} b^{2} \arcsin \left(c x \right)^{3}}{3}+d^{3} a^{2} \ln \left(c x \right)-\frac{d^{3} b^{2} \cos \left(6 \arcsin \left(c x \right)\right)}{3456}-\frac{d^{3} b^{2} \cos \left(4 \arcsin \left(c x \right)\right)}{128}-\frac{29 d^{3} b^{2} \cos \left(2 \arcsin \left(c x \right)\right)}{128}"," ",0,"-2*I*d^3*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*d^3*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*d^3*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/96*d^3*a*b*arcsin(c*x)*cos(6*arcsin(c*x))+1/8*d^3*a*b*arcsin(c*x)*cos(4*arcsin(c*x))+29/32*d^3*a*b*cos(2*arcsin(c*x))*arcsin(c*x)-I*d^3*a*b*arcsin(c*x)^2-2*I*d^3*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*d^3*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*d^3*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/576*d^3*a*b*sin(6*arcsin(c*x))-1/32*d^3*a*b*sin(4*arcsin(c*x))-29/64*d^3*a*b*sin(2*arcsin(c*x))+d^3*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d^3*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/192*d^3*b^2*cos(6*arcsin(c*x))*arcsin(c*x)^2-1/576*d^3*b^2*arcsin(c*x)*sin(6*arcsin(c*x))+1/16*d^3*b^2*cos(4*arcsin(c*x))*arcsin(c*x)^2-1/32*d^3*b^2*arcsin(c*x)*sin(4*arcsin(c*x))+29/64*d^3*b^2*arcsin(c*x)^2*cos(2*arcsin(c*x))-29/64*d^3*b^2*arcsin(c*x)*sin(2*arcsin(c*x))-1/3*I*d^3*b^2*arcsin(c*x)^3-3/2*d^3*a^2*c^2*x^2+3/4*d^3*a^2*c^4*x^4-1/6*d^3*a^2*c^6*x^6+d^3*a^2*ln(c*x)+2*d^3*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+2*d^3*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-1/3456*d^3*b^2*cos(6*arcsin(c*x))-1/128*d^3*b^2*cos(4*arcsin(c*x))-29/128*d^3*b^2*cos(2*arcsin(c*x))","A"
180,1,524,327,0.562000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^2,x)","-\frac{2 d^{3} a b \arcsin \left(c x \right) c^{6} x^{5}}{5}+2 d^{3} a b \arcsin \left(c x \right) c^{4} x^{3}-6 d^{3} a b \arcsin \left(c x \right) c^{2} x -\frac{2 d^{3} a b \,c^{5} x^{4} \sqrt{-c^{2} x^{2}+1}}{25}+\frac{14 d^{3} a b \,c^{3} x^{2} \sqrt{-c^{2} x^{2}+1}}{25}+\frac{19 b^{2} c^{2} d^{3} x}{4}-\frac{d^{3} a^{2}}{x}-\frac{2 d^{3} a b \arcsin \left(c x \right)}{x}-\frac{19 d^{3} b^{2} \arcsin \left(c x \right)^{2} c^{2} x}{8}-\frac{122 c \,d^{3} a b \sqrt{-c^{2} x^{2}+1}}{25}-\frac{19 c \,d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{4}-\frac{c \,d^{3} b^{2} \arcsin \left(c x \right) \cos \left(5 \arcsin \left(c x \right)\right)}{200}-\frac{c \,d^{3} b^{2} \sin \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{80}-\frac{c \,d^{3} b^{2} \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{8}-\frac{3 c \,d^{3} b^{2} \arcsin \left(c x \right)^{2} \sin \left(3 \arcsin \left(c x \right)\right)}{16}-2 c \,d^{3} a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c \,d^{3} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 c \,d^{3} b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+2 i b^{2} c \,d^{3} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i b^{2} c \,d^{3} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{d^{3} a^{2} c^{6} x^{5}}{5}+d^{3} a^{2} c^{4} x^{3}-3 d^{3} a^{2} c^{2} x -\frac{d^{3} b^{2} \arcsin \left(c x \right)^{2}}{x}+\frac{c \,d^{3} b^{2} \sin \left(5 \arcsin \left(c x \right)\right)}{1000}+\frac{c \,d^{3} b^{2} \sin \left(3 \arcsin \left(c x \right)\right)}{24}"," ",0,"-2/5*d^3*a*b*arcsin(c*x)*c^6*x^5+2*d^3*a*b*arcsin(c*x)*c^4*x^3-6*d^3*a*b*arcsin(c*x)*c^2*x-2/25*d^3*a*b*c^5*x^4*(-c^2*x^2+1)^(1/2)+14/25*d^3*a*b*c^3*x^2*(-c^2*x^2+1)^(1/2)+2*I*b^2*c*d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2*c*d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+19/4*b^2*c^2*d^3*x-d^3*a^2/x-2*d^3*a*b*arcsin(c*x)/x-19/8*d^3*b^2*arcsin(c*x)^2*c^2*x-122/25*c*d^3*a*b*(-c^2*x^2+1)^(1/2)-2*c*d^3*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))-19/4*c*d^3*b^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-2*c*d^3*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*d^3*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/200*c*d^3*b^2*arcsin(c*x)*cos(5*arcsin(c*x))-1/80*c*d^3*b^2*sin(5*arcsin(c*x))*arcsin(c*x)^2-1/8*c*d^3*b^2*arcsin(c*x)*cos(3*arcsin(c*x))-3/16*c*d^3*b^2*arcsin(c*x)^2*sin(3*arcsin(c*x))-1/5*d^3*a^2*c^6*x^5+d^3*a^2*c^4*x^3-3*d^3*a^2*c^2*x-d^3*b^2/x*arcsin(c*x)^2+1/1000*c*d^3*b^2*sin(5*arcsin(c*x))+1/24*c*d^3*b^2*sin(3*arcsin(c*x))","A"
181,1,884,375,1.022000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^3,x)","-6 c^{2} d^{3} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+3 i c^{2} d^{3} a b \arcsin \left(c x \right)^{2}+6 i c^{2} d^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+6 i c^{2} d^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+6 i c^{2} d^{3} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+6 i c^{2} d^{3} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{d^{3} a^{2}}{2 x^{2}}+\frac{c^{2} d^{3} b^{2} \cos \left(4 \arcsin \left(c x \right)\right)}{256}+\frac{3 c^{4} d^{3} a^{2} x^{2}}{2}-\frac{c^{6} d^{3} a^{2} x^{4}}{4}-\frac{d^{3} b^{2} \arcsin \left(c x \right)^{2}}{2 x^{2}}-\frac{5 c^{2} d^{3} b^{2} \arcsin \left(c x \right)^{2}}{8}-3 c^{2} d^{3} a^{2} \ln \left(c x \right)+c^{2} d^{3} b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 c^{2} d^{3} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)+c^{2} d^{3} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)-6 c^{2} d^{3} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)-6 c^{2} d^{3} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{5 b^{2} c^{4} d^{3} x^{2}}{8}+\frac{c^{2} d^{3} a b \sin \left(4 \arcsin \left(c x \right)\right)}{64}-\frac{5 c^{2} d^{3} a b \arcsin \left(c x \right)}{4}-\frac{c^{2} d^{3} b^{2} \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{32}+\frac{c^{2} d^{3} b^{2} \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{64}-\frac{d^{3} a b \arcsin \left(c x \right)}{x^{2}}+i c^{2} d^{3} a b +i c^{2} d^{3} b^{2} \arcsin \left(c x \right)^{3}+i c^{2} d^{3} b^{2} \arcsin \left(c x \right)-3 c^{2} d^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-3 c^{2} d^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{5 c^{4} d^{3} b^{2} \arcsin \left(c x \right)^{2} x^{2}}{4}+\frac{5 d^{3} b^{2} c^{2}}{16}-\frac{c^{2} d^{3} a b \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{16}+\frac{5 c^{3} d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{4}-\frac{c \,d^{3} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{x}+\frac{5 c^{3} d^{3} a b \sqrt{-c^{2} x^{2}+1}\, x}{4}+\frac{5 c^{4} d^{3} a b \arcsin \left(c x \right) x^{2}}{2}-\frac{c \,d^{3} a b \sqrt{-c^{2} x^{2}+1}}{x}-6 c^{2} d^{3} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"I*c^2*d^3*a*b-1/2*d^3*a^2/x^2-6*c^2*d^3*b^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+1/256*c^2*d^3*b^2*cos(4*arcsin(c*x))+3/2*c^4*d^3*a^2*x^2-1/4*c^6*d^3*a^2*x^4-1/2*d^3*b^2*arcsin(c*x)^2/x^2-6*c^2*d^3*b^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*d^3*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-5/8*c^2*d^3*b^2*arcsin(c*x)^2-3*c^2*d^3*a^2*ln(c*x)-5/8*b^2*c^4*d^3*x^2+1/64*c^2*d^3*a*b*sin(4*arcsin(c*x))+I*c^2*d^3*b^2*arcsin(c*x)^3+I*c^2*d^3*b^2*arcsin(c*x)-5/4*c^2*d^3*a*b*arcsin(c*x)-3*c^2*d^3*b^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*c^2*d^3*b^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/32*c^2*d^3*b^2*cos(4*arcsin(c*x))*arcsin(c*x)^2+1/64*c^2*d^3*b^2*arcsin(c*x)*sin(4*arcsin(c*x))-d^3*a*b*arcsin(c*x)/x^2+5/4*c^4*d^3*b^2*arcsin(c*x)^2*x^2+5/16*d^3*b^2*c^2-1/16*c^2*d^3*a*b*arcsin(c*x)*cos(4*arcsin(c*x))-6*c^2*d^3*a*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-6*c^2*d^3*a*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+5/4*c^3*d^3*b^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-c*d^3*b^2*arcsin(c*x)/x*(-c^2*x^2+1)^(1/2)+5/4*c^3*d^3*a*b*(-c^2*x^2+1)^(1/2)*x+5/2*c^4*d^3*a*b*arcsin(c*x)*x^2-c*d^3*a*b/x*(-c^2*x^2+1)^(1/2)+6*I*c^2*d^3*b^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+6*I*c^2*d^3*b^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+3*I*c^2*d^3*a*b*arcsin(c*x)^2+6*I*c^2*d^3*a*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+6*I*c^2*d^3*a*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","B"
182,1,547,342,0.886000," ","int((-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2/x^4,x)","\frac{3 c^{2} d^{3} b^{2} \arcsin \left(c x \right)^{2}}{x}-\frac{c^{6} d^{3} b^{2} \arcsin \left(c x \right)^{2} x^{3}}{3}+\frac{50 c^{3} d^{3} a b \sqrt{-c^{2} x^{2}+1}}{9}+\frac{50 c^{3} d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{9}+3 c^{4} d^{3} b^{2} \arcsin \left(c x \right)^{2} x -\frac{c^{6} d^{3} a^{2} x^{3}}{3}+3 c^{4} d^{3} a^{2} x +\frac{3 c^{2} d^{3} a^{2}}{x}-\frac{d^{3} b^{2} \arcsin \left(c x \right)^{2}}{3 x^{3}}-\frac{b^{2} c^{2} d^{3}}{3 x}-\frac{50 b^{2} c^{4} d^{3} x}{9}+\frac{2 b^{2} c^{6} d^{3} x^{3}}{27}-\frac{d^{3} a^{2}}{3 x^{3}}-\frac{2 d^{3} a b \arcsin \left(c x \right)}{3 x^{3}}+\frac{17 c^{3} d^{3} a b \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}+\frac{17 c^{3} d^{3} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{17 c^{3} d^{3} b^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{17 i b^{2} c^{3} d^{3} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3}+\frac{17 i b^{2} c^{3} d^{3} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3}-\frac{2 c^{5} d^{3} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{9}-\frac{2 c^{6} d^{3} a b \arcsin \left(c x \right) x^{3}}{3}+6 c^{4} d^{3} a b \arcsin \left(c x \right) x +\frac{6 c^{2} d^{3} a b \arcsin \left(c x \right)}{x}-\frac{2 c^{5} d^{3} a b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{c \,d^{3} a b \sqrt{-c^{2} x^{2}+1}}{3 x^{2}}-\frac{c \,d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 x^{2}}"," ",0,"3*c^2*d^3*b^2/x*arcsin(c*x)^2-1/3*c^6*d^3*b^2*arcsin(c*x)^2*x^3+50/9*c^3*d^3*a*b*(-c^2*x^2+1)^(1/2)+17/3*c^3*d^3*a*b*arctanh(1/(-c^2*x^2+1)^(1/2))+50/9*c^3*d^3*b^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+3*c^4*d^3*b^2*arcsin(c*x)^2*x-17/3*I*b^2*c^3*d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+17/3*I*b^2*c^3*d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-1/3*c^6*d^3*a^2*x^3+3*c^4*d^3*a^2*x+3*c^2*d^3*a^2/x-1/3*d^3*b^2/x^3*arcsin(c*x)^2-1/3*b^2*c^2*d^3/x-50/9*b^2*c^4*d^3*x+2/27*b^2*c^6*d^3*x^3-1/3*d^3*a^2/x^3+17/3*c^3*d^3*b^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-17/3*c^3*d^3*b^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2/3*d^3*a*b*arcsin(c*x)/x^3-2/9*c^5*d^3*b^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-2/3*c^6*d^3*a*b*arcsin(c*x)*x^3+6*c^4*d^3*a*b*arcsin(c*x)*x+6*c^2*d^3*a*b*arcsin(c*x)/x-2/9*c^5*d^3*a*b*x^2*(-c^2*x^2+1)^(1/2)-1/3*c*d^3*a*b/x^2*(-c^2*x^2+1)^(1/2)-1/3*c*d^3*b^2/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)","A"
183,0,0,316,0.585000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","\int \frac{x^{4} \left(a +b \arcsin \left(c x \right)\right)^{2}}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","F"
184,1,416,224,0.257000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","-\frac{a^{2} x^{2}}{2 c^{2} d}-\frac{a^{2} \ln \left(c x -1\right)}{2 c^{4} d}-\frac{a^{2} \ln \left(c x +1\right)}{2 c^{4} d}+\frac{i a b \arcsin \left(c x \right)^{2}}{c^{4} d}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{2 c^{3} d}-\frac{b^{2} \arcsin \left(c x \right)^{2} x^{2}}{2 c^{2} d}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{4 c^{4} d}+\frac{b^{2} x^{2}}{4 c^{2} d}-\frac{b^{2}}{8 c^{4} d}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}+\frac{i b^{2} \arcsin \left(c x \right)^{3}}{3 c^{4} d}-\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}-\frac{a b \sqrt{-c^{2} x^{2}+1}\, x}{2 c^{3} d}-\frac{a b \arcsin \left(c x \right) x^{2}}{c^{2} d}+\frac{a b \arcsin \left(c x \right)}{2 c^{4} d}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}+\frac{i a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d}"," ",0,"-1/2/c^2*a^2/d*x^2-1/2/c^4*a^2/d*ln(c*x-1)-1/2/c^4*a^2/d*ln(c*x+1)+I/c^4*a*b/d*arcsin(c*x)^2-1/2/c^3*b^2/d*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/2/c^2*b^2/d*arcsin(c*x)^2*x^2+1/4/c^4*b^2/d*arcsin(c*x)^2+1/4*b^2*x^2/c^2/d-1/8/c^4*b^2/d-1/c^4*b^2/d*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I/c^4*a*b/d*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^4/d+1/3*I/c^4*b^2/d*arcsin(c*x)^3-1/2/c^3*a*b/d*(-c^2*x^2+1)^(1/2)*x-1/c^2*a*b/d*arcsin(c*x)*x^2+1/2/c^4*a*b/d*arcsin(c*x)-2/c^4*a*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I/c^4*b^2/d*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)","A"
185,0,0,249,0.302000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","\int \frac{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","F"
186,1,258,141,0.085000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","-\frac{a^{2} \ln \left(c x -1\right)}{2 c^{2} d}-\frac{a^{2} \ln \left(c x +1\right)}{2 c^{2} d}+\frac{i b^{2} \arcsin \left(c x \right)^{3}}{3 c^{2} d}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}-\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{2} d}+\frac{i a b \arcsin \left(c x \right)^{2}}{c^{2} d}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}+\frac{i a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{2} d}"," ",0,"-1/2/c^2*a^2/d*ln(c*x-1)-1/2/c^2*a^2/d*ln(c*x+1)+1/3*I/c^2*b^2/d*arcsin(c*x)^3-1/c^2*b^2/d*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I/c^2*b^2/d*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^2/d+I/c^2*a*b/d*arcsin(c*x)^2-2/c^2*a*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I/c^2*a*b/d*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)","A"
187,1,404,189,0.154000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}+\frac{2 b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d c}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}+\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}-\frac{2 b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d c}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}-\frac{2 i a b \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}+\frac{2 i a b \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c d}-\frac{2 i a^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c d}"," ",0,"1/c/d*b^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I/c/d*b^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d/c-1/c/d*b^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I/c/d*b^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d/c+2/c*a*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I/c/d*a*b*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2/c*a*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I/c/d*a*b*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I/c/d*a^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))","B"
188,1,475,175,0.159000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d),x)","-\frac{a^{2} \ln \left(c x +1\right)}{2 d}+\frac{a^{2} \ln \left(c x \right)}{d}-\frac{a^{2} \ln \left(c x -1\right)}{2 d}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1-\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{i a b \dilog \left(1-\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{i a b \dilog \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}"," ",0,"-1/2*a^2/d*ln(c*x+1)+a^2/d*ln(c*x)-1/2*a^2/d*ln(c*x-1)-b^2/d*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*b^2/d*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d+b^2/d*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2/d*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2/d*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+b^2/d*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2/d*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*b^2/d*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+2*a*b/d*arcsin(c*x)*ln(1-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*a*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-I*a*b/d*dilog(1-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*a*b/d*dilog(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","B"
189,1,575,293,0.304000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d),x)","\frac{c \,a^{2} \ln \left(c x +1\right)}{2 d}-\frac{a^{2}}{d x}-\frac{c \,a^{2} \ln \left(c x -1\right)}{2 d}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{d x}-\frac{2 c \,b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 i c a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{2 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{2 i c \,b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 b^{2} c \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 b^{2} c \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 a b \arcsin \left(c x \right)}{d x}+\frac{2 c a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 c a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 c a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 c a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d}+\frac{2 i c \,b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i c a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}"," ",0,"1/2*c*a^2/d*ln(c*x+1)-a^2/d/x-1/2*c*a^2/d*ln(c*x-1)-b^2/d/x*arcsin(c*x)^2-2*c*b^2/d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c*b^2/d*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c*b^2/d*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+c/d*b^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*c*a*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*c*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d-c/d*b^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*c/d*b^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*c*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d-2*a*b/d*arcsin(c*x)/x+2*c*a*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*c*a*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*c*a*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*a*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+2*I*c/d*b^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*c*a*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","A"
190,1,793,250,0.526000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d),x)","\frac{i c^{2} a b}{d}+\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i c^{2} b^{2} \arcsin \left(c x \right)}{d}-\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{2 c^{2} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 c^{2} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i c^{2} a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}+\frac{i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{2 i c^{2} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 i c^{2} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d}-\frac{a b \arcsin \left(c x \right)}{d \,x^{2}}-\frac{a^{2}}{2 d \,x^{2}}+\frac{c^{2} a^{2} \ln \left(c x \right)}{d}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 d \,x^{2}}-\frac{c^{2} a^{2} \ln \left(c x +1\right)}{2 d}-\frac{c^{2} a^{2} \ln \left(c x -1\right)}{2 d}+\frac{c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d}+\frac{c^{2} b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{2 c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{b^{2} c^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d}+\frac{2 c^{2} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{2 c^{2} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{c \,b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{d x}-\frac{c a b \sqrt{-c^{2} x^{2}+1}}{d x}"," ",0,"-2*I*c^2*b^2/d*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*c^2*b^2/d*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*c^2*a*b/d*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*c^2*a*b/d*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*c^2*a*b/d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*b^2*c^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d+I*c^2*a*b/d+c^2*b^2/d*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+c^2*b^2/d*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*c^2*b^2/d*arcsin(c*x)-a*b/d*arcsin(c*x)/x^2-1/2*a^2/d/x^2+c^2*b^2/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+c^2*a^2/d*ln(c*x)-1/2*b^2/d*arcsin(c*x)^2/x^2+2*c^2*b^2/d*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*c^2*b^2/d*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*c^2*a^2/d*ln(c*x+1)-1/2*c^2*a^2/d*ln(c*x-1)+c^2*b^2/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*c^2*b^2/d*ln(I*c*x+(-c^2*x^2+1)^(1/2))-c*b^2/d*arcsin(c*x)/x*(-c^2*x^2+1)^(1/2)-c*a*b/d/x*(-c^2*x^2+1)^(1/2)-2*c^2*a*b/d*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*c^2*b^2/d*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*I*c^2*a*b/d*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*c^2*a*b/d*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-c^2*b^2/d*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","B"
191,1,725,374,0.448000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d),x)","-\frac{c \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 d \,x^{2}}-\frac{c a b \sqrt{-c^{2} x^{2}+1}}{3 d \,x^{2}}-\frac{2 c^{2} a b \arcsin \left(c x \right)}{d x}+\frac{2 c^{3} a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 c^{3} a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{2 i c^{3} a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 i c^{3} a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{2 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{2 a b \arcsin \left(c x \right)}{3 d \,x^{3}}-\frac{c^{2} a^{2}}{d x}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{3 d \,x^{3}}-\frac{c^{3} a^{2} \ln \left(c x -1\right)}{2 d}+\frac{c^{3} a^{2} \ln \left(c x +1\right)}{2 d}-\frac{2 b^{2} c^{3} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}+\frac{2 b^{2} c^{3} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{7 c^{3} a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d}+\frac{7 c^{3} a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{3 d}+\frac{c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{7 c^{3} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d}+\frac{7 i c^{3} b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d}+\frac{7 i c^{3} b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d}-\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2}}{d x}-\frac{b^{2} c^{2}}{3 d x}-\frac{a^{2}}{3 d \,x^{3}}"," ",0,"-1/3*c*b^2/d/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/3*c*a*b/d/x^2*(-c^2*x^2+1)^(1/2)-2*c^2*a*b/d*arcsin(c*x)/x+2*c^3*a*b/d*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*c^3*a*b/d*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*c^3/d*b^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*c^3*a*b/d*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*c^3*a*b/d*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*c^3/d*b^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-7/3*c^3*a*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+7/3*c^3*a*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+c^3/d*b^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-c^3/d*b^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-7/3*c^3*b^2/d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2/3*a*b/d*arcsin(c*x)/x^3+7/3*I*c^3*b^2/d*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+7/3*I*c^3*b^2/d*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-c^2*a^2/d/x-1/3*b^2/d/x^3*arcsin(c*x)^2-1/2*c^3*a^2/d*ln(c*x-1)+1/2*c^3*a^2/d*ln(c*x+1)-c^2*b^2/d/x*arcsin(c*x)^2-2*b^2*c^3*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d+2*b^2*c^3*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d-1/3*b^2*c^2/d/x-1/3*a^2/d/x^3","A"
192,1,705,325,0.622000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","\frac{3 i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}+\frac{a b \sqrt{-c^{2} x^{2}+1}}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \arcsin \left(c x \right) x}{c^{4} d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2} x}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}-\frac{3 a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}+\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}-\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}-\frac{3 i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}-\frac{a b \arcsin \left(c x \right) x}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}}{c^{5} d^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2} x}{c^{4} d^{2}}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{c^{5} d^{2}}-\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}-\frac{3 b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}-\frac{2 b^{2} x}{c^{4} d^{2}}-\frac{a^{2}}{4 c^{5} d^{2} \left(c x +1\right)}-\frac{a^{2}}{4 c^{5} d^{2} \left(c x -1\right)}+\frac{a^{2} x}{c^{4} d^{2}}+\frac{3 a^{2} \ln \left(c x -1\right)}{4 c^{5} d^{2}}-\frac{3 a^{2} \ln \left(c x +1\right)}{4 c^{5} d^{2}}+\frac{3 b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{5} d^{2}}+\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{5} d^{2}}-\frac{2 i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{5} d^{2}}"," ",0,"3*I/c^5*b^2/d^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3*I/c^5*b^2/d^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3*I/c^5*a*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3*I/c^5*a*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/c^5*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+3/c^5*a*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/c^5*a*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/c^5*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2/c^4*a*b/d^2*arcsin(c*x)*x-1/2/c^4*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x-1/c^4*a*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+2/c^5*a*b/d^2*(-c^2*x^2+1)^(1/2)+1/c^4*b^2/d^2*arcsin(c*x)^2*x+2/c^5*b^2/d^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-3/2/c^5*b^2/d^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/2/c^5*b^2/d^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I/c^5*b^2/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))+3*b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^5/d^2-3*b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^5/d^2-2*b^2*x/c^4/d^2-1/4/c^5*a^2/d^2/(c*x+1)-1/4/c^5*a^2/d^2/(c*x-1)+1/c^4*a^2/d^2*x+3/4/c^5*a^2/d^2*ln(c*x-1)-3/4/c^5*a^2/d^2*ln(c*x+1)","B"
193,1,585,243,0.663000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","\frac{a^{2}}{4 c^{4} d^{2} \left(c x +1\right)}+\frac{a^{2} \ln \left(c x +1\right)}{2 c^{4} d^{2}}-\frac{a^{2}}{4 c^{4} d^{2} \left(c x -1\right)}+\frac{a^{2} \ln \left(c x -1\right)}{2 c^{4} d^{2}}-\frac{i a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}-\frac{i a b \,x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i a b}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{i b^{2} \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 c^{4} d^{2}}+\frac{2 b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}-\frac{b^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}-\frac{i b^{2} \arcsin \left(c x \right)^{3}}{3 c^{4} d^{2}}-\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}+\frac{a b \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i a b \arcsin \left(c x \right)^{2}}{c^{4} d^{2}}-\frac{a b \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{4} d^{2}}-\frac{i b^{2} \arcsin \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"1/4/c^4*a^2/d^2/(c*x+1)+1/2/c^4*a^2/d^2*ln(c*x+1)-1/4/c^4*a^2/d^2/(c*x-1)+1/2/c^4*a^2/d^2*ln(c*x-1)-I/c^2*a*b/d^2/(c^2*x^2-1)*x^2+I/c^4*a*b/d^2/(c^2*x^2-1)+1/c^3*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+I/c^4*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)-1/2/c^4*b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)+1/c^4*b^2/d^2*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/3*I/c^4*b^2/d^2*arcsin(c*x)^3+1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/c^4/d^2+2/c^4*b^2/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))-1/c^4*b^2/d^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-I/c^4*a*b/d^2*arcsin(c*x)^2-I/c^4*b^2/d^2*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/c^3*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-I/c^2*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)*x^2-1/c^4*a*b/d^2*arcsin(c*x)/(c^2*x^2-1)+2/c^4*a*b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-I/c^4*a*b/d^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)","B"
194,1,599,262,0.398000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{4 c^{3} d^{2} \left(c x +1\right)}-\frac{a^{2} \ln \left(c x +1\right)}{4 c^{3} d^{2}}-\frac{a^{2}}{4 c^{3} d^{2} \left(c x -1\right)}+\frac{a^{2} \ln \left(c x -1\right)}{4 c^{3} d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2} x}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}-\frac{b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c^{3} d^{2}}-\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}+\frac{b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}-\frac{2 i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{3} d^{2}}-\frac{a b \arcsin \left(c x \right) x}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}-\frac{a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}-\frac{i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}+\frac{i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3} d^{2}}"," ",0,"-1/4/c^3*a^2/d^2/(c*x+1)-1/4/c^3*a^2/d^2*ln(c*x+1)-1/4/c^3*a^2/d^2/(c*x-1)+1/4/c^3*a^2/d^2*ln(c*x-1)-1/2/c^2*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x+1/c^3*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/2/c^3*b^2/d^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I/c^3*b^2/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^3/d^2+1/2/c^3*b^2/d^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I/c^3*a*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^3/d^2+I/c^3*a*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/c^2*a*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/c^3*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/c^3*a*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/c^3*a*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I/c^3*b^2/d^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I/c^3*b^2/d^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
195,1,205,83,0.048000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \ln \left(-c^{2} x^{2}+1\right)}{2 c^{2} d^{2}}-\frac{a b \arcsin \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{2 c^{2} d^{2} \left(c x +1\right)}+\frac{a b \sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{2 c^{2} d^{2} \left(c x -1\right)}"," ",0,"-1/2/c^2*a^2/d^2/(c^2*x^2-1)-1/2/c^2*b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)+1/c*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/2*b^2*ln(-c^2*x^2+1)/c^2/d^2-1/c^2*a*b/d^2/(c^2*x^2-1)*arcsin(c*x)+1/2/c^2*a*b/d^2/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)+1/2/c^2*a*b/d^2/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)","B"
196,1,593,259,0.184000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{4 c \,d^{2} \left(c x +1\right)}+\frac{a^{2} \ln \left(c x +1\right)}{4 c \,d^{2}}-\frac{a^{2}}{4 c \,d^{2} \left(c x -1\right)}-\frac{a^{2} \ln \left(c x -1\right)}{4 c \,d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}-\frac{i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}+\frac{b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 c \,d^{2}}-\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}-\frac{b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}-\frac{2 i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c \,d^{2}}-\frac{a b \arcsin \left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}+\frac{a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}+\frac{i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c \,d^{2}}"," ",0,"-1/4/c*a^2/d^2/(c*x+1)+1/4/c*a^2/d^2*ln(c*x+1)-1/4/c*a^2/d^2/(c*x-1)-1/4/c*a^2/d^2*ln(c*x-1)-1/2*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x+1/c*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+1/2/c*b^2/d^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I/c*b^2/d^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c/d^2-1/2/c*b^2/d^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-I/c*a*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c/d^2-2*I/c*b^2/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-a*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x+1/c*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/c*a*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/c*a*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I/c*b^2/d^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+I/c*a*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
197,1,829,249,0.444000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^2,x)","-\frac{2 i a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 i a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b^{2} \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i a b}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}\, c x}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b^{2} \arcsin \left(c x \right) c^{2} x^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{i a b \,c^{2} x^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{2}}+\frac{2 b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{b^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{a^{2}}{4 d^{2} \left(c x +1\right)}-\frac{a^{2}}{4 d^{2} \left(c x -1\right)}-\frac{a^{2} \ln \left(c x +1\right)}{2 d^{2}}+\frac{a^{2} \ln \left(c x \right)}{d^{2}}-\frac{a^{2} \ln \left(c x -1\right)}{2 d^{2}}"," ",0,"-1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^2+b^2/d^2*arcsin(c*x)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c*x-I*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)*c^2*x^2+a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c*x-I*a*b/d^2/(c^2*x^2-1)*c^2*x^2-a*b/d^2*arcsin(c*x)/(c^2*x^2-1)-2*a*b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*a*b/d^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+I*b^2/d^2*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*I*b^2/d^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2/d^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+I*a*b/d^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*a*b/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b/d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b/d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+I*b^2/d^2*arcsin(c*x)/(c^2*x^2-1)+I*a*b/d^2/(c^2*x^2-1)+b^2/d^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b^2/d^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)-b^2/d^2*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/4*a^2/d^2/(c*x+1)-1/4*a^2/d^2/(c*x-1)+2*b^2/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))-b^2/d^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/2*a^2/d^2*ln(c*x+1)+a^2/d^2*ln(c*x)+2*b^2/d^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2/d^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*a^2/d^2*ln(c*x-1)","B"
198,1,778,375,0.438000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{d^{2} x}-\frac{3 i c a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{3 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{d^{2} \left(c^{2} x^{2}-1\right) x}-\frac{c \,a^{2}}{4 d^{2} \left(c x +1\right)}-\frac{c \,a^{2}}{4 d^{2} \left(c x -1\right)}+\frac{3 c \,a^{2} \ln \left(c x +1\right)}{4 d^{2}}-\frac{3 c \,a^{2} \ln \left(c x -1\right)}{4 d^{2}}-\frac{3 b^{2} c \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{3 b^{2} c \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{c \,b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{3 i c a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}-\frac{3 b^{2} \arcsin \left(c x \right)^{2} c^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right) x}-\frac{3 c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}-\frac{2 c a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 c a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{2}}-\frac{2 i c \,b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{2 c \,b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{3 c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{2 i c \,b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 i c \,b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{3 c a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}-\frac{3 a b \arcsin \left(c x \right) c^{2} x}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{c a b \sqrt{-c^{2} x^{2}+1}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 c a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}"," ",0,"-a^2/d^2/x-3/2*c*b^2/d^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*c*a*b/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*a*b/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-2*I*c*b^2/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c*b^2/d^2*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c*b^2/d^2*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)/x-2*c*b^2/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/4*c*a^2/d^2/(c*x+1)-1/4*c*a^2/d^2/(c*x-1)+3/4*c*a^2/d^2*ln(c*x+1)-3/4*c*a^2/d^2*ln(c*x-1)+3*c*a*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+c*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+3/2*c*b^2/d^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3*I*c*b^2/d^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/2*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*c^2*x+2*a*b/d^2*arcsin(c*x)/(c^2*x^2-1)/x-3*c*a*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3*I*c*b^2/d^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3*a*b/d^2/(c^2*x^2-1)*arcsin(c*x)*c^2*x-3*b^2*c*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^2+3*b^2*c*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^2+3*I*c*a*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+c*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-3*I*c*a*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
199,1,903,312,0.373000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^2,x)","\frac{a b \arcsin \left(c x \right)}{d^{2} x^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 c^{2} a b \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 i c^{2} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{c^{2} a^{2} \ln \left(c x +1\right)}{d^{2}}+\frac{2 c^{2} a^{2} \ln \left(c x \right)}{d^{2}}-\frac{c^{2} a^{2} \ln \left(c x -1\right)}{d^{2}}+\frac{c^{2} a^{2}}{4 d^{2} \left(c x +1\right)}-\frac{c^{2} a^{2}}{4 d^{2} \left(c x -1\right)}+\frac{c^{2} b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{2}}-\frac{c^{2} b^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{4 c^{2} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{4 c^{2} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{b^{2} c^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{4 c^{2} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{4 c^{2} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 c^{2} a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 i c^{2} a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}-\frac{4 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{4 i c^{2} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}-\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2}}+\frac{2 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{2 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{c a b \sqrt{-c^{2} x^{2}+1}}{d^{2} x \left(c^{2} x^{2}-1\right)}+\frac{c \,b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{d^{2} x \left(c^{2} x^{2}-1\right)}-\frac{a^{2}}{2 d^{2} x^{2}}"," ",0,"4*c^2*a*b/d^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+4*c^2*a*b/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+a*b/d^2/x^2/(c^2*x^2-1)*arcsin(c*x)+2*I*c^2*a*b/d^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*c^2*b^2/d^2*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-4*I*c^2*b^2/d^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-4*I*c^2*b^2/d^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-4*I*c^2*a*b/d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-4*I*c^2*a*b/d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*c^2*a*b/d^2*arcsin(c*x)/(c^2*x^2-1)-4*c^2*a*b/d^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-c^2*a^2/d^2*ln(c*x+1)+c^2*b^2/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c^2*b^2/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+2*c^2*a^2/d^2*ln(c*x)+4*c^2*b^2/d^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+4*c^2*b^2/d^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-c^2*a^2/d^2*ln(c*x-1)+1/4*c^2*a^2/d^2/(c*x+1)-1/4*c^2*a^2/d^2/(c*x-1)-c^2*b^2/d^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*c^2*b^2/d^2*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+1/2*b^2/d^2/x^2/(c^2*x^2-1)*arcsin(c*x)^2+2*c^2*b^2/d^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*c^2*b^2/d^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-c^2*b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)+c*a*b/d^2/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+c*b^2/d^2/x/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/2*a^2/d^2/x^2-b^2*c^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^2","B"
200,1,1019,472,0.543000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^2,x)","-\frac{a^{2}}{3 d^{2} x^{3}}-\frac{5 c^{4} a b \arcsin \left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{c^{4} b^{2} x}{3 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{c a b \sqrt{-c^{2} x^{2}+1}}{3 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}+\frac{c \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{3 d^{2} x^{2} \left(c^{2} x^{2}-1\right)}+\frac{10 c^{2} a b \arcsin \left(c x \right)}{3 d^{2} \left(c^{2} x^{2}-1\right) x}+\frac{5 b^{2} c^{3} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{5 c^{3} a^{2} \ln \left(c x +1\right)}{4 d^{2}}-\frac{5 c^{3} a^{2} \ln \left(c x -1\right)}{4 d^{2}}-\frac{c^{3} a^{2}}{4 d^{2} \left(c x +1\right)}-\frac{c^{3} a^{2}}{4 d^{2} \left(c x -1\right)}-\frac{2 c^{2} a^{2}}{d^{2} x}-\frac{5 b^{2} c^{3} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{c^{2} b^{2}}{3 d^{2} \left(c^{2} x^{2}-1\right) x}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{3 d^{2} x^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}-\frac{5 c^{3} a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{5 c^{3} a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{5 i c^{3} a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}-\frac{5 i c^{3} a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}-\frac{5 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{5 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2}}+\frac{5 c^{2} b^{2} \arcsin \left(c x \right)^{2}}{3 d^{2} \left(c^{2} x^{2}-1\right) x}-\frac{5 c^{4} b^{2} \arcsin \left(c x \right)^{2} x}{2 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 c^{3} a b \sqrt{-c^{2} x^{2}+1}}{3 d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \arcsin \left(c x \right)}{3 d^{2} x^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 c^{3} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{13 c^{3} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{2}}+\frac{5 c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{2 d^{2}}+\frac{13 c^{3} a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{3 d^{2}}-\frac{13 c^{3} a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{2}}-\frac{2 i c^{3} b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{13 i c^{3} b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{2}}+\frac{13 i c^{3} b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{2}}"," ",0,"-1/3*a^2/d^2/x^3-5*c^4*a*b/d^2/(c^2*x^2-1)*arcsin(c*x)*x-1/3*c^4*b^2/d^2*x/(c^2*x^2-1)+1/3*c*a*b/d^2/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/3*c*b^2/d^2/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+10/3*c^2*a*b/d^2*arcsin(c*x)/(c^2*x^2-1)/x+5/4*c^3*a^2/d^2*ln(c*x+1)-5/4*c^3*a^2/d^2*ln(c*x-1)-1/4*c^3*a^2/d^2/(c*x+1)-1/4*c^3*a^2/d^2/(c*x-1)-2*c^2*a^2/d^2/x+1/3*c^2*b^2/d^2/(c^2*x^2-1)/x+1/3*b^2/d^2/x^3/(c^2*x^2-1)*arcsin(c*x)^2-5/2*c^3*b^2/d^2*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-13/3*c^3*b^2/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+5/2*c^3*b^2/d^2*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+13/3*c^3*a*b/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-13/3*c^3*a*b/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*c^3*b^2/d^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))+13/3*I*c^3*b^2/d^2*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+13/3*I*c^3*b^2/d^2*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-5*b^2*c^3*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^2+5*b^2*c^3*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^2+5/3*c^2*b^2/d^2*arcsin(c*x)^2/(c^2*x^2-1)/x-5/2*c^4*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x+2/3*c^3*a*b/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-5*c^3*a*b/d^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2/3*a*b/d^2/x^3/(c^2*x^2-1)*arcsin(c*x)+5*c^3*a*b/d^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2/3*c^3*b^2/d^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+5*I*c^3*a*b/d^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-5*I*c^3*a*b/d^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-5*I*c^3*b^2/d^2*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5*I*c^3*b^2/d^2*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
201,1,903,350,0.831000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\frac{3 a^{2} \ln \left(c x +1\right)}{16 c^{5} d^{3}}-\frac{3 a^{2} \ln \left(c x -1\right)}{16 c^{5} d^{3}}+\frac{5 a^{2}}{16 c^{5} d^{3} \left(c x -1\right)}-\frac{a^{2}}{16 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{5 a^{2}}{16 c^{5} d^{3} \left(c x +1\right)}+\frac{a^{2}}{16 c^{5} d^{3} \left(c x -1\right)^{2}}-\frac{3 b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}+\frac{3 b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}-\frac{3 a b \arcsin \left(c x \right) x}{4 c^{4} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{4 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{5 a b \arcsin \left(c x \right) x^{3}}{4 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{5 a b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{4 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} x}{12 c^{4} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}-\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{5} d^{3}}+\frac{7 i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 c^{5} d^{3}}-\frac{b^{2} x^{3}}{12 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}+\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}+\frac{3 i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}-\frac{3 i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}+\frac{3 a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}-\frac{3 a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{5} d^{3}}+\frac{13 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{12 c^{5} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{13 a b \sqrt{-c^{2} x^{2}+1}}{12 c^{5} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{5 b^{2} \arcsin \left(c x \right)^{2} x^{3}}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b^{2} \arcsin \left(c x \right)^{2} x}{8 c^{4} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}"," ",0,"3/16/c^5*a^2/d^3*ln(c*x+1)-3/16/c^5*a^2/d^3*ln(c*x-1)+5/16/c^5*a^2/d^3/(c*x-1)-1/16/c^5*a^2/d^3/(c*x+1)^2+5/16/c^5*a^2/d^3/(c*x+1)+1/16/c^5*a^2/d^3/(c*x-1)^2-3/4/c^4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x-5/4/c^3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+5/4/c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3-5/4/c^3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+1/12/c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x+3/8/c^5*b^2/d^3*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/8/c^5*b^2/d^3*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+7/3*I/c^5*b^2/d^3*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-1/12/c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3-3/4*b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^5/d^3+3/4*b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^5/d^3+3/4/c^5*a*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+13/12/c^5*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+13/12/c^5*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-3/4/c^5*a*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/8/c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x^3-3/8/c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x-3/4*I/c^5*b^2/d^3*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/4*I/c^5*b^2/d^3*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/4*I/c^5*a*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/4*I/c^5*a*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
202,1,472,156,0.661000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\frac{a^{2}}{16 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{3 a^{2}}{16 c^{4} d^{3} \left(c x +1\right)}+\frac{a^{2}}{16 c^{4} d^{3} \left(c x -1\right)^{2}}+\frac{3 a^{2}}{16 c^{4} d^{3} \left(c x -1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{4 c^{4} d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2} \arcsin \left(c x \right) x \sqrt{-c^{2} x^{2}+1}}{6 c^{3} d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2}}{12 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 c^{3} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \ln \left(-c^{2} x^{2}+1\right)}{3 c^{4} d^{3}}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \arcsin \left(c x \right)}{8 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{3 a b \arcsin \left(c x \right)}{8 c^{4} d^{3} \left(c x +1\right)}+\frac{a b \arcsin \left(c x \right)}{8 c^{4} d^{3} \left(c x -1\right)^{2}}+\frac{3 a b \arcsin \left(c x \right)}{8 c^{4} d^{3} \left(c x -1\right)}-\frac{a b \sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{3 c^{4} d^{3} \left(c x +1\right)}-\frac{a b \sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{24 c^{4} d^{3} \left(c x -1\right)^{2}}-\frac{a b \sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{3 c^{4} d^{3} \left(c x -1\right)}+\frac{a b \sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{24 c^{4} d^{3} \left(c x +1\right)^{2}}"," ",0,"1/16/c^4*a^2/d^3/(c*x+1)^2-3/16/c^4*a^2/d^3/(c*x+1)+1/16/c^4*a^2/d^3/(c*x-1)^2+3/16/c^4*a^2/d^3/(c*x-1)+1/4/c^4*b^2/d^3*arcsin(c*x)^2/(c^2*x^2-1)^2-1/6/c^3*b^2/d^3*arcsin(c*x)*x*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)^2-1/12/c^4*b^2/d^3/(c^2*x^2-1)-2/3/c^3*b^2/d^3*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x+1/3*b^2*ln(-c^2*x^2+1)/c^4/d^3+1/2/c^4*b^2/d^3*arcsin(c*x)^2/(c^2*x^2-1)+1/8/c^4*a*b/d^3*arcsin(c*x)/(c*x+1)^2-3/8/c^4*a*b/d^3*arcsin(c*x)/(c*x+1)+1/8/c^4*a*b/d^3*arcsin(c*x)/(c*x-1)^2+3/8/c^4*a*b/d^3*arcsin(c*x)/(c*x-1)-1/3/c^4*a*b/d^3/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)-1/24/c^4*a*b/d^3/(c*x-1)^2*(-(c*x-1)^2-2*c*x+2)^(1/2)-1/3/c^4*a*b/d^3/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)+1/24/c^4*a*b/d^3/(c*x+1)^2*(-(c*x+1)^2+2*c*x+2)^(1/2)","B"
203,1,894,348,0.625000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}-\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}-\frac{a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}+\frac{a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}-\frac{i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}+\frac{i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}+\frac{a b \arcsin \left(c x \right) x^{3}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} x}{8 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{12 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}}{12 c^{3} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{a^{2}}{16 c^{3} d^{3} \left(c x -1\right)}-\frac{a^{2}}{16 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{a^{2}}{16 c^{3} d^{3} \left(c x +1\right)}+\frac{a^{2}}{16 c^{3} d^{3} \left(c x -1\right)^{2}}-\frac{a^{2} \ln \left(c x +1\right)}{16 c^{3} d^{3}}+\frac{a^{2} \ln \left(c x -1\right)}{16 c^{3} d^{3}}-\frac{b^{2} x^{3}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}-\frac{b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c^{3} d^{3}}+\frac{b^{2} x}{12 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c^{3} d^{3}}+\frac{i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 c^{3} d^{3}}-\frac{a b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{4 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{a b \arcsin \left(c x \right) x}{4 c^{2} d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{4 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}"," ",0,"-1/4/c^3*a*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3-1/4*I/c^3*a*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/4*I/c^3*a*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/4*I/c^3*b^2/d^3*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/4*I/c^3*b^2/d^3*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/8/c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x+1/12/c^3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+1/12/c^3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)+1/4/c^3*a*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/16/c^3*a^2/d^3/(c*x-1)-1/16/c^3*a^2/d^3/(c*x+1)^2+1/16/c^3*a^2/d^3/(c*x+1)+1/16/c^3*a^2/d^3/(c*x-1)^2-1/16/c^3*a^2/d^3*ln(c*x+1)+1/16/c^3*a^2/d^3*ln(c*x-1)-1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3+1/12/c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x+1/8*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x^3-1/8/c^3*b^2/d^3*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/8/c^3*b^2/d^3*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/3*I/c^3*b^2/d^3*arctan(I*c*x+(-c^2*x^2+1)^(1/2))+1/4*b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^3/d^3-1/4*b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c^3/d^3-1/4/c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+1/4/c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x-1/4/c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2","B"
204,1,335,136,0.050000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\frac{a^{2}}{4 c^{2} d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{b^{2} \arcsin \left(c x \right)^{2}}{4 c^{2} d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2} \arcsin \left(c x \right) x \sqrt{-c^{2} x^{2}+1}}{6 c \,d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2}}{12 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \ln \left(-c^{2} x^{2}+1\right)}{6 c^{2} d^{3}}+\frac{a b \arcsin \left(c x \right)}{2 c^{2} d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{a b \sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{6 c^{2} d^{3} \left(c x +1\right)}-\frac{a b \sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{24 c^{2} d^{3} \left(c x -1\right)^{2}}+\frac{a b \sqrt{-\left(c x -1\right)^{2}-2 c x +2}}{6 c^{2} d^{3} \left(c x -1\right)}+\frac{a b \sqrt{-\left(c x +1\right)^{2}+2 c x +2}}{24 c^{2} d^{3} \left(c x +1\right)^{2}}"," ",0,"1/4/c^2*a^2/d^3/(c^2*x^2-1)^2+1/4/c^2*b^2/d^3*arcsin(c*x)^2/(c^2*x^2-1)^2-1/6/c*b^2/d^3*arcsin(c*x)*x*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)^2-1/12/c^2*b^2/d^3/(c^2*x^2-1)+1/3/c*b^2/d^3*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x-1/6*b^2*ln(-c^2*x^2+1)/c^2/d^3+1/2/c^2*a*b/d^3/(c^2*x^2-1)^2*arcsin(c*x)+1/6/c^2*a*b/d^3/(c*x+1)*(-(c*x+1)^2+2*c*x+2)^(1/2)-1/24/c^2*a*b/d^3/(c*x-1)^2*(-(c*x-1)^2-2*c*x+2)^(1/2)+1/6/c^2*a*b/d^3/(c*x-1)*(-(c*x-1)^2-2*c*x+2)^(1/2)+1/24/c^2*a*b/d^3/(c*x+1)^2*(-(c*x+1)^2+2*c*x+2)^(1/2)","B"
