1,1,75,0,0.0477089,"\int x^4 \cos ^{-1}(a x) \, dx","Int[x^4*ArcCos[a*x],x]","-\frac{\left(1-a^2 x^2\right)^{5/2}}{25 a^5}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{15 a^5}-\frac{\sqrt{1-a^2 x^2}}{5 a^5}+\frac{1}{5} x^5 \cos ^{-1}(a x)","-\frac{\left(1-a^2 x^2\right)^{5/2}}{25 a^5}+\frac{2 \left(1-a^2 x^2\right)^{3/2}}{15 a^5}-\frac{\sqrt{1-a^2 x^2}}{5 a^5}+\frac{1}{5} x^5 \cos ^{-1}(a x)",1,"-Sqrt[1 - a^2*x^2]/(5*a^5) + (2*(1 - a^2*x^2)^(3/2))/(15*a^5) - (1 - a^2*x^2)^(5/2)/(25*a^5) + (x^5*ArcCos[a*x])/5","A",4,3,8,0.3750,1,"{4628, 266, 43}"
2,1,69,0,0.0308727,"\int x^3 \cos ^{-1}(a x) \, dx","Int[x^3*ArcCos[a*x],x]","-\frac{x^3 \sqrt{1-a^2 x^2}}{16 a}-\frac{3 x \sqrt{1-a^2 x^2}}{32 a^3}+\frac{3 \sin ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)","-\frac{x^3 \sqrt{1-a^2 x^2}}{16 a}-\frac{3 x \sqrt{1-a^2 x^2}}{32 a^3}+\frac{3 \sin ^{-1}(a x)}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)",1,"(-3*x*Sqrt[1 - a^2*x^2])/(32*a^3) - (x^3*Sqrt[1 - a^2*x^2])/(16*a) + (x^4*ArcCos[a*x])/4 + (3*ArcSin[a*x])/(32*a^4)","A",4,3,8,0.3750,1,"{4628, 321, 216}"
3,1,54,0,0.0346335,"\int x^2 \cos ^{-1}(a x) \, dx","Int[x^2*ArcCos[a*x],x]","\frac{\left(1-a^2 x^2\right)^{3/2}}{9 a^3}-\frac{\sqrt{1-a^2 x^2}}{3 a^3}+\frac{1}{3} x^3 \cos ^{-1}(a x)","\frac{\left(1-a^2 x^2\right)^{3/2}}{9 a^3}-\frac{\sqrt{1-a^2 x^2}}{3 a^3}+\frac{1}{3} x^3 \cos ^{-1}(a x)",1,"-Sqrt[1 - a^2*x^2]/(3*a^3) + (1 - a^2*x^2)^(3/2)/(9*a^3) + (x^3*ArcCos[a*x])/3","A",4,3,8,0.3750,1,"{4628, 266, 43}"
4,1,45,0,0.0160866,"\int x \cos ^{-1}(a x) \, dx","Int[x*ArcCos[a*x],x]","-\frac{x \sqrt{1-a^2 x^2}}{4 a}+\frac{\sin ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)","-\frac{x \sqrt{1-a^2 x^2}}{4 a}+\frac{\sin ^{-1}(a x)}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)",1,"-(x*Sqrt[1 - a^2*x^2])/(4*a) + (x^2*ArcCos[a*x])/2 + ArcSin[a*x]/(4*a^2)","A",3,3,6,0.5000,1,"{4628, 321, 216}"
5,1,26,0,0.0075295,"\int \cos ^{-1}(a x) \, dx","Int[ArcCos[a*x],x]","x \cos ^{-1}(a x)-\frac{\sqrt{1-a^2 x^2}}{a}","x \cos ^{-1}(a x)-\frac{\sqrt{1-a^2 x^2}}{a}",1,"-(Sqrt[1 - a^2*x^2]/a) + x*ArcCos[a*x]","A",2,2,4,0.5000,1,"{4620, 261}"
6,1,51,0,0.0567818,"\int \frac{\cos ^{-1}(a x)}{x} \, dx","Int[ArcCos[a*x]/x,x]","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{2} i \cos ^{-1}(a x)^2+\cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{2} i \cos ^{-1}(a x)^2+\cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)",1,"(-I/2)*ArcCos[a*x]^2 + ArcCos[a*x]*Log[1 + E^((2*I)*ArcCos[a*x])] - (I/2)*PolyLog[2, -E^((2*I)*ArcCos[a*x])]","A",5,5,8,0.6250,1,"{4626, 3719, 2190, 2279, 2391}"
7,1,27,0,0.0224197,"\int \frac{\cos ^{-1}(a x)}{x^2} \, dx","Int[ArcCos[a*x]/x^2,x]","a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{x}","a \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{x}",1,"-(ArcCos[a*x]/x) + a*ArcTanh[Sqrt[1 - a^2*x^2]]","A",4,4,8,0.5000,1,"{4628, 266, 63, 208}"
8,1,34,0,0.015502,"\int \frac{\cos ^{-1}(a x)}{x^3} \, dx","Int[ArcCos[a*x]/x^3,x]","\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\cos ^{-1}(a x)}{2 x^2}","\frac{a \sqrt{1-a^2 x^2}}{2 x}-\frac{\cos ^{-1}(a x)}{2 x^2}",1,"(a*Sqrt[1 - a^2*x^2])/(2*x) - ArcCos[a*x]/(2*x^2)","A",2,2,8,0.2500,1,"{4628, 264}"
9,1,56,0,0.0354313,"\int \frac{\cos ^{-1}(a x)}{x^4} \, dx","Int[ArcCos[a*x]/x^4,x]","\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{3 x^3}","\frac{a \sqrt{1-a^2 x^2}}{6 x^2}+\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{3 x^3}",1,"(a*Sqrt[1 - a^2*x^2])/(6*x^2) - ArcCos[a*x]/(3*x^3) + (a^3*ArcTanh[Sqrt[1 - a^2*x^2]])/6","A",5,5,8,0.6250,1,"{4628, 266, 51, 63, 208}"
10,1,58,0,0.0221729,"\int \frac{\cos ^{-1}(a x)}{x^5} \, dx","Int[ArcCos[a*x]/x^5,x]","\frac{a^3 \sqrt{1-a^2 x^2}}{6 x}+\frac{a \sqrt{1-a^2 x^2}}{12 x^3}-\frac{\cos ^{-1}(a x)}{4 x^4}","\frac{a^3 \sqrt{1-a^2 x^2}}{6 x}+\frac{a \sqrt{1-a^2 x^2}}{12 x^3}-\frac{\cos ^{-1}(a x)}{4 x^4}",1,"(a*Sqrt[1 - a^2*x^2])/(12*x^3) + (a^3*Sqrt[1 - a^2*x^2])/(6*x) - ArcCos[a*x]/(4*x^4)","A",3,3,8,0.3750,1,"{4628, 271, 264}"
11,1,80,0,0.0466105,"\int \frac{\cos ^{-1}(a x)}{x^6} \, dx","Int[ArcCos[a*x]/x^6,x]","\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}+\frac{a \sqrt{1-a^2 x^2}}{20 x^4}+\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{5 x^5}","\frac{3 a^3 \sqrt{1-a^2 x^2}}{40 x^2}+\frac{a \sqrt{1-a^2 x^2}}{20 x^4}+\frac{3}{40} a^5 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{\cos ^{-1}(a x)}{5 x^5}",1,"(a*Sqrt[1 - a^2*x^2])/(20*x^4) + (3*a^3*Sqrt[1 - a^2*x^2])/(40*x^2) - ArcCos[a*x]/(5*x^5) + (3*a^5*ArcTanh[Sqrt[1 - a^2*x^2]])/40","A",6,5,8,0.6250,1,"{4628, 266, 51, 63, 208}"
12,1,120,0,0.1957707,"\int x^4 \cos ^{-1}(a x)^2 \, dx","Int[x^4*ArcCos[a*x]^2,x]","-\frac{8 x^3}{225 a^2}-\frac{2 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{25 a}-\frac{8 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{75 a^3}-\frac{16 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{75 a^5}-\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^2-\frac{2 x^5}{125}","-\frac{8 x^3}{225 a^2}-\frac{2 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{25 a}-\frac{8 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{75 a^3}-\frac{16 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{75 a^5}-\frac{16 x}{75 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^2-\frac{2 x^5}{125}",1,"(-16*x)/(75*a^4) - (8*x^3)/(225*a^2) - (2*x^5)/125 - (16*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(75*a^5) - (8*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(75*a^3) - (2*x^4*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(25*a) + (x^5*ArcCos[a*x]^2)/5","A",7,5,10,0.5000,1,"{4628, 4708, 4678, 8, 30}"