205,1,890,339,0.278000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}-\frac{3 b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 c \,d^{3}}-\frac{5 i b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 c \,d^{3}}+\frac{5 b^{2} \arcsin \left(c x \right)^{2} x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c^{2} b^{2} x^{3}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{2} a b \arcsin \left(c x \right) x^{3}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 c a b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 c \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 b^{2} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}+\frac{3 b^{2} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}+\frac{b^{2} x}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 a^{2} \ln \left(c x +1\right)}{16 c \,d^{3}}-\frac{3 a^{2} \ln \left(c x -1\right)}{16 c \,d^{3}}-\frac{3 a^{2}}{16 c \,d^{3} \left(c x -1\right)}-\frac{a^{2}}{16 c \,d^{3} \left(c x +1\right)^{2}}-\frac{3 a^{2}}{16 c \,d^{3} \left(c x +1\right)}+\frac{a^{2}}{16 c \,d^{3} \left(c x -1\right)^{2}}+\frac{5 a b \arcsin \left(c x \right) x}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{11 a b \sqrt{-c^{2} x^{2}+1}}{12 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{11 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{12 c \,d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{2} b^{2} \arcsin \left(c x \right)^{2} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}+\frac{3 a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}-\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}+\frac{3 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}+\frac{3 i a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}-\frac{3 i a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 c \,d^{3}}"," ",0,"3/8/c*b^2/d^3*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/8/c*b^2/d^3*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/8*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x-5/3*I/c*b^2/d^3*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-1/12*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3-3/4*c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3+3/4*c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+3/4*c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x+3/16/c*a^2/d^3*ln(c*x+1)-3/16/c*a^2/d^3*ln(c*x-1)-3/16/c*a^2/d^3/(c*x-1)-1/16/c*a^2/d^3/(c*x+1)^2-3/16/c*a^2/d^3/(c*x+1)+1/16/c*a^2/d^3/(c*x-1)^2-3/4*b^2*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c/d^3+3/4*b^2*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/c/d^3+5/4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x-11/12/c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-3/4/c*a*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/4/c*a*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-11/12/c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-3/8*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x^3-3/4*I/c*b^2/d^3*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/4*I/c*b^2/d^3*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3/4*I/c*a*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-3/4*I/c*a*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))","B"
206,1,1224,324,0.464000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^3,x)","-\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 b^{2} \arcsin \left(c x \right)^{2}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2} c^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 i b^{2} \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 a b \arcsin \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} c^{2} x^{2}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{2 a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{2 a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{4 i a b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{2 i b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{i a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{2 i a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{2 i a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{i b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{4 a b \,c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{a b \arcsin \left(c x \right) c^{2} x^{2}}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 a b c x \sqrt{-c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{4 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3} x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{a^{2} \ln \left(c x \right)}{d^{3}}+\frac{b^{2}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{5 a^{2}}{16 d^{3} \left(c x -1\right)}-\frac{a^{2} \ln \left(c x +1\right)}{2 d^{3}}-\frac{a^{2} \ln \left(c x -1\right)}{2 d^{3}}+\frac{a^{2}}{16 d^{3} \left(c x +1\right)^{2}}+\frac{5 a^{2}}{16 d^{3} \left(c x +1\right)}+\frac{a^{2}}{16 d^{3} \left(c x -1\right)^{2}}-\frac{3 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c x}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 i a b \,c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{8 i a b \,c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 i b^{2} \arcsin \left(c x \right) c^{4} x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{8 i b^{2} \arcsin \left(c x \right) c^{2} x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{8 b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}-\frac{4 b^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 d^{3}}-\frac{b^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}+\frac{2 b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"-1/2*b^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^3+3/4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2-b^2/d^3*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+b^2/d^3*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b^2/d^3*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*c^2*x^2-2*I*b^2/d^3*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2/d^3*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+3/2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)+2*a*b/d^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*a*b/d^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*a*b/d^3*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*a*b/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-4/3*I*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)-2*I*a*b/d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b/d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2*x^2+I*b^2/d^3*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-4/3*I*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)+4/3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^3*x^3*(-c^2*x^2+1)^(1/2)-a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2*x^2-3/2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c*x*(-c^2*x^2+1)^(1/2)-4/3*I*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^4*x^4+8/3*I*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2*x^2+4/3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3*x^3+a^2/d^3*ln(c*x)+1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)+8/3*b^2/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2))-4/3*b^2/d^3*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*b^2/d^3*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2/d^3*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-5/16*a^2/d^3/(c*x-1)-1/2*a^2/d^3*ln(c*x+1)-1/2*a^2/d^3*ln(c*x-1)+1/16*a^2/d^3/(c*x+1)^2+5/16*a^2/d^3/(c*x+1)+1/16*a^2/d^3/(c*x-1)^2-3/2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c*x-4/3*I*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^4*x^4+8/3*I*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2*x^2","B"
207,1,1093,458,0.538000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^3,x)","-\frac{15 b^{2} \arcsin \left(c x \right)^{2} c^{4} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{25 b^{2} \arcsin \left(c x \right)^{2} c^{2} x}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{23 c a b \sqrt{-c^{2} x^{2}+1}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{23 c \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{2 a b \arcsin \left(c x \right)}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{b^{2} c^{4} x^{3}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} c^{2} x}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{2 c \,b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{15 c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{15 c \,b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{2 c a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 c a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{2 i c \,b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 i c \,b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{11 i c \,b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{7 a b \,c^{3} x^{2} \sqrt{-c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{25 a b \arcsin \left(c x \right) c^{2} x}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{7 b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3} x^{2}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{15 a b \arcsin \left(c x \right) c^{4} x^{3}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{15 b^{2} c \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{15 b^{2} c \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{7 c \,a^{2}}{16 d^{3} \left(c x -1\right)}-\frac{c \,a^{2}}{16 d^{3} \left(c x +1\right)^{2}}-\frac{7 c \,a^{2}}{16 d^{3} \left(c x +1\right)}+\frac{c \,a^{2}}{16 d^{3} \left(c x -1\right)^{2}}+\frac{15 c \,a^{2} \ln \left(c x +1\right)}{16 d^{3}}-\frac{15 c \,a^{2} \ln \left(c x -1\right)}{16 d^{3}}-\frac{a^{2}}{d^{3} x}+\frac{15 i c a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{15 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{15 i c \,b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{15 c a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{15 c a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{15 i c a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}"," ",0,"-15/8*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*c^4*x^3+25/8*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*c^2*x-23/12*c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-15/4*c*a*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+15/4*c*a*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-23/12*c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)-15/4*I*c*a*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+15/4*I*c*a*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-15/4*I*c*b^2/d^3*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+15/4*I*c*b^2/d^3*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*c^4*x^3+1/12*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2*x-b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)^2-2*c*b^2/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+15/8*c*b^2/d^3*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-15/8*c*b^2/d^3*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*c*a*b/d^3*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*c*a*b/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+2*I*c*b^2/d^3*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+2*I*c*b^2/d^3*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+7/4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*c^3*x^2*(-c^2*x^2+1)^(1/2)+25/4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2*x+7/4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3*x^2-15/4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^4*x^3-11/3*I*c*b^2/d^3*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-7/16*c*a^2/d^3/(c*x-1)-1/16*c*a^2/d^3/(c*x+1)^2-7/16*c*a^2/d^3/(c*x+1)+1/16*c*a^2/d^3/(c*x-1)^2+15/16*c*a^2/d^3*ln(c*x+1)-15/16*c*a^2/d^3*ln(c*x-1)-a^2/d^3/x-15/4*b^2*c*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^3+15/4*b^2*c*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^3","B"
208,1,1547,427,0.590000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^3,x)","\frac{9 c^{2} a b \arcsin \left(c x \right)}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} b^{2} \arcsin \left(c x \right)^{2} x^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{a b \arcsin \left(c x \right)}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{4 i c^{2} a b}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 i c^{2} b^{2} \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{6 i c^{2} a b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 i c^{2} a b \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{6 i c^{2} a b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}-\frac{6 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 i c^{2} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{6 c^{2} a b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{6 c^{2} a b \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{6 c^{2} a b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}+\frac{9 c^{2} b^{2} \arcsin \left(c x \right)^{2}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{6 c^{2} b^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{6 c^{2} b^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{3 b^{2} c^{2} \polylog \left(3, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{2 d^{3}}+\frac{c^{2} b^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{8 c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}-\frac{7 c^{2} b^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 d^{3}}-\frac{3 c^{2} a^{2} \ln \left(c x +1\right)}{2 d^{3}}-\frac{3 c^{2} a^{2} \ln \left(c x -1\right)}{2 d^{3}}+\frac{3 c^{2} a^{2} \ln \left(c x \right)}{d^{3}}+\frac{c^{2} b^{2}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{9 c^{2} a^{2}}{16 d^{3} \left(c x -1\right)}+\frac{c^{2} a^{2}}{16 d^{3} \left(c x +1\right)^{2}}+\frac{9 c^{2} a^{2}}{16 d^{3} \left(c x +1\right)}+\frac{c^{2} a^{2}}{16 d^{3} \left(c x -1\right)^{2}}-\frac{4 i c^{6} a b \,x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{8 i c^{4} a b \,x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{4 i c^{6} b^{2} \arcsin \left(c x \right) x^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{8 i c^{4} b^{2} \arcsin \left(c x \right) x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{3}}+\frac{3 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{3 c^{2} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}-\frac{c \,b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{c a b \sqrt{-c^{2} x^{2}+1}}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}+\frac{4 c^{5} a b \,x^{3} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{3 c^{4} a b \arcsin \left(c x \right) x^{2}}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c^{3} a b x \sqrt{-c^{2} x^{2}+1}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{4 c^{5} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{a^{2}}{2 d^{3} x^{2}}-\frac{c^{4} b^{2} x^{2}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}"," ",0,"9/2*c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)-3/2*c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x^2+6*c^2*a*b/d^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-6*c^2*a*b/d^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+6*c^2*a*b/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)-4/3*I*c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)-6*I*c^2*a*b/d^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+3*I*c^2*a*b/d^3*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-6*I*c^2*a*b/d^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-4/3*I*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)+3*I*c^2*b^2/d^3*arcsin(c*x)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-6*I*c^2*b^2/d^3*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-6*I*c^2*b^2/d^3*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)^2+9/4*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2-3*c^2*b^2/d^3*arcsin(c*x)^2*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+3*c^2*b^2/d^3*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+3*c^2*b^2/d^3*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+6*c^2*b^2/d^3*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+c^2*b^2/d^3*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c^2*b^2/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-3/2*c^2*a^2/d^3*ln(c*x+1)-3/2*c^2*a^2/d^3*ln(c*x-1)+3*c^2*a^2/d^3*ln(c*x)+8/3*c^2*b^2/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2))-7/3*c^2*b^2/d^3*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+6*c^2*b^2/d^3*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+1/12*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)-9/16*c^2*a^2/d^3/(c*x-1)+1/16*c^2*a^2/d^3/(c*x+1)^2+9/16*c^2*a^2/d^3/(c*x+1)+1/16*c^2*a^2/d^3/(c*x-1)^2-3/2*b^2*c^2*polylog(3,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)/d^3-c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)+4/3*c^5*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3*(-c^2*x^2+1)^(1/2)-3*c^4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^2-1/2*c^3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x*(-c^2*x^2+1)^(1/2)+4/3*c^5*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3-1/2*c^3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-4/3*I*c^6*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^4+8/3*I*c^4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2-4/3*I*c^6*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^4+8/3*I*c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^2-1/2*a^2/d^3/x^2-1/12*c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2","B"
209,1,1352,583,0.681000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^3,x)","-\frac{a^{2}}{3 d^{3} x^{3}}-\frac{35 b^{2} c^{3} \polylog \left(3, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{35 b^{2} c^{3} \polylog \left(3, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{2 a b \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{3}}-\frac{7 c^{2} b^{2} \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{35 c^{6} b^{2} \arcsin \left(c x \right)^{2} x^{3}}{8 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{175 c^{4} b^{2} \arcsin \left(c x \right)^{2} x}{24 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{9 c^{3} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{9 c^{3} a b \sqrt{-c^{2} x^{2}+1}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{35 c^{3} a b \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{35 c^{3} a b \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{35 i c^{3} a b \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{35 i c^{3} a b \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}-\frac{35 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{35 i c^{3} b^{2} \arcsin \left(c x \right) \polylog \left(2, -i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{4 d^{3}}+\frac{35 c^{3} a^{2} \ln \left(c x +1\right)}{16 d^{3}}-\frac{35 c^{3} a^{2} \ln \left(c x -1\right)}{16 d^{3}}-\frac{3 c^{2} a^{2}}{d^{3} x}-\frac{11 c^{3} a^{2}}{16 d^{3} \left(c x -1\right)}-\frac{c^{3} a^{2}}{16 d^{3} \left(c x +1\right)^{2}}-\frac{11 c^{3} a^{2}}{16 d^{3} \left(c x +1\right)}+\frac{c^{3} a^{2}}{16 d^{3} \left(c x -1\right)^{2}}+\frac{29 c^{5} b^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{c^{2} b^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{5 c^{6} b^{2} x^{3}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{3 c^{4} b^{2} x}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{3}}-\frac{19 c^{3} a b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{19 c^{3} a b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{3 d^{3}}-\frac{19 c^{3} b^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{35 c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{35 c^{3} b^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{8 d^{3}}-\frac{17 i c^{3} b^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{19 i c^{3} b^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}+\frac{19 i c^{3} b^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3}}-\frac{14 c^{2} a b \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{c \,b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{c a b \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{35 c^{6} a b \arcsin \left(c x \right) x^{3}}{4 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{29 c^{5} a b \,x^{2} \sqrt{-c^{2} x^{2}+1}}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{175 c^{4} a b \arcsin \left(c x \right) x}{12 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}"," ",0,"-1/3*a^2/d^3/x^3-2/3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^3*arcsin(c*x)+35/4*I*c^3*a*b/d^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-35/4*I*c^3*a*b/d^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-35/4*I*c^3*b^2/d^3*arcsin(c*x)*polylog(2,I*(I*c*x+(-c^2*x^2+1)^(1/2)))+35/4*I*c^3*b^2/d^3*arcsin(c*x)*polylog(2,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-7/3*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)^2-35/8*c^6*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x^3+175/24*c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*x-9/4*c^3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-9/4*c^3*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)-35/4*c^3*a*b/d^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+35/4*c^3*a*b/d^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+35/16*c^3*a^2/d^3*ln(c*x+1)-35/16*c^3*a^2/d^3*ln(c*x-1)-3*c^2*a^2/d^3/x-11/16*c^3*a^2/d^3/(c*x-1)-1/16*c^3*a^2/d^3/(c*x+1)^2-11/16*c^3*a^2/d^3/(c*x+1)+1/16*c^3*a^2/d^3/(c*x-1)^2+29/12*c^5*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-1/3*c^2*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x-5/12*c^6*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x^3+3/4*c^4*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)*x-1/3*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x^3*arcsin(c*x)^2-19/3*c^3*a*b/d^3*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+19/3*c^3*a*b/d^3*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-19/3*c^3*b^2/d^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+35/8*c^3*b^2/d^3*arcsin(c*x)^2*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-35/8*c^3*b^2/d^3*arcsin(c*x)^2*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-17/3*I*c^3*b^2/d^3*arctan(I*c*x+(-c^2*x^2+1)^(1/2))+19/3*I*c^3*b^2/d^3*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+19/3*I*c^3*b^2/d^3*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-35/4*b^2*c^3*polylog(3,-I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^3+35/4*b^2*c^3*polylog(3,I*(I*c*x+(-c^2*x^2+1)^(1/2)))/d^3-14/3*c^2*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x*arcsin(c*x)-1/3*c*b^2/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/3*c*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*(-c^2*x^2+1)^(1/2)-35/4*c^6*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x^3+29/12*c^5*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*(-c^2*x^2+1)^(1/2)+175/12*c^4*a*b/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*x","B"
210,1,1165,326,0.579000," ","int(x^3*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right)}{4000 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{864 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{864 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+16 c^{6} x^{6}-20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-28 c^{4} x^{4}+5 i \sqrt{-c^{2} x^{2}+1}\, x c +13 c^{2} x^{2}-1\right) \left(-10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right)}{4000 c^{4} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right)}{800 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{16 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{288 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(17 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right)}{3600 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(2 i+15 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right)}{900 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/5*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d-2/15/d/c^4*(-c^2*d*x^2+d)^(3/2))+b^2*(1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)/c^4/(c^2*x^2-1)+1/864*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))/c^4/(c^2*x^2-1)+1/864*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^4/(c^2*x^2-1)+1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+16*c^6*x^6-20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-28*c^4*x^4+5*I*(-c^2*x^2+1)^(1/2)*x*c+13*c^2*x^2-1)*(-10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)/c^4/(c^2*x^2-1))+2*a*b*(1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^4/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^4/(c^2*x^2-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))/c^4/(c^2*x^2-1)-1/3600*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(17*I+15*arcsin(c*x))*cos(4*arcsin(c*x))/c^4/(c^2*x^2-1)-1/900*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(2*I+15*arcsin(c*x))*sin(4*arcsin(c*x))/c^4/(c^2*x^2-1))","C"
211,1,812,263,0.508000," ","int(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","-\frac{a^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} x^{5}}{4 c^{2} x^{2}-4}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{3}}{8 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x}{8 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{24 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{64 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4}}{8 c^{2} x^{2}-8}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{5}}{32 \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{64 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{64 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 c^{2} x^{2}-8}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{8 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{5}}{2 c^{2} x^{2}-2}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{4 \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{64 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{4 c^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a^2/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^5-3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*x^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*arcsin(c*x)^2*x-1/24*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^3+1/64*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-1/32*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*x^5+3/64*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*x^3-1/64*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*x+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5-3/4*a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x^3+1/64*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/(c^2*x^2-1)*arcsin(c*x)*x","B"
212,1,700,164,0.298000," ","int(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{216 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{216 c^{2} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{72 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/3*a^2/c^2/d*(-c^2*d*x^2+d)^(3/2)+b^2*(1/216*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))/c^2/(c^2*x^2-1)+1/216*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^2/(c^2*x^2-1))+2*a*b*(1/72*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^2/(c^2*x^2-1)-1/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^2/(c^2*x^2-1)+1/72*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))/c^2/(c^2*x^2-1))","C"
213,1,564,166,0.197000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","\frac{x \sqrt{-c^{2} d \,x^{2}+d}\, a^{2}}{2}+\frac{a^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{6 c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{4 c \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} x^{3}}{2 c^{2} x^{2}-2}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x}{2 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{3}}{4 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{4 c^{2} x^{2}-4}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 c^{2} x^{2}-2}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 c \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 c^{2} x^{2}-2}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{3}}{c^{2} x^{2}-1}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{4 c \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{c^{2} x^{2}-1}"," ",0,"1/2*x*(-c^2*d*x^2+d)^(1/2)*a^2+1/2*a^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*x-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*x^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+a*b*(-d*(c^2*x^2-1))^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x","B"
214,1,1017,384,0.382000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x,x)","-\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) a^{2}+\sqrt{-c^{2} d \,x^{2}+d}\, a^{2}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x c}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2} c^{2}}{c^{2} x^{2}-1}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{2}}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x c}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2}}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}"," ",0,"-d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*a^2+(-c^2*d*x^2+d)^(1/2)*a^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*c+b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*x^2*c^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c^2*x^2-b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)-b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
215,1,762,225,0.421000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{d x}-a^{2} c^{2} x \sqrt{-c^{2} d \,x^{2}+d}-\frac{a^{2} c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} c}{3 c^{2} x^{2}-3}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,c^{2}}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{\left(c^{2} x^{2}-1\right) x}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c}{c^{2} x^{2}-1}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, c}{c^{2} x^{2}-1}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} c}{c^{2} x^{2}-1}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) x}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c}{c^{2} x^{2}-1}"," ",0,"-a^2/d/x*(-c^2*d*x^2+d)^(3/2)-a^2*c^2*x*(-c^2*d*x^2+d)^(1/2)-a^2*c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^3*c+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)*x*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/x-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*c+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)*x*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c","B"
216,1,1082,402,0.546000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^3,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2 d \,x^{2}}+\frac{a^{2} \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right) c^{2}}{2}-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}\, c^{2}}{2}-\frac{b^{2} \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{2 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{2 x^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \arctanh \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{c^{2} x^{2}-1}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}+\frac{a b \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}}{x^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}-\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}"," ",0,"-1/2*a^2/d/x^2*(-c^2*d*x^2+d)^(3/2)+1/2*a^2*d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)*c^2-1/2*a^2*(-c^2*d*x^2+d)^(1/2)*c^2-1/2*b^2*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*c^2+b^2*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/2*b^2*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*arctanh(I*c*x+(-c^2*x^2+1)^(1/2))+b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-a*b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*c^2+a*b*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+a*b*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(2*c^2*x^2-2)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(2*c^2*x^2-2)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)","B"
217,1,3017,294,0.593000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5+20/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-6*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c+I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5+2*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^7+2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)^2*c^4-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)^2*c^2-a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-4*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*c^3/(3*c^2*x^2-3)-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^3/(3*c^2*x^2-3)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^3/(3*c^2*x^2-3)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^3/(3*c^2*x^2-3)*arcsin(c*x)^2-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^3/(3*c^2*x^2-3)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^3/(3*c^2*x^2-3)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)^2*c^8-3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)^2*c^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^6-I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5+1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^4+I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^7-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4+2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x/(c^2*x^2-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)^2-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(3/2)+2*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-2*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-3*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5","B"
218,1,1678,441,0.629000," ","int(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{7 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{35 d \,c^{4}}\right)+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d}{43904 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right) d}{16000 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d}{1152 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d}{1152 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+16 c^{6} x^{6}-20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-28 c^{4} x^{4}+5 i \sqrt{-c^{2} x^{2}+1}\, x c +13 c^{2} x^{2}-1\right) \left(-10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right) d}{16000 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d}{43904 c^{4} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d}{6272 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{128 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{384 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(2 i+35 \arcsin \left(c x \right)\right) \cos \left(6 \arcsin \left(c x \right)\right) d}{39200 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(37 i+35 \arcsin \left(c x \right)\right) \sin \left(6 \arcsin \left(c x \right)\right) d}{78400 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(7 i+15 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d}{2400 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(11 i+45 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d}{4800 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/7*x^2*(-c^2*d*x^2+d)^(5/2)/c^2/d-2/35/d/c^4*(-c^2*d*x^2+d)^(5/2))+b^2*(-1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1)+1/16000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))*d/c^4/(c^2*x^2-1)+1/1152*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1)+1/16000*(-d*(c^2*x^2-1))^(1/2)*(16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+16*c^6*x^6-20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-28*c^4*x^4+5*I*(-c^2*x^2+1)^(1/2)*x*c+13*c^2*x^2-1)*(-10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1)-1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d/c^4/(c^2*x^2-1))+2*a*b*(-1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^4/(c^2*x^2-1)-3/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^4/(c^2*x^2-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^4/(c^2*x^2-1)+3/39200*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(2*I+35*arcsin(c*x))*cos(6*arcsin(c*x))*d/c^4/(c^2*x^2-1)+1/78400*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(37*I+35*arcsin(c*x))*sin(6*arcsin(c*x))*d/c^4/(c^2*x^2-1)-1/2400*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(7*I+15*arcsin(c*x))*cos(4*arcsin(c*x))*d/c^4/(c^2*x^2-1)-1/4800*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(11*I+45*arcsin(c*x))*sin(4*arcsin(c*x))*d/c^4/(c^2*x^2-1))","C"
219,1,4469,367,0.644000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"-31/27648*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-1/12*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*x^3+1/216*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^7-1/108*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^5+1/144*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c^2/(c^2*x^2-1)*x+3/1024*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)+1/24*a^2/c^2*x*(-c^2*d*x^2+d)^(3/2)+1/12*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^6-1/8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^4+1/16*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^2+1/192*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)^2*x^2-7/2304*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2+31/27648*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)^2*x^2+3/256*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-3/1024*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/48*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-3/256*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+7/2304*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/48*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/96*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-7/2304*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)+3/256*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2-1/192*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x+1/64*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x-3/256*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+7/2304*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/256*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-11/2304*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/96*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x+1/256*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/48*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/6*a^2*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/16*a^2/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*a^2/c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/432*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x^3-1/12*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^7+1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^5+31/27648*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/96*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)^2-1/48*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^3*d-1/256*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-3/1024*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+11/2304*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-1/144*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-7/144*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^3+7/1728*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+23/27648*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-5/1024*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)-1/144*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+11/2304*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-7/144*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x^3-1/6*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^3-1/256*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)-1/216*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6+1/18*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+1/144*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-1/96*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/96*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2-1/36*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6+1/24*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-3/256*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-1/36*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^7-23/27648*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2-1/192*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)^2+7/2304*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)+5/1024*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/48*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c^2/(c^2*x^2-1)*arcsin(c*x)*x-1/16*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*d+7/2304*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)-3/256*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)-1/36*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6+1/24*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-11/2304*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/256*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-5/1024*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+23/27648*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/96*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)^2*x^2+1/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)^2-1/36*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^7+1/18*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^5+1/48*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c^2/(c^2*x^2-1)*x-11/2304*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/256*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2+1/48*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(5*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)-1/6*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^7+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5-1/96*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/32*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/6*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6-1/4*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+1/8*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+1/96*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2-11/2304*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(5*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x","C"
220,1,1151,245,0.391000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right) d}{4000 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d}{288 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d}{288 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+16 c^{6} x^{6}-20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-28 c^{4} x^{4}+5 i \sqrt{-c^{2} x^{2}+1}\, x c +13 c^{2} x^{2}-1\right) \left(-10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right) d}{4000 c^{2} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+5 \arcsin \left(c x \right)\right) d}{800 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d}{16 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d}{96 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(11 i+45 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d}{1200 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(7 i+15 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d}{600 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/5*a^2/c^2/d*(-c^2*d*x^2+d)^(5/2)+b^2*(-1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)*d/c^2/(c^2*x^2-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))*d/c^2/(c^2*x^2-1)+1/288*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d/c^2/(c^2*x^2-1)-1/4000*(-d*(c^2*x^2-1))^(1/2)*(16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+16*c^6*x^6-20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-28*c^4*x^4+5*I*(-c^2*x^2+1)^(1/2)*x*c+13*c^2*x^2-1)*(-10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)*d/c^2/(c^2*x^2-1))+2*a*b*(-1/800*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+5*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d/c^2/(c^2*x^2-1)+1/96*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/1200*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(11*I+45*arcsin(c*x))*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)-1/600*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(7*I+15*arcsin(c*x))*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1))","C"
221,1,2936,265,0.267000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"17/128*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2-15/128*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+7/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)^2-15/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)-33/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-5/32*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4+5/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-7/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-7/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)+31/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-1/16*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5-1/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+9/64*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)^2*x^2+7/64*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x+17/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-7/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+7/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)+15/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-17/128*a*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-17/128*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)-5/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x+7/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x-17/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-17/128*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^5+7/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^3*d-33/512*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-9/64*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)^2-31/512*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+31/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-31/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)+7/32*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x+33/512*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)+1/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^5-19/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^3-5/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*x-1/16*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^5-5/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^3-9/32*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*d+3/8*a^2*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+7/32*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+1/8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^2-7/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)^2*x^2+9/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x+17/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+15/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^4+9/32*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+17/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x+1/4*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4+1/4*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-7/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+9/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-15/128*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+5/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+17/128*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-15/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5+7/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/4*x*(-c^2*d*x^2+d)^(3/2)*a^2","C"
222,1,1276,529,0.454000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x,x)","\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{9 \left(c^{2} x^{2}-1\right)}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x c}{3 \left(c^{2} x^{2}-1\right)}+\frac{8 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x c}{3 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{9 \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{4} c^{4}}{3 \left(c^{2} x^{2}-1\right)}+\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{2} c^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)^{2} x^{4} c^{4}}{3 \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)^{2} x^{2} c^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} a^{2}}{3}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{68 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d}{27 \left(c^{2} x^{2}-1\right)}-a^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d +\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{4}}{27 \left(c^{2} x^{2}-1\right)}-\frac{70 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x^{2}}{27 \left(c^{2} x^{2}-1\right)}-\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)}{3 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)^{2}}{3 \left(c^{2} x^{2}-1\right)}"," ",0,"-2/9*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*c^3+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x*c-2/9*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^3*c^3-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^4*c^4+10/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*x^4*c^4+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*x^2*c^2-b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/3*(-c^2*d*x^2+d)^(3/2)*a^2+68/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)-a^2*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a^2*(-c^2*d*x^2+d)^(1/2)*d+2/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*c^4*x^4-70/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*c^2*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)^2","B"
223,1,1148,398,0.471000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x)","\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d}{\left(c^{2} x^{2}-1\right) x}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right)^{2} x^{3}}{2 \left(c^{2} x^{2}-1\right)}-a^{2} c^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{d x}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) d c}{c^{2} x^{2}-1}-\frac{3 a^{2} c^{2} d x \sqrt{-c^{2} d \,x^{2}+d}}{2}-\frac{3 a^{2} c^{2} d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right)^{2} x}{2 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} x^{3}}{4 c^{2} x^{2}-4}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} x}{4 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} d}{\left(c^{2} x^{2}-1\right) x}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} d c}{2 c^{2} x^{2}-2}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{4 c^{2} x^{2}-4}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) d c}{c^{2} x^{2}-1}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}}{c^{2} x^{2}-1}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}}{4 c^{2} x^{2}-4}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d c \sqrt{-c^{2} x^{2}+1}\, \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} d c}{2 \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{4} \arcsin \left(c x \right) x^{3}}{c^{2} x^{2}-1}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \,c^{2} \arcsin \left(c x \right) x}{c^{2} x^{2}-1}"," ",0,"1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d/(c^2*x^2-1)/x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^3*d*c+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^3-a^2*c^2*x*(-c^2*d*x^2+d)^(3/2)-a^2/d/x*(-c^2*d*x^2+d)^(5/2)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*d*c-3/2*a^2*c^2*d*x*(-c^2*d*x^2+d)^(1/2)-3/2*a^2*c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x+b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2*d/(c^2*x^2-1)/x-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c+3/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d*c-2*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+I*b^2*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^3-a*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x","B"
224,1,1372,576,0.596000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^3,x)","\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right)}-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2 d \,x^{2}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c^{2} x^{2}-1}+\frac{b^{2} d \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} d \sqrt{-c^{2} x^{2}+1}\, x}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \arcsin \left(c x \right) x^{2}}{c^{2} x^{2}-1}+\frac{a b d \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}-\frac{a^{2} c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{2}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{a b d \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}}{x^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \arcsin \left(c x \right)^{2} x^{2}}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \arctanh \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} d \,x^{2}}{c^{2} x^{2}-1}+\frac{b^{2} d \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{2 x^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d}{c^{2} x^{2}-1}+\frac{3 a^{2} c^{2} d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{3 a^{2} c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d}{2}+\frac{3 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{3 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{2} d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}-\frac{6 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{6 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{6 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}-\frac{6 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} d \arcsin \left(c x \right)^{2}}{2 c^{2} x^{2}-2}"," ",0,"-1/2*a^2/d/x^2*(-c^2*d*x^2+d)^(5/2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+b^2*d*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+3/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-3/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)*c^3*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c^2*x^2-1)*arcsin(c*x)*x^2+a*b*d*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-1/2*a^2*c^2*(-c^2*d*x^2+d)^(3/2)+a*b*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c^2*x^2-1)*arcsin(c*x)+a*b*d*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)-b^2*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c^2*x^2-1)*arcsin(c*x)^2*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*arctanh(I*c*x+(-c^2*x^2+1)^(1/2))+3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^4*d/(c^2*x^2-1)*x^2+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c^2*x^2-1)*arcsin(c*x)^2+1/2*b^2*d*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(c^2*x^2-1)+3/2*a^2*c^2*d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-3/2*a^2*c^2*(-c^2*d*x^2+d)^(1/2)*d+3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*c^2*d/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+6*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(2*c^2*x^2-2)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-6*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(2*c^2*x^2-2)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-6*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+6*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2*d/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
225,1,3281,372,0.630000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"-20/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+29/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-10/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c^2*x^2-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^3*d*c^3-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(5/2)+2/3*a^2*c^4*x*(-c^2*d*x^2+d)^(3/2)-4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+64*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7-24*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+a^2*c^4*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+2/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(5/2)+32*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^7+a^2*c^4*d*x*(-c^2*d*x^2+d)^(1/2)-16/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4+8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-16/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^6-12*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5+4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c+8*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5-16/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^7+20/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4+4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3+64*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-104*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+8*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5+146/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-28/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-16*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d*c^3/(3*c^2*x^2-3)-16/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+20/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6+73/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)^2*c^4-14/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)^2*c^2-8*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(3*c^2*x^2-3)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3-8*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(3*c^2*x^2-3)*arcsin(c*x)^2-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d*c^3-3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d*c^3+8*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(3*c^2*x^2-3)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-52*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)^2*c^6-3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+32*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)^2*c^8+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d/(24*c^4*x^4-9*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6-8*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(3*c^2*x^2-3)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+8*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(3*c^2*x^2-3)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)","B"
226,1,2146,575,0.672000," ","int(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","a^{2} \left(-\frac{x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{9 c^{2} d}-\frac{2 \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{63 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(18 i \arcsin \left(c x \right)+81 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{373248 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{175616 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{1728 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{1728 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{175616 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-18 i \arcsin \left(c x \right)+81 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{373248 c^{4} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 c^{10} x^{10}-704 c^{8} x^{8}-256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+688 c^{6} x^{6}+576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-280 c^{4} x^{4}-432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+41 c^{2} x^{2}+120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-9 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+9 \arcsin \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 c^{4} x^{4}-5 c^{2} x^{2}-4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+3 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+3 \arcsin \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d^{2}}{256 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d^{2}}{576 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-i+7 \arcsin \left(c x \right)\right) d^{2}}{25088 c^{4} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(256 i \sqrt{-c^{2} x^{2}+1}\, x^{9} c^{9}+256 c^{10} x^{10}-576 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}-704 c^{8} x^{8}+432 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+688 c^{6} x^{6}-120 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-280 c^{4} x^{4}+9 i \sqrt{-c^{2} x^{2}+1}\, x c +41 c^{2} x^{2}-1\right) \left(-i+9 \arcsin \left(c x \right)\right) d^{2}}{41472 c^{4} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/9*x^2*(-c^2*d*x^2+d)^(7/2)/c^2/d-2/63/d/c^4*(-c^2*d*x^2+d)^(7/2))+b^2*(1/373248*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(18*I*arcsin(c*x)+81*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1)-3/175616*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1)+1/1728*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)+1/1728*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1)-3/175616*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1)+1/373248*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-18*I*arcsin(c*x)+81*arcsin(c*x)^2-2)*d^2/c^4/(c^2*x^2-1))+2*a*b*(1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*c^10*x^10-704*c^8*x^8-256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+688*c^6*x^6+576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-280*c^4*x^4-432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+41*c^2*x^2+120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-9*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*c^4*x^4-5*c^2*x^2-4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+3*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/256*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d^2/c^4/(c^2*x^2-1)+1/576*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)-3/25088*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-I+7*arcsin(c*x))*d^2/c^4/(c^2*x^2-1)+1/41472*(-d*(c^2*x^2-1))^(1/2)*(256*I*(-c^2*x^2+1)^(1/2)*x^9*c^9+256*c^10*x^10-576*I*(-c^2*x^2+1)^(1/2)*x^7*c^7-704*c^8*x^8+432*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+688*c^6*x^6-120*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-280*c^4*x^4+9*I*(-c^2*x^2+1)^(1/2)*x*c+41*c^2*x^2-1)*(-I+9*arcsin(c*x))*d^2/c^4/(c^2*x^2-1))","C"
227,1,6108,488,0.759000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
228,1,1611,338,0.467000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{7 c^{2} d}+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{43904 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(16 c^{6} x^{6}-28 c^{4} x^{4}-16 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}+13 c^{2} x^{2}+20 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}-5 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(10 i \arcsin \left(c x \right)+25 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{3200 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{384 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+64 c^{8} x^{8}-112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-144 c^{6} x^{6}+56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+104 c^{4} x^{4}-7 i \sqrt{-c^{2} x^{2}+1}\, x c -25 c^{2} x^{2}+1\right) \left(-14 i \arcsin \left(c x \right)+49 \arcsin \left(c x \right)^{2}-2\right) d^{2}}{43904 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(30 i \arcsin \left(c x \right)+75 \arcsin \left(c x \right)^{2}-14\right) \cos \left(4 \arcsin \left(c x \right)\right) d^{2}}{2400 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(90 i \arcsin \left(c x \right)+75 \arcsin \left(c x \right)^{2}-22\right) \sin \left(4 \arcsin \left(c x \right)\right) d^{2}}{4800 c^{2} \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(64 c^{8} x^{8}-144 c^{6} x^{6}-64 i \sqrt{-c^{2} x^{2}+1}\, x^{7} c^{7}+104 c^{4} x^{4}+112 i \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}-25 c^{2} x^{2}-56 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+7 i \sqrt{-c^{2} x^{2}+1}\, x c +1\right) \left(i+7 \arcsin \left(c x \right)\right) d^{2}}{6272 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(4 i \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}+4 c^{4} x^{4}-3 i \sqrt{-c^{2} x^{2}+1}\, x c -5 c^{2} x^{2}+1\right) \left(-i+3 \arcsin \left(c x \right)\right) d^{2}}{128 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(11 i+70 \arcsin \left(c x \right)\right) \cos \left(6 \arcsin \left(c x \right)\right) d^{2}}{7840 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(9 i+35 \arcsin \left(c x \right)\right) \sin \left(6 \arcsin \left(c x \right)\right) d^{2}}{15680 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(i+5 \arcsin \left(c x \right)\right) \cos \left(4 \arcsin \left(c x \right)\right) d^{2}}{160 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i c^{2} x^{2}-c x \sqrt{-c^{2} x^{2}+1}-i\right) \left(3 i+5 \arcsin \left(c x \right)\right) \sin \left(4 \arcsin \left(c x \right)\right) d^{2}}{320 c^{2} \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-1/7*a^2/c^2/d*(-c^2*d*x^2+d)^(7/2)+b^2*(1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d^2/c^2/(c^2*x^2-1)-1/3200*(-d*(c^2*x^2-1))^(1/2)*(16*c^6*x^6-28*c^4*x^4-16*I*(-c^2*x^2+1)^(1/2)*x^5*c^5+13*c^2*x^2+20*I*(-c^2*x^2+1)^(1/2)*x^3*c^3-5*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(10*I*arcsin(c*x)+25*arcsin(c*x)^2-2)*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)+1/384*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)*d^2/c^2/(c^2*x^2-1)+1/43904*(-d*(c^2*x^2-1))^(1/2)*(64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+64*c^8*x^8-112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-144*c^6*x^6+56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+104*c^4*x^4-7*I*(-c^2*x^2+1)^(1/2)*x*c-25*c^2*x^2+1)*(-14*I*arcsin(c*x)+49*arcsin(c*x)^2-2)*d^2/c^2/(c^2*x^2-1)-1/2400*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(30*I*arcsin(c*x)+75*arcsin(c*x)^2-14)*cos(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/4800*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(90*I*arcsin(c*x)+75*arcsin(c*x)^2-22)*sin(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1))+2*a*b*(1/6272*(-d*(c^2*x^2-1))^(1/2)*(64*c^8*x^8-144*c^6*x^6-64*I*(-c^2*x^2+1)^(1/2)*x^7*c^7+104*c^4*x^4+112*I*(-c^2*x^2+1)^(1/2)*x^5*c^5-25*c^2*x^2-56*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+7*I*(-c^2*x^2+1)^(1/2)*x*c+1)*(I+7*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-5/128*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)*d^2/c^2/(c^2*x^2-1)+1/128*(-d*(c^2*x^2-1))^(1/2)*(4*I*(-c^2*x^2+1)^(1/2)*x^3*c^3+4*c^4*x^4-3*I*(-c^2*x^2+1)^(1/2)*x*c-5*c^2*x^2+1)*(-I+3*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/7840*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(11*I+70*arcsin(c*x))*cos(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-3/15680*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(9*I+35*arcsin(c*x))*sin(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/160*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(I+5*arcsin(c*x))*cos(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-1/320*(-d*(c^2*x^2-1))^(1/2)*(I*c^2*x^2-c*x*(-c^2*x^2+1)^(1/2)-I)*(3*I+5*arcsin(c*x))*sin(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1))","C"
229,1,5048,384,0.340000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
230,1,1574,657,0.546000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x,x)","\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{5} c^{5}}{25 \left(c^{2} x^{2}-1\right)}-\frac{22 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{3} c^{3}}{45 \left(c^{2} x^{2}-1\right)}+\frac{46 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x c}{15 \left(c^{2} x^{2}-1\right)}-\frac{22 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{45 \left(c^{2} x^{2}-1\right)}+\frac{46 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x c}{15 \left(c^{2} x^{2}-1\right)}-\frac{28 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{4} c^{4}}{15 \left(c^{2} x^{2}-1\right)}+\frac{68 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{2} c^{2}}{15 \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \sqrt{-c^{2} x^{2}+1}\, x^{5} c^{5}}{25 \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) x^{6} c^{6}}{5 \left(c^{2} x^{2}-1\right)}+\frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} a^{2}}{5}-\frac{14 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)^{2} x^{4} c^{4}}{15 \left(c^{2} x^{2}-1\right)}+\frac{34 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)^{2} x^{2} c^{2}}{15 \left(c^{2} x^{2}-1\right)}+\frac{a^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3}-a^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)+a^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}+\frac{9394 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2}}{3375 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{23 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)^{2}}{15 \left(c^{2} x^{2}-1\right)}-\frac{46 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)}{15 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{6}}{125 \left(c^{2} x^{2}-1\right)}+\frac{532 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{4}}{3375 \left(c^{2} x^{2}-1\right)}-\frac{9872 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} x^{2}}{3375 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right)^{2} x^{6} c^{6}}{5 c^{2} x^{2}-5}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}"," ",0,"2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2/25*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^5*c^5-22/45*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3*c^3+46/15*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*c+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-22/45*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*c^3+46/15*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*c-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-28/15*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^4*c^4+68/15*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2*c^2+2/25*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5*c^5+2/5*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)*x^6*c^6-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/5*(-c^2*d*x^2+d)^(5/2)*a^2+1/5*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2*x^6*c^6-14/15*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2*x^4*c^4+34/15*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2*x^2*c^2-b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/3*a^2*d*(-c^2*d*x^2+d)^(3/2)-a^2*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+a^2*(-c^2*d*x^2+d)^(1/2)*d^2+9394/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)+b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-23/15*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)^2-46/15*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*arcsin(c*x)-2/125*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*c^6*x^6+532/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*c^4*x^4-9872/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)*c^2*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))","B"
231,1,3585,521,0.565000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^2,x)","\text{output too large to display}"," ",0,"-3/8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^2+15/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)^2*x^2-31/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+65/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-15/64*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x+31/128*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-a^2/d/x*(-c^2*d*x^2+d)^(7/2)-a^2*c^2*x*(-c^2*d*x^2+d)^(5/2)-17/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-15/8*a^2*c^2*d^2*x*(-c^2*d*x^2+d)^(1/2)+b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2*d^2/(c^2*x^2-1)/x-1/64*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^5+35/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^3-33/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x-65/512*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)-15/32*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-1/4*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4-3/4*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2+15/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2-33/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-33/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x-17/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x-15/8*a^2*c^2*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-5/4*a^2*c^2*d*x*(-c^2*d*x^2+d)^(3/2)-17/32*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+31/128*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-15/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)-31/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2+79/32*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)*arcsin(c*x)*d^2*c-1/8*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^4+65/512*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2+17/64*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)^2+5/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^3*d^2*c+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)^2*x^5-11/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^3-7/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x+33/128*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+33/128*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)-63/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+63/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d^2/(c^2*x^2-1)/x+33/128*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)+33/128*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-9/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+1/16*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4-2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-33/128*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)*x^2+63/512*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-17/64*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*arcsin(c*x)^2*x^2+1/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+13/32*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^3+15/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+79/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)-15/32*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-63/512*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2-15/64*I*b^2*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)^2+31/128*I*b^2*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)+1/16*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^5-15/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*x+13/32*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^3+1/16*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^5+17/32*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)+15/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d^2*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c-7/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x-11/8*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^3+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^5-9/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-33/128*a*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d^2*c^3/(c^2*x^2-1)*x^2+1/16*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+31/128*I*a*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)","B"
232,1,1674,708,0.690000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^3,x)","-\frac{122 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2}}{27 \left(c^{2} x^{2}-1\right)}+\frac{a b \,d^{2} \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}}{x^{2} \left(c^{2} x^{2}-1\right)}+\frac{11 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \arcsin \left(c x \right)}{3 \left(c^{2} x^{2}-1\right)}-\frac{8 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right)^{2} x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \arctanh \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{c^{2} x^{2}-1}-\frac{5 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{5 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{c^{2} x^{2}-1}+\frac{10 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}-\frac{10 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right) \arcsin \left(c x \right)}{2 c^{2} x^{2}-2}-\frac{10 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}+\frac{10 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 c^{2} x^{2}-2}-\frac{a^{2} c^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{2}-\frac{a^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{7}{2}}}{2 d \,x^{2}}-\frac{5 a^{2} c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{6}+\frac{5 a^{2} c^{2} d^{\frac{5}{2}} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2}-\frac{5 a^{2} c^{2} \sqrt{-c^{2} d \,x^{2}+d}\, d^{2}}{2}-\frac{14 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{3}}{9 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} d^{2} \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{5} \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{14 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{3} \sqrt{-c^{2} x^{2}+1}\, x}{3 \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}-1\right)}-\frac{16 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{a b \,d^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right)}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d^{2} c^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} \arcsin \left(c x \right)^{2} x^{4}}{3 c^{2} x^{2}-3}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{6} x^{4}}{27 \left(c^{2} x^{2}-1\right)}+\frac{124 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{4} x^{2}}{27 \left(c^{2} x^{2}-1\right)}+\frac{11 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d^{2} c^{2} \arcsin \left(c x \right)^{2}}{6 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} d^{2} \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{2 x^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-122/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)+a*b*d^2*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)+11/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*arctanh(I*c*x+(-c^2*x^2+1)^(1/2))+5*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-5*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)^2*x^4-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^2+10*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(2*c^2*x^2-2)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-10*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(2*c^2*x^2-2)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-10*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(2*c^2*x^2-2)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+10*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(2*c^2*x^2-2)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-5*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)+5*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)-1/2*a^2*c^2*(-c^2*d*x^2+d)^(5/2)-1/2*a^2/d/x^2*(-c^2*d*x^2+d)^(7/2)-5/6*a^2*c^2*d*(-c^2*d*x^2+d)^(3/2)+5/2*a^2*c^2*d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-5/2*a^2*c^2*(-c^2*d*x^2+d)^(1/2)*d^2-14/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+2/9*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3+b^2*d^2*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+5/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-5/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2/9*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-14/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^4-16/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^2+a*b*d^2*(-d*(c^2*x^2-1))^(1/2)/x/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c-2/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^4+124/27*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x^2+11/6*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2+1/2*b^2*d^2*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/x^2/(c^2*x^2-1)","B"
233,1,3855,541,0.729000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/x^4,x)","\text{output too large to display}"," ",0,"-70*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+294*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^7+5/2*a^2*c^4*d^2*x*(-c^2*d*x^2+d)^(1/2)-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*x^3+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*x+7/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*c^4+14/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-49/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6+7/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^4+147*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^7-49/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*arcsin(c*x)*c^6-35*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(7/2)+4/3*a^2*c^4*x*(-c^2*d*x^2+d)^(5/2)+5/2*a^2*c^4*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+4/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(7/2)+5/3*a^2*c^4*d*x*(-c^2*d*x^2+d)^(3/2)+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)^2*x^3-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)^2*x-56/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+71/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-16/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c^2*x^2-1)*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)^2-5/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^3*d^2*c^3-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-46/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)*c^2+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+294*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-406*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+21*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5-28*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)*d^2*c^3/(3*c^2*x^2-3)-49/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*c^8+56/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*c^6-7/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*c^4+5*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^5-7/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4-49/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)*c^8-21*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^4/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^7+21*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c+7/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3+56/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)*c^6+380/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)*c^4+147*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^5/(c^2*x^2-1)*arcsin(c*x)^2*c^8-203*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*arcsin(c*x)^2*c^6+190/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x/(c^2*x^2-1)*arcsin(c*x)^2*c^4-14*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(3*c^2*x^2-3)*arcsin(c*x)^2-14*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(3*c^2*x^2-3)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-14*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(3*c^2*x^2-3)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)*x^3/(c^2*x^2-1)*(-c^2*x^2+1)*c^6-23/3*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x/(c^2*x^2-1)*arcsin(c*x)^2*c^2+14*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(3*c^2*x^2-3)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))*arcsin(c*x)-5*b^2*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^3+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-a*b*(-d*(c^2*x^2-1))^(1/2)*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/x^3/(c^2*x^2-1)*arcsin(c*x)-5/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*d^2*c^3-5*a*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(63*c^4*x^4-15*c^2*x^2+1)/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c^3+14/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*d^2*c^3+14*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*d^2*c^3/(3*c^2*x^2-3)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))*arcsin(c*x)","B"
234,1,1020,352,0.793000," ","int(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","a^{2} \left(-\frac{x^{4} \sqrt{-c^{2} d \,x^{2}+d}}{5 c^{2} d}+\frac{-\frac{4 x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{15 c^{2} d}-\frac{8 \sqrt{-c^{2} d \,x^{2}+d}}{15 d \,c^{4}}}{c^{2}}\right)+b^{2} \left(\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{1728 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{1728 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(25 \arcsin \left(c x \right)^{2}-2\right) \cos \left(6 \arcsin \left(c x \right)\right)}{4000 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(6 \arcsin \left(c x \right)\right)}{400 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2475 \arcsin \left(c x \right)^{2}-598\right) \cos \left(4 \arcsin \left(c x \right)\right)}{54000 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{29 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{900 c^{6} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+3 \arcsin \left(c x \right)\right)}{576 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{16 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{5 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{576 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(6 \arcsin \left(c x \right)\right)}{160 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(6 \arcsin \left(c x \right)\right)}{800 c^{6} d \left(c^{2} x^{2}-1\right)}-\frac{11 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{240 c^{6} d \left(c^{2} x^{2}-1\right)}+\frac{29 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{1800 c^{6} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/5*x^4/c^2/d*(-c^2*d*x^2+d)^(1/2)+4/5/c^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2)))+b^2*(5/1728*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))/c^6/d/(c^2*x^2-1)+5/1728*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^6/d/(c^2*x^2-1)+1/4000*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*(25*arcsin(c*x)^2-2)*cos(6*arcsin(c*x))-1/400*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*sin(6*arcsin(c*x))-1/54000*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*(2475*arcsin(c*x)^2-598)*cos(4*arcsin(c*x))+29/900*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*sin(4*arcsin(c*x)))+2*a*b*(5/576*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+3*arcsin(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^6/d/(c^2*x^2-1)-5/16*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^6/d/(c^2*x^2-1)+5/576*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-I+3*arcsin(c*x))/c^6/d/(c^2*x^2-1)+1/160*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*cos(6*arcsin(c*x))-1/800*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*sin(6*arcsin(c*x))-11/240*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))+29/1800*(-d*(c^2*x^2-1))^(1/2)/c^6/d/(c^2*x^2-1)*sin(4*arcsin(c*x)))","C"
235,1,858,297,0.945000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} x^{3} \sqrt{-c^{2} d \,x^{2}+d}}{4 c^{2} d}-\frac{3 a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{4} d}+\frac{3 a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{4} \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{8 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{8 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right)^{2}}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{16 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(5 \arcsin \left(c x \right)\right)}{128 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{64 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(5 \arcsin \left(c x \right)\right)}{512 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{15 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{128 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{7 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{64 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{31 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right)}{512 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{8 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-c^{2} x^{2}+1}}{8 c^{5} \sqrt{-d \left(c^{2} x^{2}-1\right)}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{4 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(5 \arcsin \left(c x \right)\right)}{128 c^{5} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(5 \arcsin \left(c x \right)\right)}{32 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{15 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{128 c^{5} d \left(c^{2} x^{2}-1\right)}+\frac{7 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{32 c^{5} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a^2*x^3/c^2/d*(-c^2*d*x^2+d)^(1/2)-3/8*a^2/c^4*x/d*(-c^2*d*x^2+d)^(1/2)+3/8*a^2/c^4/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*x*arcsin(c*x)^2-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*x-1/128*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*cos(5*arcsin(c*x))-1/64*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*sin(5*arcsin(c*x))*arcsin(c*x)^2+1/512*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*sin(5*arcsin(c*x))+15/128*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*cos(3*arcsin(c*x))+7/64*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*sin(3*arcsin(c*x))*arcsin(c*x)^2-31/512*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*sin(3*arcsin(c*x))-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)^2-1/8*a*b/c^5/(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*x-1/128*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*cos(5*arcsin(c*x))-1/32*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*sin(5*arcsin(c*x))+15/128*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*cos(3*arcsin(c*x))+7/32*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","B"
236,1,812,243,0.590000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","a^{2} \left(-\frac{x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}\right)+b^{2} \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{432 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-6 i \arcsin \left(c x \right)+9 \arcsin \left(c x \right)^{2}-2\right)}{432 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(9 \arcsin \left(c x \right)^{2}-2\right) \cos \left(4 \arcsin \left(c x \right)\right)}{216 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{36 c^{4} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 c^{2} x^{2}-2 i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+3 \arcsin \left(c x \right)\right)}{144 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{8 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-c^{2} x^{2}+1}\, x c +2 c^{2} x^{2}-1\right) \left(-i+3 \arcsin \left(c x \right)\right)}{144 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{24 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"a^2*(-1/3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3/d/c^4*(-c^2*d*x^2+d)^(1/2))+b^2*(1/432*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))/c^4/d/(c^2*x^2-1)+1/432*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-6*I*arcsin(c*x)+9*arcsin(c*x)^2-2)/c^4/d/(c^2*x^2-1)-1/216*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*(9*arcsin(c*x)^2-2)*cos(4*arcsin(c*x))+1/36*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*sin(4*arcsin(c*x)))+2*a*b*(1/144*(-d*(c^2*x^2-1))^(1/2)*(2*c^2*x^2-2*I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+3*arcsin(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^4/d/(c^2*x^2-1)-3/8*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^4/d/(c^2*x^2-1)+1/144*(-d*(c^2*x^2-1))^(1/2)*(2*I*(-c^2*x^2+1)^(1/2)*x*c+2*c^2*x^2-1)*(-I+3*arcsin(c*x))/c^4/d/(c^2*x^2-1)-1/24*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))+1/72*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*sin(4*arcsin(c*x)))","C"
237,1,604,180,0.431000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{6 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right)^{2}}{8 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{16 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{8 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-c^{2} x^{2}+1}}{8 c^{3} \sqrt{-d \left(c^{2} x^{2}-1\right)}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{4 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{4 c^{3} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^3+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*x*arcsin(c*x)^2-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*x+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)*cos(3*arcsin(c*x))+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*sin(3*arcsin(c*x))*arcsin(c*x)^2-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*sin(3*arcsin(c*x))-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2-1/8*a*b/c^3/(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*arcsin(c*x)*x+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*cos(3*arcsin(c*x))+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","B"
238,1,316,134,0.222000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+b^{2} \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(\arcsin \left(c x \right)^{2}-2+2 i \arcsin \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)^{2}-2-2 i \arcsin \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)+2 a b \left(-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(c^{2} x^{2}-i \sqrt{-c^{2} x^{2}+1}\, x c -1\right) \left(i+\arcsin \left(c x \right)\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \left(\arcsin \left(c x \right)-i\right)}{2 c^{2} d \left(c^{2} x^{2}-1\right)}\right)"," ",0,"-a^2/c^2/d*(-c^2*d*x^2+d)^(1/2)+b^2*(-1/2*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(arcsin(c*x)^2-2+2*I*arcsin(c*x))/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)^2-2-2*I*arcsin(c*x))/c^2/d/(c^2*x^2-1))+2*a*b*(-1/2*(-d*(c^2*x^2-1))^(1/2)*(c^2*x^2-I*(-c^2*x^2+1)^(1/2)*x*c-1)*(I+arcsin(c*x))/c^2/d/(c^2*x^2-1)-1/2*(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*(arcsin(c*x)-I)/c^2/d/(c^2*x^2-1))","C"
239,1,143,43,0.076000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{3 c d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{c d \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^3-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2","B"
240,1,388,275,0.275000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{\sqrt{d}}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(2 i \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)+\arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-\arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)-2 \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-\polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+\polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(2*I*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))-2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2)))/d/(c^2*x^2-1)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*(I*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+polylog(2,I*c*x+(-c^2*x^2+1)^(1/2)))","A"
241,1,638,187,0.378000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{d x}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, c}{\left(c^{2} x^{2}-1\right) d}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{\left(c^{2} x^{2}-1\right) x d}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c}{d \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) x d}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2/d/x*(-c^2*d*x^2+d)^(1/2)+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*c-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)*x/d*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/x/d-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)*x/d*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/x/d-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c","B"
242,1,1107,406,0.563000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{2 d \,x^{2}}-\frac{a^{2} c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 \sqrt{d}}-\frac{b^{2} \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{2 d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \arcsin \left(c x \right)^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{2 x^{2} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}-\frac{i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d \left(c^{2} x^{2}-1\right)}+\frac{i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arctanh \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{x d \left(c^{2} x^{2}-1\right)}+\frac{a b \arcsin \left(c x \right) \sqrt{-d \left(c^{2} x^{2}-1\right)}}{x^{2} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}-\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a^2/d/x^2*(-c^2*d*x^2+d)^(1/2)-1/2*a^2*c^2/d^(1/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/2*b^2*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2+b^2*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+1/2*b^2*arcsin(c*x)^2*(-d*(c^2*x^2-1))^(1/2)/x^2/d/(c^2*x^2-1)-1/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*arctanh(I*c*x+(-c^2*x^2+1)^(1/2))-a*b*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c^2+a*b*(-d*(c^2*x^2-1))^(1/2)/x/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*c+a*b*arcsin(c*x)*(-d*(c^2*x^2-1))^(1/2)/x^2/d/(c^2*x^2-1)-a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","B"
243,1,2320,301,0.709000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(1/2),x)","\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right)^{2} c^{6}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right)^{2} c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} c^{2}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d x}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d x}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{3}}-\frac{4 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c^{3}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} c^{5}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) \arcsin \left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{8 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \left(-c^{2} x^{2}+1\right) c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 a^{2} c^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d x}-\frac{2 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{4 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \left(-c^{2} x^{2}+1\right) \arcsin \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{4 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \arcsin \left(c x \right)^{2}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} \arcsin \left(c x \right) c^{8}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}\, c^{5}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{4 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}-1\right) c^{3}}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{5} c^{8}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \,c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{4 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3 d \left(c^{2} x^{2}-1\right)}+\frac{4 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{3 d \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} c^{3}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{2}}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d x}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d \,x^{2}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3} \arcsin \left(c x \right) c^{6}}{\left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right) c^{4}}{3 \left(3 c^{4} x^{4}-2 c^{2} x^{2}-1\right) d}-\frac{a^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,x^{3}}"," ",0,"b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-2*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*arcsin(c*x)^2*c^6+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*arcsin(c*x)^2*c^4+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x*arcsin(c*x)^2*c^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*(-c^2*x^2+1)*c^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*c^3+a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*c^3*(-c^2*x^2+1)^(1/2)+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^3*arcsin(c*x)-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^5*c^8-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*c^6+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^3*arcsin(c*x)^2-4*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*(-c^2*x^2+1)*arcsin(c*x)*c^6-2/3*a^2*c^2/d/x*(-c^2*d*x^2+d)^(1/2)+8/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*arcsin(c*x)*c^3-4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*(-c^2*x^2+1)*c^6-2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*(-c^2*x^2+1)*c^4-4/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-4/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c-2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3+2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*arcsin(c*x)*c^6-I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^2*(-c^2*x^2+1)^(1/2)*c^5+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x*arcsin(c*x)*c^2+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d/x^2*(-c^2*x^2+1)^(1/2)*c-4/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3-4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^5*c^8+2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*c^6+2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*c^4+2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*arcsin(c*x)*c^4+4/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^3*arcsin(c*x)^2+4/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+4/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)*c^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^5*arcsin(c*x)*c^8-4*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x^3*arcsin(c*x)*c^6+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*arcsin(c*x)*c^4-1/3*a^2/d/x^3*(-c^2*d*x^2+d)^(1/2)-4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(3*c^4*x^4-2*c^2*x^2-1)/d*x*(-c^2*x^2+1)*arcsin(c*x)*c^4","B"
244,1,1085,516,0.826000," ","int(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{4}}{3 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a^{2} x^{2}}{3 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{8 a^{2}}{3 c^{6} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{24 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(4 \arcsin \left(c x \right)\right)}{36 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{377 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{108 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{65 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{24 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(4 \arcsin \left(c x \right)\right)}{108 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2}}{3 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}-\frac{94 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{27 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{31 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{9 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}+\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{3 d^{2} c^{4} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{31 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{9 d^{2} c^{5} \left(c^{2} x^{2}-1\right)}-\frac{65 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{12 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(4 \arcsin \left(c x \right)\right)}{36 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{d^{2} c^{6} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(4 \arcsin \left(c x \right)\right)}{12 d^{2} c^{6} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a^2*x^4/c^2/d/(-c^2*d*x^2+d)^(1/2)-4/3*a^2/c^4*x^2/d/(-c^2*d*x^2+d)^(1/2)+8/3*a^2/c^6/d/(-c^2*d*x^2+d)^(1/2)+1/24*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*cos(4*arcsin(c*x))*arcsin(c*x)^2-1/36*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)*sin(4*arcsin(c*x))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+377/108*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)-65/24*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)^2-1/108*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*cos(4*arcsin(c*x))+5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arcsin(c*x)^2*x^2-94/27*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*x^2+31/9*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^4/(c^2*x^2-1)*arcsin(c*x)*x^2+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+31/9*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-65/12*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)-1/36*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*sin(4*arcsin(c*x))-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+1/12*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/c^6/(c^2*x^2-1)*arcsin(c*x)*cos(4*arcsin(c*x))","B"
245,1,973,402,0.935000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{3}}{2 c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a^{2} x}{2 c^{4} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{4} d \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{2 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{9 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \arcsin \left(c x \right)^{2}}{8 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{16 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sin \left(3 \arcsin \left(c x \right)\right)}{16 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{2 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{9 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{4 c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{4 c^{5} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a^2*x^3/c^2/d/(-c^2*d*x^2+d)^(1/2)+3/2*a^2/c^4*x/d/(-c^2*d*x^2+d)^(1/2)-3/2*a^2/c^4/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)^3-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^5/d^2/(c^2*x^2-1)+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)^2-1/8*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^5/d^2/(c^2*x^2-1)-9/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*x*arcsin(c*x)^2+1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*x-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)*cos(3*arcsin(c*x))-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*sin(3*arcsin(c*x))*arcsin(c*x)^2+1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*sin(3*arcsin(c*x))+3/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)^2+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/8*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)-9/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)*x-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*cos(3*arcsin(c*x))-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^2/(c^2*x^2-1)*arcsin(c*x)*sin(3*arcsin(c*x))","B"
246,1,830,401,0.544000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2} x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a^{2}}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a^2/d/c^4/(-c^2*d*x^2+d)^(1/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x^2-4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)","B"
247,1,581,248,0.412000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{3 d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{2} c^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{d^{2} c^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)^3+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/d^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/d^2/c^2/(c^2*x^2-1)*x-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)^2+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/c^3/(c^2*x^2-1)*arcsin(c*x)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/c^2/(c^2*x^2-1)*x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/c^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","B"
248,1,540,213,0.198000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/c^2/d/(-c^2*d*x^2+d)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)","B"
249,1,425,199,0.155000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*x/d/(-c^2*d*x^2+d)^(1/2)+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/c/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/d^2/(c^2*x^2-1)*x-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)","B"
250,1,1096,490,0.405000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2}}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{3}{2}}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2/d/(-c^2*d*x^2+d)^(1/2)-a^2/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-4*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))","B"
251,1,807,346,0.380000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a^{2}}{d x \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a^{2} c^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, c}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{\left(c^{2} x^{2}-1\right) d^{2} x}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{4 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2}}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) d^{2} x}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{4}-1\right) c}{\left(c^{2} x^{2}-1\right) d^{2}}"," ",0,"-a^2/d/x/(-c^2*d*x^2+d)^(1/2)+2*a^2*c^2/d*x/(-c^2*d*x^2+d)^(1/2)+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*c-2*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/d^2*x*c^2+b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/(c^2*x^2-1)/d^2/x-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+4*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*arcsin(c*x)*c-4*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/d^2*x*c^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/(c^2*x^2-1)/d^2/x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/d^2*ln((I*c*x+(-c^2*x^2+1)^(1/2))^4-1)*c","B"