13,1,98,0,0.1696625,"\int x^3 \cos ^{-1}(a x)^2 \, dx","Int[x^3*ArcCos[a*x]^2,x]","-\frac{3 x^2}{32 a^2}-\frac{x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{8 a}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{16 a^3}-\frac{3 \cos ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^2-\frac{x^4}{32}","-\frac{3 x^2}{32 a^2}-\frac{x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{8 a}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{16 a^3}-\frac{3 \cos ^{-1}(a x)^2}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^2-\frac{x^4}{32}",1,"(-3*x^2)/(32*a^2) - x^4/32 - (3*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(16*a^3) - (x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(8*a) - (3*ArcCos[a*x]^2)/(32*a^4) + (x^4*ArcCos[a*x]^2)/4","A",6,4,10,0.4000,1,"{4628, 4708, 4642, 30}"
14,1,82,0,0.1255993,"\int x^2 \cos ^{-1}(a x)^2 \, dx","Int[x^2*ArcCos[a*x]^2,x]","-\frac{2 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{9 a}-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^2-\frac{2 x^3}{27}","-\frac{2 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{9 a}-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{9 a^3}-\frac{4 x}{9 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^2-\frac{2 x^3}{27}",1,"(-4*x)/(9*a^2) - (2*x^3)/27 - (4*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(9*a^3) - (2*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(9*a) + (x^3*ArcCos[a*x]^2)/3","A",5,5,10,0.5000,1,"{4628, 4708, 4678, 8, 30}"
15,1,60,0,0.0966761,"\int x \cos ^{-1}(a x)^2 \, dx","Int[x*ArcCos[a*x]^2,x]","-\frac{x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{2 a}-\frac{\cos ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^2-\frac{x^2}{4}","-\frac{x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{2 a}-\frac{\cos ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^2-\frac{x^2}{4}",1,"-x^2/4 - (x*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(2*a) - ArcCos[a*x]^2/(4*a^2) + (x^2*ArcCos[a*x]^2)/2","A",4,4,8,0.5000,1,"{4628, 4708, 4642, 30}"
16,1,35,0,0.0468431,"\int \cos ^{-1}(a x)^2 \, dx","Int[ArcCos[a*x]^2,x]","-\frac{2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+x \cos ^{-1}(a x)^2-2 x","-\frac{2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+x \cos ^{-1}(a x)^2-2 x",1,"-2*x - (2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/a + x*ArcCos[a*x]^2","A",3,3,6,0.5000,1,"{4620, 4678, 8}"
17,1,73,0,0.0933503,"\int \frac{\cos ^{-1}(a x)^2}{x} \, dx","Int[ArcCos[a*x]^2/x,x]","-i \cos ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{3} i \cos ^{-1}(a x)^3+\cos ^{-1}(a x)^2 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)","-i \cos ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{3} i \cos ^{-1}(a x)^3+\cos ^{-1}(a x)^2 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)",1,"(-I/3)*ArcCos[a*x]^3 + ArcCos[a*x]^2*Log[1 + E^((2*I)*ArcCos[a*x])] - I*ArcCos[a*x]*PolyLog[2, -E^((2*I)*ArcCos[a*x])] + PolyLog[3, -E^((2*I)*ArcCos[a*x])]/2","A",6,6,10,0.6000,1,"{4626, 3719, 2190, 2531, 2282, 6589}"
18,1,74,0,0.1069365,"\int \frac{\cos ^{-1}(a x)^2}{x^2} \, dx","Int[ArcCos[a*x]^2/x^2,x]","2 i a \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^2}{x}-4 i a \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)","2 i a \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-2 i a \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^2}{x}-4 i a \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)",1,"-(ArcCos[a*x]^2/x) - (4*I)*a*ArcCos[a*x]*ArcTan[E^(I*ArcCos[a*x])] + (2*I)*a*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - (2*I)*a*PolyLog[2, I*E^(I*ArcCos[a*x])]","A",7,5,10,0.5000,1,"{4628, 4710, 4181, 2279, 2391}"
19,1,43,0,0.0783459,"\int \frac{\cos ^{-1}(a x)^2}{x^3} \, dx","Int[ArcCos[a*x]^2/x^3,x]","\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\cos ^{-1}(a x)^2}{2 x^2}","\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{x}+a^2 \log (x)-\frac{\cos ^{-1}(a x)^2}{2 x^2}",1,"(a*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/x - ArcCos[a*x]^2/(2*x^2) + a^2*Log[x]","A",3,3,10,0.3000,1,"{4628, 4682, 29}"
20,1,124,0,0.176919,"\int \frac{\cos ^{-1}(a x)^2}{x^4} \, dx","Int[ArcCos[a*x]^2/x^4,x]","\frac{1}{3} i a^3 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-\frac{1}{3} i a^3 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{3 x^2}-\frac{a^2}{3 x}-\frac{2}{3} i a^3 \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^2}{3 x^3}","\frac{1}{3} i a^3 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-\frac{1}{3} i a^3 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{3 x^2}-\frac{a^2}{3 x}-\frac{2}{3} i a^3 \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) + (a*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(3*x^2) - ArcCos[a*x]^2/(3*x^3) - ((2*I)/3)*a^3*ArcCos[a*x]*ArcTan[E^(I*ArcCos[a*x])] + (I/3)*a^3*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - (I/3)*a^3*PolyLog[2, I*E^(I*ArcCos[a*x])]","A",9,7,10,0.7000,1,"{4628, 4702, 4710, 4181, 2279, 2391, 30}"
21,1,87,0,0.1517411,"\int \frac{\cos ^{-1}(a x)^2}{x^5} \, dx","Int[ArcCos[a*x]^2/x^5,x]","-\frac{a^2}{12 x^2}+\frac{a^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{3 x}+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{6 x^3}+\frac{1}{3} a^4 \log (x)-\frac{\cos ^{-1}(a x)^2}{4 x^4}","-\frac{a^2}{12 x^2}+\frac{a^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{3 x}+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{6 x^3}+\frac{1}{3} a^4 \log (x)-\frac{\cos ^{-1}(a x)^2}{4 x^4}",1,"-a^2/(12*x^2) + (a*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(6*x^3) + (a^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(3*x) - ArcCos[a*x]^2/(4*x^4) + (a^4*Log[x])/3","A",5,5,10,0.5000,1,"{4628, 4702, 4682, 29, 30}"