252,1,1490,641,0.655000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x)","-\frac{4 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{3 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right) x^{2}}-\frac{3 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d^{2} \left(c^{2} x^{2}-1\right) x^{2}}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} c^{2}}{2 d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 a^{2} c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{3}{2}}}-\frac{a^{2}}{2 d \,x^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a^{2} c^{2}}{2 d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right) d^{2}}-\frac{3 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 \left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{\left(c^{2} x^{2}-1\right) d^{2}}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{\left(c^{2} x^{2}-1\right) d^{2}}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{d^{2} \left(c^{2} x^{2}-1\right) x}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c}{d^{2} \left(c^{2} x^{2}-1\right) x}"," ",0,"3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-4*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x^2*arcsin(c*x)^2-3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*c^2+a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x^2*arcsin(c*x)-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2*c^2-3/2*a^2*c^2/d^(3/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)-1/2*a^2/d/x^2/(-c^2*d*x^2+d)^(1/2)+3/2*a^2*c^2/d/(-c^2*d*x^2+d)^(1/2)-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x*(-c^2*x^2+1)^(1/2)*c+b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/x*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c+3/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-3/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/d^2*c^2*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))","B"
253,1,2845,470,0.749000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(3/2),x)","\text{output too large to display}"," ",0,"8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*arcsin(c*x)*c^4+16/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*arcsin(c*x)^2-10/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-10/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+32/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*c^3+64/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*(-c^2*x^2+1)*c^8-32/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*(-c^2*x^2+1)*c^6-8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*(-c^2*x^2+1)*c^4-16/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*(-c^2*x^2+1)*arcsin(c*x)*c^4+64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*(-c^2*x^2+1)*arcsin(c*x)*c^8-32/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*(-c^2*x^2+1)*arcsin(c*x)*c^6+7/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*c^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x*c^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^3*arcsin(c*x)^2+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^7*c^10-40/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*c^8-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*arcsin(c*x)^2*c^6+8*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*arcsin(c*x)^2*c^4+4*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x*arcsin(c*x)^2*c^2+8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*(-c^2*x^2+1)*c^8-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*(-c^2*x^2+1)*c^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*c^3+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*c^3+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^3*arcsin(c*x)-1/3*a^2/d/x^3/(-c^2*d*x^2+d)^(1/2)-128/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5-4/3*a^2*c^2/d/x/(-c^2*d*x^2+d)^(1/2)+8/3*a^2*c^4/d*x/(-c^2*d*x^2+d)^(1/2)-32*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*arcsin(c*x)*c^8+8*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*arcsin(c*x)*c^6-8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^2*(-c^2*x^2+1)^(1/2)*c^5+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3+64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^7*arcsin(c*x)*c^10+8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*c^4+64/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^7*c^10-32*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^5*c^8+8*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*c^6+1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x^2*(-c^2*x^2+1)^(1/2)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)*c^3-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^2/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c^3+8*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2/x*arcsin(c*x)*c^2-128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^3*arcsin(c*x)*c^6+16*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x*arcsin(c*x)*c^4+10/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+10/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*c^3*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^4*x^4-7*c^2*x^2-1)/d^2*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5","B"
254,1,1201,505,0.814000," ","int(x^5*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 a^{2} x^{2}}{c^{4} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{10 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{8 a^{2}}{3 c^{6} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{11 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{11 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{11 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{6} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{5}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{5}}-\frac{a^{2} x^{4}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{6}}"," ",0,"2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)+4*a^2/c^4*x^2/d/(-c^2*d*x^2+d)^(3/2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6+2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*x^2+b^2*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*x^2-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6*arcsin(c*x)-b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)^2*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arcsin(c*x)^2*x^2-8/3*a^2/c^6/d/(-c^2*d*x^2+d)^(3/2)+11/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-11/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)*x^2+4*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arcsin(c*x)*x^2-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^5*(-c^2*x^2+1)^(1/2)*x-11/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+11/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^5*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+11/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-11/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^6/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-a^2*x^4/c^2/d/(-c^2*d*x^2+d)^(3/2)-5/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^6*arcsin(c*x)^2","B"
255,1,1304,393,1.003000," ","int(x^4*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{a^{2} x^{3}}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{a^{2} x}{c^{4} d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{4} d^{2} \sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}+\frac{8 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{3}}-\frac{8 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{4 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{3}}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}-\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{3}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}-\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}+\frac{8 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3}}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2}}{c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{5}}-\frac{16 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{4}}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{8 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 c^{5} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}"," ",0,"1/3*a^2*x^3/c^2/d/(-c^2*d*x^2+d)^(3/2)-a^2/c^4/d^2*x/(-c^2*d*x^2+d)^(1/2)+a^2/c^4/d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^3*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^2-4/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)^2*x^3-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*arcsin(c*x)^2*x-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^3*x^2*(-c^2*x^2+1)^(1/2)+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*x-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*x^3-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)+8/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)^3-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)^2+1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*(-c^2*x^2+1)^(1/2)-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^5*(-c^2*x^2+1)^(1/2)-16/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^4*arcsin(c*x)*x+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^5/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-8/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^5/d^3/(c^2*x^2-1)*arcsin(c*x)^2+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)*x^3","B"
256,1,829,315,0.562000," ","int(x^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{a^{2} x^{2}}{c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{2 a^{2}}{3 d \,c^{4} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}+\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{2}}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{3}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2} c^{4}}-\frac{5 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{3 c^{4} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*x^2/c^2/d/(-c^2*d*x^2+d)^(3/2)-2/3*a^2/d/c^4/(-c^2*d*x^2+d)^(3/2)+b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arcsin(c*x)^2*x^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*x^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arcsin(c*x)^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4+5/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-5/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-5/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^2*arcsin(c*x)*x^2-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^3*(-c^2*x^2+1)^(1/2)*x-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2/c^4*arcsin(c*x)-5/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)+5/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^4/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)","B"
257,1,3277,312,0.497000," ","int(x^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+2/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*arcsin(c*x)*x^7-a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*x^4+1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*(-c^2*x^2+1)*arcsin(c*x)*x^3-2/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^3/(c^2*x^2-1)*arcsin(c*x)^2-1/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^3/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*x^2*(-c^2*x^2+1)^(1/2)+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*x^4-I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3*(-c^2*x^2+1)^(1/2)*x^6+2/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*arcsin(c*x)*x^5-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*arcsin(c*x)*x^7-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*arcsin(c*x)*x^5+a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*x^2+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*x^7+2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*x^5+1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*(-c^2*x^2+1)*x^3-1/3*a^2/c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3+1/3*a^2/c^2*x/d/(-c^2*d*x^2+d)^(3/2)+I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^6-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*(-c^2*x^2+1)*arcsin(c*x)*x^5-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^4+4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*x^2-4/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^3/(c^2*x^2-1)*arcsin(c*x)-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*(-c^2*x^2+1)*x^5-2/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+2*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6-4*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+8/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*(-c^2*x^2+1)*x^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*x^7+b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*x^5+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*arcsin(c*x)^2*x^3+b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^4*arcsin(c*x)^2*x^7-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*arcsin(c*x)^2*x^5+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*c^2*(-c^2*x^2+1)*x^5+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^2*(-c^2*x^2+1)*x-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)-1/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*arcsin(c*x)*x^3+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*arcsin(c*x)*x^3-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)/c^3*(-c^2*x^2+1)^(1/2)-1/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^8*x^8-9*c^6*x^6+10*c^4*x^4-5*c^2*x^2+1)*x^3","B"
258,1,762,281,0.293000," ","int(x*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\frac{a^{2}}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) c^{2}}-\frac{a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right)}{3 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}"," ",0,"1/3*a^2/c^2/d/(-c^2*d*x^2+d)^(3/2)-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2+1/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c*(-c^2*x^2+1)^(1/2)*x+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/c^2*arcsin(c*x)-1/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)+1/3*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)","B"
259,1,2896,293,0.235000," ","int((a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*(-c^2*x^2+1)*x^5+14/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^2-10/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*(-c^2*x^2+1)*x^3-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*x^4+8/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*arcsin(c*x)+4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^5-10/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^3-16/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x+1/3*a^2*x/d/(-c^2*d*x^2+d)^(3/2)+2/3*a^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^2-I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*(-c^2*x^2+1)^(1/2)*x^4-14/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^5+4/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*arcsin(c*x)^2+16/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^3+4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*arcsin(c*x)*x^7+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*(-c^2*x^2+1)*x-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-4/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+7/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*x^2*(-c^2*x^2+1)^(1/2)+2/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+16/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^3+2*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+4/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^7-14/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^5+34/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^3-4*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^5-8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)+28/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2-4*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x-3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^5-4*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)^2*x+13/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^3+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^7+17/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)^2*x^3-4/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^3+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^5+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)^2*x^5+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)-8*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x-2*I*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x","B"
260,1,1373,580,0.481000," ","int((a+b*arcsin(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x)","-\frac{2 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{14 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x c}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x c}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 i a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2} c^{2}}{d^{3} \left(c^{2} x^{2}-1\right)^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{7 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{7 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{7 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{a^{2}}{d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{d^{\frac{5}{2}}}+\frac{a^{2}}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{3 d^{3} \left(c^{2} x^{2}-1\right)^{2}}"," ",0,"-1/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)*x*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)*x^2*c^2+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*c+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-14/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*c^2*x^2-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))+8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)^2*x^2*c^2-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-7/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+7/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+7/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-7/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2+a^2/d^2/(-c^2*d*x^2+d)^(1/2)-a^2/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+1/3*a^2/d/(-c^2*d*x^2+d)^(3/2)+4/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)^2*arcsin(c*x)^2","B"
261,1,3777,443,0.492000," ","int((a+b*arcsin(c*x))^2/x^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"4/3*a^2*c^2*x/d/(-c^2*d*x^2+d)^(3/2)+280/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*arcsin(c*x)*c^6-8/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^4*(-c^2*x^2+1)^(1/2)*c^5+64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^9*arcsin(c*x)*c^10-224/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*arcsin(c*x)*c^8-10/3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)*c-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/d^3/(c^2*x^2-1)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2-1)*c+64/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^9*c^10-224/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*c^8+280/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*c^6-48*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*c^4+8*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*c^2-128/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*arcsin(c*x)*c^6+112*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*arcsin(c*x)*c^4-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*(-c^2*x^2+1)^(1/2)*c^3-88*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*arcsin(c*x)*c^2+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+5/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+16/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*arcsin(c*x)^2-48*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*arcsin(c*x)*c^4+17/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*(-c^2*x^2+1)^(1/2)*c^3+8*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*arcsin(c*x)*c^2-24*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-8/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-10/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*c*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+3*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*(-c^2*x^2+1)^(1/2)*c+18*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3/x*arcsin(c*x)-8*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*(-c^2*x^2+1)*c^2-88/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*(-c^2*x^2+1)*c^6+80/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*(-c^2*x^2+1)*c^4+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^9*c^10-40*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*c^8+160/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*c^6-29*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*c^4+5*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*c^2+9*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3/x*arcsin(c*x)^2+8/3*a^2*c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+272/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3-128/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^4*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5-a^2/d/x/(-c^2*d*x^2+d)^(3/2)+32/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*(-c^2*x^2+1)*c^8-64/3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*arcsin(c*x)^2*c^6+56*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*arcsin(c*x)^2*c^4-44*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*arcsin(c*x)^2*c^2+3*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c-3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*(-c^2*x^2+1)^(1/2)*c+136/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^3-8*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*(-c^2*x^2+1)*arcsin(c*x)*c^2+64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*(-c^2*x^2+1)*arcsin(c*x)*c^8-64/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^4*(-c^2*x^2+1)^(1/2)*arcsin(c*x)^2*c^5-160/3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*(-c^2*x^2+1)*arcsin(c*x)*c^6-48*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c-160/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^5*(-c^2*x^2+1)*c^6+40*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*(-c^2*x^2+1)*c^4+64/3*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^7*(-c^2*x^2+1)*c^8-8*I*a*b*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x*(-c^2*x^2+1)*c^2+32/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^2*x^2-1)*arcsin(c*x)*c+40*I*b^2*(-d*(c^2*x^2-1))^(1/2)/(8*c^6*x^6-25*c^4*x^4+26*c^2*x^2-9)/d^3*x^3*(-c^2*x^2+1)*arcsin(c*x)*c^4","B"
262,1,1876,739,0.744000," ","int((a+b*arcsin(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x)","-\frac{a^{2}}{2 d \,x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a^{2} c^{2}}{6 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{5 a^{2} c^{2}}{2 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}-\frac{5 a^{2} c^{2} \ln \left(\frac{2 d +2 \sqrt{d}\, \sqrt{-c^{2} d \,x^{2}+d}}{x}\right)}{2 d^{\frac{5}{2}}}+\frac{5 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{26 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arctan \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{20 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) c^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}-\frac{5 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right)^{2} c^{4}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)}{2 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{13 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{13 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right)^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{2 d^{3} \left(c^{2} x^{2}-1\right)}+\frac{13 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{13 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{3 d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{5 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} \arcsin \left(c x \right) c^{4}}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x \sqrt{-c^{2} x^{2}+1}\, c^{3}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, c}{d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x}-\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}+\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, -i c x -\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{5 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \polylog \left(3, i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} c^{4}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}+\frac{10 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} c^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2}}{2 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right) x^{2}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2}}{3 d^{3} \left(c^{4} x^{4}-2 c^{2} x^{2}+1\right)}"," ",0,"-1/2*a^2/d/x^2/(-c^2*d*x^2+d)^(3/2)+5/6*a^2*c^2/d/(-c^2*d*x^2+d)^(3/2)+5/2*a^2*c^2/d^2/(-c^2*d*x^2+d)^(1/2)-5/2*a^2*c^2/d^(5/2)*ln((2*d+2*d^(1/2)*(-c^2*d*x^2+d)^(1/2))/x)+5*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-26/3*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arctan(I*c*x+(-c^2*x^2+1)^(1/2))-5*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-5*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-5*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+5*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-5/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)^2*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-13/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+13/3*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+13/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-13/3*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+5/2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*arcsin(c*x)^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^3+20/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)*c^2-a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)-5/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*arcsin(c*x)^2*c^4-b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+5*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*polylog(3,-I*c*x-(-c^2*x^2+1)^(1/2))-5*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*polylog(3,I*c*x+(-c^2*x^2+1)^(1/2))+b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*c^2/d^3/(c^2*x^2-1)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c-5*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*arcsin(c*x)*c^4+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x*(-c^2*x^2+1)^(1/2)*c^3-a*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x*(-c^2*x^2+1)^(1/2)*c-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*x^2*c^4+10/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*arcsin(c*x)^2*c^2-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)/x^2*arcsin(c*x)^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)/d^3/(c^4*x^4-2*c^2*x^2+1)*c^2","B"
263,1,5229,517,0.789000," ","int((a+b*arcsin(c*x))^2/x^4/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
264,1,129,133,0.125000," ","int(x^4*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\frac{-16 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+8 a^{4} x^{4} \arcsin \left(a x \right)+2 a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}-24 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x a +24 a^{2} x^{2} \arcsin \left(a x \right)+8 \arcsin \left(a x \right)^{3}+15 a x \sqrt{-a^{2} x^{2}+1}-15 \arcsin \left(a x \right)}{64 a^{5}}"," ",0,"1/64*(-16*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x^3*a^3+8*a^4*x^4*arcsin(a*x)+2*a^3*x^3*(-a^2*x^2+1)^(1/2)-24*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x*a+24*a^2*x^2*arcsin(a*x)+8*arcsin(a*x)^3+15*a*x*(-a^2*x^2+1)^(1/2)-15*arcsin(a*x))/a^5","A"
265,1,127,106,0.111000," ","int(x^3*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\left(9 a^{4} x^{4} \arcsin \left(a x \right)^{2}+9 \arcsin \left(a x \right)^{2} x^{2} a^{2}+6 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-2 a^{4} x^{4}-38 a^{2} x^{2}-18 \arcsin \left(a x \right)^{2}+36 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a +40\right) \sqrt{-a^{2} x^{2}+1}}{27 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/27/a^4*(9*a^4*x^4*arcsin(a*x)^2+9*arcsin(a*x)^2*x^2*a^2+6*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3-2*a^4*x^4-38*a^2*x^2-18*arcsin(a*x)^2+36*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a+40)*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
266,1,71,75,0.145000," ","int(x^2*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\frac{-6 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x a +6 a^{2} x^{2} \arcsin \left(a x \right)+2 \arcsin \left(a x \right)^{3}+3 a x \sqrt{-a^{2} x^{2}+1}-3 \arcsin \left(a x \right)}{12 a^{3}}"," ",0,"1/12*(-6*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x*a+6*a^2*x^2*arcsin(a*x)+2*arcsin(a*x)^3+3*a*x*(-a^2*x^2+1)^(1/2)-3*arcsin(a*x))/a^3","A"
267,1,80,51,0.099000," ","int(x*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\arcsin \left(a x \right)^{2} x^{2} a^{2}-\arcsin \left(a x \right)^{2}+2 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a -2 a^{2} x^{2}+2\right)}{a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a^2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)*(arcsin(a*x)^2*x^2*a^2-arcsin(a*x)^2+2*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a-2*a^2*x^2+2)","A"
268,1,12,11,0.004000," ","int(arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\frac{\arcsin \left(a x \right)^{3}}{3 a}"," ",0,"1/3*arcsin(a*x)^3/a","A"
269,1,161,130,0.125000," ","int(arcsin(a*x)^2/x/(-a^2*x^2+1)^(1/2),x)","\arcsin \left(a x \right)^{2} \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)-2 i \arcsin \left(a x \right) \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)+2 \polylog \left(3, i a x +\sqrt{-a^{2} x^{2}+1}\right)-\arcsin \left(a x \right)^{2} \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)+2 i \arcsin \left(a x \right) \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)-2 \polylog \left(3, -i a x -\sqrt{-a^{2} x^{2}+1}\right)"," ",0,"arcsin(a*x)^2*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-2*I*arcsin(a*x)*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))+2*polylog(3,I*a*x+(-a^2*x^2+1)^(1/2))-arcsin(a*x)^2*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+2*I*arcsin(a*x)*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))-2*polylog(3,-I*a*x-(-a^2*x^2+1)^(1/2))","A"
270,1,148,92,0.221000," ","int(arcsin(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x)","\frac{\left(i a x -\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{2}}{x}+2 a \arcsin \left(a x \right) \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)+2 a \arcsin \left(a x \right) \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)-2 i \arcsin \left(a x \right)^{2} a -2 i \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right) a -2 i \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right) a"," ",0,"(I*a*x-(-a^2*x^2+1)^(1/2))/x*arcsin(a*x)^2+2*a*arcsin(a*x)*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+2*a*arcsin(a*x)*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-2*I*arcsin(a*x)^2*a-2*I*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))*a-2*I*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))*a","A"
271,1,269,195,0.329000," ","int(arcsin(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) \left(a^{2} x^{2} \arcsin \left(a x \right)-2 a x \sqrt{-a^{2} x^{2}+1}-\arcsin \left(a x \right)\right)}{2 \left(a^{2} x^{2}-1\right) x^{2}}+\frac{a^{2} \arcsin \left(a x \right)^{2} \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)}{2}-i a^{2} \arcsin \left(a x \right) \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)-\frac{a^{2} \arcsin \left(a x \right)^{2} \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)}{2}+i a^{2} \arcsin \left(a x \right) \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)+a^{2} \polylog \left(3, i a x +\sqrt{-a^{2} x^{2}+1}\right)-a^{2} \polylog \left(3, -i a x -\sqrt{-a^{2} x^{2}+1}\right)-2 \arctanh \left(i a x +\sqrt{-a^{2} x^{2}+1}\right) a^{2}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)/x^2*arcsin(a*x)*(a^2*x^2*arcsin(a*x)-2*a*x*(-a^2*x^2+1)^(1/2)-arcsin(a*x))+1/2*a^2*arcsin(a*x)^2*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-I*a^2*arcsin(a*x)*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))-1/2*a^2*arcsin(a*x)^2*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+I*a^2*arcsin(a*x)*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))+a^2*polylog(3,I*a*x+(-a^2*x^2+1)^(1/2))-a^2*polylog(3,-I*a*x-(-a^2*x^2+1)^(1/2))-2*arctanh(I*a*x+(-a^2*x^2+1)^(1/2))*a^2","A"
272,1,52,36,0.053000," ","int(arcsin(a*x)^2/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{3}}{3 a c \left(a^{2} x^{2}-1\right)}"," ",0,"-1/3*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c/(a^2*x^2-1)*arcsin(a*x)^3","A"
273,1,169,183,0.208000," ","int(arcsin(a*x)^2/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i \sqrt{-a^{2} x^{2}+1}+a x \right) \arcsin \left(a x \right)^{2}}{c^{2} a \left(a^{2} x^{2}-1\right)}+\frac{i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \arcsin \left(a x \right) \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)+2 \arcsin \left(a x \right)^{2}+\polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)\right)}{c^{2} a \left(a^{2} x^{2}-1\right)}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(I*(-a^2*x^2+1)^(1/2)+a*x)*arcsin(a*x)^2/c^2/a/(a^2*x^2-1)+I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/c^2/a/(a^2*x^2-1)*(2*I*arcsin(a*x)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+2*arcsin(a*x)^2+polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2))","A"
274,1,365,265,0.273000," ","int(arcsin(a*x)^2/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}-2 i \sqrt{-a^{2} x^{2}+1}-3 a x \right) \left(-2 i \arcsin \left(a x \right) x^{4} a^{4}-2 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+i \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-a^{4} x^{4}+3 \arcsin \left(a x \right)^{2} x^{2} a^{2}+4 i \arcsin \left(a x \right) x^{2} a^{2}+3 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a -i \sqrt{-a^{2} x^{2}+1}\, x a +3 a^{2} x^{2}-4 \arcsin \left(a x \right)^{2}-2 i \arcsin \left(a x \right)-2\right)}{3 c^{3} \left(3 a^{6} x^{6}-10 a^{4} x^{4}+11 a^{2} x^{2}-4\right) a}+\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \arcsin \left(a x \right) \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)+2 \arcsin \left(a x \right)^{2}+\polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)\right)}{3 a \,c^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/3*(-c*(a^2*x^2-1))^(1/2)*(2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3-2*I*(-a^2*x^2+1)^(1/2)-3*a*x)*(-2*I*arcsin(a*x)*x^4*a^4-2*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3+I*(-a^2*x^2+1)^(1/2)*x^3*a^3-a^4*x^4+3*arcsin(a*x)^2*x^2*a^2+4*I*arcsin(a*x)*x^2*a^2+3*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a-I*(-a^2*x^2+1)^(1/2)*x*a+3*a^2*x^2-4*arcsin(a*x)^2-2*I*arcsin(a*x)-2)/c^3/(3*a^6*x^6-10*a^4*x^4+11*a^2*x^2-4)/a+2/3*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*I*arcsin(a*x)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+2*arcsin(a*x)^2+polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2))/a/c^3/(a^2*x^2-1)","A"
275,1,556,358,0.345000," ","int(arcsin(a*x)^2/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{5} x^{5}-20 a^{3} x^{3}+8 i \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+15 a x -16 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+8 i \sqrt{-a^{2} x^{2}+1}\right) \left(-280 i \arcsin \left(a x \right) x^{6} a^{6}+64 \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x^{7} a^{7}+126 i \sqrt{-a^{2} x^{2}+1}\, x^{5} a^{5}+32 x^{8} a^{8}-156 i \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-248 \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x^{5} a^{5}-328 i \arcsin \left(a x \right) x^{2} a^{2}-142 a^{6} x^{6}+80 a^{4} x^{4} \arcsin \left(a x \right)^{2}+456 i \arcsin \left(a x \right) x^{4} a^{4}+340 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+62 i \sqrt{-a^{2} x^{2}+1}\, x a +265 a^{4} x^{4}-190 \arcsin \left(a x \right)^{2} x^{2} a^{2}-32 i \sqrt{-a^{2} x^{2}+1}\, x^{7} a^{7}-165 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a +88 i \arcsin \left(a x \right)-235 a^{2} x^{2}+128 \arcsin \left(a x \right)^{2}+64 i \arcsin \left(a x \right) x^{8} a^{8}+80\right)}{30 c^{4} \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 a^{6} x^{6}-517 a^{4} x^{4}+287 a^{2} x^{2}-64\right) a}+\frac{8 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \arcsin \left(a x \right) \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)+2 \arcsin \left(a x \right)^{2}+\polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)\right)}{15 a \,c^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/30*(-c*(a^2*x^2-1))^(1/2)*(8*a^5*x^5-20*a^3*x^3+8*I*(-a^2*x^2+1)^(1/2)*x^4*a^4+15*a*x-16*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+8*I*(-a^2*x^2+1)^(1/2))*(-280*I*arcsin(a*x)*x^6*a^6+64*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x^7*a^7+126*I*(-a^2*x^2+1)^(1/2)*x^5*a^5+32*x^8*a^8-156*I*(-a^2*x^2+1)^(1/2)*x^3*a^3-248*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x^5*a^5-328*I*arcsin(a*x)*x^2*a^2-142*a^6*x^6+80*a^4*x^4*arcsin(a*x)^2+456*I*arcsin(a*x)*x^4*a^4+340*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3+62*I*(-a^2*x^2+1)^(1/2)*x*a+265*a^4*x^4-190*arcsin(a*x)^2*x^2*a^2-32*I*(-a^2*x^2+1)^(1/2)*x^7*a^7-165*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a+88*I*arcsin(a*x)-235*a^2*x^2+128*arcsin(a*x)^2+64*I*arcsin(a*x)*x^8*a^8+80)/c^4/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a+8/15*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*I*arcsin(a*x)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+2*arcsin(a*x)^2+polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2))/a/c^4/(a^2*x^2-1)","A"
276,0,0,1228,22.230000," ","int(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{3} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","F"
277,0,0,696,10.615000," ","int(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","F"
278,0,0,333,4.483000," ","int(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)*(a+b*arcsin(c*x))^2,x)","F"
279,0,0,29,0.594000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{-c^{2} d \,x^{2}+d}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d),x)","F"
280,0,0,253,0.747000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{2}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^2,x)","F"
281,0,0,594,0.838000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{3}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^3,x)","F"
282,0,0,895,12.278000," ","int(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","F"
283,0,0,463,4.897000," ","int(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int x^{m} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
284,0,0,187,1.793000," ","int(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int x^{m} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
285,0,0,29,0.932000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","F"
286,0,0,29,0.815000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","F"
287,0,0,29,0.849000," ","int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\int \frac{x^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","F"
288,0,0,24,0.702000," ","int(x^m*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsin \left(a x \right)^{2}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsin(a*x)^2/(-a^2*x^2+1)^(1/2),x)","F"
289,1,278,322,0.142000," ","int((-a^2*c*x^2+c)^3*arcsin(a*x)^3,x)","-\frac{c^{3} \left(1929375 \arcsin \left(a x \right)^{3} a^{7} x^{7}+826875 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{6} x^{6}-8103375 \arcsin \left(a x \right)^{3} a^{5} x^{5}-236250 \arcsin \left(a x \right) a^{7} x^{7}-3869775 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{4} x^{4}-33750 a^{6} x^{6} \sqrt{-a^{2} x^{2}+1}+13505625 a^{3} x^{3} \arcsin \left(a x \right)^{3}+1547910 \arcsin \left(a x \right) a^{5} x^{5}+8345925 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{2} x^{2}+269082 a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}-13505625 a x \arcsin \left(a x \right)^{3}-5563950 a^{3} x^{3} \arcsin \left(a x \right)-23825025 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}-1495874 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}+47650050 a x \arcsin \left(a x \right)+44658302 \sqrt{-a^{2} x^{2}+1}\right)}{13505625 a}"," ",0,"-1/13505625/a*c^3*(1929375*arcsin(a*x)^3*a^7*x^7+826875*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^6*x^6-8103375*arcsin(a*x)^3*a^5*x^5-236250*arcsin(a*x)*a^7*x^7-3869775*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^4*x^4-33750*a^6*x^6*(-a^2*x^2+1)^(1/2)+13505625*a^3*x^3*arcsin(a*x)^3+1547910*arcsin(a*x)*a^5*x^5+8345925*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^2*x^2+269082*a^4*x^4*(-a^2*x^2+1)^(1/2)-13505625*a*x*arcsin(a*x)^3-5563950*a^3*x^3*arcsin(a*x)-23825025*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)-1495874*a^2*x^2*(-a^2*x^2+1)^(1/2)+47650050*a*x*arcsin(a*x)+44658302*(-a^2*x^2+1)^(1/2))","A"
290,1,206,237,0.090000," ","int((-a^2*c*x^2+c)^2*arcsin(a*x)^3,x)","\frac{c^{2} \left(3375 \arcsin \left(a x \right)^{3} a^{5} x^{5}+2025 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{4} x^{4}-11250 a^{3} x^{3} \arcsin \left(a x \right)^{3}-810 \arcsin \left(a x \right) a^{5} x^{5}-8550 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{2} x^{2}-162 a^{4} x^{4} \sqrt{-a^{2} x^{2}+1}+16875 a x \arcsin \left(a x \right)^{3}+5700 a^{3} x^{3} \arcsin \left(a x \right)+33525 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}+1684 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-67050 a x \arcsin \left(a x \right)-63682 \sqrt{-a^{2} x^{2}+1}\right)}{16875 a}"," ",0,"1/16875/a*c^2*(3375*arcsin(a*x)^3*a^5*x^5+2025*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^4*x^4-11250*a^3*x^3*arcsin(a*x)^3-810*arcsin(a*x)*a^5*x^5-8550*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^2*x^2-162*a^4*x^4*(-a^2*x^2+1)^(1/2)+16875*a*x*arcsin(a*x)^3+5700*a^3*x^3*arcsin(a*x)+33525*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)+1684*a^2*x^2*(-a^2*x^2+1)^(1/2)-67050*a*x*arcsin(a*x)-63682*(-a^2*x^2+1)^(1/2))","A"
291,1,132,136,0.081000," ","int((-a^2*c*x^2+c)*arcsin(a*x)^3,x)","-\frac{c \left(9 a^{3} x^{3} \arcsin \left(a x \right)^{3}+9 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, a^{2} x^{2}-27 a x \arcsin \left(a x \right)^{3}-6 a^{3} x^{3} \arcsin \left(a x \right)-63 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}-2 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}+126 a x \arcsin \left(a x \right)+122 \sqrt{-a^{2} x^{2}+1}\right)}{27 a}"," ",0,"-1/27/a*c*(9*a^3*x^3*arcsin(a*x)^3+9*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*a^2*x^2-27*a*x*arcsin(a*x)^3-6*a^3*x^3*arcsin(a*x)-63*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)-2*a^2*x^2*(-a^2*x^2+1)^(1/2)+126*a*x*arcsin(a*x)+122*(-a^2*x^2+1)^(1/2))","A"
292,0,0,245,0.133000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c),x)","\int \frac{\arcsin \left(a x \right)^{3}}{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(arcsin(a*x)^3/(-a^2*c*x^2+c),x)","F"
293,1,486,391,0.246000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^2,x)","-\frac{\arcsin \left(a x \right)^{3} x}{2 \left(a^{2} x^{2}-1\right) c^{2}}+\frac{3 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}}{2 a \left(a^{2} x^{2}-1\right) c^{2}}+\frac{\arcsin \left(a x \right)^{3} \ln \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{2}}-\frac{3 i \arcsin \left(a x \right)^{2} \polylog \left(2, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{2}}+\frac{3 \arcsin \left(a x \right) \polylog \left(3, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}+\frac{3 i \polylog \left(4, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}-\frac{\arcsin \left(a x \right)^{3} \ln \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{2}}+\frac{3 i \arcsin \left(a x \right)^{2} \polylog \left(2, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{2}}-\frac{3 \arcsin \left(a x \right) \polylog \left(3, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}-\frac{3 i \polylog \left(4, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}-\frac{3 \arcsin \left(a x \right) \ln \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}+\frac{3 \arcsin \left(a x \right) \ln \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}+\frac{3 i \dilog \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}-\frac{3 i \dilog \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{a \,c^{2}}"," ",0,"-1/2/(a^2*x^2-1)*arcsin(a*x)^3/c^2*x+3/2/a/(a^2*x^2-1)*arcsin(a*x)^2/c^2*(-a^2*x^2+1)^(1/2)+1/2/a/c^2*arcsin(a*x)^3*ln(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))-3/2*I*arcsin(a*x)^2*polylog(2,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2+3*arcsin(a*x)*polylog(3,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2+3*I*polylog(4,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2-1/2/a/c^2*arcsin(a*x)^3*ln(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))+3/2*I*arcsin(a*x)^2*polylog(2,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2-3*arcsin(a*x)*polylog(3,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2-3*I*polylog(4,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^2-3/a/c^2*arcsin(a*x)*ln(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))+3/a/c^2*arcsin(a*x)*ln(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))+3*I/a/c^2*dilog(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))-3*I/a/c^2*dilog(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))","A"
294,1,726,483,0.344000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^3,x)","-\frac{3 a^{2} \arcsin \left(a x \right)^{3} x^{3}}{8 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{9 a \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x^{2}}{8 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{a^{2} \arcsin \left(a x \right) x^{3}}{4 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{a \,x^{2} \sqrt{-a^{2} x^{2}+1}}{4 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{5 \arcsin \left(a x \right)^{3} x}{8 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{11 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}}{8 a \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{\arcsin \left(a x \right) x}{4 \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}-\frac{\sqrt{-a^{2} x^{2}+1}}{4 a \left(a^{4} x^{4}-2 a^{2} x^{2}+1\right) c^{3}}+\frac{3 \arcsin \left(a x \right)^{3} \ln \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{8 a \,c^{3}}-\frac{9 i \polylog \left(4, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{4 a \,c^{3}}+\frac{9 \arcsin \left(a x \right) \polylog \left(3, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{4 a \,c^{3}}-\frac{5 i \dilog \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{3}}-\frac{3 \arcsin \left(a x \right)^{3} \ln \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{8 a \,c^{3}}+\frac{9 i \polylog \left(4, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{4 a \,c^{3}}-\frac{9 \arcsin \left(a x \right) \polylog \left(3, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{4 a \,c^{3}}+\frac{9 i \arcsin \left(a x \right)^{2} \polylog \left(2, -i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{8 a \,c^{3}}-\frac{5 \arcsin \left(a x \right) \ln \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{3}}+\frac{5 \arcsin \left(a x \right) \ln \left(1-i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{3}}-\frac{9 i \arcsin \left(a x \right)^{2} \polylog \left(2, i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{8 a \,c^{3}}+\frac{5 i \dilog \left(1+i \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)\right)}{2 a \,c^{3}}"," ",0,"-3/8*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)^3*x^3+9/8*a/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x^2-1/4*a^2/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)*x^3+1/4*a/(a^4*x^4-2*a^2*x^2+1)/c^3*x^2*(-a^2*x^2+1)^(1/2)+5/8/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)^3*x-11/8/a/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)+1/4/(a^4*x^4-2*a^2*x^2+1)/c^3*arcsin(a*x)*x-1/4/a/(a^4*x^4-2*a^2*x^2+1)/c^3*(-a^2*x^2+1)^(1/2)+3/8/a/c^3*arcsin(a*x)^3*ln(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))+9/4*I*polylog(4,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3+9/4*arcsin(a*x)*polylog(3,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3-9/8*I*arcsin(a*x)^2*polylog(2,I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3-3/8/a/c^3*arcsin(a*x)^3*ln(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))-5/2*I/a/c^3*dilog(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))-9/4*arcsin(a*x)*polylog(3,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3-9/4*I*polylog(4,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3-5/2/a/c^3*arcsin(a*x)*ln(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))+5/2/a/c^3*arcsin(a*x)*ln(1-I*(I*a*x+(-a^2*x^2+1)^(1/2)))+5/2*I/a/c^3*dilog(1+I*(I*a*x+(-a^2*x^2+1)^(1/2)))+9/8*I*arcsin(a*x)^2*polylog(2,-I*(I*a*x+(-a^2*x^2+1)^(1/2)))/a/c^3","A"
295,1,699,461,0.336000," ","int((-a^2*c*x^2+c)^(5/2)*arcsin(a*x)^3,x)","-\frac{5 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{4} c^{2}}{64 a \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-32 i \sqrt{-a^{2} x^{2}+1}\, x^{6} a^{6}+32 x^{7} a^{7}+48 i \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}-64 a^{5} x^{5}-18 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+38 a^{3} x^{3}+i \sqrt{-a^{2} x^{2}+1}-6 a x \right) \left(18 i \arcsin \left(a x \right)^{2}+36 \arcsin \left(a x \right)^{3}-i-6 \arcsin \left(a x \right)\right) c^{2}}{13824 a \left(a^{2} x^{2}-1\right)}+\frac{15 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}-i \sqrt{-a^{2} x^{2}+1}-2 a x \right) \left(-6 i \arcsin \left(a x \right)^{2}+4 \arcsin \left(a x \right)^{3}+3 i-6 \arcsin \left(a x \right)\right) c^{2}}{512 a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i x^{2} a^{2}-a x \sqrt{-a^{2} x^{2}+1}-i\right) \left(2088 i \arcsin \left(a x \right)^{2}+2304 \arcsin \left(a x \right)^{3}-251 i-924 \arcsin \left(a x \right)\right) \cos \left(5 \arcsin \left(a x \right)\right) c^{2}}{110592 a \left(a^{2} x^{2}-1\right)}+\frac{5 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i \sqrt{-a^{2} x^{2}+1}\, x a +a^{2} x^{2}-1\right) \left(360 i \arcsin \left(a x \right)^{2}+576 \arcsin \left(a x \right)^{3}-47 i-204 \arcsin \left(a x \right)\right) \sin \left(5 \arcsin \left(a x \right)\right) c^{2}}{110592 a \left(a^{2} x^{2}-1\right)}-\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i x^{2} a^{2}-a x \sqrt{-a^{2} x^{2}+1}-i\right) \left(264 i \arcsin \left(a x \right)^{2}+128 \arcsin \left(a x \right)^{3}-123 i-228 \arcsin \left(a x \right)\right) \cos \left(3 \arcsin \left(a x \right)\right) c^{2}}{4096 a \left(a^{2} x^{2}-1\right)}+\frac{9 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i \sqrt{-a^{2} x^{2}+1}\, x a +a^{2} x^{2}-1\right) \left(72 i \arcsin \left(a x \right)^{2}+64 \arcsin \left(a x \right)^{3}-39 i-84 \arcsin \left(a x \right)\right) \sin \left(3 \arcsin \left(a x \right)\right) c^{2}}{4096 a \left(a^{2} x^{2}-1\right)}"," ",0,"-5/64*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/(a^2*x^2-1)*arcsin(a*x)^4*c^2+1/13824*(-c*(a^2*x^2-1))^(1/2)*(-32*I*(-a^2*x^2+1)^(1/2)*x^6*a^6+32*x^7*a^7+48*I*(-a^2*x^2+1)^(1/2)*x^4*a^4-64*a^5*x^5-18*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+38*a^3*x^3+I*(-a^2*x^2+1)^(1/2)-6*a*x)*(18*I*arcsin(a*x)^2+36*arcsin(a*x)^3-I-6*arcsin(a*x))*c^2/a/(a^2*x^2-1)+15/512*(-c*(a^2*x^2-1))^(1/2)*(2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3-I*(-a^2*x^2+1)^(1/2)-2*a*x)*(-6*I*arcsin(a*x)^2+4*arcsin(a*x)^3+3*I-6*arcsin(a*x))*c^2/a/(a^2*x^2-1)-1/110592*(-c*(a^2*x^2-1))^(1/2)*(I*x^2*a^2-a*x*(-a^2*x^2+1)^(1/2)-I)*(2088*I*arcsin(a*x)^2+2304*arcsin(a*x)^3-251*I-924*arcsin(a*x))*cos(5*arcsin(a*x))*c^2/a/(a^2*x^2-1)+5/110592*(-c*(a^2*x^2-1))^(1/2)*(I*(-a^2*x^2+1)^(1/2)*x*a+a^2*x^2-1)*(360*I*arcsin(a*x)^2+576*arcsin(a*x)^3-47*I-204*arcsin(a*x))*sin(5*arcsin(a*x))*c^2/a/(a^2*x^2-1)-3/4096*(-c*(a^2*x^2-1))^(1/2)*(I*x^2*a^2-a*x*(-a^2*x^2+1)^(1/2)-I)*(264*I*arcsin(a*x)^2+128*arcsin(a*x)^3-123*I-228*arcsin(a*x))*cos(3*arcsin(a*x))*c^2/a/(a^2*x^2-1)+9/4096*(-c*(a^2*x^2-1))^(1/2)*(I*(-a^2*x^2+1)^(1/2)*x*a+a^2*x^2-1)*(72*I*arcsin(a*x)^2+64*arcsin(a*x)^3-39*I-84*arcsin(a*x))*sin(3*arcsin(a*x))*c^2/a/(a^2*x^2-1)","C"
296,1,474,313,0.234000," ","int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^3,x)","-\frac{3 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{4} c}{32 a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-8 i \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+8 a^{5} x^{5}+8 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}-12 a^{3} x^{3}-i \sqrt{-a^{2} x^{2}+1}+4 a x \right) \left(24 i \arcsin \left(a x \right)^{2}+32 \arcsin \left(a x \right)^{3}-3 i-12 \arcsin \left(a x \right)\right) c}{2048 a \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}-i \sqrt{-a^{2} x^{2}+1}-2 a x \right) \left(-6 i \arcsin \left(a x \right)^{2}+4 \arcsin \left(a x \right)^{3}+3 i-6 \arcsin \left(a x \right)\right) c}{32 a \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i x^{2} a^{2}-a x \sqrt{-a^{2} x^{2}+1}-i\right) \left(408 i \arcsin \left(a x \right)^{2}+224 \arcsin \left(a x \right)^{3}-195 i-372 \arcsin \left(a x \right)\right) \cos \left(3 \arcsin \left(a x \right)\right) c}{2048 a \left(a^{2} x^{2}-1\right)}+\frac{9 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i \sqrt{-a^{2} x^{2}+1}\, x a +a^{2} x^{2}-1\right) \left(40 i \arcsin \left(a x \right)^{2}+32 \arcsin \left(a x \right)^{3}-21 i-44 \arcsin \left(a x \right)\right) \sin \left(3 \arcsin \left(a x \right)\right) c}{2048 a \left(a^{2} x^{2}-1\right)}"," ",0,"-3/32*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/(a^2*x^2-1)*arcsin(a*x)^4*c-1/2048*(-c*(a^2*x^2-1))^(1/2)*(-8*I*(-a^2*x^2+1)^(1/2)*x^4*a^4+8*a^5*x^5+8*I*(-a^2*x^2+1)^(1/2)*x^2*a^2-12*a^3*x^3-I*(-a^2*x^2+1)^(1/2)+4*a*x)*(24*I*arcsin(a*x)^2+32*arcsin(a*x)^3-3*I-12*arcsin(a*x))*c/a/(a^2*x^2-1)+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3-I*(-a^2*x^2+1)^(1/2)-2*a*x)*(-6*I*arcsin(a*x)^2+4*arcsin(a*x)^3+3*I-6*arcsin(a*x))*c/a/(a^2*x^2-1)-1/2048*(-c*(a^2*x^2-1))^(1/2)*(I*x^2*a^2-a*x*(-a^2*x^2+1)^(1/2)-I)*(408*I*arcsin(a*x)^2+224*arcsin(a*x)^3-195*I-372*arcsin(a*x))*cos(3*arcsin(a*x))*c/a/(a^2*x^2-1)+9/2048*(-c*(a^2*x^2-1))^(1/2)*(I*(-a^2*x^2+1)^(1/2)*x*a+a^2*x^2-1)*(40*I*arcsin(a*x)^2+32*arcsin(a*x)^3-21*I-44*arcsin(a*x))*sin(3*arcsin(a*x))*c/a/(a^2*x^2-1)","C"
297,1,260,183,0.207000," ","int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^3,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{4}}{8 a \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}+i \sqrt{-a^{2} x^{2}+1}-2 a x \right) \left(6 i \arcsin \left(a x \right)^{2}+4 \arcsin \left(a x \right)^{3}-3 i-6 \arcsin \left(a x \right)\right)}{32 a \left(a^{2} x^{2}-1\right)}+\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}-i \sqrt{-a^{2} x^{2}+1}-2 a x \right) \left(-6 i \arcsin \left(a x \right)^{2}+4 \arcsin \left(a x \right)^{3}+3 i-6 \arcsin \left(a x \right)\right)}{32 a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/8*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/(a^2*x^2-1)*arcsin(a*x)^4+1/32*(-c*(a^2*x^2-1))^(1/2)*(-2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3+I*(-a^2*x^2+1)^(1/2)-2*a*x)*(6*I*arcsin(a*x)^2+4*arcsin(a*x)^3-3*I-6*arcsin(a*x))/a/(a^2*x^2-1)+1/32*(-c*(a^2*x^2-1))^(1/2)*(2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3-I*(-a^2*x^2+1)^(1/2)-2*a*x)*(-6*I*arcsin(a*x)^2+4*arcsin(a*x)^3+3*I-6*arcsin(a*x))/a/(a^2*x^2-1)","C"
298,1,52,36,0.046000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{4}}{4 a c \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c/(a^2*x^2-1)*arcsin(a*x)^4","A"