22,1,201,0,0.4026145,"\int x^4 \cos ^{-1}(a x)^3 \, dx","Int[x^4*ArcCos[a*x]^3,x]","\frac{6 \left(1-a^2 x^2\right)^{5/2}}{625 a^5}-\frac{76 \left(1-a^2 x^2\right)^{3/2}}{1125 a^5}+\frac{298 \sqrt{1-a^2 x^2}}{375 a^5}-\frac{3 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \cos ^{-1}(a x)}{75 a^2}-\frac{4 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a^3}-\frac{8 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a^5}-\frac{16 x \cos ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^3-\frac{6}{125} x^5 \cos ^{-1}(a x)","\frac{6 \left(1-a^2 x^2\right)^{5/2}}{625 a^5}-\frac{76 \left(1-a^2 x^2\right)^{3/2}}{1125 a^5}+\frac{298 \sqrt{1-a^2 x^2}}{375 a^5}-\frac{3 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a}-\frac{8 x^3 \cos ^{-1}(a x)}{75 a^2}-\frac{4 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a^3}-\frac{8 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{25 a^5}-\frac{16 x \cos ^{-1}(a x)}{25 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^3-\frac{6}{125} x^5 \cos ^{-1}(a x)",1,"(298*Sqrt[1 - a^2*x^2])/(375*a^5) - (76*(1 - a^2*x^2)^(3/2))/(1125*a^5) + (6*(1 - a^2*x^2)^(5/2))/(625*a^5) - (16*x*ArcCos[a*x])/(25*a^4) - (8*x^3*ArcCos[a*x])/(75*a^2) - (6*x^5*ArcCos[a*x])/125 - (8*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(25*a^5) - (4*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(25*a^3) - (3*x^4*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(25*a) + (x^5*ArcCos[a*x]^3)/5","A",14,7,10,0.7000,1,"{4628, 4708, 4678, 4620, 261, 266, 43}"
23,1,167,0,0.3149797,"\int x^3 \cos ^{-1}(a x)^3 \, dx","Int[x^3*ArcCos[a*x]^3,x]","\frac{3 x^3 \sqrt{1-a^2 x^2}}{128 a}+\frac{45 x \sqrt{1-a^2 x^2}}{256 a^3}-\frac{3 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \cos ^{-1}(a x)}{32 a^2}-\frac{9 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{32 a^3}-\frac{45 \sin ^{-1}(a x)}{256 a^4}-\frac{3 \cos ^{-1}(a x)^3}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^3-\frac{3}{32} x^4 \cos ^{-1}(a x)","\frac{3 x^3 \sqrt{1-a^2 x^2}}{128 a}+\frac{45 x \sqrt{1-a^2 x^2}}{256 a^3}-\frac{3 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{16 a}-\frac{9 x^2 \cos ^{-1}(a x)}{32 a^2}-\frac{9 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{32 a^3}-\frac{45 \sin ^{-1}(a x)}{256 a^4}-\frac{3 \cos ^{-1}(a x)^3}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^3-\frac{3}{32} x^4 \cos ^{-1}(a x)",1,"(45*x*Sqrt[1 - a^2*x^2])/(256*a^3) + (3*x^3*Sqrt[1 - a^2*x^2])/(128*a) - (9*x^2*ArcCos[a*x])/(32*a^2) - (3*x^4*ArcCos[a*x])/32 - (9*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(32*a^3) - (3*x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(16*a) - (3*ArcCos[a*x]^3)/(32*a^4) + (x^4*ArcCos[a*x]^3)/4 - (45*ArcSin[a*x])/(256*a^4)","A",11,5,10,0.5000,1,"{4628, 4708, 4642, 321, 216}"
24,1,136,0,0.2409023,"\int x^2 \cos ^{-1}(a x)^3 \, dx","Int[x^2*ArcCos[a*x]^3,x]","-\frac{2 \left(1-a^2 x^2\right)^{3/2}}{27 a^3}+\frac{14 \sqrt{1-a^2 x^2}}{9 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{3 a}-\frac{2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{3 a^3}-\frac{4 x \cos ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^3-\frac{2}{9} x^3 \cos ^{-1}(a x)","-\frac{2 \left(1-a^2 x^2\right)^{3/2}}{27 a^3}+\frac{14 \sqrt{1-a^2 x^2}}{9 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{3 a}-\frac{2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{3 a^3}-\frac{4 x \cos ^{-1}(a x)}{3 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^3-\frac{2}{9} x^3 \cos ^{-1}(a x)",1,"(14*Sqrt[1 - a^2*x^2])/(9*a^3) - (2*(1 - a^2*x^2)^(3/2))/(27*a^3) - (4*x*ArcCos[a*x])/(3*a^2) - (2*x^3*ArcCos[a*x])/9 - (2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(3*a^3) - (x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(3*a) + (x^3*ArcCos[a*x]^3)/3","A",9,7,10,0.7000,1,"{4628, 4708, 4678, 4620, 261, 266, 43}"
25,1,99,0,0.1559689,"\int x \cos ^{-1}(a x)^3 \, dx","Int[x*ArcCos[a*x]^3,x]","\frac{3 x \sqrt{1-a^2 x^2}}{8 a}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{4 a}-\frac{3 \sin ^{-1}(a x)}{8 a^2}-\frac{\cos ^{-1}(a x)^3}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^3-\frac{3}{4} x^2 \cos ^{-1}(a x)","\frac{3 x \sqrt{1-a^2 x^2}}{8 a}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{4 a}-\frac{3 \sin ^{-1}(a x)}{8 a^2}-\frac{\cos ^{-1}(a x)^3}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^3-\frac{3}{4} x^2 \cos ^{-1}(a x)",1,"(3*x*Sqrt[1 - a^2*x^2])/(8*a) - (3*x^2*ArcCos[a*x])/4 - (3*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(4*a) - ArcCos[a*x]^3/(4*a^2) + (x^2*ArcCos[a*x]^3)/2 - (3*ArcSin[a*x])/(8*a^2)","A",6,5,8,0.6250,1,"{4628, 4708, 4642, 321, 216}"
26,1,60,0,0.0810922,"\int \cos ^{-1}(a x)^3 \, dx","Int[ArcCos[a*x]^3,x]","\frac{6 \sqrt{1-a^2 x^2}}{a}-\frac{3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{a}+x \cos ^{-1}(a x)^3-6 x \cos ^{-1}(a x)","\frac{6 \sqrt{1-a^2 x^2}}{a}-\frac{3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{a}+x \cos ^{-1}(a x)^3-6 x \cos ^{-1}(a x)",1,"(6*Sqrt[1 - a^2*x^2])/a - 6*x*ArcCos[a*x] - (3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/a + x*ArcCos[a*x]^3","A",4,3,6,0.5000,1,"{4620, 4678, 261}"
27,1,101,0,0.1105185,"\int \frac{\cos ^{-1}(a x)^3}{x} \, dx","Int[ArcCos[a*x]^3/x,x]","-\frac{3}{2} i \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3}{2} \cos ^{-1}(a x) \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3}{4} i \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{4} i \cos ^{-1}(a x)^4+\cos ^{-1}(a x)^3 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)","-\frac{3}{2} i \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3}{2} \cos ^{-1}(a x) \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3}{4} i \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{4} i \cos ^{-1}(a x)^4+\cos ^{-1}(a x)^3 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)",1,"(-I/4)*ArcCos[a*x]^4 + ArcCos[a*x]^3*Log[1 + E^((2*I)*ArcCos[a*x])] - ((3*I)/2)*ArcCos[a*x]^2*PolyLog[2, -E^((2*I)*ArcCos[a*x])] + (3*ArcCos[a*x]*PolyLog[3, -E^((2*I)*ArcCos[a*x])])/2 + ((3*I)/4)*PolyLog[4, -E^((2*I)*ArcCos[a*x])]","A",7,7,10,0.7000,1,"{4626, 3719, 2190, 2531, 6609, 2282, 6589}"
28,1,122,0,0.1749375,"\int \frac{\cos ^{-1}(a x)^3}{x^2} \, dx","Int[ArcCos[a*x]^3/x^2,x]","6 i a \cos ^{-1}(a x) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-6 i a \cos ^{-1}(a x) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{x}-6 i a \cos ^{-1}(a x)^2 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)","6 i a \cos ^{-1}(a x) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-6 i a \cos ^{-1}(a x) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-6 a \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+6 a \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{x}-6 i a \cos ^{-1}(a x)^2 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)",1,"-(ArcCos[a*x]^3/x) - (6*I)*a*ArcCos[a*x]^2*ArcTan[E^(I*ArcCos[a*x])] + (6*I)*a*ArcCos[a*x]*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - (6*I)*a*ArcCos[a*x]*PolyLog[2, I*E^(I*ArcCos[a*x])] - 6*a*PolyLog[3, (-I)*E^(I*ArcCos[a*x])] + 6*a*PolyLog[3, I*E^(I*ArcCos[a*x])]","A",9,6,10,0.6000,1,"{4628, 4710, 4181, 2531, 2282, 6589}"
29,1,102,0,0.1753425,"\int \frac{\cos ^{-1}(a x)^3}{x^3} \, dx","Int[ArcCos[a*x]^3/x^3,x]","-\frac{3}{2} i a^2 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x}-\frac{3}{2} i a^2 \cos ^{-1}(a x)^2+3 a^2 \cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{2 x^2}","-\frac{3}{2} i a^2 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{3 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x}-\frac{3}{2} i a^2 \cos ^{-1}(a x)^2+3 a^2 \cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{2 x^2}",1,"((-3*I)/2)*a^2*ArcCos[a*x]^2 + (3*a*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(2*x) - ArcCos[a*x]^3/(2*x^2) + 3*a^2*ArcCos[a*x]*Log[1 + E^((2*I)*ArcCos[a*x])] - ((3*I)/2)*a^2*PolyLog[2, -E^((2*I)*ArcCos[a*x])]","A",7,7,10,0.7000,1,"{4628, 4682, 4626, 3719, 2190, 2279, 2391}"
30,1,192,0,0.3038685,"\int \frac{\cos ^{-1}(a x)^3}{x^4} \, dx","Int[ArcCos[a*x]^3/x^4,x]","i a^3 \cos ^{-1}(a x) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-i a^3 \cos ^{-1}(a x) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x^2}+a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a^2 \cos ^{-1}(a x)}{x}-i a^3 \cos ^{-1}(a x)^2 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{3 x^3}","i a^3 \cos ^{-1}(a x) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-i a^3 \cos ^{-1}(a x) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-a^3 \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+a^3 \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x^2}+a^3 \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\frac{a^2 \cos ^{-1}(a x)}{x}-i a^3 \cos ^{-1}(a x)^2 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{3 x^3}",1,"-((a^2*ArcCos[a*x])/x) + (a*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(2*x^2) - ArcCos[a*x]^3/(3*x^3) - I*a^3*ArcCos[a*x]^2*ArcTan[E^(I*ArcCos[a*x])] + a^3*ArcTanh[Sqrt[1 - a^2*x^2]] + I*a^3*ArcCos[a*x]*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - I*a^3*ArcCos[a*x]*PolyLog[2, I*E^(I*ArcCos[a*x])] - a^3*PolyLog[3, (-I)*E^(I*ArcCos[a*x])] + a^3*PolyLog[3, I*E^(I*ArcCos[a*x])]","A",14,10,10,1.000,1,"{4628, 4702, 4710, 4181, 2531, 2282, 6589, 266, 63, 208}"
31,1,169,0,0.2895686,"\int \frac{\cos ^{-1}(a x)^3}{x^5} \, dx","Int[ArcCos[a*x]^3/x^5,x]","-\frac{1}{2} i a^4 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{a^3 \sqrt{1-a^2 x^2}}{4 x}+\frac{a^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x}-\frac{a^2 \cos ^{-1}(a x)}{4 x^2}+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{4 x^3}-\frac{1}{2} i a^4 \cos ^{-1}(a x)^2+a^4 \cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{4 x^4}","-\frac{1}{2} i a^4 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{a^3 \sqrt{1-a^2 x^2}}{4 x}+\frac{a^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{2 x}-\frac{a^2 \cos ^{-1}(a x)}{4 x^2}+\frac{a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^2}{4 x^3}-\frac{1}{2} i a^4 \cos ^{-1}(a x)^2+a^4 \cos ^{-1}(a x) \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^3}{4 x^4}",1,"(a^3*Sqrt[1 - a^2*x^2])/(4*x) - (a^2*ArcCos[a*x])/(4*x^2) - (I/2)*a^4*ArcCos[a*x]^2 + (a*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(4*x^3) + (a^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^2)/(2*x) - ArcCos[a*x]^3/(4*x^4) + a^4*ArcCos[a*x]*Log[1 + E^((2*I)*ArcCos[a*x])] - (I/2)*a^4*PolyLog[2, -E^((2*I)*ArcCos[a*x])]","A",10,9,10,0.9000,1,"{4628, 4702, 4682, 4626, 3719, 2190, 2279, 2391, 264}"
32,1,282,0,0.8742225,"\int x^5 \cos ^{-1}(a x)^4 \, dx","Int[x^5*ArcCos[a*x]^4,x]","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}-\frac{x^5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a}+\frac{x^5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{54 a}-\frac{5 x^4 \cos ^{-1}(a x)^2}{48 a^2}-\frac{5 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{36 a^3}+\frac{65 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{864 a^3}-\frac{5 x^2 \cos ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{24 a^5}+\frac{245 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{576 a^5}-\frac{5 \cos ^{-1}(a x)^4}{96 a^6}+\frac{245 \cos ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \cos ^{-1}(a x)^4-\frac{1}{18} x^6 \cos ^{-1}(a x)^2+\frac{x^6}{324}","\frac{65 x^4}{3456 a^2}+\frac{245 x^2}{1152 a^4}-\frac{x^5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a}+\frac{x^5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{54 a}-\frac{5 x^4 \cos ^{-1}(a x)^2}{48 a^2}-\frac{5 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{36 a^3}+\frac{65 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{864 a^3}-\frac{5 x^2 \cos ^{-1}(a x)^2}{16 a^4}-\frac{5 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{24 a^5}+\frac{245 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{576 a^5}-\frac{5 \cos ^{-1}(a x)^4}{96 a^6}+\frac{245 \cos ^{-1}(a x)^2}{1152 a^6}+\frac{1}{6} x^6 \cos ^{-1}(a x)^4-\frac{1}{18} x^6 \cos ^{-1}(a x)^2+\frac{x^6}{324}",1,"(245*x^2)/(1152*a^4) + (65*x^4)/(3456*a^2) + x^6/324 + (245*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(576*a^5) + (65*x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(864*a^3) + (x^5*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(54*a) + (245*ArcCos[a*x]^2)/(1152*a^6) - (5*x^2*ArcCos[a*x]^2)/(16*a^4) - (5*x^4*ArcCos[a*x]^2)/(48*a^2) - (x^6*ArcCos[a*x]^2)/18 - (5*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(24*a^5) - (5*x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(36*a^3) - (x^5*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(9*a) - (5*ArcCos[a*x]^4)/(96*a^6) + (x^6*ArcCos[a*x]^4)/6","A",23,4,10,0.4000,1,"{4628, 4708, 4642, 30}"