299,1,203,246,0.207000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(i \sqrt{-a^{2} x^{2}+1}+a x \right) \arcsin \left(a x \right)^{3}}{a \,c^{2} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \left(-4 i \arcsin \left(a x \right)^{3}+6 \arcsin \left(a x \right)^{2} \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)-6 i \arcsin \left(a x \right) \polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)+3 \polylog \left(3, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)\right)}{2 a \,c^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(I*(-a^2*x^2+1)^(1/2)+a*x)*arcsin(a*x)^3/a/c^2/(a^2*x^2-1)-1/2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)*(-4*I*arcsin(a*x)^3+6*arcsin(a*x)^2*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)-6*I*arcsin(a*x)*polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2)+3*polylog(3,-(I*a*x+(-a^2*x^2+1)^(1/2))^2))/a/c^2/(a^2*x^2-1)","A"
300,1,661,376,0.295000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+2 a^{3} x^{3}-2 i \sqrt{-a^{2} x^{2}+1}-3 a x \right) \arcsin \left(a x \right) \left(-6 i \arcsin \left(a x \right) x^{4} a^{4}-6 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+6 i \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-6 a^{4} x^{4}+6 \arcsin \left(a x \right)^{2} x^{2} a^{2}+12 i \arcsin \left(a x \right) x^{2} a^{2}+9 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a -6 i \sqrt{-a^{2} x^{2}+1}\, x a +18 a^{2} x^{2}-8 \arcsin \left(a x \right)^{2}-6 i \arcsin \left(a x \right)-12\right)}{6 c^{3} \left(3 a^{6} x^{6}-10 a^{4} x^{4}+11 a^{2} x^{2}-4\right) a}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \ln \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)}{a \,c^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{a \,c^{3} \left(a^{2} x^{2}-1\right)}+\frac{4 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \arcsin \left(a x \right)^{3}}{3 a \,c^{3} \left(a^{2} x^{2}-1\right)}-\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{2} \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{a \,c^{3} \left(a^{2} x^{2}-1\right)}+\frac{2 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \arcsin \left(a x \right) \polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{a \,c^{3} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \polylog \left(3, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{a \,c^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/6*(-c*(a^2*x^2-1))^(1/2)*(2*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+2*a^3*x^3-2*I*(-a^2*x^2+1)^(1/2)-3*a*x)*arcsin(a*x)*(-6*I*arcsin(a*x)*x^4*a^4-6*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3+6*I*(-a^2*x^2+1)^(1/2)*x^3*a^3-6*a^4*x^4+6*arcsin(a*x)^2*x^2*a^2+12*I*arcsin(a*x)*x^2*a^2+9*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a-6*I*(-a^2*x^2+1)^(1/2)*x*a+18*a^2*x^2-8*arcsin(a*x)^2-6*I*arcsin(a*x)-12)/c^3/(3*a^6*x^6-10*a^4*x^4+11*a^2*x^2-4)/a+2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^3/(a^2*x^2-1)*ln(I*a*x+(-a^2*x^2+1)^(1/2))-(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^3/(a^2*x^2-1)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+4/3*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/a/c^3/(a^2*x^2-1)*arcsin(a*x)^3-2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^3/(a^2*x^2-1)*arcsin(a*x)^2*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+2*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/a/c^3/(a^2*x^2-1)*arcsin(a*x)*polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2)-(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^3/(a^2*x^2-1)*polylog(3,-(I*a*x+(-a^2*x^2+1)^(1/2))^2)","A"
301,1,1017,509,0.401000," ","int(arcsin(a*x)^3/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{5} x^{5}-20 a^{3} x^{3}+8 i \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+15 a x -16 i \sqrt{-a^{2} x^{2}+1}\, x^{2} a^{2}+8 i \sqrt{-a^{2} x^{2}+1}\right) \left(24 i x^{8} a^{8}-96 i x^{6} a^{6}+144 i x^{4} a^{4}+192 \arcsin \left(a x \right) x^{8} a^{8}-852 \arcsin \left(a x \right) x^{6} a^{6}-380 \arcsin \left(a x \right)^{3} x^{2} a^{2}+756 i \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x^{5} a^{5}-936 i \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x^{3} a^{3}+372 i \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x a -192 i \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right) x^{7} a^{7}+1368 i \arcsin \left(a x \right)^{2} x^{4} a^{4}-984 i \arcsin \left(a x \right)^{2} x^{2} a^{2}+192 i \arcsin \left(a x \right)^{2} x^{8} a^{8}-840 i \arcsin \left(a x \right)^{2} x^{6} a^{6}+192 \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{2} x^{7} a^{7}-744 \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{2} x^{5} a^{5}+264 i \arcsin \left(a x \right)^{2}+256 \arcsin \left(a x \right)^{3}+480 \arcsin \left(a x \right)+1590 a^{4} x^{4} \arcsin \left(a x \right)+160 a^{4} x^{4} \arcsin \left(a x \right)^{3}-45 a x \sqrt{-a^{2} x^{2}+1}+105 a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}-1410 a^{2} x^{2} \arcsin \left(a x \right)+24 i+24 \sqrt{-a^{2} x^{2}+1}\, x^{7} a^{7}-96 i x^{2} a^{2}+1020 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-495 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x a -84 \sqrt{-a^{2} x^{2}+1}\, a^{5} x^{5}\right)}{60 c^{4} \left(40 a^{10} x^{10}-215 x^{8} a^{8}+469 a^{6} x^{6}-517 a^{4} x^{4}+287 a^{2} x^{2}-64\right) a}+\frac{2 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \ln \left(i a x +\sqrt{-a^{2} x^{2}+1}\right)}{a \,c^{4} \left(a^{2} x^{2}-1\right)}-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{a \,c^{4} \left(a^{2} x^{2}-1\right)}+\frac{16 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \arcsin \left(a x \right)^{3}}{15 a \,c^{4} \left(a^{2} x^{2}-1\right)}-\frac{8 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{2} \ln \left(1+\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{5 a \,c^{4} \left(a^{2} x^{2}-1\right)}+\frac{8 i \sqrt{-a^{2} x^{2}+1}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \arcsin \left(a x \right) \polylog \left(2, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{5 a \,c^{4} \left(a^{2} x^{2}-1\right)}-\frac{4 \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{-a^{2} x^{2}+1}\, \polylog \left(3, -\left(i a x +\sqrt{-a^{2} x^{2}+1}\right)^{2}\right)}{5 a \,c^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/60*(-c*(a^2*x^2-1))^(1/2)*(8*a^5*x^5-20*a^3*x^3+8*I*(-a^2*x^2+1)^(1/2)*x^4*a^4+15*a*x-16*I*(-a^2*x^2+1)^(1/2)*x^2*a^2+8*I*(-a^2*x^2+1)^(1/2))*(192*arcsin(a*x)*x^8*a^8-852*arcsin(a*x)*x^6*a^6-380*arcsin(a*x)^3*x^2*a^2+24*I*x^8*a^8-96*I*x^6*a^6+144*I*x^4*a^4-96*I*x^2*a^2+756*I*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x^5*a^5-936*I*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x^3*a^3+372*I*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x*a+192*(-a^2*x^2+1)^(1/2)*arcsin(a*x)^2*x^7*a^7-744*(-a^2*x^2+1)^(1/2)*arcsin(a*x)^2*x^5*a^5+1368*I*arcsin(a*x)^2*x^4*a^4-984*I*arcsin(a*x)^2*x^2*a^2+192*I*arcsin(a*x)^2*x^8*a^8-840*I*arcsin(a*x)^2*x^6*a^6+264*I*arcsin(a*x)^2-192*I*(-a^2*x^2+1)^(1/2)*arcsin(a*x)*x^7*a^7+24*I+256*arcsin(a*x)^3+480*arcsin(a*x)+1590*a^4*x^4*arcsin(a*x)+160*a^4*x^4*arcsin(a*x)^3-45*a*x*(-a^2*x^2+1)^(1/2)+105*a^3*x^3*(-a^2*x^2+1)^(1/2)-1410*a^2*x^2*arcsin(a*x)+24*(-a^2*x^2+1)^(1/2)*x^7*a^7+1020*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x^3*a^3-495*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x*a-84*(-a^2*x^2+1)^(1/2)*a^5*x^5)/c^4/(40*a^10*x^10-215*a^8*x^8+469*a^6*x^6-517*a^4*x^4+287*a^2*x^2-64)/a+2*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*ln(I*a*x+(-a^2*x^2+1)^(1/2))-(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+16/15*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/a/c^4/(a^2*x^2-1)*arcsin(a*x)^3-8/5*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*arcsin(a*x)^2*ln(1+(I*a*x+(-a^2*x^2+1)^(1/2))^2)+8/5*I*(-a^2*x^2+1)^(1/2)*(-c*(a^2*x^2-1))^(1/2)/a/c^4/(a^2*x^2-1)*arcsin(a*x)*polylog(2,-(I*a*x+(-a^2*x^2+1)^(1/2))^2)-4/5*(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)/a/c^4/(a^2*x^2-1)*polylog(3,-(I*a*x+(-a^2*x^2+1)^(1/2))^2)","A"
302,0,0,24,0.696000," ","int(x^m*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsin \left(a x \right)^{3}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","F"
303,1,159,163,0.126000," ","int(x^4*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\frac{-32 \arcsin \left(a x \right)^{3} \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}+24 a^{4} x^{4} \arcsin \left(a x \right)^{2}+12 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-3 a^{4} x^{4}-48 \arcsin \left(a x \right)^{3} \sqrt{-a^{2} x^{2}+1}\, x a +72 \arcsin \left(a x \right)^{2} x^{2} a^{2}+12 \arcsin \left(a x \right)^{4}+90 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a -45 a^{2} x^{2}-45 \arcsin \left(a x \right)^{2}}{128 a^{5}}"," ",0,"1/128*(-32*arcsin(a*x)^3*(-a^2*x^2+1)^(1/2)*x^3*a^3+24*a^4*x^4*arcsin(a*x)^2+12*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x^3*a^3-3*a^4*x^4-48*arcsin(a*x)^3*(-a^2*x^2+1)^(1/2)*x*a+72*arcsin(a*x)^2*x^2*a^2+12*arcsin(a*x)^4+90*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a-45*a^2*x^2-45*arcsin(a*x)^2)/a^5","A"
304,1,180,135,0.121000," ","int(x^3*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\left(9 a^{4} x^{4} \arcsin \left(a x \right)^{3}+9 \arcsin \left(a x \right)^{3} x^{2} a^{2}+9 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-6 a^{4} x^{4} \arcsin \left(a x \right)-114 a^{2} x^{2} \arcsin \left(a x \right)-2 a^{3} x^{3} \sqrt{-a^{2} x^{2}+1}-18 \arcsin \left(a x \right)^{3}+54 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x a +120 \arcsin \left(a x \right)-120 a x \sqrt{-a^{2} x^{2}+1}\right) \sqrt{-a^{2} x^{2}+1}}{27 a^{4} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/27/a^4*(9*a^4*x^4*arcsin(a*x)^3+9*arcsin(a*x)^3*x^2*a^2+9*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x^3*a^3-6*a^4*x^4*arcsin(a*x)-114*a^2*x^2*arcsin(a*x)-2*a^3*x^3*(-a^2*x^2+1)^(1/2)-18*arcsin(a*x)^3+54*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x*a+120*arcsin(a*x)-120*a*x*(-a^2*x^2+1)^(1/2))*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)","A"
305,1,85,91,0.139000," ","int(x^2*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\frac{-4 \arcsin \left(a x \right)^{3} \sqrt{-a^{2} x^{2}+1}\, x a +6 \arcsin \left(a x \right)^{2} x^{2} a^{2}+\arcsin \left(a x \right)^{4}+6 \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, x a -3 a^{2} x^{2}-3 \arcsin \left(a x \right)^{2}}{8 a^{3}}"," ",0,"1/8*(-4*arcsin(a*x)^3*(-a^2*x^2+1)^(1/2)*x*a+6*arcsin(a*x)^2*x^2*a^2+arcsin(a*x)^4+6*arcsin(a*x)*(-a^2*x^2+1)^(1/2)*x*a-3*a^2*x^2-3*arcsin(a*x)^2)/a^3","A"
306,1,107,63,0.102000," ","int(x*arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\arcsin \left(a x \right)^{3} x^{2} a^{2}-\arcsin \left(a x \right)^{3}+3 \arcsin \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, x a -6 a^{2} x^{2} \arcsin \left(a x \right)+6 \arcsin \left(a x \right)-6 a x \sqrt{-a^{2} x^{2}+1}\right)}{a^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a^2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)*(arcsin(a*x)^3*x^2*a^2-arcsin(a*x)^3+3*arcsin(a*x)^2*(-a^2*x^2+1)^(1/2)*x*a-6*a^2*x^2*arcsin(a*x)+6*arcsin(a*x)-6*a*x*(-a^2*x^2+1)^(1/2))","A"
307,1,12,11,0.008000," ","int(arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\frac{\arcsin \left(a x \right)^{4}}{4 a}"," ",0,"1/4*arcsin(a*x)^4/a","A"
308,1,221,190,0.128000," ","int(arcsin(a*x)^3/x/(-a^2*x^2+1)^(1/2),x)","-\arcsin \left(a x \right)^{3} \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)+\arcsin \left(a x \right)^{3} \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)-6 \arcsin \left(a x \right) \polylog \left(3, -i a x -\sqrt{-a^{2} x^{2}+1}\right)+6 \arcsin \left(a x \right) \polylog \left(3, i a x +\sqrt{-a^{2} x^{2}+1}\right)+3 i \arcsin \left(a x \right)^{2} \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)-3 i \arcsin \left(a x \right)^{2} \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)-6 i \polylog \left(4, -i a x -\sqrt{-a^{2} x^{2}+1}\right)+6 i \polylog \left(4, i a x +\sqrt{-a^{2} x^{2}+1}\right)"," ",0,"-arcsin(a*x)^3*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+arcsin(a*x)^3*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-6*arcsin(a*x)*polylog(3,-I*a*x-(-a^2*x^2+1)^(1/2))+6*arcsin(a*x)*polylog(3,I*a*x+(-a^2*x^2+1)^(1/2))+3*I*arcsin(a*x)^2*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))-3*I*arcsin(a*x)^2*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))-6*I*polylog(4,-I*a*x-(-a^2*x^2+1)^(1/2))+6*I*polylog(4,I*a*x+(-a^2*x^2+1)^(1/2))","A"
309,1,208,123,0.226000," ","int(arcsin(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x)","\frac{\left(i a x -\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{3}}{x}-2 i \arcsin \left(a x \right)^{3} a +3 \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{2} a -6 i \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right) a +3 \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{2} a -6 i \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right) a +6 \polylog \left(3, -i a x -\sqrt{-a^{2} x^{2}+1}\right) a +6 \polylog \left(3, i a x +\sqrt{-a^{2} x^{2}+1}\right) a"," ",0,"(I*a*x-(-a^2*x^2+1)^(1/2))/x*arcsin(a*x)^3-2*I*arcsin(a*x)^3*a+3*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))*arcsin(a*x)^2*a-6*I*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))*arcsin(a*x)*a+3*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))*arcsin(a*x)^2*a-6*I*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))*arcsin(a*x)*a+6*polylog(3,-I*a*x-(-a^2*x^2+1)^(1/2))*a+6*polylog(3,I*a*x+(-a^2*x^2+1)^(1/2))*a","A"
310,1,428,328,0.352000," ","int(arcsin(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \arcsin \left(a x \right)^{2} \left(a^{2} x^{2} \arcsin \left(a x \right)-3 a x \sqrt{-a^{2} x^{2}+1}-\arcsin \left(a x \right)\right)}{2 \left(a^{2} x^{2}-1\right) x^{2}}-\frac{\ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{3} a^{2}}{2}+\frac{\ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right) \arcsin \left(a x \right)^{3} a^{2}}{2}-3 a^{2} \arcsin \left(a x \right) \ln \left(1+i a x +\sqrt{-a^{2} x^{2}+1}\right)+\frac{3 i a^{2} \arcsin \left(a x \right)^{2} \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)}{2}-3 a^{2} \arcsin \left(a x \right) \polylog \left(3, -i a x -\sqrt{-a^{2} x^{2}+1}\right)+3 a^{2} \arcsin \left(a x \right) \ln \left(1-i a x -\sqrt{-a^{2} x^{2}+1}\right)-\frac{3 i a^{2} \arcsin \left(a x \right)^{2} \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)}{2}+3 a^{2} \arcsin \left(a x \right) \polylog \left(3, i a x +\sqrt{-a^{2} x^{2}+1}\right)+3 i a^{2} \polylog \left(2, -i a x -\sqrt{-a^{2} x^{2}+1}\right)-3 i a^{2} \polylog \left(4, -i a x -\sqrt{-a^{2} x^{2}+1}\right)-3 i a^{2} \polylog \left(2, i a x +\sqrt{-a^{2} x^{2}+1}\right)+3 i a^{2} \polylog \left(4, i a x +\sqrt{-a^{2} x^{2}+1}\right)"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)/(a^2*x^2-1)/x^2*arcsin(a*x)^2*(a^2*x^2*arcsin(a*x)-3*a*x*(-a^2*x^2+1)^(1/2)-arcsin(a*x))-1/2*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))*arcsin(a*x)^3*a^2+1/2*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))*arcsin(a*x)^3*a^2-3*a^2*arcsin(a*x)*ln(1+I*a*x+(-a^2*x^2+1)^(1/2))+3/2*I*a^2*arcsin(a*x)^2*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))-3*a^2*arcsin(a*x)*polylog(3,-I*a*x-(-a^2*x^2+1)^(1/2))+3*a^2*arcsin(a*x)*ln(1-I*a*x-(-a^2*x^2+1)^(1/2))-3/2*I*a^2*arcsin(a*x)^2*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))+3*a^2*arcsin(a*x)*polylog(3,I*a*x+(-a^2*x^2+1)^(1/2))+3*I*a^2*polylog(2,-I*a*x-(-a^2*x^2+1)^(1/2))-3*I*a^2*polylog(4,-I*a*x-(-a^2*x^2+1)^(1/2))-3*I*a^2*polylog(2,I*a*x+(-a^2*x^2+1)^(1/2))+3*I*a^2*polylog(4,I*a*x+(-a^2*x^2+1)^(1/2))","A"
311,1,42,59,0.115000," ","int((-a^2*c*x^2+c)^3/arcsin(a*x),x)","\frac{c^{3} \left(35 \Ci \left(\arcsin \left(a x \right)\right)+21 \Ci \left(3 \arcsin \left(a x \right)\right)+7 \Ci \left(5 \arcsin \left(a x \right)\right)+\Ci \left(7 \arcsin \left(a x \right)\right)\right)}{64 a}"," ",0,"1/64/a*c^3*(35*Ci(arcsin(a*x))+21*Ci(3*arcsin(a*x))+7*Ci(5*arcsin(a*x))+Ci(7*arcsin(a*x)))","A"
312,1,33,44,0.059000," ","int((-a^2*c*x^2+c)^2/arcsin(a*x),x)","\frac{c^{2} \left(10 \Ci \left(\arcsin \left(a x \right)\right)+5 \Ci \left(3 \arcsin \left(a x \right)\right)+\Ci \left(5 \arcsin \left(a x \right)\right)\right)}{16 a}"," ",0,"1/16/a*c^2*(10*Ci(arcsin(a*x))+5*Ci(3*arcsin(a*x))+Ci(5*arcsin(a*x)))","A"
313,1,22,25,0.060000," ","int((-a^2*c*x^2+c)/arcsin(a*x),x)","\frac{c \left(3 \Ci \left(\arcsin \left(a x \right)\right)+\Ci \left(3 \arcsin \left(a x \right)\right)\right)}{4 a}"," ",0,"1/4/a*c*(3*Ci(arcsin(a*x))+Ci(3*arcsin(a*x)))","A"
314,0,0,22,0.129000," ","int(1/(-a^2*c*x^2+c)/arcsin(a*x),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right) \arcsin \left(a x \right)}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)/arcsin(a*x),x)","F"
315,0,0,22,0.465000," ","int(1/(-a^2*c*x^2+c)^2/arcsin(a*x),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{2} \arcsin \left(a x \right)}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^2/arcsin(a*x),x)","F"
316,1,193,192,0.089000," ","int(x^4*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","-\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{16 c^{5} b}-\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{16 c^{5} b}-\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{32 c^{5} b}-\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{32 c^{5} b}+\frac{\Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right)}{32 c^{5} b}+\frac{\Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right)}{32 c^{5} b}+\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{16 b \,c^{5}}"," ",0,"-1/16/c^5/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)-1/16/c^5/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)-1/32/c^5/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)-1/32/c^5/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+1/32/c^5/b*Si(6*arcsin(c*x)+6*a/b)*sin(6*a/b)+1/32/c^5/b*Ci(6*arcsin(c*x)+6*a/b)*cos(6*a/b)+1/16*ln(a+b*arcsin(c*x))/b/c^5","A"
317,1,138,171,0.077000," ","int(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","\frac{\Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)-2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)+\Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-\Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)-\Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)}{16 c^{4} b}"," ",0,"1/16/c^4*(Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b)-2*Ci(arcsin(c*x)+a/b)*sin(a/b)+2*Si(arcsin(c*x)+a/b)*cos(a/b)+Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)-Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)-Si(5*arcsin(c*x)+5*a/b)*cos(5*a/b))/b","A"
318,1,77,76,0.069000," ","int(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","-\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{8 c^{3} b}-\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{8 c^{3} b}+\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{8 b \,c^{3}}"," ",0,"-1/8/c^3/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)-1/8/c^3/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)+1/8*ln(a+b*arcsin(c*x))/b/c^3","A"
319,1,92,113,0.074000," ","int(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","\frac{\Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-\Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{4 c^{2} b}"," ",0,"1/4/c^2*(Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)-Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)+Si(arcsin(c*x)+a/b)*cos(a/b)-Ci(arcsin(c*x)+a/b)*sin(a/b))/b","A"
320,1,77,76,0.080000," ","int((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{2 c b}+\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{2 c b}+\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{2 b c}"," ",0,"1/2/c/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)+1/2/c/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+1/2*ln(a+b*arcsin(c*x))/b/c","A"
321,0,0,76,0.503000," ","int((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x)),x)","F"
322,0,0,44,0.569000," ","int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x)),x)","F"
323,0,0,28,2.986000," ","int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x)),x)","F"
324,0,0,28,4.546000," ","int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x)),x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x)),x)","F"
325,1,184,229,0.092000," ","int(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","-\frac{\Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)-\Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)-3 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)+3 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)-3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)+\Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right)-\Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right)+3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)}{64 c^{4} b}"," ",0,"-1/64/c^4*(Si(5*arcsin(c*x)+5*a/b)*cos(5*a/b)-Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b)-3*Si(arcsin(c*x)+a/b)*cos(a/b)+3*Ci(arcsin(c*x)+a/b)*sin(a/b)-3*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)+Si(7*arcsin(c*x)+7*a/b)*cos(7*a/b)-Ci(7*arcsin(c*x)+7*a/b)*sin(7*a/b)+3*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b))/b","A"
326,1,193,192,0.095000," ","int(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","-\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{16 c^{3} b}-\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{16 c^{3} b}+\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{32 c^{3} b}+\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{32 c^{3} b}-\frac{\Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right)}{32 c^{3} b}-\frac{\Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right)}{32 c^{3} b}+\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{16 b \,c^{3}}"," ",0,"-1/16/c^3/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)-1/16/c^3/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)+1/32/c^3/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)+1/32/c^3/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)-1/32/c^3/b*Si(6*arcsin(c*x)+6*a/b)*sin(6*a/b)-1/32/c^3/b*Ci(6*arcsin(c*x)+6*a/b)*cos(6*a/b)+1/16*ln(a+b*arcsin(c*x))/b/c^3","A"
327,1,139,171,0.072000," ","int(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\frac{3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+\Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)-\Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)}{16 c^{2} b}"," ",0,"1/16/c^2*(3*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)-3*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)+2*Si(arcsin(c*x)+a/b)*cos(a/b)-2*Ci(arcsin(c*x)+a/b)*sin(a/b)+Si(5*arcsin(c*x)+5*a/b)*cos(5*a/b)-Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b))/b","A"
328,1,135,134,0.092000," ","int((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{8 c b}+\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{8 c b}+\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{2 c b}+\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{2 c b}+\frac{3 \ln \left(a +b \arcsin \left(c x \right)\right)}{8 b c}"," ",0,"1/8/c/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)+1/8/c/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)+1/2/c/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)+1/2/c/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+3/8*ln(a+b*arcsin(c*x))/b/c","A"
329,0,0,129,0.619000," ","int((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x)),x)","F"
330,0,0,98,0.523000," ","int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x)),x)","F"
331,0,0,28,3.145000," ","int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x)),x)","F"
332,0,0,28,3.858000," ","int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x)),x)","F"
333,1,185,229,0.079000," ","int(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\frac{6 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-6 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+8 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-\Si \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \cos \left(\frac{9 a}{b}\right)+\Ci \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \sin \left(\frac{9 a}{b}\right)-8 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)-3 \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right)+3 \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right)}{256 c^{4} b}"," ",0,"1/256/c^4*(6*Si(arcsin(c*x)+a/b)*cos(a/b)-6*Ci(arcsin(c*x)+a/b)*sin(a/b)+8*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)-Si(9*arcsin(c*x)+9*a/b)*cos(9*a/b)+Ci(9*arcsin(c*x)+9*a/b)*sin(9*a/b)-8*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)-3*Si(7*arcsin(c*x)+7*a/b)*cos(7*a/b)+3*Ci(7*arcsin(c*x)+7*a/b)*sin(7*a/b))/b","A"
334,1,251,250,0.079000," ","int(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","-\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{32 c^{3} b}+\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{32 c^{3} b}-\frac{\Si \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \sin \left(\frac{8 a}{b}\right)}{128 c^{3} b}-\frac{\Ci \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \cos \left(\frac{8 a}{b}\right)}{128 c^{3} b}+\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{32 c^{3} b}-\frac{\Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right)}{32 c^{3} b}-\frac{\Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right)}{32 c^{3} b}-\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{32 c^{3} b}+\frac{5 \ln \left(a +b \arcsin \left(c x \right)\right)}{128 b \,c^{3}}"," ",0,"-1/32/c^3/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)+1/32/c^3/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)-1/128/c^3/b*Si(8*arcsin(c*x)+8*a/b)*sin(8*a/b)-1/128/c^3/b*Ci(8*arcsin(c*x)+8*a/b)*cos(8*a/b)+1/32/c^3/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)-1/32/c^3/b*Si(6*arcsin(c*x)+6*a/b)*sin(6*a/b)-1/32/c^3/b*Ci(6*arcsin(c*x)+6*a/b)*cos(6*a/b)-1/32/c^3/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)+5/128*ln(a+b*arcsin(c*x))/b/c^3","A"
335,1,185,229,0.075000," ","int(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\frac{9 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-9 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+5 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-5 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+\Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right)-\Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right)+5 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)-5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)}{64 c^{2} b}"," ",0,"1/64/c^2*(9*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)-9*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)+5*Si(arcsin(c*x)+a/b)*cos(a/b)-5*Ci(arcsin(c*x)+a/b)*sin(a/b)+Si(7*arcsin(c*x)+7*a/b)*cos(7*a/b)-Ci(7*arcsin(c*x)+7*a/b)*sin(7*a/b)+5*Si(5*arcsin(c*x)+5*a/b)*cos(5*a/b)-5*Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b))/b","A"
336,1,193,192,0.084000," ","int((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\frac{\Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right)}{32 c b}+\frac{\Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right)}{32 c b}+\frac{3 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{16 c b}+\frac{3 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{16 c b}+\frac{15 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{32 c b}+\frac{15 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{32 c b}+\frac{5 \ln \left(a +b \arcsin \left(c x \right)\right)}{16 b c}"," ",0,"1/32/c/b*Si(6*arcsin(c*x)+6*a/b)*sin(6*a/b)+1/32/c/b*Ci(6*arcsin(c*x)+6*a/b)*cos(6*a/b)+3/16/c/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)+3/16/c/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)+15/32/c/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)+15/32/c/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+5/16*ln(a+b*arcsin(c*x))/b/c","A"
337,0,0,181,0.717000," ","int((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x)),x)","F"
338,0,0,152,0.612000," ","int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x)),x)","F"
339,0,0,28,3.289000," ","int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x)),x)","F"
340,0,0,28,4.434000," ","int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x)),x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x)),x)","F"
341,1,36,35,0.149000," ","int(x^4/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\Ci \left(2 \arcsin \left(a x \right)\right)}{2 a^{5}}+\frac{\Ci \left(4 \arcsin \left(a x \right)\right)}{8 a^{5}}+\frac{3 \ln \left(\arcsin \left(a x \right)\right)}{8 a^{5}}"," ",0,"-1/2*Ci(2*arcsin(a*x))/a^5+1/8*Ci(4*arcsin(a*x))/a^5+3/8*ln(arcsin(a*x))/a^5","A"
342,1,21,23,0.129000," ","int(x^3/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\Si \left(3 \arcsin \left(a x \right)\right)-3 \Si \left(\arcsin \left(a x \right)\right)}{4 a^{4}}"," ",0,"-1/4*(Si(3*arcsin(a*x))-3*Si(arcsin(a*x)))/a^4","A"
343,1,24,23,0.099000," ","int(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\Ci \left(2 \arcsin \left(a x \right)\right)}{2 a^{3}}+\frac{\ln \left(\arcsin \left(a x \right)\right)}{2 a^{3}}"," ",0,"-1/2*Ci(2*arcsin(a*x))/a^3+1/2*ln(arcsin(a*x))/a^3","A"
344,1,24,23,0.000000," ","int(x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\Ci \left(2 \arcsin \left(a x \right)\right)}{2 a^{3}}+\frac{\ln \left(\arcsin \left(a x \right)\right)}{2 a^{3}}"," ",0,"-1/2*Ci(2*arcsin(a*x))/a^3+1/2*ln(arcsin(a*x))/a^3","A"
345,1,10,9,0.073000," ","int(x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\Si \left(\arcsin \left(a x \right)\right)}{a^{2}}"," ",0,"Si(arcsin(a*x))/a^2","A"
346,1,10,9,0.007000," ","int(1/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{\ln \left(\arcsin \left(a x \right)\right)}{a}"," ",0,"ln(arcsin(a*x))/a","A"
347,0,0,24,0.146000," ","int(1/x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{1}{x \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
348,0,0,24,0.293000," ","int(1/x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
349,1,139,171,0.088000," ","int(x^5/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)-\Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)-5 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)+5 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+10 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-10 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{16 c^{6} b}"," ",0,"1/16/c^6*(Si(5*arcsin(c*x)+5*a/b)*cos(5*a/b)-Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b)-5*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)+5*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)+10*Si(arcsin(c*x)+a/b)*cos(a/b)-10*Ci(arcsin(c*x)+a/b)*sin(a/b))/b","A"
350,1,135,134,0.093000," ","int(x^4/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)}{8 c^{5} b}+\frac{\Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)}{8 c^{5} b}-\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{2 c^{5} b}-\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{2 c^{5} b}+\frac{3 \ln \left(a +b \arcsin \left(c x \right)\right)}{8 b \,c^{5}}"," ",0,"1/8/c^5/b*Si(4*arcsin(c*x)+4*a/b)*sin(4*a/b)+1/8/c^5/b*Ci(4*arcsin(c*x)+4*a/b)*cos(4*a/b)-1/2/c^5/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)-1/2/c^5/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+3/8*ln(a+b*arcsin(c*x))/b/c^5","A"
351,1,93,113,0.085000," ","int(x^3/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+3 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-3 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)-\Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)}{4 c^{4} b}"," ",0,"1/4/c^4*(Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)+3*Si(arcsin(c*x)+a/b)*cos(a/b)-3*Ci(arcsin(c*x)+a/b)*sin(a/b)-Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b))/b","A"
352,1,77,76,0.097000," ","int(x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","-\frac{\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)}{2 c^{3} b}-\frac{\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)}{2 c^{3} b}+\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{2 b \,c^{3}}"," ",0,"-1/2/c^3/b*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)-1/2/c^3/b*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)+1/2*ln(a+b*arcsin(c*x))/b/c^3","A"
353,1,46,54,0.076000," ","int(x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{c^{2} b}"," ",0,"1/c^2*(Si(arcsin(c*x)+a/b)*cos(a/b)-Ci(arcsin(c*x)+a/b)*sin(a/b))/b","A"
354,1,17,16,0.006000," ","int(1/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\frac{\ln \left(a +b \arcsin \left(c x \right)\right)}{b c}"," ",0,"ln(a+b*arcsin(c*x))/b/c","A"
355,0,0,28,0.161000," ","int(1/x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
356,0,0,28,0.115000," ","int(1/x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
357,0,0,28,0.557000," ","int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
358,0,0,26,0.401000," ","int(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
359,0,0,25,0.254000," ","int(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
360,0,0,28,2.622000," ","int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
361,0,0,28,0.627000," ","int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
362,0,0,28,2.799000," ","int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
363,0,0,26,2.451000," ","int(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
364,0,0,25,1.885000," ","int(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
365,0,0,28,5.464000," ","int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
366,0,0,28,5.641000," ","int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
367,0,0,28,1.523000," ","int(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m} \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{a +b \arcsin \left(c x \right)}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
368,0,0,28,1.305000," ","int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{a +b \arcsin \left(c x \right)}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
369,0,0,28,0.843000," ","int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m} \sqrt{-c^{2} x^{2}+1}}{a +b \arcsin \left(c x \right)}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","F"
370,0,0,28,0.197000," ","int(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m}}{\sqrt{-c^{2} x^{2}+1}\, \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x)),x)","F"
371,0,0,28,0.660000," ","int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x)),x)","F"
372,0,0,28,0.881000," ","int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x)),x)","F"
373,0,0,24,0.246000," ","int(x^m/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m}}{\arcsin \left(a x \right) \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m/arcsin(a*x)/(-a^2*x^2+1)^(1/2),x)","F"
374,1,105,85,0.174000," ","int((-a^2*c*x^2+c)^3/arcsin(a*x)^2,x)","-\frac{c^{3} \left(35 \Si \left(\arcsin \left(a x \right)\right) \arcsin \left(a x \right)+63 \Si \left(3 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+35 \Si \left(5 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+7 \Si \left(7 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+35 \sqrt{-a^{2} x^{2}+1}+\cos \left(7 \arcsin \left(a x \right)\right)+21 \cos \left(3 \arcsin \left(a x \right)\right)+7 \cos \left(5 \arcsin \left(a x \right)\right)\right)}{64 a \arcsin \left(a x \right)}"," ",0,"-1/64/a*c^3*(35*Si(arcsin(a*x))*arcsin(a*x)+63*Si(3*arcsin(a*x))*arcsin(a*x)+35*Si(5*arcsin(a*x))*arcsin(a*x)+7*Si(7*arcsin(a*x))*arcsin(a*x)+35*(-a^2*x^2+1)^(1/2)+cos(7*arcsin(a*x))+21*cos(3*arcsin(a*x))+7*cos(5*arcsin(a*x)))/arcsin(a*x)","A"
375,1,83,70,0.088000," ","int((-a^2*c*x^2+c)^2/arcsin(a*x)^2,x)","-\frac{c^{2} \left(10 \Si \left(\arcsin \left(a x \right)\right) \arcsin \left(a x \right)+15 \Si \left(3 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+5 \Si \left(5 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+10 \sqrt{-a^{2} x^{2}+1}+5 \cos \left(3 \arcsin \left(a x \right)\right)+\cos \left(5 \arcsin \left(a x \right)\right)\right)}{16 a \arcsin \left(a x \right)}"," ",0,"-1/16/a*c^2*(10*Si(arcsin(a*x))*arcsin(a*x)+15*Si(3*arcsin(a*x))*arcsin(a*x)+5*Si(5*arcsin(a*x))*arcsin(a*x)+10*(-a^2*x^2+1)^(1/2)+5*cos(3*arcsin(a*x))+cos(5*arcsin(a*x)))/arcsin(a*x)","A"
376,1,59,49,0.079000," ","int((-a^2*c*x^2+c)/arcsin(a*x)^2,x)","-\frac{c \left(3 \Si \left(\arcsin \left(a x \right)\right) \arcsin \left(a x \right)+3 \Si \left(3 \arcsin \left(a x \right)\right) \arcsin \left(a x \right)+3 \sqrt{-a^{2} x^{2}+1}+\cos \left(3 \arcsin \left(a x \right)\right)\right)}{4 a \arcsin \left(a x \right)}"," ",0,"-1/4/a*c*(3*Si(arcsin(a*x))*arcsin(a*x)+3*Si(3*arcsin(a*x))*arcsin(a*x)+3*(-a^2*x^2+1)^(1/2)+cos(3*arcsin(a*x)))/arcsin(a*x)","A"
377,0,0,54,0.135000," ","int(1/(-a^2*c*x^2+c)/arcsin(a*x)^2,x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right) \arcsin \left(a x \right)^{2}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)/arcsin(a*x)^2,x)","F"
378,0,0,55,0.507000," ","int(1/(-a^2*c*x^2+c)^2/arcsin(a*x)^2,x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{2} \arcsin \left(a x \right)^{2}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^2/arcsin(a*x)^2,x)","F"
379,0,0,15,2.289000," ","int(1/(-x^2+1)/arcsin(x)^2-x/(-x^2+1)^(3/2)/arcsin(x),x)","\int \frac{1}{\left(-x^{2}+1\right) \arcsin \left(x \right)^{2}}-\frac{x}{\left(-x^{2}+1\right)^{\frac{3}{2}} \arcsin \left(x \right)}\, dx"," ",0,"int(1/(-x^2+1)/arcsin(x)^2-x/(-x^2+1)^(3/2)/arcsin(x),x)","F"
380,0,0,28,0.930000," ","int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{m} \sqrt{-c^{2} x^{2}+1}}{\left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","F"
381,1,340,202,0.088000," ","int(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","-\frac{5 \arcsin \left(c x \right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b +5 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b -2 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b -2 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b -3 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b -3 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +5 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a +5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a -2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a -2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a -3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +2 x b c -\sin \left(5 \arcsin \left(c x \right)\right) b +\sin \left(3 \arcsin \left(c x \right)\right) b}{16 c^{4} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/16/c^4*(5*arcsin(c*x)*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b+5*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*b-2*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b-2*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b-3*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b-3*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+5*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a+5*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*a-2*Si(arcsin(c*x)+a/b)*sin(a/b)*a-2*Ci(arcsin(c*x)+a/b)*cos(a/b)*a-3*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a-3*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+2*x*b*c-sin(5*arcsin(c*x))*b+sin(3*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
382,1,136,90,0.074000," ","int(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","\frac{4 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -4 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b +4 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -4 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a +\cos \left(4 \arcsin \left(c x \right)\right) b -b}{8 c^{3} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/8/c^3*(4*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-4*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b+4*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-4*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a+cos(4*arcsin(c*x))*b-b)/(a+b*arcsin(c*x))/b^2","A"
383,1,223,142,0.073000," ","int(x*(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","\frac{3 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +3 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +\arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +\arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a +3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -x b c -\sin \left(3 \arcsin \left(c x \right)\right) b}{4 c^{2} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/4/c^2*(3*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b+3*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+3*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a+3*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+Si(arcsin(c*x)+a/b)*sin(a/b)*a+Ci(arcsin(c*x)+a/b)*cos(a/b)*a-x*b*c-sin(3*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
384,1,134,84,0.094000," ","int((-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))^2,x)","-\frac{2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b -2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(2 \arcsin \left(c x \right)\right) b +b}{2 c \,b^{2} \left(a +b \arcsin \left(c x \right)\right)}"," ",0,"-1/2/c*(2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b-2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a-2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+cos(2*arcsin(c*x))*b+b)/b^2/(a+b*arcsin(c*x))","A"
385,0,0,102,0.836000," ","int((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x/(a+b*arcsin(c*x))^2,x)","F"
386,0,0,54,0.746000," ","int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^2/(a+b*arcsin(c*x))^2,x)","F"
387,0,0,28,4.548000," ","int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^3/(a+b*arcsin(c*x))^2,x)","F"
388,0,0,28,6.534000," ","int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x))^2,x)","\int \frac{\sqrt{-c^{2} x^{2}+1}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(1/2)/x^4/(a+b*arcsin(c*x))^2,x)","F"
389,0,0,28,1.371000," ","int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{m} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{\left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
390,1,455,262,0.087000," ","int(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","-\frac{7 \arcsin \left(c x \right) \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) b -9 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b -9 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +5 \arcsin \left(c x \right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b +5 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b -3 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b -3 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +7 \arcsin \left(c x \right) \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) b +7 \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) a -9 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a -9 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +5 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a +5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a -3 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a -3 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a +7 \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) a +3 x b c -\sin \left(7 \arcsin \left(c x \right)\right) b +3 \sin \left(3 \arcsin \left(c x \right)\right) b -\sin \left(5 \arcsin \left(c x \right)\right) b}{64 c^{4} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/64/c^4*(7*arcsin(c*x)*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*b-9*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b-9*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+5*arcsin(c*x)*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b+5*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*b-3*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b-3*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+7*arcsin(c*x)*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*b+7*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*a-9*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a-9*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+5*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a+5*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*a-3*Si(arcsin(c*x)+a/b)*sin(a/b)*a-3*Ci(arcsin(c*x)+a/b)*cos(a/b)*a+7*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*a+3*x*b*c-sin(7*arcsin(c*x))*b+3*sin(3*arcsin(c*x))*b-sin(5*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
391,1,364,208,0.105000," ","int(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\frac{8 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -8 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b -2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +6 \arcsin \left(c x \right) \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) b -6 \arcsin \left(c x \right) \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) b +8 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -8 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a -2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a +2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +6 \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) a -6 \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) a +2 \cos \left(4 \arcsin \left(c x \right)\right) b -\cos \left(2 \arcsin \left(c x \right)\right) b +\cos \left(6 \arcsin \left(c x \right)\right) b -2 b}{32 c^{3} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/32/c^3*(8*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-8*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b-2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b+2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+6*arcsin(c*x)*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*b-6*arcsin(c*x)*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*b+8*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-8*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a-2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a+2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+6*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*a-6*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*a+2*cos(4*arcsin(c*x))*b-cos(2*arcsin(c*x))*b+cos(6*arcsin(c*x))*b-2*b)/(a+b*arcsin(c*x))/b^2","A"
392,1,341,202,0.078000," ","int(x*(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\frac{9 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +9 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +2 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +2 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +5 \arcsin \left(c x \right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b +5 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b +9 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a +9 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a +5 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a +5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a -2 x b c -3 \sin \left(3 \arcsin \left(c x \right)\right) b -\sin \left(5 \arcsin \left(c x \right)\right) b}{16 c^{2} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/16/c^2*(9*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b+9*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+2*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+2*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+5*arcsin(c*x)*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b+5*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*b+9*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a+9*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+2*Si(arcsin(c*x)+a/b)*sin(a/b)*a+2*Ci(arcsin(c*x)+a/b)*cos(a/b)*a+5*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a+5*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*a-2*x*b*c-3*sin(3*arcsin(c*x))*b-sin(5*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
393,1,250,146,0.095000," ","int((-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","-\frac{4 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -4 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b +8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b -8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +4 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -4 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a +8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(4 \arcsin \left(c x \right)\right) b +4 \cos \left(2 \arcsin \left(c x \right)\right) b +3 b}{8 c \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/8/c*(4*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-4*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b+8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b-8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+4*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-4*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a+8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a-8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+cos(4*arcsin(c*x))*b+4*cos(2*arcsin(c*x))*b+3*b)/(a+b*arcsin(c*x))/b^2","A"
394,0,0,168,0.798000," ","int((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x/(a+b*arcsin(c*x))^2,x)","F"
395,0,0,100,0.663000," ","int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^2/(a+b*arcsin(c*x))^2,x)","F"
396,0,0,28,1.824000," ","int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^3/(a+b*arcsin(c*x))^2,x)","F"
397,0,0,68,5.812000," ","int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(3/2)/x^4/(a+b*arcsin(c*x))^2,x)","F"
398,0,0,28,1.596000," ","int(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{m} \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{\left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
399,1,454,262,0.109000," ","int(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\frac{6 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +6 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b -9 \arcsin \left(c x \right) \Si \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \sin \left(\frac{9 a}{b}\right) b -9 \arcsin \left(c x \right) \Ci \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \cos \left(\frac{9 a}{b}\right) b +24 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +24 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b -21 \arcsin \left(c x \right) \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) b -21 \arcsin \left(c x \right) \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) b +6 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +6 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -9 \Si \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \sin \left(\frac{9 a}{b}\right) a -9 \Ci \left(9 \arcsin \left(c x \right)+\frac{9 a}{b}\right) \cos \left(\frac{9 a}{b}\right) a +24 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a +24 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a -21 \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) a -21 \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) a -6 x b c +\sin \left(9 \arcsin \left(c x \right)\right) b -8 \sin \left(3 \arcsin \left(c x \right)\right) b +3 \sin \left(7 \arcsin \left(c x \right)\right) b}{256 c^{4} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/256/c^4*(6*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+6*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b-9*arcsin(c*x)*Si(9*arcsin(c*x)+9*a/b)*sin(9*a/b)*b-9*arcsin(c*x)*Ci(9*arcsin(c*x)+9*a/b)*cos(9*a/b)*b+24*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b+24*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b-21*arcsin(c*x)*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*b-21*arcsin(c*x)*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*b+6*Si(arcsin(c*x)+a/b)*sin(a/b)*a+6*Ci(arcsin(c*x)+a/b)*cos(a/b)*a-9*Si(9*arcsin(c*x)+9*a/b)*sin(9*a/b)*a-9*Ci(9*arcsin(c*x)+9*a/b)*cos(9*a/b)*a+24*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a+24*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a-21*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*a-21*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*a-6*x*b*c+sin(9*arcsin(c*x))*b-8*sin(3*arcsin(c*x))*b+3*sin(7*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
400,1,478,266,0.093000," ","int(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\frac{16 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -16 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b +8 \arcsin \left(c x \right) \Si \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \cos \left(\frac{8 a}{b}\right) b -8 \arcsin \left(c x \right) \Ci \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \sin \left(\frac{8 a}{b}\right) b -8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +24 \arcsin \left(c x \right) \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) b -24 \arcsin \left(c x \right) \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) b +16 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -16 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a +8 \Si \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \cos \left(\frac{8 a}{b}\right) a -8 \Ci \left(8 \arcsin \left(c x \right)+\frac{8 a}{b}\right) \sin \left(\frac{8 a}{b}\right) a -8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a +8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +24 \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) a -24 \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) a +4 \cos \left(4 \arcsin \left(c x \right)\right) b +\cos \left(8 \arcsin \left(c x \right)\right) b -4 \cos \left(2 \arcsin \left(c x \right)\right) b +4 \cos \left(6 \arcsin \left(c x \right)\right) b -5 b}{128 c^{3} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/128/c^3*(16*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-16*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b+8*arcsin(c*x)*Si(8*arcsin(c*x)+8*a/b)*cos(8*a/b)*b-8*arcsin(c*x)*Ci(8*arcsin(c*x)+8*a/b)*sin(8*a/b)*b-8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b+8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+24*arcsin(c*x)*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*b-24*arcsin(c*x)*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*b+16*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-16*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a+8*Si(8*arcsin(c*x)+8*a/b)*cos(8*a/b)*a-8*Ci(8*arcsin(c*x)+8*a/b)*sin(8*a/b)*a-8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a+8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+24*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*a-24*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*a+4*cos(4*arcsin(c*x))*b+cos(8*arcsin(c*x))*b-4*cos(2*arcsin(c*x))*b+4*cos(6*arcsin(c*x))*b-5*b)/(a+b*arcsin(c*x))/b^2","A"