33,1,250,0,0.6692385,"\int x^4 \cos ^{-1}(a x)^4 \, dx","Int[x^4*ArcCos[a*x]^4,x]","\frac{1088 x^3}{16875 a^2}-\frac{4 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{25 a}+\frac{24 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{625 a}-\frac{16 x^3 \cos ^{-1}(a x)^2}{75 a^2}-\frac{16 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{75 a^3}+\frac{1088 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{5625 a^3}-\frac{32 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{75 a^5}+\frac{16576 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{5625 a^5}+\frac{16576 x}{5625 a^4}-\frac{32 x \cos ^{-1}(a x)^2}{25 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^4-\frac{12}{125} x^5 \cos ^{-1}(a x)^2+\frac{24 x^5}{3125}","\frac{1088 x^3}{16875 a^2}-\frac{4 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{25 a}+\frac{24 x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{625 a}-\frac{16 x^3 \cos ^{-1}(a x)^2}{75 a^2}-\frac{16 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{75 a^3}+\frac{1088 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{5625 a^3}-\frac{32 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{75 a^5}+\frac{16576 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{5625 a^5}+\frac{16576 x}{5625 a^4}-\frac{32 x \cos ^{-1}(a x)^2}{25 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^4-\frac{12}{125} x^5 \cos ^{-1}(a x)^2+\frac{24 x^5}{3125}",1,"(16576*x)/(5625*a^4) + (1088*x^3)/(16875*a^2) + (24*x^5)/3125 + (16576*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(5625*a^5) + (1088*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(5625*a^3) + (24*x^4*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(625*a) - (32*x*ArcCos[a*x]^2)/(25*a^4) - (16*x^3*ArcCos[a*x]^2)/(75*a^2) - (12*x^5*ArcCos[a*x]^2)/125 - (32*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(75*a^5) - (16*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(75*a^3) - (4*x^4*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(25*a) + (x^5*ArcCos[a*x]^4)/5","A",19,6,10,0.6000,1,"{4628, 4708, 4678, 4620, 8, 30}"
34,1,198,0,0.5195836,"\int x^3 \cos ^{-1}(a x)^4 \, dx","Int[x^3*ArcCos[a*x]^4,x]","\frac{45 x^2}{128 a^2}-\frac{x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{4 a}+\frac{3 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{32 a}-\frac{9 x^2 \cos ^{-1}(a x)^2}{16 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{8 a^3}+\frac{45 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{64 a^3}-\frac{3 \cos ^{-1}(a x)^4}{32 a^4}+\frac{45 \cos ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^4-\frac{3}{16} x^4 \cos ^{-1}(a x)^2+\frac{3 x^4}{128}","\frac{45 x^2}{128 a^2}-\frac{x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{4 a}+\frac{3 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{32 a}-\frac{9 x^2 \cos ^{-1}(a x)^2}{16 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{8 a^3}+\frac{45 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{64 a^3}-\frac{3 \cos ^{-1}(a x)^4}{32 a^4}+\frac{45 \cos ^{-1}(a x)^2}{128 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^4-\frac{3}{16} x^4 \cos ^{-1}(a x)^2+\frac{3 x^4}{128}",1,"(45*x^2)/(128*a^2) + (3*x^4)/128 + (45*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(64*a^3) + (3*x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(32*a) + (45*ArcCos[a*x]^2)/(128*a^4) - (9*x^2*ArcCos[a*x]^2)/(16*a^2) - (3*x^4*ArcCos[a*x]^2)/16 - (3*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(8*a^3) - (x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(4*a) - (3*ArcCos[a*x]^4)/(32*a^4) + (x^4*ArcCos[a*x]^4)/4","A",14,4,10,0.4000,1,"{4628, 4708, 4642, 30}"
35,1,166,0,0.3657335,"\int x^2 \cos ^{-1}(a x)^4 \, dx","Int[x^2*ArcCos[a*x]^4,x]","-\frac{4 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a}-\frac{8 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a^3}+\frac{8 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a}+\frac{160 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a^3}+\frac{160 x}{27 a^2}-\frac{8 x \cos ^{-1}(a x)^2}{3 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^4-\frac{4}{9} x^3 \cos ^{-1}(a x)^2+\frac{8 x^3}{81}","-\frac{4 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a}-\frac{8 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{9 a^3}+\frac{8 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a}+\frac{160 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a^3}+\frac{160 x}{27 a^2}-\frac{8 x \cos ^{-1}(a x)^2}{3 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^4-\frac{4}{9} x^3 \cos ^{-1}(a x)^2+\frac{8 x^3}{81}",1,"(160*x)/(27*a^2) + (8*x^3)/81 + (160*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(27*a^3) + (8*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(27*a) - (8*x*ArcCos[a*x]^2)/(3*a^2) - (4*x^3*ArcCos[a*x]^2)/9 - (8*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(9*a^3) - (4*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(9*a) + (x^3*ArcCos[a*x]^4)/3","A",11,6,10,0.6000,1,"{4628, 4708, 4678, 4620, 8, 30}"
36,1,112,0,0.2370459,"\int x \cos ^{-1}(a x)^4 \, dx","Int[x*ArcCos[a*x]^4,x]","-\frac{x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{a}+\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{2 a}-\frac{\cos ^{-1}(a x)^4}{4 a^2}+\frac{3 \cos ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^4-\frac{3}{2} x^2 \cos ^{-1}(a x)^2+\frac{3 x^2}{4}","-\frac{x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{a}+\frac{3 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{2 a}-\frac{\cos ^{-1}(a x)^4}{4 a^2}+\frac{3 \cos ^{-1}(a x)^2}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^4-\frac{3}{2} x^2 \cos ^{-1}(a x)^2+\frac{3 x^2}{4}",1,"(3*x^2)/4 + (3*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(2*a) + (3*ArcCos[a*x]^2)/(4*a^2) - (3*x^2*ArcCos[a*x]^2)/2 - (x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/a - ArcCos[a*x]^4/(4*a^2) + (x^2*ArcCos[a*x]^4)/2","A",7,4,8,0.5000,1,"{4628, 4708, 4642, 30}"
37,1,69,0,0.1203689,"\int \cos ^{-1}(a x)^4 \, dx","Int[ArcCos[a*x]^4,x]","-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{a}+\frac{24 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+x \cos ^{-1}(a x)^4-12 x \cos ^{-1}(a x)^2+24 x","-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{a}+\frac{24 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+x \cos ^{-1}(a x)^4-12 x \cos ^{-1}(a x)^2+24 x",1,"24*x + (24*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/a - 12*x*ArcCos[a*x]^2 - (4*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/a + x*ArcCos[a*x]^4","A",5,3,6,0.5000,1,"{4620, 4678, 8}"
38,1,119,0,0.1254826,"\int \frac{\cos ^{-1}(a x)^4}{x} \, dx","Int[ArcCos[a*x]^4/x,x]","-2 i \cos ^{-1}(a x)^3 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+3 i \cos ^{-1}(a x) \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{5} i \cos ^{-1}(a x)^5+\cos ^{-1}(a x)^4 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)","-2 i \cos ^{-1}(a x)^3 \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+3 i \cos ^{-1}(a x) \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{3}{2} \text{PolyLog}\left(5,-e^{2 i \cos ^{-1}(a x)}\right)-\frac{1}{5} i \cos ^{-1}(a x)^5+\cos ^{-1}(a x)^4 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)",1,"(-I/5)*ArcCos[a*x]^5 + ArcCos[a*x]^4*Log[1 + E^((2*I)*ArcCos[a*x])] - (2*I)*ArcCos[a*x]^3*PolyLog[2, -E^((2*I)*ArcCos[a*x])] + 3*ArcCos[a*x]^2*PolyLog[3, -E^((2*I)*ArcCos[a*x])] + (3*I)*ArcCos[a*x]*PolyLog[4, -E^((2*I)*ArcCos[a*x])] - (3*PolyLog[5, -E^((2*I)*ArcCos[a*x])])/2","A",8,7,10,0.7000,1,"{4626, 3719, 2190, 2531, 6609, 2282, 6589}"
39,1,176,0,0.2040318,"\int \frac{\cos ^{-1}(a x)^4}{x^2} \, dx","Int[ArcCos[a*x]^4/x^2,x]","12 i a \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-12 i a \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-24 a \cos ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+24 a \cos ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-i e^{i \cos ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{x}-8 i a \cos ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)","12 i a \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-12 i a \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-24 a \cos ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+24 a \cos ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)-24 i a \text{PolyLog}\left(4,-i e^{i \cos ^{-1}(a x)}\right)+24 i a \text{PolyLog}\left(4,i e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{x}-8 i a \cos ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)",1,"-(ArcCos[a*x]^4/x) - (8*I)*a*ArcCos[a*x]^3*ArcTan[E^(I*ArcCos[a*x])] + (12*I)*a*ArcCos[a*x]^2*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - (12*I)*a*ArcCos[a*x]^2*PolyLog[2, I*E^(I*ArcCos[a*x])] - 24*a*ArcCos[a*x]*PolyLog[3, (-I)*E^(I*ArcCos[a*x])] + 24*a*ArcCos[a*x]*PolyLog[3, I*E^(I*ArcCos[a*x])] - (24*I)*a*PolyLog[4, (-I)*E^(I*ArcCos[a*x])] + (24*I)*a*PolyLog[4, I*E^(I*ArcCos[a*x])]","A",11,7,10,0.7000,1,"{4628, 4710, 4181, 2531, 6609, 2282, 6589}"
40,1,121,0,0.2133447,"\int \frac{\cos ^{-1}(a x)^4}{x^3} \, dx","Int[ArcCos[a*x]^4/x^3,x]","-6 i a^2 \cos ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{2 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{x}-2 i a^2 \cos ^{-1}(a x)^3+6 a^2 \cos ^{-1}(a x)^2 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{2 x^2}","-6 i a^2 \cos ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(a x)}\right)+\frac{2 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{x}-2 i a^2 \cos ^{-1}(a x)^3+6 a^2 \cos ^{-1}(a x)^2 \log \left(1+e^{2 i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{2 x^2}",1,"(-2*I)*a^2*ArcCos[a*x]^3 + (2*a*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/x - ArcCos[a*x]^4/(2*x^2) + 6*a^2*ArcCos[a*x]^2*Log[1 + E^((2*I)*ArcCos[a*x])] - (6*I)*a^2*ArcCos[a*x]*PolyLog[2, -E^((2*I)*ArcCos[a*x])] + 3*a^2*PolyLog[3, -E^((2*I)*ArcCos[a*x])]","A",8,8,10,0.8000,1,"{4628, 4682, 4626, 3719, 2190, 2531, 2282, 6589}"
41,1,304,0,0.4207705,"\int \frac{\cos ^{-1}(a x)^4}{x^4} \, dx","Int[ArcCos[a*x]^4/x^4,x]","2 i a^3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-2 i a^3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-4 a^3 \cos ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+4 a^3 \cos ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-i e^{i \cos ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,i e^{i \cos ^{-1}(a x)}\right)+\frac{2 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{3 x^2}-\frac{2 a^2 \cos ^{-1}(a x)^2}{x}-\frac{4}{3} i a^3 \cos ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-8 i a^3 \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{3 x^3}","2 i a^3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-2 i a^3 \cos ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-4 a^3 \cos ^{-1}(a x) \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(a x)}\right)+4 a^3 \cos ^{-1}(a x) \text{PolyLog}\left(3,i e^{i \cos ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)-4 i a^3 \text{PolyLog}\left(4,-i e^{i \cos ^{-1}(a x)}\right)+4 i a^3 \text{PolyLog}\left(4,i e^{i \cos ^{-1}(a x)}\right)+\frac{2 a \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^3}{3 x^2}-\frac{2 a^2 \cos ^{-1}(a x)^2}{x}-\frac{4}{3} i a^3 \cos ^{-1}(a x)^3 \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-8 i a^3 \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)-\frac{\cos ^{-1}(a x)^4}{3 x^3}",1,"(-2*a^2*ArcCos[a*x]^2)/x + (2*a*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^3)/(3*x^2) - ArcCos[a*x]^4/(3*x^3) - (8*I)*a^3*ArcCos[a*x]*ArcTan[E^(I*ArcCos[a*x])] - ((4*I)/3)*a^3*ArcCos[a*x]^3*ArcTan[E^(I*ArcCos[a*x])] + (4*I)*a^3*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] + (2*I)*a^3*ArcCos[a*x]^2*PolyLog[2, (-I)*E^(I*ArcCos[a*x])] - (4*I)*a^3*PolyLog[2, I*E^(I*ArcCos[a*x])] - (2*I)*a^3*ArcCos[a*x]^2*PolyLog[2, I*E^(I*ArcCos[a*x])] - 4*a^3*ArcCos[a*x]*PolyLog[3, (-I)*E^(I*ArcCos[a*x])] + 4*a^3*ArcCos[a*x]*PolyLog[3, I*E^(I*ArcCos[a*x])] - (4*I)*a^3*PolyLog[4, (-I)*E^(I*ArcCos[a*x])] + (4*I)*a^3*PolyLog[4, I*E^(I*ArcCos[a*x])]","A",19,10,10,1.000,1,"{4628, 4702, 4710, 4181, 2531, 6609, 2282, 6589, 2279, 2391}"