401,1,455,260,0.109000," ","int(x*(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\frac{27 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +27 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +5 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +5 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +7 \arcsin \left(c x \right) \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) b +7 \arcsin \left(c x \right) \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) b +25 \arcsin \left(c x \right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b +25 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b +27 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a +27 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +5 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +5 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a +7 \Si \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \sin \left(\frac{7 a}{b}\right) a +7 \Ci \left(7 \arcsin \left(c x \right)+\frac{7 a}{b}\right) \cos \left(\frac{7 a}{b}\right) a +25 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a +25 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a -5 x b c -9 \sin \left(3 \arcsin \left(c x \right)\right) b -\sin \left(7 \arcsin \left(c x \right)\right) b -5 \sin \left(5 \arcsin \left(c x \right)\right) b}{64 c^{2} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/64/c^2*(27*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b+27*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+5*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+5*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+7*arcsin(c*x)*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*b+7*arcsin(c*x)*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*b+25*arcsin(c*x)*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b+25*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*b+27*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a+27*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+5*Si(arcsin(c*x)+a/b)*sin(a/b)*a+5*Ci(arcsin(c*x)+a/b)*cos(a/b)*a+7*Si(7*arcsin(c*x)+7*a/b)*sin(7*a/b)*a+7*Ci(7*arcsin(c*x)+7*a/b)*cos(7*a/b)*a+25*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a+25*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*a-5*x*b*c-9*sin(3*arcsin(c*x))*b-sin(7*arcsin(c*x))*b-5*sin(5*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
402,1,364,205,0.102000," ","int((-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","-\frac{6 \arcsin \left(c x \right) \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) b -6 \arcsin \left(c x \right) \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) b +24 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -24 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b +30 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b -30 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +6 \Si \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \cos \left(\frac{6 a}{b}\right) a -6 \Ci \left(6 \arcsin \left(c x \right)+\frac{6 a}{b}\right) \sin \left(\frac{6 a}{b}\right) a +24 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -24 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a +30 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -30 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(6 \arcsin \left(c x \right)\right) b +6 \cos \left(4 \arcsin \left(c x \right)\right) b +15 \cos \left(2 \arcsin \left(c x \right)\right) b +10 b}{32 c \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/32/c*(6*arcsin(c*x)*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*b-6*arcsin(c*x)*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*b+24*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-24*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b+30*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b-30*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+6*Si(6*arcsin(c*x)+6*a/b)*cos(6*a/b)*a-6*Ci(6*arcsin(c*x)+6*a/b)*sin(6*a/b)*a+24*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-24*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a+30*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a-30*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+cos(6*arcsin(c*x))*b+6*cos(4*arcsin(c*x))*b+15*cos(2*arcsin(c*x))*b+10*b)/(a+b*arcsin(c*x))/b^2","A"
403,0,0,222,1.015000," ","int((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x/(a+b*arcsin(c*x))^2,x)","F"
404,0,0,104,0.849000," ","int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^2/(a+b*arcsin(c*x))^2,x)","F"
405,0,0,28,5.249000," ","int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{3} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^3/(a+b*arcsin(c*x))^2,x)","F"
406,0,0,28,6.349000," ","int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}}}{x^{4} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((-c^2*x^2+1)^(5/2)/x^4/(a+b*arcsin(c*x))^2,x)","F"
407,0,0,48,0.287000," ","int(x^m/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{x^{m}}{\left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(x^m/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","F"
408,1,341,192,0.109000," ","int(x^5/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\frac{5 \arcsin \left(c x \right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b +5 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b -15 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b -15 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +10 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +10 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +5 \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a +5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a -15 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a -15 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +10 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +10 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -10 x b c -\sin \left(5 \arcsin \left(c x \right)\right) b +5 \sin \left(3 \arcsin \left(c x \right)\right) b}{16 c^{6} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/16/c^6*(5*arcsin(c*x)*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b+5*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*b-15*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b-15*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b+10*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+10*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+5*Si(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a+5*Ci(5*arcsin(c*x)+5*a/b)*cos(5*a/b)*a-15*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a-15*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a+10*Si(arcsin(c*x)+a/b)*sin(a/b)*a+10*Ci(arcsin(c*x)+a/b)*cos(a/b)*a-10*x*b*c-sin(5*arcsin(c*x))*b+5*sin(3*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
409,1,250,137,0.112000," ","int(x^4/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{4 \arcsin \left(c x \right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -4 \arcsin \left(c x \right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b -8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +4 \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -4 \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a -8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a +8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(4 \arcsin \left(c x \right)\right) b -4 \cos \left(2 \arcsin \left(c x \right)\right) b +3 b}{8 c^{5} b^{2} \left(a +b \arcsin \left(c x \right)\right)}"," ",0,"-1/8/c^5*(4*arcsin(c*x)*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*b-4*arcsin(c*x)*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*b-8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b+8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+4*Si(4*arcsin(c*x)+4*a/b)*cos(4*a/b)*a-4*Ci(4*arcsin(c*x)+4*a/b)*sin(4*a/b)*a-8*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a+8*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+cos(4*arcsin(c*x))*b-4*cos(2*arcsin(c*x))*b+3*b)/b^2/(a+b*arcsin(c*x))","A"
410,1,227,134,0.108000," ","int(x^3/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{3 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +3 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b -3 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b -3 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a +3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a -3 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a -3 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a +3 x b c -\sin \left(3 \arcsin \left(c x \right)\right) b}{4 c^{4} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/4/c^4*(3*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b+3*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b-3*arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b-3*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+3*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a+3*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a-3*Si(arcsin(c*x)+a/b)*sin(a/b)*a-3*Ci(arcsin(c*x)+a/b)*cos(a/b)*a+3*x*b*c-sin(3*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2","A"
411,1,136,79,0.102000," ","int(x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\frac{2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b -2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) \arcsin \left(c x \right) b +2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(2 \arcsin \left(c x \right)\right) b -b}{2 c^{3} b^{2} \left(a +b \arcsin \left(c x \right)\right)}"," ",0,"1/2/c^3*(2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*arcsin(c*x)*b-2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*arcsin(c*x)*b+2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a-2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+cos(2*arcsin(c*x))*b-b)/b^2/(a+b*arcsin(c*x))","A"
412,1,108,72,0.092000," ","int(x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\frac{\arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +\arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -x b c}{c^{2} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/c^2*(arcsin(c*x)*Si(arcsin(c*x)+a/b)*sin(a/b)*b+arcsin(c*x)*Ci(arcsin(c*x)+a/b)*cos(a/b)*b+Si(arcsin(c*x)+a/b)*sin(a/b)*a+Ci(arcsin(c*x)+a/b)*cos(a/b)*a-x*b*c)/(a+b*arcsin(c*x))/b^2","A"
413,1,19,18,0.007000," ","int(1/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","-\frac{1}{b c \left(a +b \arcsin \left(c x \right)\right)}"," ",0,"-1/b/c/(a+b*arcsin(c*x))","A"
414,0,0,46,0.189000," ","int(1/x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x \left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","F"
415,0,0,46,0.231000," ","int(1/x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","\int \frac{1}{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(1/x^2/(a+b*arcsin(c*x))^2/(-c^2*x^2+1)^(1/2),x)","F"
416,0,0,28,0.730000," ","int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
417,0,0,28,0.830000," ","int(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{3}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
418,0,0,68,0.668000," ","int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
419,0,0,26,0.344000," ","int(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
420,0,0,63,0.331000," ","int(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
421,0,0,28,3.829000," ","int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
422,0,0,28,0.980000," ","int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
423,0,0,28,0.934000," ","int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{m}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
424,0,0,28,4.556000," ","int(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{3}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
425,0,0,28,4.093000," ","int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x^{2}}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
426,0,0,26,2.803000," ","int(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{x}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
427,0,0,63,0.648000," ","int(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
428,0,0,28,7.731000," ","int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{x \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
429,0,0,28,8.148000," ","int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{x^{2} \left(-c^{2} x^{2}+1\right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
430,1,12,11,0.012000," ","int(1/arcsin(a*x)^3/(-a^2*x^2+1)^(1/2),x)","-\frac{1}{2 a \arcsin \left(a x \right)^{2}}"," ",0,"-1/2/a/arcsin(a*x)^2","A"
431,1,287,199,0.242000," ","int(x^3*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","-\frac{d \left(2 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{6 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+2 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{6 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-6 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-6 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \sin \left(\frac{2 a +2 b \arcsin \left(c x \right)}{b}-\frac{2 a}{b}\right)-\sin \left(\frac{6 a +6 b \arcsin \left(c x \right)}{b}-\frac{6 a}{b}\right)\right)}{16 c^{4} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/16/c^4*d/b*(2*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(6*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)+2*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(6*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)-6*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-6*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+3*sin(2*(a+b*arcsin(c*x))/b-2*a/b)-sin(6*(a+b*arcsin(c*x))/b-6*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
432,1,441,291,0.343000," ","int(x^2*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","\frac{d \left(\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-2 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+2 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-2 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right)+\cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right)+\cos \left(\frac{5 a +5 b \arcsin \left(c x \right)}{b}-\frac{5 a}{b}\right)\right)}{8 c^{3} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/8/c^3*d/b*(5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-2*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+2*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-2*cos((a+b*arcsin(c*x))/b-a/b)+cos(3*(a+b*arcsin(c*x))/b-3*a/b)+cos(5*(a+b*arcsin(c*x))/b-5*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
433,1,281,195,0.212000," ","int(x*(-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","-\frac{d \left(-2 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}-2 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}-4 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-4 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+2 \sin \left(\frac{2 a +2 b \arcsin \left(c x \right)}{b}-\frac{2 a}{b}\right)+\sin \left(\frac{4 a +4 b \arcsin \left(c x \right)}{b}-\frac{4 a}{b}\right)\right)}{4 c^{2} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/4/c^2*d/b/(a+b*arcsin(c*x))^(1/2)*(-2*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)-2*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)-4*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-4*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+2*sin(2*(a+b*arcsin(c*x))/b-2*a/b)+sin(4*(a+b*arcsin(c*x))/b-4*a/b))","A"
434,1,297,202,0.203000," ","int((-c^2*d*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","-\frac{d \left(\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right)+\cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right)\right)}{2 c b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/2/c*d/b*(3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+3*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-3*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+3*cos((a+b*arcsin(c*x))/b-a/b)+cos(3*(a+b*arcsin(c*x))/b-3*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
435,0,0,142,0.855000," ","int((-c^2*d*x^2+d)/x/(a+b*arcsin(c*x))^(3/2),x)","\int \frac{-c^{2} d \,x^{2}+d}{x \left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)/x/(a+b*arcsin(c*x))^(3/2),x)","F"
436,1,551,381,0.302000," ","int(x^3*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","-\frac{d^{2} \left(4 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{6 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+4 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{6 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-4 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}-4 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}-12 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-12 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+4 \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{8 a}{b}\right) \FresnelC \left(\frac{4 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}+4 \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{8 a}{b}\right) \mathrm{S}\left(\frac{4 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}+6 \sin \left(\frac{2 a +2 b \arcsin \left(c x \right)}{b}-\frac{2 a}{b}\right)+2 \sin \left(\frac{4 a +4 b \arcsin \left(c x \right)}{b}-\frac{4 a}{b}\right)-2 \sin \left(\frac{6 a +6 b \arcsin \left(c x \right)}{b}-\frac{6 a}{b}\right)-\sin \left(\frac{8 a +8 b \arcsin \left(c x \right)}{b}-\frac{8 a}{b}\right)\right)}{64 c^{4} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/64/c^4*d^2/b*(4*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(6*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)+4*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(6*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)-4*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)-4*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)-12*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-12*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+4*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(8*a/b)*FresnelC(4/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)+4*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(8*a/b)*FresnelS(4/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)+6*sin(2*(a+b*arcsin(c*x))/b-2*a/b)+2*sin(4*(a+b*arcsin(c*x))/b-4*a/b)-2*sin(6*(a+b*arcsin(c*x))/b-6*a/b)-sin(8*(a+b*arcsin(c*x))/b-8*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
437,1,590,395,0.316000," ","int(x^2*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","\frac{d^{2} \left(\sqrt{7}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{7 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{7}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}-\sqrt{7}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{7 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{7}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}+3 \sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-3 \sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-5 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+5 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right)+3 \cos \left(\frac{5 a +5 b \arcsin \left(c x \right)}{b}-\frac{5 a}{b}\right)+\cos \left(\frac{7 a +7 b \arcsin \left(c x \right)}{b}-\frac{7 a}{b}\right)-5 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right)\right)}{32 c^{3} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/32/c^3*d^2/b*(7^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*cos(7*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*7^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)-7^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*sin(7*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*7^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)+3*5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-3*5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-5*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+5*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+cos(3*(a+b*arcsin(c*x))/b-3*a/b)+3*cos(5*(a+b*arcsin(c*x))/b-5*a/b)+cos(7*(a+b*arcsin(c*x))/b-7*a/b)-5*cos((a+b*arcsin(c*x))/b-a/b))/(a+b*arcsin(c*x))^(1/2)","A"
438,1,426,299,0.245000," ","int(x*(-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","\frac{d^{2} \left(2 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{6 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+2 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{6 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{6}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}+8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}+10 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+10 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-4 \sin \left(\frac{4 a +4 b \arcsin \left(c x \right)}{b}-\frac{4 a}{b}\right)-\sin \left(\frac{6 a +6 b \arcsin \left(c x \right)}{b}-\frac{6 a}{b}\right)-5 \sin \left(\frac{2 a +2 b \arcsin \left(c x \right)}{b}-\frac{2 a}{b}\right)\right)}{16 c^{2} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/16/c^2*d^2/b*(2*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(6*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)+2*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(6*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*6^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*Pi^(1/2)+8*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)+8*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*2^(1/2)+10*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+10*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-4*sin(4*(a+b*arcsin(c*x))/b-4*a/b)-sin(6*(a+b*arcsin(c*x))/b-6*a/b)-5*sin(2*(a+b*arcsin(c*x))/b-2*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
439,1,446,302,0.232000," ","int((-c^2*d*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","-\frac{d^{2} \left(5 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-5 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+10 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-10 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+10 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right)+5 \cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right)+\cos \left(\frac{5 a +5 b \arcsin \left(c x \right)}{b}-\frac{5 a}{b}\right)\right)}{8 c b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/8/c*d^2/b*(5*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-5*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+10*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-10*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+10*cos((a+b*arcsin(c*x))/b-a/b)+5*cos(3*(a+b*arcsin(c*x))/b-3*a/b)+cos(5*(a+b*arcsin(c*x))/b-5*a/b))/(a+b*arcsin(c*x))^(1/2)","A"
440,0,0,236,1.038000," ","int((-c^2*d*x^2+d)^2/x/(a+b*arcsin(c*x))^(3/2),x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{2}}{x \left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c^2*d*x^2+d)^2/x/(a+b*arcsin(c*x))^(3/2),x)","F"
441,0,0,32,0.608000," ","int(x*arcsin(x)^(3/2)/(-x^2+1)^2-3/8*x/(-x^2+1)/arcsin(x)^(1/2),x)","\int \frac{x \arcsin \left(x \right)^{\frac{3}{2}}}{\left(-x^{2}+1\right)^{2}}-\frac{3 x}{8 \left(-x^{2}+1\right) \sqrt{\arcsin \left(x \right)}}\, dx"," ",0,"int(x*arcsin(x)^(3/2)/(-x^2+1)^2-3/8*x/(-x^2+1)/arcsin(x)^(1/2),x)","F"
442,0,0,181,0.472000," ","int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(1/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arcsin \left(a x \right)}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(1/2),x)","F"
443,0,0,104,0.450000," ","int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(1/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\arcsin \left(a x \right)}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(1/2),x)","F"
444,1,38,36,0.064000," ","int(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsin \left(a x \right)^{\frac{3}{2}} \sqrt{-a^{2} x^{2}+1}}{3 a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"2/3*arcsin(a*x)^(3/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
445,0,0,78,0.500000," ","int(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\sqrt{\arcsin \left(a x \right)}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
446,0,0,157,0.632000," ","int(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{\sqrt{\arcsin \left(a x \right)}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arcsin(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","F"
447,0,0,293,0.392000," ","int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(3/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsin \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(3/2),x)","F"
448,0,0,177,0.430000," ","int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(3/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \arcsin \left(a x \right)^{\frac{3}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(3/2),x)","F"
449,1,38,36,0.059000," ","int(arcsin(a*x)^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsin \left(a x \right)^{\frac{5}{2}} \sqrt{-a^{2} x^{2}+1}}{5 a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"2/5*arcsin(a*x)^(5/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
450,0,0,78,0.462000," ","int(arcsin(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\arcsin \left(a x \right)^{\frac{3}{2}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
451,0,0,349,0.384000," ","int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(5/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsin \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)*arcsin(a*x)^(5/2),x)","F"
452,0,0,199,0.411000," ","int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(5/2),x)","\int \sqrt{-a^{2} c \,x^{2}+c}\, \arcsin \left(a x \right)^{\frac{5}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)*arcsin(a*x)^(5/2),x)","F"
453,1,38,36,0.060000," ","int(arcsin(a*x)^(5/2)/(-a^2*c*x^2+c)^(1/2),x)","\frac{2 \arcsin \left(a x \right)^{\frac{7}{2}} \sqrt{-a^{2} x^{2}+1}}{7 a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"2/7*arcsin(a*x)^(7/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
454,0,0,78,0.464000," ","int(arcsin(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{\arcsin \left(a x \right)^{\frac{5}{2}}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x)","F"
455,0,0,180,0.456000," ","int((a^2-x^2)^(3/2)*arcsin(x/a)^(1/2),x)","\int \left(a^{2}-x^{2}\right)^{\frac{3}{2}} \sqrt{\arcsin \left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2-x^2)^(3/2)*arcsin(x/a)^(1/2),x)","F"
456,0,0,100,0.436000," ","int((a^2-x^2)^(1/2)*arcsin(x/a)^(1/2),x)","\int \sqrt{a^{2}-x^{2}}\, \sqrt{\arcsin \left(\frac{x}{a}\right)}\, dx"," ",0,"int((a^2-x^2)^(1/2)*arcsin(x/a)^(1/2),x)","F"
457,1,38,34,0.070000," ","int(arcsin(x/a)^(1/2)/(a^2-x^2)^(1/2),x)","\frac{2 \arcsin \left(\frac{x}{a}\right)^{\frac{3}{2}} a \sqrt{\frac{a^{2}-x^{2}}{a^{2}}}}{3 \sqrt{a^{2}-x^{2}}}"," ",0,"2/3*arcsin(x/a)^(3/2)*a/(a^2-x^2)^(1/2)*((a^2-x^2)/a^2)^(1/2)","A"
458,0,0,77,0.499000," ","int(arcsin(x/a)^(1/2)/(a^2-x^2)^(3/2),x)","\int \frac{\sqrt{\arcsin \left(\frac{x}{a}\right)}}{\left(a^{2}-x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(x/a)^(1/2)/(a^2-x^2)^(3/2),x)","F"
459,0,0,155,0.559000," ","int(arcsin(x/a)^(1/2)/(a^2-x^2)^(5/2),x)","\int \frac{\sqrt{\arcsin \left(\frac{x}{a}\right)}}{\left(a^{2}-x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int(arcsin(x/a)^(1/2)/(a^2-x^2)^(5/2),x)","F"
460,0,0,289,0.391000," ","int((a^2-x^2)^(3/2)*arcsin(x/a)^(3/2),x)","\int \left(a^{2}-x^{2}\right)^{\frac{3}{2}} \arcsin \left(\frac{x}{a}\right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2-x^2)^(3/2)*arcsin(x/a)^(3/2),x)","F"
461,0,0,173,0.426000," ","int((a^2-x^2)^(1/2)*arcsin(x/a)^(3/2),x)","\int \sqrt{a^{2}-x^{2}}\, \arcsin \left(\frac{x}{a}\right)^{\frac{3}{2}}\, dx"," ",0,"int((a^2-x^2)^(1/2)*arcsin(x/a)^(3/2),x)","F"
462,1,38,34,0.062000," ","int(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x)","\frac{2 \arcsin \left(\frac{x}{a}\right)^{\frac{5}{2}} a \sqrt{\frac{a^{2}-x^{2}}{a^{2}}}}{5 \sqrt{a^{2}-x^{2}}}"," ",0,"2/5*arcsin(x/a)^(5/2)*a/(a^2-x^2)^(1/2)*((a^2-x^2)/a^2)^(1/2)","A"
463,0,0,77,0.429000," ","int(arcsin(x/a)^(3/2)/(a^2-x^2)^(3/2),x)","\int \frac{\arcsin \left(\frac{x}{a}\right)^{\frac{3}{2}}}{\left(a^{2}-x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(arcsin(x/a)^(3/2)/(a^2-x^2)^(3/2),x)","F"
464,1,20,19,0.129000," ","int(x/(-x^2+1)^(1/2)/arcsin(x)^(1/2),x)","\mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{\arcsin \left(x \right)}}{\sqrt{\pi}}\right) \sqrt{2}\, \sqrt{\pi}"," ",0,"FresnelS(2^(1/2)/Pi^(1/2)*arcsin(x)^(1/2))*2^(1/2)*Pi^(1/2)","A"
465,0,0,196,0.415000," ","int((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\sqrt{\arcsin \left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x)","F"
466,0,0,136,0.389000," ","int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\sqrt{\arcsin \left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x)","F"
467,0,0,81,0.444000," ","int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(1/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\sqrt{\arcsin \left(a x \right)}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(1/2),x)","F"
468,1,38,36,0.055000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(1/2),x)","\frac{2 \sqrt{\arcsin \left(a x \right)}\, \sqrt{-a^{2} x^{2}+1}}{a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"2*arcsin(a*x)^(1/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
469,0,0,22,0.477000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\arcsin \left(a x \right)}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(1/2),x)","F"
470,0,0,22,0.582000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\arcsin \left(a x \right)}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(1/2),x)","F"
471,0,0,193,0.382000," ","int((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{\arcsin \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x)","F"
472,0,0,135,0.381000," ","int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arcsin \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x)","F"
473,0,0,82,0.415000," ","int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\arcsin \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x)","F"
474,1,38,36,0.057000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(3/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}}{\sqrt{\arcsin \left(a x \right)}\, a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"-2/arcsin(a*x)^(1/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
475,0,0,90,0.469000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsin \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(3/2),x)","F"
476,0,0,90,0.584000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arcsin \left(a x \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(3/2),x)","F"
477,0,0,168,0.386000," ","int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{\arcsin \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x)","F"
478,0,0,104,0.419000," ","int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x)","\int \frac{\sqrt{-a^{2} c \,x^{2}+c}}{\arcsin \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x)","F"
479,1,38,36,0.058000," ","int(1/(-a^2*c*x^2+c)^(1/2)/arcsin(a*x)^(5/2),x)","-\frac{2 \sqrt{-a^{2} x^{2}+1}}{3 \arcsin \left(a x \right)^{\frac{3}{2}} a \sqrt{-c \left(a^{2} x^{2}-1\right)}}"," ",0,"-2/3/arcsin(a*x)^(3/2)/a/(-c*(a^2*x^2-1))^(1/2)*(-a^2*x^2+1)^(1/2)","A"
480,0,0,90,0.467000," ","int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \arcsin \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(3/2)/arcsin(a*x)^(5/2),x)","F"
481,0,0,90,0.585000," ","int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(5/2),x)","\int \frac{1}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \arcsin \left(a x \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(-a^2*c*x^2+c)^(5/2)/arcsin(a*x)^(5/2),x)","F"
482,0,0,241,0.567000," ","int(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","\int x^{2} \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","F"
483,0,0,355,0.266000," ","int(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","\int x \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","F"
484,0,0,237,0.258000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","\int \sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n,x)","F"
485,0,0,198,0.658000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x,x)","\int \frac{\sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x,x)","F"
486,0,0,81,0.387000," ","int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x^2,x)","\int \frac{\sqrt{-c^{2} d \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(1/2)*(a+b*arcsin(c*x))^n/x^2,x)","F"
487,0,0,630,0.466000," ","int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","\int x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","F"
488,0,0,541,0.186000," ","int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","\int x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","F"
489,0,0,432,0.136000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","\int \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n,x)","F"
490,0,0,388,0.278000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x,x)","F"
491,0,0,273,0.401000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x^2,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^n/x^2,x)","F"
492,0,0,840,0.477000," ","int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","\int x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","F"
493,0,0,743,0.190000," ","int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","\int x \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","F"
494,0,0,644,0.132000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","\int \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n,x)","F"
495,0,0,752,0.274000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}}{x}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x,x)","F"
496,0,0,465,0.370000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x^2,x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{n}}{x^{2}}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^n/x^2,x)","F"
497,0,0,24,0.428000," ","int(x^m*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{m} \arcsin \left(a x \right)^{n}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^m*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","F"
498,0,0,147,0.464000," ","int(x^3*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \arcsin \left(a x \right)^{n}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^3*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","F"
499,0,0,101,0.405000," ","int(x^2*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \arcsin \left(a x \right)^{n}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^2*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","F"
500,0,0,67,0.100000," ","int(x*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","\int \frac{x \arcsin \left(a x \right)^{n}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x*arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","F"
501,1,18,17,0.006000," ","int(arcsin(a*x)^n/(-a^2*x^2+1)^(1/2),x)","\frac{\arcsin \left(a x \right)^{1+n}}{a \left(1+n \right)}"," ",0,"arcsin(a*x)^(1+n)/a/(1+n)","A"
502,0,0,24,0.176000," ","int(arcsin(a*x)^n/x/(-a^2*x^2+1)^(1/2),x)","\int \frac{\arcsin \left(a x \right)^{n}}{x \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arcsin(a*x)^n/x/(-a^2*x^2+1)^(1/2),x)","F"
503,0,0,24,0.270000," ","int(arcsin(a*x)^n/x^2/(-a^2*x^2+1)^(1/2),x)","\int \frac{\arcsin \left(a x \right)^{n}}{x^{2} \sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arcsin(a*x)^n/x^2/(-a^2*x^2+1)^(1/2),x)","F"
504,0,0,318,0.442000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","F"
505,0,0,229,0.277000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","F"
506,0,0,112,0.277000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","\int \sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))*(-c*f*x+f)^(1/2),x)","F"
507,0,0,123,0.322000," ","int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}}{\sqrt{c d x +d}}\, dx"," ",0,"int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(1/2),x)","F"
508,0,0,144,0.378000," ","int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(3/2),x)","F"
509,0,0,141,0.321000," ","int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right) \sqrt{-c f x +f}}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))*(-c*f*x+f)^(1/2)/(c*d*x+d)^(5/2),x)","F"
510,0,0,348,0.276000," ","int((c*d*x+d)^(5/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(5/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","F"
511,0,0,190,0.272000," ","int((c*d*x+d)^(3/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","F"
512,0,0,229,0.278000," ","int((c*d*x+d)^(1/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","\int \sqrt{c d x +d}\, \left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*f*x+f)^(3/2)*(a+b*arcsin(c*x)),x)","F"
513,0,0,210,0.318000," ","int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{c d x +d}}\, dx"," ",0,"int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x)","F"
514,0,0,224,0.339000," ","int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x)","F"
515,0,0,284,0.345000," ","int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-c*f*x+f)^(3/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x)","F"
516,0,0,265,0.274000," ","int((c*d*x+d)^(5/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(5/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","F"
517,0,0,348,0.276000," ","int((c*d*x+d)^(3/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","F"
518,0,0,318,0.283000," ","int((c*d*x+d)^(1/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","\int \sqrt{c d x +d}\, \left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*f*x+f)^(5/2)*(a+b*arcsin(c*x)),x)","F"
519,0,0,295,0.320000," ","int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{c d x +d}}\, dx"," ",0,"int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(1/2),x)","F"
520,0,0,405,0.362000," ","int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(3/2),x)","F"
521,0,0,368,0.363000," ","int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x)","\int \frac{\left(-c f x +f \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-c*f*x+f)^(5/2)*(a+b*arcsin(c*x))/(c*d*x+d)^(5/2),x)","F"
522,0,0,295,0.323000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c f x +f}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","F"
523,0,0,210,0.324000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c f x +f}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","F"
524,0,0,123,0.331000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)}{\sqrt{-c f x +f}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(1/2),x)","F"
525,0,0,47,0.314000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(1/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\sqrt{c d x +d}\, \sqrt{-c f x +f}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(1/2),x)","F"
526,0,0,89,0.342000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(1/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{3}{2}} \sqrt{-c f x +f}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(1/2),x)","F"
527,0,0,229,0.339000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(1/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{5}{2}} \sqrt{-c f x +f}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(1/2),x)","F"
528,0,0,403,0.361000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","F"
529,0,0,224,0.345000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","F"
530,0,0,144,0.348000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(3/2),x)","F"
531,0,0,88,0.339000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(3/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\sqrt{c d x +d}\, \left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(3/2),x)","F"
532,0,0,84,0.333000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(3/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(3/2),x)","F"
533,0,0,219,0.333000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(3/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{5}{2}} \left(-c f x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(3/2),x)","F"
534,0,0,367,0.372000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","F"
535,0,0,284,0.350000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","F"
536,0,0,142,0.326000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)}{\left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))/(-c*f*x+f)^(5/2),x)","F"
537,0,0,229,0.338000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(5/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\sqrt{c d x +d}\, \left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(1/2)/(-c*f*x+f)^(5/2),x)","F"
538,0,0,219,0.337000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(5/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(3/2)/(-c*f*x+f)^(5/2),x)","F"
539,0,0,160,0.329000," ","int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(5/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(c d x +d \right)^{\frac{5}{2}} \left(-c f x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(c*d*x+d)^(5/2)/(-c*f*x+f)^(5/2),x)","F"
540,0,0,523,0.369000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c e x +e}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x)","F"
541,0,0,385,0.312000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c e x +e}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2),x)","F"
542,0,0,186,0.311000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int \sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
543,0,0,202,0.349000," ","int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c e x +e}}{\sqrt{c d x +d}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(1/2),x)","F"
544,0,0,515,0.292000," ","int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c e x +e}}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(3/2),x)","F"
545,0,0,422,0.352000," ","int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c e x +e}}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2*(-c*e*x+e)^(1/2)/(c*d*x+d)^(5/2),x)","F"
546,0,0,593,0.309000," ","int((c*d*x+d)^(5/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
547,0,0,306,0.303000," ","int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
548,0,0,385,0.315000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int \sqrt{c d x +d}\, \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
549,0,0,348,0.350000," ","int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}}\, dx"," ",0,"int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x)","F"
550,0,0,681,0.293000," ","int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x)","F"
551,0,0,472,0.290000," ","int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x)","F"
552,0,0,426,0.311000," ","int((c*d*x+d)^(5/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","\int \left(c d x +d \right)^{\frac{5}{2}} \left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","F"
553,0,0,593,0.309000," ","int((c*d*x+d)^(3/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","F"
554,0,0,523,0.318000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","\int \sqrt{c d x +d}\, \left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2,x)","F"
555,0,0,483,0.357000," ","int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}}\, dx"," ",0,"int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2),x)","F"
556,0,0,855,0.296000," ","int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2),x)","F"
557,0,0,637,0.292000," ","int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x)","\int \frac{\left(-c e x +e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((-c*e*x+e)^(5/2)*(a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2),x)","F"
558,0,0,483,0.359000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{-c e x +e}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","F"
559,0,0,348,0.360000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{-c e x +e}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","F"
560,0,0,203,0.361000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{-c e x +e}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(1/2),x)","F"
561,0,0,47,0.352000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
562,0,0,448,0.372000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(1/2),x)","F"
563,0,0,817,0.369000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{5}{2}} \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(1/2),x)","F"
564,0,0,855,0.295000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","F"
565,0,0,680,0.300000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","F"
566,0,0,515,0.300000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(3/2),x)","F"
567,0,0,447,0.367000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(3/2),x)","F"
568,0,0,213,0.356000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
569,0,0,652,0.371000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{5}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(3/2),x)","F"
570,0,0,642,0.299000," ","int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","\int \frac{\left(c d x +d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(5/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","F"
571,0,0,476,0.296000," ","int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","F"
572,0,0,426,0.362000," ","int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","\int \frac{\sqrt{c d x +d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(a+b*arcsin(c*x))^2/(-c*e*x+e)^(5/2),x)","F"
573,0,0,817,0.376000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(5/2),x)","F"
574,0,0,652,0.371000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(5/2),x)","F"
575,0,0,334,0.368000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{5}{2}} \left(-c e x +e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(5/2)/(-c*e*x+e)^(5/2),x)","F"
576,0,0,295,0.995000," ","int(x^2*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int x^{2} \sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^2*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
577,0,0,191,0.557000," ","int(x*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int x \sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x*(c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
578,0,0,186,0.000000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int \sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
579,0,0,420,0.436000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x,x)","\int \frac{\sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}{x}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x,x)","F"
580,0,0,245,1.000000," ","int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x)","\int \frac{\sqrt{c d x +d}\, \sqrt{-c e x +e}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((c*d*x+d)^(1/2)*(-c*e*x+e)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x)","F"
581,0,0,433,1.046000," ","int(x^2*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int x^{2} \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x^2*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
582,0,0,290,0.571000," ","int(x*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int x \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int(x*(c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
583,0,0,306,0.000000," ","int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","\int \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2,x)","F"
584,0,0,605,0.428000," ","int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x,x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{x}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x,x)","F"
585,0,0,459,1.022000," ","int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x)","\int \frac{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{x^{2}}\, dx"," ",0,"int((c*d*x+d)^(3/2)*(-c*e*x+e)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x)","F"
586,0,0,214,0.669000," ","int(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
587,0,0,157,0.801000," ","int(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{x \left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
588,0,0,47,0.000000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
589,0,0,295,0.425000," ","int((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{x \sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
590,0,0,210,1.288000," ","int((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{x^{2} \sqrt{c d x +d}\, \sqrt{-c e x +e}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(1/2)/(-c*e*x+e)^(1/2),x)","F"
591,0,0,283,0.657000," ","int(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{x^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
592,0,0,241,0.852000," ","int(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{x \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
593,0,0,213,0.000000," ","int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
594,0,0,553,0.434000," ","int((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{x \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/x/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
595,0,0,395,1.272000," ","int((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{x^{2} \left(c d x +d \right)^{\frac{3}{2}} \left(-c e x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/x^2/(c*d*x+d)^(3/2)/(-c*e*x+e)^(3/2),x)","F"
596,1,201,132,0.008000," ","int(x^4*(e*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e \,c^{7} x^{7}+\frac{1}{5} c^{7} x^{5} d \right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) e \,c^{7} x^{7}}{7}+\frac{\arcsin \left(c x \right) c^{7} x^{5} d}{5}-\frac{e \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{c^{2} d \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}\right)}{c^{2}}}{c^{5}}"," ",0,"1/c^5*(a/c^2*(1/7*e*c^7*x^7+1/5*c^7*x^5*d)+b/c^2*(1/7*arcsin(c*x)*e*c^7*x^7+1/5*arcsin(c*x)*c^7*x^5*d-1/7*e*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-1/5*c^2*d*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))))","A"
597,1,177,131,0.006000," ","int(x^3*(e*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e \,c^{6} x^{6}+\frac{1}{4} x^{4} c^{6} d \right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) e \,c^{6} x^{6}}{6}+\frac{\arcsin \left(c x \right) c^{6} x^{4} d}{4}-\frac{e \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}-\frac{c^{2} d \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*e*c^6*x^6+1/4*x^4*c^6*d)+b/c^2*(1/6*arcsin(c*x)*e*c^6*x^6+1/4*arcsin(c*x)*c^6*x^4*d-1/6*e*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/4*c^2*d*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))))","A"
598,1,161,104,0.005000," ","int(x^2*(e*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e \,c^{5} x^{5}+\frac{1}{3} c^{5} d \,x^{3}\right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) e \,c^{5} x^{5}}{5}+\frac{\arcsin \left(c x \right) c^{5} d \,x^{3}}{3}-\frac{e \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{c^{2} d \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}\right)}{c^{2}}}{c^{3}}"," ",0,"1/c^3*(a/c^2*(1/5*e*c^5*x^5+1/3*c^5*d*x^3)+b/c^2*(1/5*arcsin(c*x)*e*c^5*x^5+1/3*arcsin(c*x)*c^5*d*x^3-1/5*e*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/3*c^2*d*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))))","A"
599,1,137,110,0.004000," ","int(x*(e*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{4} e \,c^{4} x^{4}+\frac{1}{2} x^{2} c^{4} d \right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) e \,c^{4} x^{4}}{4}+\frac{\arcsin \left(c x \right) c^{4} d \,x^{2}}{2}-\frac{e \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}-\frac{c^{2} d \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}\right)}{c^{2}}}{c^{2}}"," ",0,"1/c^2*(a/c^2*(1/4*e*c^4*x^4+1/2*x^2*c^4*d)+b/c^2*(1/4*arcsin(c*x)*e*c^4*x^4+1/2*arcsin(c*x)*c^4*d*x^2-1/4*e*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/2*c^2*d*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))))","A"
600,1,111,71,0.005000," ","int((e*x^2+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) c^{3} x^{3} e}{3}+\arcsin \left(c x \right) c^{3} d x -\frac{e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+c^{2} d \sqrt{-c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b/c^2*(1/3*arcsin(c*x)*c^3*x^3*e+arcsin(c*x)*c^3*d*x-1/3*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+c^2*d*(-c^2*x^2+1)^(1/2)))","A"
601,1,167,138,0.256000," ","int((e*x^2+d)*(a+b*arcsin(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)-\frac{i b d \arcsin \left(c x \right)^{2}}{2}+d b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)+d b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-i d b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{b \arcsin \left(c x \right) e \cos \left(2 \arcsin \left(c x \right)\right)}{4 c^{2}}+\frac{b e \sin \left(2 \arcsin \left(c x \right)\right)}{8 c^{2}}"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)-1/2*I*b*d*arcsin(c*x)^2+d*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))+d*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*d*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-I*d*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-1/4*b/c^2*arcsin(c*x)*e*cos(2*arcsin(c*x))+1/8*b/c^2*e*sin(2*arcsin(c*x))","A"
602,1,79,62,0.008000," ","int((e*x^2+d)*(a+b*arcsin(c*x))/x^2,x)","c \left(\frac{a \left(c e x -\frac{c d}{x}\right)}{c^{2}}+\frac{b \left(\arcsin \left(c x \right) e c x -\frac{\arcsin \left(c x \right) c d}{x}+e \sqrt{-c^{2} x^{2}+1}-c^{2} d \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{2}}\right)"," ",0,"c*(a/c^2*(c*e*x-c*d/x)+b/c^2*(arcsin(c*x)*e*c*x-arcsin(c*x)*c*d/x+e*(-c^2*x^2+1)^(1/2)-c^2*d*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
603,1,174,127,0.865000," ","int((e*x^2+d)*(a+b*arcsin(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}-\frac{i b e \arcsin \left(c x \right)^{2}}{2}+\frac{i c^{2} d b}{2}-\frac{b c d \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{d b \arcsin \left(c x \right)}{2 x^{2}}+b e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+b e \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i b e \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-i b e \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"a*e*ln(c*x)-1/2*d*a/x^2-1/2*I*b*e*arcsin(c*x)^2+1/2*I*c^2*d*b-1/2*b*c*d*(-c^2*x^2+1)^(1/2)/x-1/2*d*b*arcsin(c*x)/x^2+b*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+b*e*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*b*e*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-I*b*e*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
604,1,120,75,0.012000," ","int((e*x^2+d)*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{d}{3 c \,x^{3}}-\frac{e}{c x}\right)}{c^{2}}+\frac{b \left(-\frac{\arcsin \left(c x \right) d}{3 c \,x^{3}}-\frac{\arcsin \left(c x \right) e}{c x}-e \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{c^{2} d \left(-\frac{\sqrt{-c^{2} x^{2}+1}}{2 c^{2} x^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2}\right)}{3}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-1/3/c*d/x^3-e/c/x)+b/c^2*(-1/3*arcsin(c*x)/c*d/x^3-arcsin(c*x)*e/c/x-e*arctanh(1/(-c^2*x^2+1)^(1/2))+1/3*c^2*d*(-1/2/c^2/x^2*(-c^2*x^2+1)^(1/2)-1/2*arctanh(1/(-c^2*x^2+1)^(1/2)))))","A"
605,1,339,215,0.006000," ","int(x^4*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{2} c^{9} x^{9}+\frac{2}{7} c^{9} e d \,x^{7}+\frac{1}{5} d^{2} c^{9} x^{5}\right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{9} x^{9}}{9}+\frac{2 \arcsin \left(c x \right) c^{9} e d \,x^{7}}{7}+\frac{\arcsin \left(c x \right) d^{2} c^{9} x^{5}}{5}-\frac{e^{2} \left(-\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{8 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{63}-\frac{16 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{105}-\frac{64 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{315}-\frac{128 \sqrt{-c^{2} x^{2}+1}}{315}\right)}{9}-\frac{2 c^{2} e d \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{d^{2} c^{4} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}\right)}{c^{4}}}{c^{5}}"," ",0,"1/c^5*(a/c^4*(1/9*e^2*c^9*x^9+2/7*c^9*e*d*x^7+1/5*d^2*c^9*x^5)+b/c^4*(1/9*arcsin(c*x)*e^2*c^9*x^9+2/7*arcsin(c*x)*c^9*e*d*x^7+1/5*arcsin(c*x)*d^2*c^9*x^5-1/9*e^2*(-1/9*c^8*x^8*(-c^2*x^2+1)^(1/2)-8/63*c^6*x^6*(-c^2*x^2+1)^(1/2)-16/105*c^4*x^4*(-c^2*x^2+1)^(1/2)-64/315*c^2*x^2*(-c^2*x^2+1)^(1/2)-128/315*(-c^2*x^2+1)^(1/2))-2/7*c^2*e*d*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-1/5*d^2*c^4*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))))","A"