42,1,55,0,0.0907464,"\int \frac{x^6}{\cos ^{-1}(a x)} \, dx","Int[x^6/ArcCos[a*x],x]","-\frac{5 \text{Si}\left(\cos ^{-1}(a x)\right)}{64 a^7}-\frac{9 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{5 \text{Si}\left(5 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{\text{Si}\left(7 \cos ^{-1}(a x)\right)}{64 a^7}","-\frac{5 \text{Si}\left(\cos ^{-1}(a x)\right)}{64 a^7}-\frac{9 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{5 \text{Si}\left(5 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{\text{Si}\left(7 \cos ^{-1}(a x)\right)}{64 a^7}",1,"(-5*SinIntegral[ArcCos[a*x]])/(64*a^7) - (9*SinIntegral[3*ArcCos[a*x]])/(64*a^7) - (5*SinIntegral[5*ArcCos[a*x]])/(64*a^7) - SinIntegral[7*ArcCos[a*x]]/(64*a^7)","A",7,3,10,0.3000,1,"{4636, 4406, 3299}"
43,1,43,0,0.0788047,"\int \frac{x^5}{\cos ^{-1}(a x)} \, dx","Int[x^5/ArcCos[a*x],x]","-\frac{5 \text{Si}\left(2 \cos ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{8 a^6}-\frac{\text{Si}\left(6 \cos ^{-1}(a x)\right)}{32 a^6}","-\frac{5 \text{Si}\left(2 \cos ^{-1}(a x)\right)}{32 a^6}-\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{8 a^6}-\frac{\text{Si}\left(6 \cos ^{-1}(a x)\right)}{32 a^6}",1,"(-5*SinIntegral[2*ArcCos[a*x]])/(32*a^6) - SinIntegral[4*ArcCos[a*x]]/(8*a^6) - SinIntegral[6*ArcCos[a*x]]/(32*a^6)","A",6,3,10,0.3000,1,"{4636, 4406, 3299}"
44,1,41,0,0.0748271,"\int \frac{x^4}{\cos ^{-1}(a x)} \, dx","Int[x^4/ArcCos[a*x],x]","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{16 a^5}-\frac{\text{Si}\left(5 \cos ^{-1}(a x)\right)}{16 a^5}","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{8 a^5}-\frac{3 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{16 a^5}-\frac{\text{Si}\left(5 \cos ^{-1}(a x)\right)}{16 a^5}",1,"-SinIntegral[ArcCos[a*x]]/(8*a^5) - (3*SinIntegral[3*ArcCos[a*x]])/(16*a^5) - SinIntegral[5*ArcCos[a*x]]/(16*a^5)","A",6,3,10,0.3000,1,"{4636, 4406, 3299}"
45,1,29,0,0.06382,"\int \frac{x^3}{\cos ^{-1}(a x)} \, dx","Int[x^3/ArcCos[a*x],x]","-\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{4 a^4}-\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{8 a^4}","-\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{4 a^4}-\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{8 a^4}",1,"-SinIntegral[2*ArcCos[a*x]]/(4*a^4) - SinIntegral[4*ArcCos[a*x]]/(8*a^4)","A",5,3,10,0.3000,1,"{4636, 4406, 3299}"
46,1,27,0,0.0600118,"\int \frac{x^2}{\cos ^{-1}(a x)} \, dx","Int[x^2/ArcCos[a*x],x]","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{4 a^3}-\frac{\text{Si}\left(3 \cos ^{-1}(a x)\right)}{4 a^3}","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{4 a^3}-\frac{\text{Si}\left(3 \cos ^{-1}(a x)\right)}{4 a^3}",1,"-SinIntegral[ArcCos[a*x]]/(4*a^3) - SinIntegral[3*ArcCos[a*x]]/(4*a^3)","A",5,3,10,0.3000,1,"{4636, 4406, 3299}"
47,1,14,0,0.0348895,"\int \frac{x}{\cos ^{-1}(a x)} \, dx","Int[x/ArcCos[a*x],x]","-\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{2 a^2}","-\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{2 a^2}",1,"-SinIntegral[2*ArcCos[a*x]]/(2*a^2)","A",4,4,8,0.5000,1,"{4636, 4406, 12, 3299}"
48,1,10,0,0.0153486,"\int \frac{1}{\cos ^{-1}(a x)} \, dx","Int[ArcCos[a*x]^(-1),x]","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{a}","-\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{a}",1,"-(SinIntegral[ArcCos[a*x]]/a)","A",2,2,6,0.3333,1,"{4624, 3299}"
49,0,0,0,0.0134597,"\int \frac{1}{x \cos ^{-1}(a x)} \, dx","Int[1/(x*ArcCos[a*x]),x]","\int \frac{1}{x \cos ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0141143,"\int \frac{1}{x^2 \cos ^{-1}(a x)} \, dx","Int[1/(x^2*ArcCos[a*x]),x]","\int \frac{1}{x^2 \cos ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \cos ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*ArcCos[a*x]), x]","A",0,0,0,0,-1,"{}"
51,1,82,0,0.0789818,"\int \frac{x^6}{\cos ^{-1}(a x)^2} \, dx","Int[x^6/ArcCos[a*x]^2,x]","-\frac{5 \text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{64 a^7}-\frac{27 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{25 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{7 \text{CosIntegral}\left(7 \cos ^{-1}(a x)\right)}{64 a^7}+\frac{x^6 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}","-\frac{5 \text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{64 a^7}-\frac{27 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{25 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{64 a^7}-\frac{7 \text{CosIntegral}\left(7 \cos ^{-1}(a x)\right)}{64 a^7}+\frac{x^6 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}",1,"(x^6*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - (5*CosIntegral[ArcCos[a*x]])/(64*a^7) - (27*CosIntegral[3*ArcCos[a*x]])/(64*a^7) - (25*CosIntegral[5*ArcCos[a*x]])/(64*a^7) - (7*CosIntegral[7*ArcCos[a*x]])/(64*a^7)","A",6,2,10,0.2000,1,"{4632, 3302}"
52,1,70,0,0.0640758,"\int \frac{x^5}{\cos ^{-1}(a x)^2} \, dx","Int[x^5/ArcCos[a*x]^2,x]","-\frac{5 \text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{16 a^6}-\frac{\text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{2 a^6}-\frac{3 \text{CosIntegral}\left(6 \cos ^{-1}(a x)\right)}{16 a^6}+\frac{x^5 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}","-\frac{5 \text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{16 a^6}-\frac{\text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{2 a^6}-\frac{3 \text{CosIntegral}\left(6 \cos ^{-1}(a x)\right)}{16 a^6}+\frac{x^5 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}",1,"(x^5*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - (5*CosIntegral[2*ArcCos[a*x]])/(16*a^6) - CosIntegral[4*ArcCos[a*x]]/(2*a^6) - (3*CosIntegral[6*ArcCos[a*x]])/(16*a^6)","A",5,2,10,0.2000,1,"{4632, 3302}"