606,1,303,217,0.009000," ","int(x^3*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{2} c^{8} x^{8}+\frac{1}{3} c^{8} e d \,x^{6}+\frac{1}{4} x^{4} c^{8} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{8} x^{8}}{8}+\frac{\arcsin \left(c x \right) c^{8} e d \,x^{6}}{3}+\frac{\arcsin \left(c x \right) d^{2} c^{8} x^{4}}{4}-\frac{e^{2} \left(-\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{8}-\frac{7 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{48}-\frac{35 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{192}-\frac{35 c x \sqrt{-c^{2} x^{2}+1}}{128}+\frac{35 \arcsin \left(c x \right)}{128}\right)}{8}-\frac{c^{2} e d \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{3}-\frac{d^{2} c^{4} \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}\right)}{c^{4}}}{c^{4}}"," ",0,"1/c^4*(a/c^4*(1/8*e^2*c^8*x^8+1/3*c^8*e*d*x^6+1/4*x^4*c^8*d^2)+b/c^4*(1/8*arcsin(c*x)*e^2*c^8*x^8+1/3*arcsin(c*x)*c^8*e*d*x^6+1/4*arcsin(c*x)*d^2*c^8*x^4-1/8*e^2*(-1/8*c^7*x^7*(-c^2*x^2+1)^(1/2)-7/48*c^5*x^5*(-c^2*x^2+1)^(1/2)-35/192*c^3*x^3*(-c^2*x^2+1)^(1/2)-35/128*c*x*(-c^2*x^2+1)^(1/2)+35/128*arcsin(c*x))-1/3*c^2*e*d*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/4*d^2*c^4*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))))","A"
607,1,279,176,0.005000," ","int(x^2*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{2} c^{7} x^{7}+\frac{2}{5} c^{7} e d \,x^{5}+\frac{1}{3} d^{2} c^{7} x^{3}\right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{7} x^{7}}{7}+\frac{2 \arcsin \left(c x \right) c^{7} e d \,x^{5}}{5}+\frac{\arcsin \left(c x \right) d^{2} c^{7} x^{3}}{3}-\frac{e^{2} \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{2 c^{2} e d \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{d^{2} c^{4} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}\right)}{c^{4}}}{c^{3}}"," ",0,"1/c^3*(a/c^4*(1/7*e^2*c^7*x^7+2/5*c^7*e*d*x^5+1/3*d^2*c^7*x^3)+b/c^4*(1/7*arcsin(c*x)*e^2*c^7*x^7+2/5*arcsin(c*x)*c^7*e*d*x^5+1/3*arcsin(c*x)*d^2*c^7*x^3-1/7*e^2*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-2/5*c^2*e*d*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/3*d^2*c^4*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))))","A"
608,1,243,167,0.005000," ","int(x*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e^{2} c^{6} x^{6}+\frac{1}{2} c^{6} e d \,x^{4}+\frac{1}{2} x^{2} c^{6} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{6} x^{6}}{6}+\frac{\arcsin \left(c x \right) c^{6} e d \,x^{4}}{2}+\frac{\arcsin \left(c x \right) d^{2} c^{6} x^{2}}{2}-\frac{e^{2} \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}-\frac{c^{2} e d \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{2}-\frac{d^{2} c^{4} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}\right)}{c^{4}}}{c^{2}}"," ",0,"1/c^2*(a/c^4*(1/6*e^2*c^6*x^6+1/2*c^6*e*d*x^4+1/2*x^2*c^6*d^2)+b/c^4*(1/6*arcsin(c*x)*e^2*c^6*x^6+1/2*arcsin(c*x)*c^6*e*d*x^4+1/2*arcsin(c*x)*d^2*c^6*x^2-1/6*e^2*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/2*c^2*e*d*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/2*d^2*c^4*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))))","A"
609,1,209,134,0.005000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} e d \,x^{3}+d^{2} c^{5} x \right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \arcsin \left(c x \right) c^{5} e d \,x^{3}}{3}+\arcsin \left(c x \right) d^{2} c^{5} x -\frac{e^{2} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{2 c^{2} e d \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+d^{2} c^{4} \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*e*d*x^3+d^2*c^5*x)+b/c^4*(1/5*arcsin(c*x)*e^2*c^5*x^5+2/3*arcsin(c*x)*c^5*e*d*x^3+arcsin(c*x)*d^2*c^5*x-1/5*e^2*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-2/3*c^2*e*d*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+d^2*c^4*(-c^2*x^2+1)^(1/2)))","A"
610,1,262,225,0.327000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))/x,x)","\frac{a \,e^{2} x^{4}}{4}+a e d \,x^{2}+a \,d^{2} \ln \left(c x \right)-\frac{i b \,d^{2} \arcsin \left(c x \right)^{2}}{2}+b \,d^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+b \,d^{2} \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i b \,d^{2} \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-i b \,d^{2} \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{b \arcsin \left(c x \right) e^{2} \cos \left(4 \arcsin \left(c x \right)\right)}{32 c^{4}}-\frac{b \,e^{2} \sin \left(4 \arcsin \left(c x \right)\right)}{128 c^{4}}-\frac{b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) d e}{2 c^{2}}-\frac{b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) e^{2}}{8 c^{4}}+\frac{b \sin \left(2 \arcsin \left(c x \right)\right) d e}{4 c^{2}}+\frac{b \sin \left(2 \arcsin \left(c x \right)\right) e^{2}}{16 c^{4}}"," ",0,"1/4*a*e^2*x^4+a*e*d*x^2+a*d^2*ln(c*x)-1/2*I*b*d^2*arcsin(c*x)^2+b*d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+b*d^2*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-I*b*d^2*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-I*b*d^2*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/32*b/c^4*arcsin(c*x)*e^2*cos(4*arcsin(c*x))-1/128*b/c^4*e^2*sin(4*arcsin(c*x))-1/2*b/c^2*cos(2*arcsin(c*x))*arcsin(c*x)*d*e-1/8*b/c^4*cos(2*arcsin(c*x))*arcsin(c*x)*e^2+1/4*b/c^2*sin(2*arcsin(c*x))*d*e+1/16*b/c^4*sin(2*arcsin(c*x))*e^2","A"
611,1,168,114,0.008000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))/x^2,x)","c \left(\frac{a \left(\frac{e^{2} c^{3} x^{3}}{3}+2 c^{3} e d x -\frac{d^{2} c^{3}}{x}\right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{3} x^{3}}{3}+2 \arcsin \left(c x \right) c^{3} e d x -\frac{\arcsin \left(c x \right) d^{2} c^{3}}{x}-\frac{e^{2} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+2 c^{2} e d \sqrt{-c^{2} x^{2}+1}-d^{2} c^{4} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{4}}\right)"," ",0,"c*(a/c^4*(1/3*e^2*c^3*x^3+2*c^3*e*d*x-d^2*c^3/x)+b/c^4*(1/3*arcsin(c*x)*e^2*c^3*x^3+2*arcsin(c*x)*c^3*e*d*x-arcsin(c*x)*d^2*c^3/x-1/3*e^2*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+2*c^2*e*d*(-c^2*x^2+1)^(1/2)-d^2*c^4*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
612,1,248,189,0.900000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a e d \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}-i b d e \arcsin \left(c x \right)^{2}+\frac{b \,e^{2} x \sqrt{-c^{2} x^{2}+1}}{4 c}+\frac{b \arcsin \left(c x \right) x^{2} e^{2}}{2}-\frac{b \,e^{2} \arcsin \left(c x \right)}{4 c^{2}}+\frac{i c^{2} b \,d^{2}}{2}-\frac{b c \,d^{2} \sqrt{-c^{2} x^{2}+1}}{2 x}-\frac{b \arcsin \left(c x \right) d^{2}}{2 x^{2}}+2 b e d \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+2 b e d \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i b e d \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-2 i b e d \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)"," ",0,"1/2*a*x^2*e^2+2*a*e*d*ln(c*x)-1/2*a*d^2/x^2-I*b*d*e*arcsin(c*x)^2+1/4*b*e^2*x*(-c^2*x^2+1)^(1/2)/c+1/2*b*arcsin(c*x)*x^2*e^2-1/4*b*e^2*arcsin(c*x)/c^2+1/2*I*c^2*b*d^2-1/2*b*c*d^2*(-c^2*x^2+1)^(1/2)/x-1/2*b*arcsin(c*x)*d^2/x^2+2*b*e*d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+2*b*e*d*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b*e*d*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))-2*I*b*e*d*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))","A"
613,1,156,114,0.011000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(\frac{a \left(c x \,e^{2}-\frac{d^{2} c}{3 x^{3}}-\frac{2 c e d}{x}\right)}{c^{4}}+\frac{b \left(\arcsin \left(c x \right) c x \,e^{2}-\frac{\arcsin \left(c x \right) d^{2} c}{3 x^{3}}-\frac{2 \arcsin \left(c x \right) c e d}{x}+e^{2} \sqrt{-c^{2} x^{2}+1}+\frac{d^{2} c^{4} \left(-\frac{\sqrt{-c^{2} x^{2}+1}}{2 c^{2} x^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2}\right)}{3}-2 c^{2} e d \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{4}}\right)"," ",0,"c^3*(a/c^4*(c*x*e^2-1/3*d^2*c/x^3-2*c*e*d/x)+b/c^4*(arcsin(c*x)*c*x*e^2-1/3*arcsin(c*x)*d^2*c/x^3-2*arcsin(c*x)*c*e*d/x+e^2*(-c^2*x^2+1)^(1/2)+1/3*d^2*c^4*(-1/2/c^2/x^2*(-c^2*x^2+1)^(1/2)-1/2*arctanh(1/(-c^2*x^2+1)^(1/2)))-2*c^2*e*d*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
614,1,497,309,0.005000," ","int(x^4*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{11} e^{3} c^{11} x^{11}+\frac{1}{3} c^{11} d \,e^{2} x^{9}+\frac{3}{7} c^{11} d^{2} e \,x^{7}+\frac{1}{5} c^{11} x^{5} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{11} x^{11}}{11}+\frac{\arcsin \left(c x \right) c^{11} d \,e^{2} x^{9}}{3}+\frac{3 \arcsin \left(c x \right) c^{11} d^{2} e \,x^{7}}{7}+\frac{\arcsin \left(c x \right) c^{11} x^{5} d^{3}}{5}-\frac{e^{3} \left(-\frac{c^{10} x^{10} \sqrt{-c^{2} x^{2}+1}}{11}-\frac{10 c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{99}-\frac{80 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{693}-\frac{32 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{231}-\frac{128 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{693}-\frac{256 \sqrt{-c^{2} x^{2}+1}}{693}\right)}{11}-\frac{c^{2} d \,e^{2} \left(-\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{8 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{63}-\frac{16 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{105}-\frac{64 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{315}-\frac{128 \sqrt{-c^{2} x^{2}+1}}{315}\right)}{3}-\frac{3 c^{4} d^{2} e \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{d^{3} c^{6} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}\right)}{c^{6}}}{c^{5}}"," ",0,"1/c^5*(a/c^6*(1/11*e^3*c^11*x^11+1/3*c^11*d*e^2*x^9+3/7*c^11*d^2*e*x^7+1/5*c^11*x^5*d^3)+b/c^6*(1/11*arcsin(c*x)*e^3*c^11*x^11+1/3*arcsin(c*x)*c^11*d*e^2*x^9+3/7*arcsin(c*x)*c^11*d^2*e*x^7+1/5*arcsin(c*x)*c^11*x^5*d^3-1/11*e^3*(-1/11*c^10*x^10*(-c^2*x^2+1)^(1/2)-10/99*c^8*x^8*(-c^2*x^2+1)^(1/2)-80/693*c^6*x^6*(-c^2*x^2+1)^(1/2)-32/231*c^4*x^4*(-c^2*x^2+1)^(1/2)-128/693*c^2*x^2*(-c^2*x^2+1)^(1/2)-256/693*(-c^2*x^2+1)^(1/2))-1/3*c^2*d*e^2*(-1/9*c^8*x^8*(-c^2*x^2+1)^(1/2)-8/63*c^6*x^6*(-c^2*x^2+1)^(1/2)-16/105*c^4*x^4*(-c^2*x^2+1)^(1/2)-64/315*c^2*x^2*(-c^2*x^2+1)^(1/2)-128/315*(-c^2*x^2+1)^(1/2))-3/7*c^4*d^2*e*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-1/5*d^3*c^6*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))))","A"
615,1,449,354,0.014000," ","int(x^3*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{10} e^{3} c^{10} x^{10}+\frac{3}{8} c^{10} d \,e^{2} x^{8}+\frac{1}{2} c^{10} d^{2} e \,x^{6}+\frac{1}{4} x^{4} c^{10} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{10} x^{10}}{10}+\frac{3 \arcsin \left(c x \right) c^{10} d \,e^{2} x^{8}}{8}+\frac{\arcsin \left(c x \right) c^{10} d^{2} e \,x^{6}}{2}+\frac{\arcsin \left(c x \right) c^{10} x^{4} d^{3}}{4}-\frac{e^{3} \left(-\frac{c^{9} x^{9} \sqrt{-c^{2} x^{2}+1}}{10}-\frac{9 c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{80}-\frac{21 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{160}-\frac{21 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{128}-\frac{63 c x \sqrt{-c^{2} x^{2}+1}}{256}+\frac{63 \arcsin \left(c x \right)}{256}\right)}{10}-\frac{3 c^{2} d \,e^{2} \left(-\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{8}-\frac{7 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{48}-\frac{35 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{192}-\frac{35 c x \sqrt{-c^{2} x^{2}+1}}{128}+\frac{35 \arcsin \left(c x \right)}{128}\right)}{8}-\frac{c^{4} d^{2} e \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{2}-\frac{d^{3} c^{6} \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}\right)}{c^{6}}}{c^{4}}"," ",0,"1/c^4*(a/c^6*(1/10*e^3*c^10*x^10+3/8*c^10*d*e^2*x^8+1/2*c^10*d^2*e*x^6+1/4*x^4*c^10*d^3)+b/c^6*(1/10*arcsin(c*x)*e^3*c^10*x^10+3/8*arcsin(c*x)*c^10*d*e^2*x^8+1/2*arcsin(c*x)*c^10*d^2*e*x^6+1/4*arcsin(c*x)*c^10*x^4*d^3-1/10*e^3*(-1/10*c^9*x^9*(-c^2*x^2+1)^(1/2)-9/80*c^7*x^7*(-c^2*x^2+1)^(1/2)-21/160*c^5*x^5*(-c^2*x^2+1)^(1/2)-21/128*c^3*x^3*(-c^2*x^2+1)^(1/2)-63/256*c*x*(-c^2*x^2+1)^(1/2)+63/256*arcsin(c*x))-3/8*c^2*d*e^2*(-1/8*c^7*x^7*(-c^2*x^2+1)^(1/2)-7/48*c^5*x^5*(-c^2*x^2+1)^(1/2)-35/192*c^3*x^3*(-c^2*x^2+1)^(1/2)-35/128*c*x*(-c^2*x^2+1)^(1/2)+35/128*arcsin(c*x))-1/2*c^4*d^2*e*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/4*d^3*c^6*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))))","A"
616,1,417,259,0.005000," ","int(x^2*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{3} c^{9} x^{9}+\frac{3}{7} c^{9} d \,e^{2} x^{7}+\frac{3}{5} c^{9} d^{2} e \,x^{5}+\frac{1}{3} c^{9} x^{3} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{9} x^{9}}{9}+\frac{3 \arcsin \left(c x \right) c^{9} d \,e^{2} x^{7}}{7}+\frac{3 \arcsin \left(c x \right) c^{9} d^{2} e \,x^{5}}{5}+\frac{\arcsin \left(c x \right) c^{9} x^{3} d^{3}}{3}-\frac{e^{3} \left(-\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{8 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{63}-\frac{16 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{105}-\frac{64 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{315}-\frac{128 \sqrt{-c^{2} x^{2}+1}}{315}\right)}{9}-\frac{3 c^{2} d \,e^{2} \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{3 c^{4} d^{2} e \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{d^{3} c^{6} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}\right)}{c^{6}}}{c^{3}}"," ",0,"1/c^3*(a/c^6*(1/9*e^3*c^9*x^9+3/7*c^9*d*e^2*x^7+3/5*c^9*d^2*e*x^5+1/3*c^9*x^3*d^3)+b/c^6*(1/9*arcsin(c*x)*e^3*c^9*x^9+3/7*arcsin(c*x)*c^9*d*e^2*x^7+3/5*arcsin(c*x)*c^9*d^2*e*x^5+1/3*arcsin(c*x)*c^9*x^3*d^3-1/9*e^3*(-1/9*c^8*x^8*(-c^2*x^2+1)^(1/2)-8/63*c^6*x^6*(-c^2*x^2+1)^(1/2)-16/105*c^4*x^4*(-c^2*x^2+1)^(1/2)-64/315*c^2*x^2*(-c^2*x^2+1)^(1/2)-128/315*(-c^2*x^2+1)^(1/2))-3/7*c^2*d*e^2*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-3/5*c^4*d^2*e*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/3*d^3*c^6*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))))","A"
617,1,369,238,0.005000," ","int(x*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{3} c^{8} x^{8}+\frac{1}{2} c^{8} d \,e^{2} x^{6}+\frac{3}{4} c^{8} d^{2} e \,x^{4}+\frac{1}{2} x^{2} c^{8} d^{3}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{8} x^{8}}{8}+\frac{\arcsin \left(c x \right) c^{8} d \,e^{2} x^{6}}{2}+\frac{3 \arcsin \left(c x \right) c^{8} d^{2} e \,x^{4}}{4}+\frac{\arcsin \left(c x \right) c^{8} x^{2} d^{3}}{2}-\frac{e^{3} \left(-\frac{c^{7} x^{7} \sqrt{-c^{2} x^{2}+1}}{8}-\frac{7 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{48}-\frac{35 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{192}-\frac{35 c x \sqrt{-c^{2} x^{2}+1}}{128}+\frac{35 \arcsin \left(c x \right)}{128}\right)}{8}-\frac{c^{2} d \,e^{2} \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{2}-\frac{3 c^{4} d^{2} e \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}-\frac{d^{3} c^{6} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}\right)}{c^{6}}}{c^{2}}"," ",0,"1/c^2*(a/c^6*(1/8*e^3*c^8*x^8+1/2*c^8*d*e^2*x^6+3/4*c^8*d^2*e*x^4+1/2*x^2*c^8*d^3)+b/c^6*(1/8*arcsin(c*x)*e^3*c^8*x^8+1/2*arcsin(c*x)*c^8*d*e^2*x^6+3/4*arcsin(c*x)*c^8*d^2*e*x^4+1/2*arcsin(c*x)*c^8*x^2*d^3-1/8*e^3*(-1/8*c^7*x^7*(-c^2*x^2+1)^(1/2)-7/48*c^5*x^5*(-c^2*x^2+1)^(1/2)-35/192*c^3*x^3*(-c^2*x^2+1)^(1/2)-35/128*c*x*(-c^2*x^2+1)^(1/2)+35/128*arcsin(c*x))-1/2*c^2*d*e^2*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-3/4*c^4*d^2*e*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/2*d^3*c^6*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))))","A"
618,1,325,205,0.006000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+d^{3} c^{7} x \right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \arcsin \left(c x \right) c^{7} d \,e^{2} x^{5}}{5}+\arcsin \left(c x \right) c^{7} d^{2} e \,x^{3}+\arcsin \left(c x \right) d^{3} c^{7} x -\frac{e^{3} \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{3 c^{2} d \,e^{2} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-c^{4} d^{2} e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+d^{3} c^{6} \sqrt{-c^{2} x^{2}+1}\right)}{c^{6}}}{c}"," ",0,"1/c*(a/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+d^3*c^7*x)+b/c^6*(1/7*arcsin(c*x)*e^3*c^7*x^7+3/5*arcsin(c*x)*c^7*d*e^2*x^5+arcsin(c*x)*c^7*d^2*e*x^3+arcsin(c*x)*d^3*c^7*x-1/7*e^3*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-3/5*c^2*d*e^2*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-c^4*d^2*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+d^3*c^6*(-c^2*x^2+1)^(1/2)))","A"
619,1,391,335,0.436000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x))/x,x)","\frac{a \,e^{3} x^{6}}{6}+\frac{3 a d \,e^{2} x^{4}}{4}+\frac{3 a \,d^{2} e \,x^{2}}{2}+d^{3} a \ln \left(c x \right)-\frac{i b \,d^{3} \arcsin \left(c x \right)^{2}}{2}+d^{3} b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)+d^{3} b \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-i d^{3} b \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-i d^{3} b \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{b \arcsin \left(c x \right) e^{3} \cos \left(6 \arcsin \left(c x \right)\right)}{192 c^{6}}+\frac{b \,e^{3} \sin \left(6 \arcsin \left(c x \right)\right)}{1152 c^{6}}+\frac{3 b \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) d \,e^{2}}{32 c^{4}}+\frac{b \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) e^{3}}{32 c^{6}}-\frac{3 b \sin \left(4 \arcsin \left(c x \right)\right) d \,e^{2}}{128 c^{4}}-\frac{b \sin \left(4 \arcsin \left(c x \right)\right) e^{3}}{128 c^{6}}-\frac{3 b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) d^{2} e}{4 c^{2}}-\frac{3 b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) d \,e^{2}}{8 c^{4}}-\frac{5 b \cos \left(2 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) e^{3}}{64 c^{6}}+\frac{3 b \sin \left(2 \arcsin \left(c x \right)\right) d^{2} e}{8 c^{2}}+\frac{3 b \sin \left(2 \arcsin \left(c x \right)\right) d \,e^{2}}{16 c^{4}}+\frac{5 b \sin \left(2 \arcsin \left(c x \right)\right) e^{3}}{128 c^{6}}"," ",0,"1/6*a*e^3*x^6+3/4*a*d*e^2*x^4+3/2*a*d^2*e*x^2+d^3*a*ln(c*x)-I*d^3*b*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+d^3*b*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+d^3*b*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-1/2*I*b*d^3*arcsin(c*x)^2-I*d^3*b*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))-1/192*b/c^6*arcsin(c*x)*e^3*cos(6*arcsin(c*x))+1/1152*b/c^6*e^3*sin(6*arcsin(c*x))+3/32*b/c^4*cos(4*arcsin(c*x))*arcsin(c*x)*d*e^2+1/32*b/c^6*cos(4*arcsin(c*x))*arcsin(c*x)*e^3-3/128*b/c^4*sin(4*arcsin(c*x))*d*e^2-1/128*b/c^6*sin(4*arcsin(c*x))*e^3-3/4*b/c^2*cos(2*arcsin(c*x))*arcsin(c*x)*d^2*e-3/8*b/c^4*cos(2*arcsin(c*x))*arcsin(c*x)*d*e^2-5/64*b/c^6*cos(2*arcsin(c*x))*arcsin(c*x)*e^3+3/8*b/c^2*sin(2*arcsin(c*x))*d^2*e+3/16*b/c^4*sin(2*arcsin(c*x))*d*e^2+5/128*b/c^6*sin(2*arcsin(c*x))*e^3","A"
620,1,264,174,0.010000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x))/x^2,x)","c \left(\frac{a \left(\frac{e^{3} c^{5} x^{5}}{5}+c^{5} d \,e^{2} x^{3}+3 c^{5} d^{2} e x -\frac{d^{3} c^{5}}{x}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{5} x^{5}}{5}+\arcsin \left(c x \right) c^{5} d \,e^{2} x^{3}+3 \arcsin \left(c x \right) c^{5} d^{2} e x -\frac{\arcsin \left(c x \right) d^{3} c^{5}}{x}-\frac{e^{3} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-c^{2} d \,e^{2} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+3 c^{4} d^{2} e \sqrt{-c^{2} x^{2}+1}-d^{3} c^{6} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{6}}\right)"," ",0,"c*(a/c^6*(1/5*e^3*c^5*x^5+c^5*d*e^2*x^3+3*c^5*d^2*e*x-d^3*c^5/x)+b/c^6*(1/5*arcsin(c*x)*e^3*c^5*x^5+arcsin(c*x)*c^5*d*e^2*x^3+3*arcsin(c*x)*c^5*d^2*e*x-arcsin(c*x)*d^3*c^5/x-1/5*e^3*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-c^2*d*e^2*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+3*c^4*d^2*e*(-c^2*x^2+1)^(1/2)-d^3*c^6*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
621,1,360,256,0.734000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x))/x^3,x)","\frac{a \,e^{3} x^{4}}{4}+\frac{3 a \,x^{2} d \,e^{2}}{2}+3 a \,d^{2} e \ln \left(c x \right)-\frac{a \,d^{3}}{2 x^{2}}+3 b \,d^{2} e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)-\frac{b \sin \left(4 \arcsin \left(c x \right)\right) e^{3}}{128 c^{4}}+\frac{b \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right) e^{3}}{32 c^{4}}-3 i b \,d^{2} e \polylog \left(2, i c x +\sqrt{-c^{2} x^{2}+1}\right)-3 i b \,d^{2} e \polylog \left(2, -i c x -\sqrt{-c^{2} x^{2}+1}\right)+\frac{3 b \sqrt{-c^{2} x^{2}+1}\, x d \,e^{2}}{4 c}+\frac{i c^{2} b \,d^{3}}{2}+3 b \,d^{2} e \arcsin \left(c x \right) \ln \left(1-i c x -\sqrt{-c^{2} x^{2}+1}\right)-\frac{3 i b \,d^{2} e \arcsin \left(c x \right)^{2}}{2}-\frac{b c \,d^{3} \sqrt{-c^{2} x^{2}+1}}{2 x}+\frac{b \sqrt{-c^{2} x^{2}+1}\, x \,e^{3}}{8 c^{3}}-\frac{3 b \arcsin \left(c x \right) d \,e^{2}}{4 c^{2}}-\frac{b \arcsin \left(c x \right) e^{3}}{8 c^{4}}+\frac{b \arcsin \left(c x \right) x^{2} e^{3}}{4 c^{2}}+\frac{3 b \arcsin \left(c x \right) x^{2} d \,e^{2}}{2}-\frac{b \arcsin \left(c x \right) d^{3}}{2 x^{2}}"," ",0,"1/4*a*e^3*x^4+3/2*a*x^2*d*e^2+3*a*d^2*e*ln(c*x)-1/2*a*d^3/x^2+3*b*d^2*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/128/c^4*b*sin(4*arcsin(c*x))*e^3+1/32/c^4*b*cos(4*arcsin(c*x))*arcsin(c*x)*e^3-3*I*b*d^2*e*polylog(2,-I*c*x-(-c^2*x^2+1)^(1/2))+1/2*I*c^2*b*d^3+3/4/c*b*(-c^2*x^2+1)^(1/2)*x*d*e^2-3*I*b*d^2*e*polylog(2,I*c*x+(-c^2*x^2+1)^(1/2))+3*b*d^2*e*arcsin(c*x)*ln(1-I*c*x-(-c^2*x^2+1)^(1/2))-3/2*I*b*d^2*e*arcsin(c*x)^2-1/2*b*c*d^3*(-c^2*x^2+1)^(1/2)/x+1/8/c^3*b*(-c^2*x^2+1)^(1/2)*x*e^3-3/4/c^2*b*arcsin(c*x)*d*e^2-1/8/c^4*b*arcsin(c*x)*e^3+1/4/c^2*b*arcsin(c*x)*x^2*e^3+3/2*b*arcsin(c*x)*x^2*d*e^2-1/2*b*arcsin(c*x)*d^3/x^2","A"
622,1,249,166,0.012000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x))/x^4,x)","c^{3} \left(\frac{a \left(\frac{e^{3} c^{3} x^{3}}{3}+3 c^{3} x d \,e^{2}-\frac{d^{3} c^{3}}{3 x^{3}}-\frac{3 c^{3} d^{2} e}{x}\right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} c^{3} x^{3}}{3}+3 \arcsin \left(c x \right) c^{3} x d \,e^{2}-\frac{\arcsin \left(c x \right) d^{3} c^{3}}{3 x^{3}}-\frac{3 \arcsin \left(c x \right) c^{3} d^{2} e}{x}-\frac{e^{3} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+3 c^{2} d \,e^{2} \sqrt{-c^{2} x^{2}+1}+\frac{d^{3} c^{6} \left(-\frac{\sqrt{-c^{2} x^{2}+1}}{2 c^{2} x^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2}\right)}{3}-3 c^{4} d^{2} e \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)\right)}{c^{6}}\right)"," ",0,"c^3*(a/c^6*(1/3*e^3*c^3*x^3+3*c^3*x*d*e^2-1/3*d^3*c^3/x^3-3*c^3*d^2*e/x)+b/c^6*(1/3*arcsin(c*x)*e^3*c^3*x^3+3*arcsin(c*x)*c^3*x*d*e^2-1/3*arcsin(c*x)*d^3*c^3/x^3-3*arcsin(c*x)*c^3*d^2*e/x-1/3*e^3*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+3*c^2*d*e^2*(-c^2*x^2+1)^(1/2)+1/3*d^3*c^6*(-1/2/c^2/x^2*(-c^2*x^2+1)^(1/2)-1/2*arctanh(1/(-c^2*x^2+1)^(1/2)))-3*c^4*d^2*e*arctanh(1/(-c^2*x^2+1)^(1/2))))","A"
623,1,465,289,0.005000," ","int((e*x^2+d)^4*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{9} e^{4} c^{9} x^{9}+\frac{4}{7} c^{9} d \,e^{3} x^{7}+\frac{6}{5} c^{9} d^{2} e^{2} x^{5}+\frac{4}{3} c^{9} d^{3} e \,x^{3}+c^{9} d^{4} x \right)}{c^{8}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{4} c^{9} x^{9}}{9}+\frac{4 \arcsin \left(c x \right) c^{9} d \,e^{3} x^{7}}{7}+\frac{6 \arcsin \left(c x \right) c^{9} d^{2} e^{2} x^{5}}{5}+\frac{4 \arcsin \left(c x \right) c^{9} d^{3} e \,x^{3}}{3}+\arcsin \left(c x \right) c^{9} d^{4} x -\frac{e^{4} \left(-\frac{c^{8} x^{8} \sqrt{-c^{2} x^{2}+1}}{9}-\frac{8 c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{63}-\frac{16 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{105}-\frac{64 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{315}-\frac{128 \sqrt{-c^{2} x^{2}+1}}{315}\right)}{9}-\frac{4 c^{2} d \,e^{3} \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{6 c^{4} d^{2} e^{2} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{4 c^{6} d^{3} e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+c^{8} d^{4} \sqrt{-c^{2} x^{2}+1}\right)}{c^{8}}}{c}"," ",0,"1/c*(a/c^8*(1/9*e^4*c^9*x^9+4/7*c^9*d*e^3*x^7+6/5*c^9*d^2*e^2*x^5+4/3*c^9*d^3*e*x^3+c^9*d^4*x)+b/c^8*(1/9*arcsin(c*x)*e^4*c^9*x^9+4/7*arcsin(c*x)*c^9*d*e^3*x^7+6/5*arcsin(c*x)*c^9*d^2*e^2*x^5+4/3*arcsin(c*x)*c^9*d^3*e*x^3+arcsin(c*x)*c^9*d^4*x-1/9*e^4*(-1/9*c^8*x^8*(-c^2*x^2+1)^(1/2)-8/63*c^6*x^6*(-c^2*x^2+1)^(1/2)-16/105*c^4*x^4*(-c^2*x^2+1)^(1/2)-64/315*c^2*x^2*(-c^2*x^2+1)^(1/2)-128/315*(-c^2*x^2+1)^(1/2))-4/7*c^2*d*e^3*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-6/5*c^4*d^2*e^2*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-4/3*c^6*d^3*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+c^8*d^4*(-c^2*x^2+1)^(1/2)))","A"
624,1,376,597,3.851000," ","int(x^4*(a+b*arcsin(c*x))/(e*x^2+d),x)","\frac{a \,x^{3}}{3 e}-\frac{a d x}{e^{2}}+\frac{a \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{e^{2} \sqrt{d e}}-\frac{b d \sqrt{-c^{2} x^{2}+1}}{c \,e^{2}}-\frac{b d x \arcsin \left(c x \right)}{e^{2}}+\frac{b \sqrt{-c^{2} x^{2}+1}}{4 c^{3} e}+\frac{b \arcsin \left(c x \right) x}{4 c^{2} e}+\frac{c b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{2 e^{2}}+\frac{c b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{2 e^{2}}-\frac{b \cos \left(3 \arcsin \left(c x \right)\right)}{36 c^{3} e}-\frac{b \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{12 c^{3} e}"," ",0,"1/3*a/e*x^3-a*d*x/e^2+a*d^2/e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-b*d*(-c^2*x^2+1)^(1/2)/c/e^2-b*d*x*arcsin(c*x)/e^2+1/4*b*(-c^2*x^2+1)^(1/2)/c^3/e+1/4/c^2*b/e*arcsin(c*x)*x+1/2*c*b*d^2/e^2*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/2*c*b*d^2/e^2*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-1/36/c^3*b/e*cos(3*arcsin(c*x))-1/12/c^3*b*arcsin(c*x)/e*sin(3*arcsin(c*x))","C"
625,1,2854,536,0.920000," ","int(x^3*(a+b*arcsin(c*x))/(e*x^2+d),x)","\text{output too large to display}"," ",0,"-2*c^2*b/e^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d^2-2*c^4*b/e^4*d^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+I*c^4*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d^3/e^4+I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d^2/e^3+b/e^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d*(c^2*d*(c^2*d+e))^(1/2)+1/2*b/e/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d+2*I*c^4*b*arcsin(c*x)^2*d^3/e^4+2*I*c^2*b*arcsin(c*x)^2*d^2/e^3-1/2*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^3*(c^2*d*(c^2*d+e))^(1/2)-I*b*d*arcsin(c*x)^2/e^3*(c^2*d*(c^2*d+e))^(1/2)-1/2*I*b*arcsin(c*x)^2/e/(c^2*d+e)*d-1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e/(c^2*d+e)*d-1/4*b*arcsin(c*x)/c^2/e+1/2*a/e*x^2-1/2*a*d/e^2*ln(c^2*e*x^2+c^2*d)+1/2*b*arcsin(c*x)/e*x^2-1/2*b/e^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d-5/2*I*c^2*b*d^2*arcsin(c*x)^2/e^2/(c^2*d+e)-5/4*I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2/(c^2*d+e)*d^2+1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e^2*d/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))+I*b*(c^2*d*(c^2*d+e))^(1/2)/e^2*d/(c^2*d+e)*arcsin(c*x)^2-3/2*b/e^2*d/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b/e/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)+4*c^4*b/e^3*d^3/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+5/2*c^2*b/e^2*d^2/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+2*c^6*b/e^4*d^4/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+2*c^2*b/e^4*d^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)+1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-1/4*I*b*(c^2*d*(c^2*d+e))^(1/2)/e^2*d/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))+3/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)*d-2*I*c^4*b*d^3*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)-1/8*I/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-I*c^6*b*d^4*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^4/(c^2*d+e)+1/8*I/c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-2*I*c^2*b*arcsin(c*x)^2*d^2/e^4*(c^2*d*(c^2*d+e))^(1/2)-2*I*c^6*b*d^4*arcsin(c*x)^2/e^4/(c^2*d+e)-I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d^2/e^4*(c^2*d*(c^2*d+e))^(1/2)-4*I*c^4*b*d^3*arcsin(c*x)^2/e^3/(c^2*d+e)-2*c^4*b/e^4*d^3/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)-3*c^2*b/e^3*d^2/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)+I*c^4*b*d^3*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+2*I*c^4*b*d^3*arcsin(c*x)^2/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3*I*c^2*b*d^2*arcsin(c*x)^2/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3/2*I*c^2*b*d^2*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/4*b*x*(-c^2*x^2+1)^(1/2)/c/e+I*b*d*arcsin(c*x)^2/e^2+1/2*I*b*d/e^2*sum((_R1^2*e-4*c^2*d-2*e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^2","C"
626,1,285,533,0.626000," ","int(x^2*(a+b*arcsin(c*x))/(e*x^2+d),x)","\frac{a x}{e}-\frac{a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{e \sqrt{d e}}+\frac{b \sqrt{-c^{2} x^{2}+1}}{c e}+\frac{b x \arcsin \left(c x \right)}{e}-\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{2 e}-\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{2 e}"," ",0,"a*x/e-a*d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+b*(-c^2*x^2+1)^(1/2)/c/e+b*x*arcsin(c*x)/e-1/2*c*b*d/e*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-1/2*c*b*d/e*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
627,1,2749,476,0.407000," ","int(x*(a+b*arcsin(c*x))/(e*x^2+d),x)","\text{Expression too large to display}"," ",0,"-1/2*b/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+1/2*b/e*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)+1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/(c^2*d+e)+1/2*I*b*arcsin(c*x)^2/(c^2*d+e)-1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e-I*b/e*arcsin(c*x)^2-1/2*I*b/e*sum((_R1^2*e-4*c^2*d-2*e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-b/e^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)+I*b*arcsin(c*x)^2/e^2*(c^2*d*(c^2*d+e))^(1/2)+1/2*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2*(c^2*d*(c^2*d+e))^(1/2)+3/2*b/e/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-2*I*c^2*b*d*arcsin(c*x)^2/e^2-I*c^4*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d^2/e^3-I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^2+1/2*a/e*ln(c^2*e*x^2+c^2*d)-2*I*c^4*b*arcsin(c*x)^2*d^2/e^3-3/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/4*I*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-I*b*(c^2*d*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arcsin(c*x)^2+2*c^2*b/e^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d+2*c^4*b/e^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d^2+3*c^2*b/e^2*d/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)+2*c^4*b/e^3*d^2/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)-I*c^4*b*d^2*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-3/2*I*c^2*b*d*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-3*I*c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e^2*d/(c^2*d+e)*arcsin(c*x)^2-2*I*c^4*b*d^2*arcsin(c*x)^2/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/4/c^2*b/d/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-2*c^2*b/e^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d*(c^2*d*(c^2*d+e))^(1/2)-2*c^6*b/e^3*d^3/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)-4*c^4*b/e^2*d^2/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)-5/2*c^2*b/e/(c^2*d+e)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d+I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^3*(c^2*d*(c^2*d+e))^(1/2)+I*c^6*b*d^3*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)+1/8*I/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))-1/8*I/c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+2*I*c^2*b*arcsin(c*x)^2*d/e^3*(c^2*d*(c^2*d+e))^(1/2)+2*I*c^6*b*d^3*arcsin(c*x)^2/e^3/(c^2*d+e)+5/4*I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e*d/(c^2*d+e)+4*I*c^4*b*arcsin(c*x)^2/e^2/(c^2*d+e)*d^2+5/2*I*c^2*b*arcsin(c*x)^2/e/(c^2*d+e)*d+2*I*c^4*b*d^2*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2/(c^2*d+e)","C"
628,1,236,497,0.087000," ","int((a+b*arcsin(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{2}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{2}"," ",0,"a/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*c*b*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/2*c*b*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
629,1,355,523,0.329000," ","int((a+b*arcsin(c*x))/x/(e*x^2+d),x)","-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d}+\frac{a \ln \left(c x \right)}{d}+\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d}+\frac{b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}-\frac{i b \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i b \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right) e}{4 d}"," ",0,"-1/2*a/d*ln(c^2*e*x^2+c^2*d)+a/d*ln(c*x)+1/4*I*b*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))/d+b/d*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b/d*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*b*dilog(I*c*x+(-c^2*x^2+1)^(1/2))/d+1/4*I*b*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))*e/d","C"
630,1,363,535,0.939000," ","int((a+b*arcsin(c*x))/x^2/(e*x^2+d),x)","-\frac{a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{d \sqrt{d e}}-\frac{a}{d x}-\frac{b \arcsin \left(c x \right)}{d x}-\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{8 c \,d^{2}}+\frac{b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{8 c \,d^{2}}-\frac{c b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d}+\frac{c b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d}"," ",0,"-a*e/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d/x-b*arcsin(c*x)/d/x-1/8*b/c/d^2*e*sum((4*_R1^2*c^2*d+_R1^2*e-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/8*b/c/d^2*e*sum((_R1^2*e-4*c^2*d-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-c*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)","C"
631,1,419,575,0.447000," ","int((a+b*arcsin(c*x))/x^3/(e*x^2+d),x)","\frac{a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}-\frac{a}{2 d \,x^{2}}-\frac{a e \ln \left(c x \right)}{d^{2}}+\frac{i c^{2} b}{2 d}-\frac{b c \sqrt{-c^{2} x^{2}+1}}{2 d x}-\frac{b \arcsin \left(c x \right)}{2 d \,x^{2}}-\frac{i b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{2}}-\frac{b e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b e \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b e \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{2}}"," ",0,"1/2*a*e/d^2*ln(c^2*e*x^2+c^2*d)-1/2*a/d/x^2-a/d^2*e*ln(c*x)+1/2*I*c^2*b/d-1/2*b*c*(-c^2*x^2+1)^(1/2)/d/x-1/2*b*arcsin(c*x)/d/x^2-1/4*I*b/d^2*e*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-b/d^2*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*b/d^2*e*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b/d^2*e*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-1/4*I*b/d^2*e^2*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
632,1,472,596,1.030000," ","int((a+b*arcsin(c*x))/x^4/(e*x^2+d),x)","\frac{a \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{d^{2} \sqrt{d e}}-\frac{a}{3 d \,x^{3}}+\frac{a e}{d^{2} x}-\frac{b c \sqrt{-c^{2} x^{2}+1}}{6 d \,x^{2}}+\frac{b \arcsin \left(c x \right) e}{d^{2} x}-\frac{b \arcsin \left(c x \right)}{3 d \,x^{3}}-\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{8 c \,d^{3}}-\frac{c^{3} b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{6 d}+\frac{c^{3} b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{6 d}+\frac{b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{8 c \,d^{3}}+\frac{c b e \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{c b e \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{2}}"," ",0,"a*e^2/d^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/3*a/d/x^3+a/d^2*e/x-1/6*b*c*(-c^2*x^2+1)^(1/2)/d/x^2+b*arcsin(c*x)/d^2*e/x-1/3*b*arcsin(c*x)/d/x^3-1/8/c*b/d^3*e^2*sum((_R1^2*e-4*c^2*d-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-1/6*c^3*b/d*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+1/6*c^3*b/d*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)+1/8/c*b/d^3*e^2*sum((4*_R1^2*c^2*d+_R1^2*e-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+c*b/d^2*e*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-c*b/d^2*e*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)","C"
633,1,2907,545,0.926000," ","int(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"5/4*I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^2/(c^2*d+e)-2*I*c^2*b*arcsin(c*x)^2*d/e^4*(c^2*d*(c^2*d+e))^(1/2)-I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^4*(c^2*d*(c^2*d+e))^(1/2)+5/2*I*c^2*b*arcsin(c*x)^2*d/e^2/(c^2*d+e)+2*I*c^6*b*d^3*arcsin(c*x)^2/e^4/(c^2*d+e)+4*I*c^4*b*d^2*arcsin(c*x)^2/e^3/(c^2*d+e)+1/2*a/e^2*ln(c^2*e*x^2+c^2*d)-1/4*I*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))-2*I*c^4*b*arcsin(c*x)^2*d^2/e^4-2*I*c^2*b*arcsin(c*x)^2*d/e^3-I*c^4*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*d^2/e^4-I*c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*d/e^3-3/2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/2*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))+I*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arcsin(c*x)^2+1/2*c^2*b*arcsin(c*x)/e^2*d/(c^2*e*x^2+c^2*d)+2*c^2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^3*d+2*c^4*b*d^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^4+3/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/2*I*b*(c^2*d*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))+1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)+2*I*c^4*b*d^2*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)-2*c^6*b*d^3*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^4/(c^2*d+e)-4*c^4*b*d^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^3/(c^2*d+e)-5/2*c^2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)*d/e^2/(c^2*d+e)+2*c^2*b*d*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^4*(c^2*d*(c^2*d+e))^(1/2)+I*c^6*b*d^3*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^4/(c^2*d+e)-1/2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e/(c^2*d+e)+b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^3*(c^2*d*(c^2*d+e))^(1/2)+1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e/(c^2*d+e)-I*b*arcsin(c*x)^2/e^3*(c^2*d*(c^2*d+e))^(1/2)-1/2*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3*(c^2*d*(c^2*d+e))^(1/2)+1/2*I*b*arcsin(c*x)^2/e/(c^2*d+e)+1/2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^2-1/2*I*b/e^2*sum((_R1^2*e-4*c^2*d-2*e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-I*b*arcsin(c*x)^2/e^2-1/4*I*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^2+2*I*c^4*b*d^2*arcsin(c*x)^2/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+I*c^4*b*d^2*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/4/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/d/(c^2*d+e)*arcsin(c*x)*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))-2*c^4*b*d^2*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-3*c^2*b*d*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/4/c^2*b*ln(1-e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))*arcsin(c*x)/d/e/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/8*I/c^2*b*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/d/e/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3/2*I*c^2*b*d*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+3*I*c^2*b*d*arcsin(c*x)^2/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/8*I/c^2*b*(c^2*d*(c^2*d+e))^(1/2)/e/d/(c^2*d+e)*polylog(2,e*(I*c*x+(-c^2*x^2+1)^(1/2))^2/(2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e))","C"
634,1,414,72,0.042000," ","int(x*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \arcsin \left(c x \right)}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x +\frac{\sqrt{-c^{2} e d}}{e}}\right)}{4 e \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}-\frac{c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x -\frac{\sqrt{-c^{2} e d}}{e}}\right)}{4 e \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}"," ",0,"-1/2*c^2*a/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arcsin(c*x)+1/4*c^2*b/e/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x+(-c^2*e*d)^(1/2)/e))-1/4*c^2*b/e/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x-(-c^2*e*d)^(1/2)/e))","B"
635,1,491,588,0.425000," ","int((a+b*arcsin(c*x))/x/(e*x^2+d)^2,x)","\frac{a \,c^{2}}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{2}}+\frac{a \ln \left(c x \right)}{d^{2}}+\frac{b \,c^{2} \arcsin \left(c x \right)}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right)}{2 d^{2} \left(c^{2} d +e \right)}+\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{2}}+\frac{b \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}-\frac{i b \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right) e}{4 d^{2}}"," ",0,"1/2*a*c^2/d/(c^2*e*x^2+c^2*d)-1/2*a/d^2*ln(c^2*e*x^2+c^2*d)+a/d^2*ln(c*x)+1/2*b*c^2*arcsin(c*x)/d/(c^2*e*x^2+c^2*d)+1/2*I*b*(c^2*d*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))+1/4*I*b/d^2*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+b/d^2*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-I*b/d^2*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*b/d^2*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+1/4*I*b/d^2*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))*e","C"
636,1,679,638,0.590000," ","int((a+b*arcsin(c*x))/x^3/(e*x^2+d)^2,x)","-\frac{c^{2} a e}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{d^{3}}-\frac{a}{2 d^{2} x^{2}}-\frac{2 a e \ln \left(c x \right)}{d^{3}}-\frac{i b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right) e}{2 \left(c^{2} d +e \right) d^{3}}+\frac{i c^{4} b}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) d}-\frac{c^{3} b x \sqrt{-c^{2} x^{2}+1}\, e}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) d^{2}}-\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}}{2 x \left(c^{2} e \,x^{2}+c^{2} d \right) d}-\frac{c^{2} b \arcsin \left(c x \right) e}{d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \arcsin \left(c x \right)}{2 x^{2} \left(c^{2} e \,x^{2}+c^{2} d \right) d}-\frac{i b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{2 d^{3}}-\frac{i b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{2 d^{3}}-\frac{2 b e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{2 i b e \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}+\frac{i c^{4} b \,x^{2} e}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) d^{2}}-\frac{2 i b e \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3}}"," ",0,"-1/2*c^2*a*e/d^2/(c^2*e*x^2+c^2*d)+a*e/d^3*ln(c^2*e*x^2+c^2*d)-1/2*a/d^2/x^2-2*a/d^3*e*ln(c*x)+1/2*I*c^4*b/(c^2*e*x^2+c^2*d)/d-1/2*I*b*(c^2*d*(c^2*d+e))^(1/2)/(c^2*d+e)/d^3*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))*e-1/2*c^3*b*x/(c^2*e*x^2+c^2*d)/d^2*(-c^2*x^2+1)^(1/2)*e-1/2*c^3*b/x/(c^2*e*x^2+c^2*d)/d*(-c^2*x^2+1)^(1/2)-c^2*b*arcsin(c*x)*e/d^2/(c^2*e*x^2+c^2*d)-1/2*c^2*b/x^2/(c^2*e*x^2+c^2*d)/d*arcsin(c*x)-1/2*I*b/d^3*e^2*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/2*I*c^4*b*x^2/(c^2*e*x^2+c^2*d)/d^2*e-2*b/d^3*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*I*b/d^3*e*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+2*I*b/d^3*e*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-2*I*b/d^3*e*dilog(I*c*x+(-c^2*x^2+1)^(1/2))","C"
637,1,1738,697,3.076000," ","int(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","\frac{a x}{e^{2}}+\frac{c^{2} a d x}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e^{2} \sqrt{d e}}+\frac{b \sqrt{-c^{2} x^{2}+1}}{c \,e^{2}}+\frac{b x \arcsin \left(c x \right)}{e^{2}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5} \left(c^{2} d +e \right)}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{4} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5} \left(c^{2} d +e \right)}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{4} \left(c^{2} d +e \right)}+\frac{c^{2} b \arcsin \left(c x \right) d x}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{3} \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{5} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5}}-\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{3} \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{5} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{5}}-\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{4 e^{2}}-\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 e^{2}}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d^{2}}{e^{5}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{2 e^{4}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d^{2}}{e^{5}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{2 e^{4}}"," ",0,"a*x/e^2+1/2*c^2*a/e^2*d*x/(c^2*e*x^2+c^2*d)-3/2*a/e^2*d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+b*(-c^2*x^2+1)^(1/2)/c/e^2+b*x*arcsin(c*x)/e^2-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/2*c^2*b*arcsin(c*x)*d*x/e^2/(c^2*e*x^2+c^2*d)-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)-c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^5*(c^2*d*(c^2*d+e))^(1/2)-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)+c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^5*(c^2*d*(c^2*d+e))^(1/2)-3/4*c*b/e^2*d*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-3/4*c*b/e^2*d*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d^2/e^5+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^4+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d^2/e^5+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^4","C"
638,1,1677,660,1.104000," ","int(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{c^{2} b \arcsin \left(c x \right) x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{4 e}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 e}+\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{4}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 e^{3}}+\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d^{2} \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{4} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, d \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{4}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{4}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 e^{3}}"," ",0,"-1/2*c^2*a/e*x/(c^2*e*x^2+c^2*d)+1/2*a/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*c^2*b*arcsin(c*x)/e*x/(c^2*e*x^2+c^2*d)+1/4*c*b/e*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/4*c*b/e*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*d-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^4+c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*d+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^4-c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3","C"
639,1,1687,672,0.886000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \arcsin \left(c x \right) x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d \left(c^{2} d +e \right) e^{2}}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{e^{3}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \,e^{3}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 d \,e^{2}}-\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d \left(c^{2} d +e \right) e^{2}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{e^{3}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \,e^{3}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 d \,e^{2}}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{4 d}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d}"," ",0,"1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)+1/2*a/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*c^2*b*arcsin(c*x)*x/d/(c^2*e*x^2+c^2*d)-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*d+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^2+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3-c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^3*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^2-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*d-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^2-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3+c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^3*(c^2*d*(c^2*d+e))^(1/2)+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^2+1/4*c*b/d*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/4*c*b/d*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
640,1,1839,707,4.596000," ","int((a+b*arcsin(c*x))/x^2/(e*x^2+d)^2,x)","-\frac{a e \,c^{2} x}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d^{2} \sqrt{d e}}-\frac{a}{d^{2} x}-\frac{3 b \,c^{2} x \arcsin \left(c x \right) e}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \,c^{2} \arcsin \left(c x \right)}{x d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \,c^{5} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}-\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \left(c^{2} d +e \right) e^{2}}+\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{d \left(c^{2} d +e \right) e}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d^{2} \left(c^{2} d +e \right) e}-\frac{b \,c^{3} \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{d \,e^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d^{2} e^{2}}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{2 d^{2} e}+\frac{b \,c^{5} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{\left(c^{2} d +e \right) e^{2}}+\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d \left(c^{2} d +e \right) e^{2}}+\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{d \left(c^{2} d +e \right) e}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{2 d^{2} \left(c^{2} d +e \right) e}-\frac{b \,c^{3} \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{d \,e^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{d^{2} e^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{2 d^{2} e}+\frac{3 b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{16 c \,d^{3}}-\frac{c b \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2}}+\frac{c b \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-1\right)}{d^{2}}-\frac{3 b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(4 \textit{\_R1}^{2} c^{2} d +\textit{\_R1}^{2} e -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{16 c \,d^{3}}"," ",0,"-1/2*a/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-3/2*a/d^2*e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d^2/x-3/2*b*c^2*x*arcsin(c*x)/d^2/(c^2*e*x^2+c^2*d)*e-b*c^2/x*arcsin(c*x)/d/(c^2*e*x^2+c^2*d)+b*c^5*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^2-b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)+b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)/e-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/(c^2*d+e)/e*(c^2*d*(c^2*d+e))^(1/2)-b*c^3*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/e^2+c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/e^2*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/e+b*c^5*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^2+b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e^2*(c^2*d*(c^2*d+e))^(1/2)+b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)/e+1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/(c^2*d+e)/e*(c^2*d*(c^2*d+e))^(1/2)-b*c^3*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/e^2-c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/e^2*(c^2*d*(c^2*d+e))^(1/2)-1/2*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/e+3/16*b/c/d^3*e*sum((_R1^2*e-4*c^2*d-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-c*b/d^2*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+c*b/d^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-1)-3/16*b/c/d^3*e*sum((4*_R1^2*c^2*d+_R1^2*e-e)/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
641,1,5124,662,2.878000," ","int(x^5*(a+b*arcsin(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
642,1,1055,133,0.019000," ","int(x^3*(a+b*arcsin(c*x))/(e*x^2+d)^3,x)","-\frac{c^{2} a}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} a d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} b \arcsin \left(c x \right)}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} b \arcsin \left(c x \right) d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{3 c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x +\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{2} \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}-\frac{3 c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x -\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{2} \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}-\frac{c^{2} b \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{16 e^{2} \left(c^{2} d +e \right) \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}-\frac{c^{2} b \sqrt{-c^{2} e d}\, \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x -\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{3} \left(c^{2} d +e \right) \sqrt{\frac{c^{2} d +e}{e}}}-\frac{c^{2} b \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{16 e^{2} \left(c^{2} d +e \right) \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}+\frac{c^{2} b \sqrt{-c^{2} e d}\, \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x +\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{3} \left(c^{2} d +e \right) \sqrt{\frac{c^{2} d +e}{e}}}"," ",0,"-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arcsin(c*x)/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arcsin(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2+3/16*c^2*b/e^2/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x+(-c^2*e*d)^(1/2)/e))-3/16*c^2*b/e^2/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x-(-c^2*e*d)^(1/2)/e))-1/16*c^2*b/e^2/(c^2*d+e)/(c*x-(-c^2*e*d)^(1/2)/e)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2)-1/16*c^2*b/e^3*(-c^2*e*d)^(1/2)/(c^2*d+e)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x-(-c^2*e*d)^(1/2)/e))-1/16*c^2*b/e^2/(c^2*d+e)/(c*x+(-c^2*e*d)^(1/2)/e)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2)+1/16*c^2*b/e^3*(-c^2*e*d)^(1/2)/(c^2*d+e)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x+(-c^2*e*d)^(1/2)/e))","B"
643,1,1017,118,0.011000," ","int(x*(a+b*arcsin(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{4} b \arcsin \left(c x \right)}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x +\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e d \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}-\frac{c^{2} b \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x -\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e d \sqrt{-c^{2} e d}\, \sqrt{\frac{c^{2} d +e}{e}}}+\frac{c^{2} b \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{16 e d \left(c^{2} d +e \right) \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}+\frac{c^{2} b \sqrt{-c^{2} e d}\, \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}-\frac{2 \sqrt{-c^{2} e d}\, \left(c x -\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x -\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{2} d \left(c^{2} d +e \right) \sqrt{\frac{c^{2} d +e}{e}}}+\frac{c^{2} b \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{16 e d \left(c^{2} d +e \right) \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}-\frac{c^{2} b \sqrt{-c^{2} e d}\, \ln \left(\frac{\frac{2 c^{2} d +2 e}{e}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+2 \sqrt{\frac{c^{2} d +e}{e}}\, \sqrt{-\left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)^{2}+\frac{2 \sqrt{-c^{2} e d}\, \left(c x +\frac{\sqrt{-c^{2} e d}}{e}\right)}{e}+\frac{c^{2} d +e}{e}}}{c x +\frac{\sqrt{-c^{2} e d}}{e}}\right)}{16 e^{2} d \left(c^{2} d +e \right) \sqrt{\frac{c^{2} d +e}{e}}}"," ",0,"-1/4*c^4*a/e/(c^2*e*x^2+c^2*d)^2-1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)+1/16*c^2*b/e/d/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x+(-c^2*e*d)^(1/2)/e))-1/16*c^2*b/e/d/(-c^2*e*d)^(1/2)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x-(-c^2*e*d)^(1/2)/e))+1/16*c^2*b/e/d/(c^2*d+e)/(c*x-(-c^2*e*d)^(1/2)/e)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2)+1/16*c^2*b/e^2/d*(-c^2*e*d)^(1/2)/(c^2*d+e)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x-(-c^2*e*d)^(1/2)/e)^2-2*(-c^2*e*d)^(1/2)/e*(c*x-(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x-(-c^2*e*d)^(1/2)/e))+1/16*c^2*b/e/d/(c^2*d+e)/(c*x+(-c^2*e*d)^(1/2)/e)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2)-1/16*c^2*b/e^2/d*(-c^2*e*d)^(1/2)/(c^2*d+e)/((c^2*d+e)/e)^(1/2)*ln((2*(c^2*d+e)/e+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+2*((c^2*d+e)/e)^(1/2)*(-(c*x+(-c^2*e*d)^(1/2)/e)^2+2*(-c^2*e*d)^(1/2)/e*(c*x+(-c^2*e*d)^(1/2)/e)+(c^2*d+e)/e)^(1/2))/(c*x+(-c^2*e*d)^(1/2)/e))","B"
644,1,1379,700,0.720000," ","int((a+b*arcsin(c*x))/x/(e*x^2+d)^3,x)","-\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{3}}+\frac{3 b \,c^{4} \arcsin \left(c x \right) e}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i b \,c^{6}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{5 i b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right) e}{8 d^{3} \left(c^{2} d +e \right)^{2}}+\frac{3 i b \,c^{2} \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right)}{4 d^{2} \left(c^{2} d +e \right)^{2}}+\frac{i b \,c^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right) e}{4 d^{2} \left(c^{2} d +e \right)}+\frac{a \,c^{4}}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{a \,c^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \,c^{6} x^{4} e^{2}}{8 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i b \,c^{6} x^{2} e}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{3 b \,c^{6} \arcsin \left(c x \right)}{4 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{b \,c^{6} \arcsin \left(c x \right) x^{2} e}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{b \,c^{5} \sqrt{-c^{2} x^{2}+1}\, x^{3} e^{2}}{8 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{b \,c^{5} \sqrt{-c^{2} x^{2}+1}\, x e}{8 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{b \,c^{4} \arcsin \left(c x \right) x^{2} e^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{a \ln \left(c x \right)}{d^{3}}+\frac{b \,c^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} d +e \right)}+\frac{b e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{i b e \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{i b \,c^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} d +e \right)}+\frac{i b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{3} \left(c^{2} d +e \right)}-\frac{i b e \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{i b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{3} \left(c^{2} d +e \right)}+\frac{i b \,c^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{2} \left(c^{2} d +e \right)}-\frac{i b \,c^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{2} \left(c^{2} d +e \right)}"," ",0,"-1/2*a/d^3*ln(c^2*e*x^2+c^2*d)+5/8*I*b*(c^2*d*(c^2*d+e))^(1/2)/d^3/(c^2*d+e)^2*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))*e+3/4*I*b*c^2*(c^2*d*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)^2*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))+1/4*I*b*c^2/d^2/(c^2*d+e)*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))*e+3/4*b*c^4/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*e+I*b/d^3/(c^2*d+e)*e*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+b*c^2/d^2/(c^2*d+e)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+I*b*c^2/d^2/(c^2*d+e)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))+1/4*I*b/d^3/(c^2*d+e)*e*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-I*b/d^3/(c^2*d+e)*e*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+1/4*I*b/d^3/(c^2*d+e)*e^2*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/4*I*b*c^2/d^2/(c^2*d+e)*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-I*b*c^2/d^2/(c^2*d+e)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))+b/d^3/(c^2*d+e)*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+1/4*a*c^4/d/(c^2*e*x^2+c^2*d)^2+1/2*a*c^2/d^2/(c^2*e*x^2+c^2*d)+3/4*b*c^6/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)+1/8*I*b*c^6/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)+1/8*I*b*c^6/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^4*e^2+1/4*I*b*c^6/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^2*e+1/2*b*c^6/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*x^2*e-1/8*b*c^5/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*x^3*e^2-1/8*b*c^5/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*x*e+1/2*b*c^4/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*x^2*e^2+a/d^3*ln(c*x)","C"
645,1,1816,757,0.957000," ","int((a+b*arcsin(c*x))/x^3/(e*x^2+d)^3,x)","\frac{3 i c^{2} b e \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}-\frac{c^{2} a e}{d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{4} a e}{4 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{3 a e \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 d^{4}}-\frac{3 a e \ln \left(c x \right)}{d^{4}}-\frac{c^{7} b \sqrt{-c^{2} x^{2}+1}}{2 x \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{6} b \arcsin \left(c x \right)}{2 x^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{9 c^{4} b \arcsin \left(c x \right) e^{2}}{4 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{9 c^{6} b \arcsin \left(c x \right) e}{4 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{a}{2 d^{3} x^{2}}-\frac{3 i c^{2} b e \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}-\frac{9 i b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right) e^{2}}{8 d^{4} \left(c^{2} d +e \right)^{2}}-\frac{3 i c^{2} b e \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{3} \left(c^{2} d +e \right)}-\frac{3 i c^{2} b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{3} \left(c^{2} d +e \right)}-\frac{3 c^{2} b e \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{3} \left(c^{2} d +e \right)}+\frac{3 i c^{6} b e}{8 d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{3 i c^{6} b \,x^{2} e^{2}}{4 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i c^{8} b \,x^{4} e^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{3 i c^{6} b \,x^{4} e^{3}}{8 d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i c^{8} b \,x^{2} e}{d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{5 i c^{2} b \sqrt{c^{2} d \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e -4 c^{2} d -2 e}{4 \sqrt{d^{2} c^{4}+c^{2} e d}}\right) e}{4 d^{3} \left(c^{2} d +e \right)^{2}}-\frac{7 c^{5} b x \sqrt{-c^{2} x^{2}+1}\, e^{2}}{8 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{-c^{2} x^{2}+1}\, e}{2 x d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{5} b \,x^{3} \sqrt{-c^{2} x^{2}+1}\, e^{3}}{8 d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{4} b \,x^{2} \arcsin \left(c x \right) e^{3}}{2 d^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{7} b \sqrt{-c^{2} x^{2}+1}\, x^{3} e^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{7} b \sqrt{-c^{2} x^{2}+1}\, x e}{d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{6} b \arcsin \left(c x \right) x^{2} e^{2}}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b \arcsin \left(c x \right) e}{2 x^{2} d \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 b \,e^{2} \arcsin \left(c x \right) \ln \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 i b \,e^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2} e -4 c^{2} d -e \right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{4} \left(c^{2} d +e \right)}+\frac{3 i b \,e^{2} \dilog \left(1+i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 i b \,e^{2} \dilog \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{d^{4} \left(c^{2} d +e \right)}-\frac{3 i b \,e^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{4 d^{4} \left(c^{2} d +e \right)}+\frac{i c^{8} b}{2 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}"," ",0,"-3/4*I*c^2*b/d^3*e/(c^2*d+e)*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-c^2*a*e/d^3/(c^2*e*x^2+c^2*d)+1/2*I*c^8*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)-1/4*c^4*a*e/d^2/(c^2*e*x^2+c^2*d)^2-3*c^2*b/d^3/(c^2*d+e)*e*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))+3/2*a*e/d^4*ln(c^2*e*x^2+c^2*d)-3*a/d^4*e*ln(c*x)-3*b/d^4*e^2/(c^2*d+e)*arcsin(c*x)*ln(1+I*c*x+(-c^2*x^2+1)^(1/2))-1/2*c^7*b/x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)-1/2*c^6*b/x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)-3/4*I*b/d^4*e^2/(c^2*d+e)*sum((_R1^2*e-4*c^2*d-e)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+3*I*b/d^4*e^2/(c^2*d+e)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*I*b/d^4*e^2/(c^2*d+e)*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-3/4*I*b/d^4*e^3/(c^2*d+e)*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-9/4*c^4*b/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*e^2-3/4*I*c^2*b/d^3*e^2/(c^2*d+e)*sum((_R1^2-1)/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-9/4*c^6*b/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*e-1/2*a/d^3/x^2+3*I*c^2*b/d^3*e/(c^2*d+e)*dilog(1+I*c*x+(-c^2*x^2+1)^(1/2))-3*I*c^2*b/d^3/(c^2*d+e)*e*dilog(I*c*x+(-c^2*x^2+1)^(1/2))-9/8*I*b*(c^2*d*(c^2*d+e))^(1/2)/d^4/(c^2*d+e)^2*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))*e^2+3/8*I*c^6*b/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*e-7/8*c^5*b*x/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*e^2-5/4*I*c^2*b*(c^2*d*(c^2*d+e))^(1/2)/d^3/(c^2*d+e)^2*arctanh(1/4*(2*(I*c*x+(-c^2*x^2+1)^(1/2))^2*e-4*c^2*d-2*e)/(c^4*d^2+c^2*d*e)^(1/2))*e+3/4*I*c^6*b*x^2/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*e^2+1/2*I*c^8*b*x^4/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*e^2+3/8*I*c^6*b*x^4/d^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*e^3-1/2*c^5*b/x/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*e-3/8*c^5*b*x^3/d^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*e^3-3/2*c^4*b*x^2/d^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*e^3-1/2*c^7*b/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*x^3*e^2-c^7*b/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-c^2*x^2+1)^(1/2)*x*e-3/2*c^6*b/d^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*x^2*e^2-1/2*c^4*b/x^2/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsin(c*x)*e+I*c^8*b*x^2/d/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*e","C"
646,1,3107,926,2.017000," ","int(x^4*(a+b*arcsin(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-3/8*c^4*b/e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x*d-5/8*c^6*b/e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3*d-3/8*c^6*b/e^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x*d^2+1/8*c^5*b/e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-c^2*x^2+1)^(1/2)*x^2*d+c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^2*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d/e^5/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-7/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)*d+7/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)*d+3/8*a/e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+9/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^4/(c^2*d+e)^2*d^2+5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d-5/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^4*(c^2*d*(c^2*d+e))^(1/2)-5/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)+5/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^4*(c^2*d*(c^2*d+e))^(1/2)+5/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-7/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^4*d+9/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^4/(c^2*d+e)^2*d^2+5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d-7/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^4*d+c^7*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^5/(c^2*d+e)^2-c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))*d^2/e^5/(c^2*d+e)+c^7*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*d^3*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^5/(c^2*d+e)^2-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))*d^2/e^5/(c^2*d+e)+1/8*c^5*b/e^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*d^2*(-c^2*x^2+1)^(1/2)-3/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e^2*d*x-5/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^3+3/16*c^3*b/e^2/(c^2*d+e)*d*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+3/16*c^3*b/e^2/(c^2*d+e)*d*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-5/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^3-5/8*c^4*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3-5/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x^3+3/16*c*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+3/16*c*b/e/(c^2*d+e)*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))","C"
647,1,2259,942,2.178000," ","int(x^2*(a+b*arcsin(c*x))/(e*x^2+d)^3,x)","\frac{c^{4} b e \arcsin \left(c x \right) x^{3}}{8 d \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{6} b \arcsin \left(c x \right) x d}{8 e \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} d \,e^{2}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} d \left(c^{2} d +e \right)}-\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} d \left(c^{2} d +e \right)}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} d \,e^{2}}-\frac{c^{5} b \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{4} b \arcsin \left(c x \right) x}{8 \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{6} b \arcsin \left(c x \right) x^{3}}{8 \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{4 \left(c^{2} d +e \right)^{2} e^{2}}+\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{4 \left(c^{2} d +e \right) e^{3}}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{4 \left(c^{2} d +e \right) e^{3}}-\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{4 \left(c^{2} d +e \right)^{2} e^{2}}+\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{16 e \left(c^{2} d +e \right)}+\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{16 e \left(c^{2} d +e \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} e -2 c^{2} d -e \right)}\right)}{16 d \left(c^{2} d +e \right)}+\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(e \,\textit{\_Z}^{4}+\left(-4 c^{2} d -2 e \right) \textit{\_Z}^{2}+e \right)}{\sum}\frac{\textit{\_R1} \left(i \arcsin \left(c x \right) \ln \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -i c x -\sqrt{-c^{2} x^{2}+1}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} e -2 c^{2} d -e}\right)}{16 d \left(c^{2} d +e \right)}-\frac{c^{5} b d \sqrt{-c^{2} x^{2}+1}}{8 e \left(c^{2} d +e \right) \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right)}{8 e^{2} d \left(c^{2} d +e \right)}-\frac{c^{3} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c^{5} b \sqrt{-\left(2 c^{2} d -2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctan \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(-2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}-e \right) e}}\right) d}{4 e^{3} \left(c^{2} d +e \right)^{2}}+\frac{c b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right)}{8 e^{2} d \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) d}{4 e^{3} \left(c^{2} d +e \right)^{2}}+\frac{c^{3} b \sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}\, \arctanh \left(\frac{e \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{\sqrt{\left(2 c^{2} d +2 \sqrt{c^{2} d \left(c^{2} d +e \right)}+e \right) e}}\right) \sqrt{c^{2} d \left(c^{2} d +e \right)}}{4 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c^{4} a x}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} e}+\frac{c^{4} a \,x^{3}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d e \sqrt{d e}}"," ",0,"1/8*c^4*b*e/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3-1/8*c^6*b/e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x*d-1/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-1/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)+1/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)-1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/e^2+1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^3-1/8*c^5*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-c^2*x^2+1)^(1/2)*x^2-1/8*c^4*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x+1/8*c^6*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3+1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^3-1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/e^2+1/16*c^3*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/16*c^3*b/e/(c^2*d+e)*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/16*c*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/16*c*b/d/(c^2*d+e)*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d/(c^2*d+e)+1/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d/(c^2*d+e)-1/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+1/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-1/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d-1/8*c^5*b/e*d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-c^2*x^2+1)^(1/2)-1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x+1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/d*x^3+1/8*a/d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))","C"
648,1,3110,939,1.121000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-c^7*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)-c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*(c^2*d*(c^2*d+e))^(1/2)+3/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e/d^2/(c^2*d+e)-c^7*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/(c^2*d+e)^2*d+5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d/(c^2*d+e)+5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d/(c^2*d+e)-3/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d/(c^2*d+e)^2/e+3/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e/d^2/(c^2*d+e)-3/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d/(c^2*d+e)^2/e+1/4*c^4*a*x/d/(c^2*e*x^2+c^2*d)^2+3/16*c^3*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+3/16*c^3*b/d/(c^2*d+e)*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+1/8*c^5*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-c^2*x^2+1)^(1/2)+3/8*c^2*a/d^2*x/(c^2*e*x^2+c^2*d)+3/8*a/d^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+3/16*c*b/d^2/(c^2*d+e)*e*sum(1/_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))+3/16*c*b/d^2/(c^2*d+e)*e*sum(_R1/(_R1^2*e-2*c^2*d-e)*(I*arcsin(c*x)*ln((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)+dilog((_R1-I*c*x-(-c^2*x^2+1)^(1/2))/_R1)),_R1=RootOf(e*_Z^4+(-4*c^2*d-2*e)*_Z^2+e))-7/4*c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/e^2-7/4*c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/e^2+c^5*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)/e^3+c^5*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)/e^3+5/8*c^6*b/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x+3/8*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/d^2/(c^2*d+e)^2/e*(c^2*d*(c^2*d+e))^(1/2)-3/4*c*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^2/d^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-5/4*c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)+c^3*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)-3/8*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/d^2/(c^2*d+e)^2/e*(c^2*d*(c^2*d+e))^(1/2)+3/4*c*b*(-(2*c^2*d-2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctan(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((-2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)-e)*e)^(1/2))/e^2/d^2/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)+1/8*c^5*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-c^2*x^2+1)^(1/2)*x^2*e+3/8*c^4*b/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3*e^2+5/8*c^4*b/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x*e+3/8*c^6*b*e/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsin(c*x)*x^3+5/4*c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/(c^2*d+e)^2/d/e^2*(c^2*d*(c^2*d+e))^(1/2)-c^3*b*((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2)*arctanh(e*(I*c*x+(-c^2*x^2+1)^(1/2))/((2*c^2*d+2*(c^2*d*(c^2*d+e))^(1/2)+e)*e)^(1/2))/e^3/d/(c^2*d+e)*(c^2*d*(c^2*d+e))^(1/2)","C"
649,0,0,20,0.878000," ","int((e*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","\int \sqrt{e \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arcsin(c*x)),x)","F"
650,0,0,20,0.799000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(e*x^2+d)^(1/2),x)","F"
651,0,0,60,0.688000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(e*x^2+d)^(3/2),x)","F"
652,0,0,122,0.718000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(e*x^2+d)^(5/2),x)","F"
653,0,0,192,0.746000," ","int((a+b*arcsin(c*x))/(e*x^2+d)^(7/2),x)","\int \frac{a +b \arcsin \left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))/(e*x^2+d)^(7/2),x)","F"
654,0,0,474,44.158000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arcsin(c*x)),x)","F"
655,0,0,285,15.848000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arcsin(c*x)),x)","F"
656,0,0,155,4.862000," ","int((f*x)^m*(e*x^2+d)*(a+b*arcsin(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arcsin(c*x)),x)","F"
657,0,0,25,1.487000," ","int((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \arcsin \left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d),x)","F"
658,0,0,25,1.036000," ","int((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \arcsin \left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsin(c*x))/(e*x^2+d)^2,x)","F"
659,1,1194,509,0.174000," ","int((e*x^2+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{7} e^{3} c^{7} x^{7}+\frac{3}{5} c^{7} d \,e^{2} x^{5}+c^{7} d^{2} e \,x^{3}+d^{3} c^{7} x \right)}{c^{6}}+\frac{b^{2} \left(\frac{e^{3} \left(55125 \arcsin \left(c x \right)^{2} c^{7} x^{7}+15750 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{6} x^{6}-231525 \arcsin \left(c x \right)^{2} c^{5} x^{5}-2250 c^{7} x^{7}-73710 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}+385875 \arcsin \left(c x \right)^{2} c^{3} x^{3}+14742 c^{5} x^{5}+158970 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-385875 c x \arcsin \left(c x \right)^{2}-52990 c^{3} x^{3}-453810 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+453810 c x \right)}{385875}+\frac{c^{2} d \,e^{2} \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{1125}+\frac{e^{3} \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{1125}+\frac{c^{4} d^{2} e \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{2 c^{2} d \,e^{2} \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{e^{3} \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+d^{3} c^{6} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+3 c^{4} d^{2} e \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+3 c^{2} d \,e^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+e^{3} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{6}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) e^{3} c^{7} x^{7}}{7}+\frac{3 \arcsin \left(c x \right) c^{7} d \,e^{2} x^{5}}{5}+\arcsin \left(c x \right) c^{7} d^{2} e \,x^{3}+\arcsin \left(c x \right) d^{3} c^{7} x -\frac{e^{3} \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{3 c^{2} d \,e^{2} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-c^{4} d^{2} e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+d^{3} c^{6} \sqrt{-c^{2} x^{2}+1}\right)}{c^{6}}}{c}"," ",0,"1/c*(a^2/c^6*(1/7*e^3*c^7*x^7+3/5*c^7*d*e^2*x^5+c^7*d^2*e*x^3+d^3*c^7*x)+b^2/c^6*(1/385875*e^3*(55125*arcsin(c*x)^2*c^7*x^7+15750*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^6*x^6-231525*arcsin(c*x)^2*c^5*x^5-2250*c^7*x^7-73710*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4+385875*arcsin(c*x)^2*c^3*x^3+14742*c^5*x^5+158970*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-385875*c*x*arcsin(c*x)^2-52990*c^3*x^3-453810*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+453810*c*x)+1/1125*c^2*d*e^2*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+1/1125*e^3*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+1/9*c^4*d^2*e*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+2/9*c^2*d*e^2*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/9*e^3*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+d^3*c^6*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+3*c^4*d^2*e*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+3*c^2*d*e^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+e^3*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^6*(1/7*arcsin(c*x)*e^3*c^7*x^7+3/5*arcsin(c*x)*c^7*d*e^2*x^5+arcsin(c*x)*c^7*d^2*e*x^3+arcsin(c*x)*d^3*c^7*x-1/7*e^3*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-3/5*c^2*d*e^2*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-c^4*d^2*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+d^3*c^6*(-c^2*x^2+1)^(1/2)))","B"
660,1,635,299,0.127000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} e d \,x^{3}+d^{2} c^{5} x \right)}{c^{4}}+\frac{b^{2} \left(\frac{e^{2} \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{3375}+\frac{2 c^{2} e d \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{2 e^{2} \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+d^{2} c^{4} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+2 c^{2} e d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+e^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \arcsin \left(c x \right) c^{5} e d \,x^{3}}{3}+\arcsin \left(c x \right) d^{2} c^{5} x -\frac{e^{2} \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{2 c^{2} e d \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+d^{2} c^{4} \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a^2/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*e*d*x^3+d^2*c^5*x)+b^2/c^4*(1/3375*e^2*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+2/27*c^2*e*d*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+2/27*e^2*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+d^2*c^4*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+2*c^2*e*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+e^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^4*(1/5*arcsin(c*x)*e^2*c^5*x^5+2/3*arcsin(c*x)*c^5*e*d*x^3+arcsin(c*x)*d^2*c^5*x-1/5*e^2*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-2/3*c^2*e*d*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+d^2*c^4*(-c^2*x^2+1)^(1/2)))","B"
661,1,276,140,0.099000," ","int((e*x^2+d)*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{3} c^{3} x^{3} e +c^{3} d x \right)}{c^{2}}+\frac{b^{2} \left(\frac{e \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+c^{2} d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+e \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) c^{3} x^{3} e}{3}+\arcsin \left(c x \right) c^{3} d x -\frac{e \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}+c^{2} d \sqrt{-c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a^2/c^2*(1/3*c^3*x^3*e+c^3*d*x)+b^2/c^2*(1/27*e*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+c^2*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+e*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^2*(1/3*arcsin(c*x)*c^3*x^3*e+arcsin(c*x)*c^3*d*x-1/3*e*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+c^2*d*(-c^2*x^2+1)^(1/2)))","A"
662,1,72,45,0.016000," ","int((a+b*arcsin(c*x))^2,x)","\frac{c x \,a^{2}+b^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+2 a b \left(c x \arcsin \left(c x \right)+\sqrt{-c^{2} x^{2}+1}\right)}{c}"," ",0,"1/c*(c*x*a^2+b^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+2*a*b*(c*x*arcsin(c*x)+(-c^2*x^2+1)^(1/2)))","A"
663,0,0,773,1.394000," ","int((a+b*arcsin(c*x))^2/(e*x^2+d),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(e*x^2+d),x)","F"
664,0,0,22,0.702000," ","int((e*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","\int \sqrt{e \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((e*x^2+d)^(1/2)*(a+b*arcsin(c*x))^2,x)","F"
665,0,0,22,0.717000," ","int((a+b*arcsin(c*x))^2/(e*x^2+d)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(e*x^2+d)^(1/2),x)","F"
666,0,0,22,0.683000," ","int((a+b*arcsin(c*x))^2/(e*x^2+d)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(e*x^2+d)^(3/2),x)","F"
667,0,0,22,0.556000," ","int((a+b*arcsin(c*x))^2/(e*x^2+d)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(e*x^2+d)^(5/2),x)","F"
668,1,310,367,0.084000," ","int((e*x^2+d)^2/(a+b*arcsin(c*x)),x)","\frac{16 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c^{4} d^{2}+16 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c^{4} d^{2}-8 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) c^{2} d e -8 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) c^{2} d e +8 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c^{2} d e +8 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c^{2} d e +\sin \left(\frac{5 a}{b}\right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) e^{2}+\cos \left(\frac{5 a}{b}\right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) e^{2}-3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) e^{2}-3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) e^{2}+2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) e^{2}+2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) e^{2}}{16 c^{5} b}"," ",0,"1/16/c^5*(16*Si(arcsin(c*x)+a/b)*sin(a/b)*c^4*d^2+16*Ci(arcsin(c*x)+a/b)*cos(a/b)*c^4*d^2-8*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*c^2*d*e-8*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*c^2*d*e+8*Si(arcsin(c*x)+a/b)*sin(a/b)*c^2*d*e+8*Ci(arcsin(c*x)+a/b)*cos(a/b)*c^2*d*e+sin(5*a/b)*Si(5*arcsin(c*x)+5*a/b)*e^2+cos(5*a/b)*Ci(5*arcsin(c*x)+5*a/b)*e^2-3*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*e^2-3*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*e^2+2*Si(arcsin(c*x)+a/b)*sin(a/b)*e^2+2*Ci(arcsin(c*x)+a/b)*cos(a/b)*e^2)/b","A"
669,1,142,171,0.069000," ","int((e*x^2+d)/(a+b*arcsin(c*x)),x)","-\frac{-4 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c^{2} d -4 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c^{2} d +\Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) e +\Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) e -\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) e -\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) e}{4 c^{3} b}"," ",0,"-1/4/c^3*(-4*Si(arcsin(c*x)+a/b)*sin(a/b)*c^2*d-4*Ci(arcsin(c*x)+a/b)*cos(a/b)*c^2*d+Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*e+Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*e-Si(arcsin(c*x)+a/b)*sin(a/b)*e-Ci(arcsin(c*x)+a/b)*cos(a/b)*e)/b","A"
670,1,48,53,0.062000," ","int(1/(a+b*arcsin(c*x)),x)","\frac{\frac{\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b}+\frac{\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)}{b}}{c}"," ",0,"1/c*(Si(arcsin(c*x)+a/b)*sin(a/b)/b+Ci(arcsin(c*x)+a/b)*cos(a/b)/b)","A"
671,0,0,22,0.846000," ","int(1/(e*x^2+d)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsin(c*x)),x)","F"
672,0,0,22,3.198000," ","int(1/(e*x^2+d)^2/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsin(c*x)),x)","F"
673,0,0,22,0.432000," ","int((e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x)","\int \frac{\sqrt{e \,x^{2}+d}}{a +b \arcsin \left(c x \right)}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x)","F"
674,0,0,22,0.451000," ","int(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\sqrt{e \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x)),x)","F"
675,0,0,22,0.408000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x)),x)","F"
676,0,0,22,0.433000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x)),x)","F"
677,1,795,472,0.268000," ","int((e*x^2+d)^2/(a+b*arcsin(c*x))^2,x)","-\frac{8 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,c^{2} d e -8 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,c^{2} d e +16 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,c^{4} d^{2}-16 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,c^{4} d^{2}-24 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a \,c^{2} d e +2 \sqrt{-c^{2} x^{2}+1}\, b \,e^{2}+\cos \left(5 \arcsin \left(c x \right)\right) b \,e^{2}+24 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a \,c^{2} d e -24 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b \,c^{2} d e +24 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b \,c^{2} d e +8 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,c^{2} d e -8 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,c^{2} d e -8 \cos \left(3 \arcsin \left(c x \right)\right) b \,c^{2} d e -2 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,e^{2}+16 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,c^{4} d^{2}-16 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,c^{4} d^{2}+5 \arcsin \left(c x \right) \cos \left(\frac{5 a}{b}\right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) b \,e^{2}-5 \arcsin \left(c x \right) \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b \,e^{2}-9 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b \,e^{2}+9 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b \,e^{2}+2 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,e^{2}+9 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a \,e^{2}+5 \cos \left(\frac{5 a}{b}\right) \Si \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) a \,e^{2}-5 \Ci \left(5 \arcsin \left(c x \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a \,e^{2}-9 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a \,e^{2}-2 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,e^{2}+8 \sqrt{-c^{2} x^{2}+1}\, b \,c^{2} d e -3 \cos \left(3 \arcsin \left(c x \right)\right) b \,e^{2}+16 \sqrt{-c^{2} x^{2}+1}\, b \,c^{4} d^{2}+2 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,e^{2}}{16 c^{5} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"-1/16/c^5*(2*(-c^2*x^2+1)^(1/2)*b*e^2+cos(5*arcsin(c*x))*b*e^2+24*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a*c^2*d*e+8*Si(arcsin(c*x)+a/b)*cos(a/b)*a*c^2*d*e-8*Ci(arcsin(c*x)+a/b)*sin(a/b)*a*c^2*d*e+16*arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*c^4*d^2-16*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*c^4*d^2-2*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*e^2-8*cos(3*arcsin(c*x))*b*c^2*d*e-24*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b*c^2*d*e+24*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b*c^2*d*e+8*arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*c^2*d*e-8*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*c^2*d*e+16*Si(arcsin(c*x)+a/b)*cos(a/b)*a*c^4*d^2-16*Ci(arcsin(c*x)+a/b)*sin(a/b)*a*c^4*d^2+5*arcsin(c*x)*cos(5*a/b)*Si(5*arcsin(c*x)+5*a/b)*b*e^2-5*arcsin(c*x)*Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*b*e^2+8*(-c^2*x^2+1)^(1/2)*b*c^2*d*e-9*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b*e^2+9*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b*e^2+2*Si(arcsin(c*x)+a/b)*cos(a/b)*a*e^2+9*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a*e^2-3*cos(3*arcsin(c*x))*b*e^2-24*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a*c^2*d*e+5*cos(5*a/b)*Si(5*arcsin(c*x)+5*a/b)*a*e^2-5*Ci(5*arcsin(c*x)+5*a/b)*sin(5*a/b)*a*e^2-9*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a*e^2+16*(-c^2*x^2+1)^(1/2)*b*c^4*d^2-2*Ci(arcsin(c*x)+a/b)*sin(a/b)*a*e^2+2*arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*e^2)/(a+b*arcsin(c*x))/b^2","A"
678,1,367,237,0.194000," ","int((e*x^2+d)/(a+b*arcsin(c*x))^2,x)","\frac{-4 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,c^{2} d +4 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,c^{2} d -4 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,c^{2} d +4 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,c^{2} d +3 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b e -3 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b e -\arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b e +\arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b e -4 \sqrt{-c^{2} x^{2}+1}\, b \,c^{2} d +3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a e -3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a e -\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a e +\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a e +\cos \left(3 \arcsin \left(c x \right)\right) b e -\sqrt{-c^{2} x^{2}+1}\, b e}{4 c^{3} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/4/c^3*(-4*arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*c^2*d+4*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*c^2*d-4*Si(arcsin(c*x)+a/b)*cos(a/b)*a*c^2*d+4*Ci(arcsin(c*x)+a/b)*sin(a/b)*a*c^2*d+3*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b*e-3*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b*e-arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*e+arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*e-4*(-c^2*x^2+1)^(1/2)*b*c^2*d+3*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a*e-3*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a*e-Si(arcsin(c*x)+a/b)*cos(a/b)*a*e+Ci(arcsin(c*x)+a/b)*sin(a/b)*a*e+cos(3*arcsin(c*x))*b*e-(-c^2*x^2+1)^(1/2)*b*e)/(a+b*arcsin(c*x))/b^2","A"
679,1,76,84,0.000000," ","int(1/(a+b*arcsin(c*x))^2,x)","\frac{-\frac{\sqrt{-c^{2} x^{2}+1}}{\left(a +b \arcsin \left(c x \right)\right) b}-\frac{\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b^{2}}}{c}"," ",0,"1/c*(-(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))/b-(Si(arcsin(c*x)+a/b)*cos(a/b)-Ci(arcsin(c*x)+a/b)*sin(a/b))/b^2)","A"
680,0,0,22,1.069000," ","int(1/(e*x^2+d)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsin(c*x))^2,x)","F"
681,0,0,22,3.976000," ","int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^2,x)","F"
682,0,0,22,0.446000," ","int((e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{\sqrt{e \,x^{2}+d}}{\left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x)","F"
683,0,0,22,0.447000," ","int(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\sqrt{e \,x^{2}+d}\, \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(1/2)/(a+b*arcsin(c*x))^2,x)","F"
684,0,0,22,0.405000," ","int(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(3/2)/(a+b*arcsin(c*x))^2,x)","F"
685,0,0,22,0.423000," ","int(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x^2+d)^(5/2)/(a+b*arcsin(c*x))^2,x)","F"
686,1,1137,581,0.503000," ","int((e*x^2+d)^2*(a+b*arcsin(c*x))^(1/2),x)","-\frac{-200 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{2} d e +200 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{2} d e -75 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}+75 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}+1200 \arcsin \left(c x \right) \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) b \,c^{2} d e +1200 \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a \,c^{2} d e +450 \arcsin \left(c x \right) \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) b \,e^{2}+450 \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a \,e^{2}+3600 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{4} d^{2}-3600 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{4} d^{2}+1800 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{2} d e -1800 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,c^{2} d e +450 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}-450 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}-7200 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b \,c^{4} d^{2}-7200 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a \,c^{4} d^{2}-3600 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b \,c^{2} d e -3600 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a \,c^{2} d e -900 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b \,e^{2}-900 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a \,e^{2}+9 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \cos \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}-9 \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{5}\, \sin \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b \,e^{2}-90 \arcsin \left(c x \right) \sin \left(\frac{5 a +5 b \arcsin \left(c x \right)}{b}-\frac{5 a}{b}\right) b \,e^{2}-90 \sin \left(\frac{5 a +5 b \arcsin \left(c x \right)}{b}-\frac{5 a}{b}\right) a \,e^{2}}{7200 c^{5} \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-1/7200/c^5*(-200*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*3^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^2*d*e+200*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*3^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^2*d*e-75*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*3^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2+75*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*3^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2+1200*arcsin(c*x)*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*b*c^2*d*e+1200*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*a*c^2*d*e+450*arcsin(c*x)*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*b*e^2+450*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*a*e^2+3600*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^4*d^2-3600*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^4*d^2+1800*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^2*d*e-1800*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*c^2*d*e+450*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2-450*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2-7200*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b*c^4*d^2-7200*sin((a+b*arcsin(c*x))/b-a/b)*a*c^4*d^2-3600*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b*c^2*d*e-3600*sin((a+b*arcsin(c*x))/b-a/b)*a*c^2*d*e-900*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b*e^2-900*sin((a+b*arcsin(c*x))/b-a/b)*a*e^2+9*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*5^(1/2)*cos(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2-9*(a+b*arcsin(c*x))^(1/2)*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*5^(1/2)*sin(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b*e^2-90*arcsin(c*x)*sin(5*(a+b*arcsin(c*x))/b-5*a/b)*b*e^2-90*sin(5*(a+b*arcsin(c*x))/b-5*a/b)*a*e^2)/(a+b*arcsin(c*x))^(1/2)","A"
687,1,542,284,0.324000," ","int((e*x^2+d)*(a+b*arcsin(c*x))^(1/2),x)","\frac{-36 \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b \,c^{2} d +36 \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b \,c^{2} d +\cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b e -\sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b e -9 \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b e +9 \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sqrt{\pi}\, \sqrt{2}\, b e +72 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b \,c^{2} d +72 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a \,c^{2} d +18 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b e -6 \arcsin \left(c x \right) \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) b e +18 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a e -6 \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a e}{72 c^{3} \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/72/c^3*(-36*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*c^2*d+36*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*c^2*d+cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*e-sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*3^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*e-9*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*e+9*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*Pi^(1/2)*2^(1/2)*b*e+72*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b*c^2*d+72*sin((a+b*arcsin(c*x))/b-a/b)*a*c^2*d+18*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b*e-6*arcsin(c*x)*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*b*e+18*sin((a+b*arcsin(c*x))/b-a/b)*a*e-6*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*a*e)/(a+b*arcsin(c*x))^(1/2)","A"
688,1,178,95,0.006000," ","int((a+b*arcsin(c*x))^(1/2),x)","\frac{-\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b +\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b +2 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b +2 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a}{2 c \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/2/c/(a+b*arcsin(c*x))^(1/2)*(-2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b+2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*b+2*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*b+2*sin((a+b*arcsin(c*x))/b-a/b)*a)","A"
689,0,0,22,0.581000," ","int((a+b*arcsin(c*x))^(1/2)/(e*x^2+d),x)","\int \frac{\sqrt{a +b \arcsin \left(c x \right)}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsin(c*x))^(1/2)/(e*x^2+d),x)","F"
690,0,0,22,1.263000," ","int((a+b*arcsin(c*x))^(1/2)/(e*x^2+d)^2,x)","\int \frac{\sqrt{a +b \arcsin \left(c x \right)}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsin(c*x))^(1/2)/(e*x^2+d)^2,x)","F"
691,1,835,374,0.435000," ","int((e*x^2+d)*(a+b*arcsin(c*x))^(3/2),x)","\frac{-108 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} c^{2} d -108 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} c^{2} d +\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} e +\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} e -27 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} e -27 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(c x \right)}\, b^{2} e +144 \arcsin \left(c x \right)^{2} \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2} c^{2} d +288 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b \,c^{2} d +216 \arcsin \left(c x \right) \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2} c^{2} d +36 \arcsin \left(c x \right)^{2} \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2} e -12 \arcsin \left(c x \right)^{2} \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) b^{2} e +144 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a^{2} c^{2} d +216 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b \,c^{2} d +72 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b e +54 \arcsin \left(c x \right) \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2} e -24 \arcsin \left(c x \right) \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a b e -6 \arcsin \left(c x \right) \cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) b^{2} e +36 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a^{2} e +54 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b e -12 \sin \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a^{2} e -6 \cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) a b e}{144 c^{3} \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/144/c^3*(-108*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*c^2*d-108*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*c^2*d+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*e+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*e-27*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*e-27*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(a+b*arcsin(c*x))^(1/2)*b^2*e+144*arcsin(c*x)^2*sin((a+b*arcsin(c*x))/b-a/b)*b^2*c^2*d+288*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*a*b*c^2*d+216*arcsin(c*x)*cos((a+b*arcsin(c*x))/b-a/b)*b^2*c^2*d+36*arcsin(c*x)^2*sin((a+b*arcsin(c*x))/b-a/b)*b^2*e-12*arcsin(c*x)^2*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*b^2*e+144*sin((a+b*arcsin(c*x))/b-a/b)*a^2*c^2*d+216*cos((a+b*arcsin(c*x))/b-a/b)*a*b*c^2*d+72*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*a*b*e+54*arcsin(c*x)*cos((a+b*arcsin(c*x))/b-a/b)*b^2*e-24*arcsin(c*x)*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*a*b*e-6*arcsin(c*x)*cos(3*(a+b*arcsin(c*x))/b-3*a/b)*b^2*e+36*sin((a+b*arcsin(c*x))/b-a/b)*a^2*e+54*cos((a+b*arcsin(c*x))/b-a/b)*a*b*e-12*sin(3*(a+b*arcsin(c*x))/b-3*a/b)*a^2*e-6*cos(3*(a+b*arcsin(c*x))/b-3*a/b)*a*b*e)/(a+b*arcsin(c*x))^(1/2)","B"
692,1,270,123,0.002000," ","int((a+b*arcsin(c*x))^(3/2),x)","\frac{-3 \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \cos \left(\frac{a}{b}\right) \sqrt{\frac{1}{b}}\, b^{2}-3 \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, b^{2}+4 \arcsin \left(c x \right)^{2} \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2}+8 \arcsin \left(c x \right) \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b +6 \arcsin \left(c x \right) \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) b^{2}+4 \sin \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a^{2}+6 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) a b}{4 c \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/4/c/(a+b*arcsin(c*x))^(1/2)*(-3*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*cos(a/b)*(1/b)^(1/2)*b^2-3*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*(1/b)^(1/2)*b^2+4*arcsin(c*x)^2*sin((a+b*arcsin(c*x))/b-a/b)*b^2+8*arcsin(c*x)*sin((a+b*arcsin(c*x))/b-a/b)*a*b+6*arcsin(c*x)*cos((a+b*arcsin(c*x))/b-a/b)*b^2+4*sin((a+b*arcsin(c*x))/b-a/b)*a^2+6*cos((a+b*arcsin(c*x))/b-a/b)*a*b)","B"
693,0,0,22,0.559000," ","int((a+b*arcsin(c*x))^(3/2)/(e*x^2+d),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsin(c*x))^(3/2)/(e*x^2+d),x)","F"
694,0,0,22,1.319000," ","int((a+b*arcsin(c*x))^(3/2)/(e*x^2+d)^2,x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((a+b*arcsin(c*x))^(3/2)/(e*x^2+d)^2,x)","F"
695,1,545,529,0.415000," ","int((e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x)","-\frac{\sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{5}\, \left(-48 \sqrt{5}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{4} d^{2}-48 \sqrt{5}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{4} d^{2}+8 \sqrt{5}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d e +8 \sqrt{5}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d e -24 \sqrt{5}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d e -24 \sqrt{5}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d e +3 \sqrt{5}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}+3 \sqrt{5}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}-6 \sqrt{5}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}-6 \sqrt{5}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}-3 \cos \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}-3 \sin \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e^{2}\right)}{240 c^{5}}"," ",0,"-1/240/c^5*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*5^(1/2)*(-48*5^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^4*d^2-48*5^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^4*d^2+8*5^(1/2)*3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d*e+8*5^(1/2)*3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d*e-24*5^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d*e-24*5^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d*e+3*5^(1/2)*3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2+3*5^(1/2)*3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2-6*5^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2-6*5^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2-3*cos(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2-3*sin(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e^2)","A"
696,1,248,253,0.247000," ","int((e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \left(12 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d +12 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d -\cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, e -\sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, e +3 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e +3 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e \right)}{12 c^{3}}"," ",0,"1/12/c^3*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(12*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d+12*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d-cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*3^(1/2)*e-sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*3^(1/2)*e+3*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e+3*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e)","A"
697,1,83,81,0.000000," ","int(1/(a+b*arcsin(c*x))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(\cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{c}"," ",0,"2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b))/c","A"
698,0,0,22,0.556000," ","int(1/(e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \sqrt{a +b \arcsin \left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsin(c*x))^(1/2),x)","F"
699,0,0,22,1.232000," ","int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \sqrt{a +b \arcsin \left(c x \right)}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(1/2),x)","F"
700,1,446,320,0.349000," ","int((e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","\frac{-4 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d +4 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2} d +\sqrt{\frac{1}{b}}\, \sqrt{3}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e -\sqrt{\frac{1}{b}}\, \sqrt{3}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e -\sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e +\sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) e -4 \cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) c^{2} d +\cos \left(\frac{3 a +3 b \arcsin \left(c x \right)}{b}-\frac{3 a}{b}\right) e -\cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right) e}{2 c^{3} b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"1/2/c^3/b*(-4*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d+4*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*c^2*d+(1/b)^(1/2)*3^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e-(1/b)^(1/2)*3^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e-(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e+(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)*e-4*cos((a+b*arcsin(c*x))/b-a/b)*c^2*d+cos(3*(a+b*arcsin(c*x))/b-3*a/b)*e-cos((a+b*arcsin(c*x))/b-a/b)*e)/(a+b*arcsin(c*x))^(1/2)","A"
701,1,149,113,0.000000," ","int(1/(a+b*arcsin(c*x))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(c x \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\cos \left(\frac{a +b \arcsin \left(c x \right)}{b}-\frac{a}{b}\right)\right)}{c b \sqrt{a +b \arcsin \left(c x \right)}}"," ",0,"-2/c/b*((1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)-(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(c*x))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(c*x))^(1/2)/b)+cos((a+b*arcsin(c*x))/b-a/b))/(a+b*arcsin(c*x))^(1/2)","A"
702,0,0,22,0.553000," ","int(1/(e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right) \left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)/(a+b*arcsin(c*x))^(3/2),x)","F"
703,0,0,22,1.235000," ","int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","\int \frac{1}{\left(e \,x^{2}+d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x^2+d)^2/(a+b*arcsin(c*x))^(3/2),x)","F"