53,1,68,0,0.062514,"\int \frac{x^4}{\cos ^{-1}(a x)^2} \, dx","Int[x^4/ArcCos[a*x]^2,x]","-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{8 a^5}-\frac{9 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{16 a^5}-\frac{5 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{16 a^5}+\frac{x^4 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}","-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{8 a^5}-\frac{9 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{16 a^5}-\frac{5 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{16 a^5}+\frac{x^4 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}",1,"(x^4*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - CosIntegral[ArcCos[a*x]]/(8*a^5) - (9*CosIntegral[3*ArcCos[a*x]])/(16*a^5) - (5*CosIntegral[5*ArcCos[a*x]])/(16*a^5)","A",5,2,10,0.2000,1,"{4632, 3302}"
54,1,56,0,0.0502264,"\int \frac{x^3}{\cos ^{-1}(a x)^2} \, dx","Int[x^3/ArcCos[a*x]^2,x]","-\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{2 a^4}-\frac{\text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{2 a^4}+\frac{x^3 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}","-\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{2 a^4}-\frac{\text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{2 a^4}+\frac{x^3 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}",1,"(x^3*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - CosIntegral[2*ArcCos[a*x]]/(2*a^4) - CosIntegral[4*ArcCos[a*x]]/(2*a^4)","A",4,2,10,0.2000,1,"{4632, 3302}"
55,1,54,0,0.0461439,"\int \frac{x^2}{\cos ^{-1}(a x)^2} \, dx","Int[x^2/ArcCos[a*x]^2,x]","-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{4 a^3}-\frac{3 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{4 a^3}+\frac{x^2 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}","-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{4 a^3}-\frac{3 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{4 a^3}+\frac{x^2 \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}",1,"(x^2*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - CosIntegral[ArcCos[a*x]]/(4*a^3) - (3*CosIntegral[3*ArcCos[a*x]])/(4*a^3)","A",4,2,10,0.2000,1,"{4632, 3302}"
56,1,38,0,0.0244747,"\int \frac{x}{\cos ^{-1}(a x)^2} \, dx","Int[x/ArcCos[a*x]^2,x]","\frac{x \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}-\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{a^2}","\frac{x \sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}-\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{a^2}",1,"(x*Sqrt[1 - a^2*x^2])/(a*ArcCos[a*x]) - CosIntegral[2*ArcCos[a*x]]/a^2","A",2,2,8,0.2500,1,"{4632, 3302}"
57,1,35,0,0.0811583,"\int \frac{1}{\cos ^{-1}(a x)^2} \, dx","Int[ArcCos[a*x]^(-2),x]","\frac{\sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{a}","\frac{\sqrt{1-a^2 x^2}}{a \cos ^{-1}(a x)}-\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{a}",1,"Sqrt[1 - a^2*x^2]/(a*ArcCos[a*x]) - CosIntegral[ArcCos[a*x]]/a","A",3,3,6,0.5000,1,"{4622, 4724, 3302}"
58,0,0,0,0.0119504,"\int \frac{1}{x \cos ^{-1}(a x)^2} \, dx","Int[1/(x*ArcCos[a*x]^2),x]","\int \frac{1}{x \cos ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^2), x]","A",0,0,0,0,-1,"{}"
59,0,0,0,0.0134958,"\int \frac{1}{x^2 \cos ^{-1}(a x)^2} \, dx","Int[1/(x^2*ArcCos[a*x]^2),x]","\int \frac{1}{x^2 \cos ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \cos ^{-1}(a x)^2},x\right)",0,"Defer[Int][1/(x^2*ArcCos[a*x]^2), x]","A",0,0,0,0,-1,"{}"
60,1,98,0,0.3444571,"\int \frac{x^4}{\cos ^{-1}(a x)^3} \, dx","Int[x^4/ArcCos[a*x]^3,x]","\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Si}\left(5 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{x^4 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \cos ^{-1}(a x)}+\frac{5 x^5}{2 \cos ^{-1}(a x)}","\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{16 a^5}+\frac{27 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{25 \text{Si}\left(5 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{x^4 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{2 x^3}{a^2 \cos ^{-1}(a x)}+\frac{5 x^5}{2 \cos ^{-1}(a x)}",1,"(x^4*Sqrt[1 - a^2*x^2])/(2*a*ArcCos[a*x]^2) - (2*x^3)/(a^2*ArcCos[a*x]) + (5*x^5)/(2*ArcCos[a*x]) + SinIntegral[ArcCos[a*x]]/(16*a^5) + (27*SinIntegral[3*ArcCos[a*x]])/(32*a^5) + (25*SinIntegral[5*ArcCos[a*x]])/(32*a^5)","A",14,5,10,0.5000,1,"{4634, 4720, 4636, 4406, 3299}"
61,1,83,0,0.3048967,"\int \frac{x^3}{\cos ^{-1}(a x)^3} \, dx","Int[x^3/ArcCos[a*x]^3,x]","\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{a^4}+\frac{x^3 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \cos ^{-1}(a x)}+\frac{2 x^4}{\cos ^{-1}(a x)}","\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{2 a^4}+\frac{\text{Si}\left(4 \cos ^{-1}(a x)\right)}{a^4}+\frac{x^3 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{3 x^2}{2 a^2 \cos ^{-1}(a x)}+\frac{2 x^4}{\cos ^{-1}(a x)}",1,"(x^3*Sqrt[1 - a^2*x^2])/(2*a*ArcCos[a*x]^2) - (3*x^2)/(2*a^2*ArcCos[a*x]) + (2*x^4)/ArcCos[a*x] + SinIntegral[2*ArcCos[a*x]]/(2*a^4) + SinIntegral[4*ArcCos[a*x]]/a^4","A",12,6,10,0.6000,1,"{4634, 4720, 4636, 4406, 3299, 12}"
62,1,82,0,0.2430801,"\int \frac{x^2}{\cos ^{-1}(a x)^3} \, dx","Int[x^2/ArcCos[a*x]^3,x]","\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{8 a^3}+\frac{x^2 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{x}{a^2 \cos ^{-1}(a x)}+\frac{3 x^3}{2 \cos ^{-1}(a x)}","\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{8 a^3}+\frac{9 \text{Si}\left(3 \cos ^{-1}(a x)\right)}{8 a^3}+\frac{x^2 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{x}{a^2 \cos ^{-1}(a x)}+\frac{3 x^3}{2 \cos ^{-1}(a x)}",1,"(x^2*Sqrt[1 - a^2*x^2])/(2*a*ArcCos[a*x]^2) - x/(a^2*ArcCos[a*x]) + (3*x^3)/(2*ArcCos[a*x]) + SinIntegral[ArcCos[a*x]]/(8*a^3) + (9*SinIntegral[3*ArcCos[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{4634, 4720, 4636, 4406, 3299, 4624}"
63,1,63,0,0.1646394,"\int \frac{x}{\cos ^{-1}(a x)^3} \, dx","Int[x/ArcCos[a*x]^3,x]","\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{a^2}+\frac{x \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{1}{2 a^2 \cos ^{-1}(a x)}+\frac{x^2}{\cos ^{-1}(a x)}","\frac{\text{Si}\left(2 \cos ^{-1}(a x)\right)}{a^2}+\frac{x \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}-\frac{1}{2 a^2 \cos ^{-1}(a x)}+\frac{x^2}{\cos ^{-1}(a x)}",1,"(x*Sqrt[1 - a^2*x^2])/(2*a*ArcCos[a*x]^2) - 1/(2*a^2*ArcCos[a*x]) + x^2/ArcCos[a*x] + SinIntegral[2*ArcCos[a*x]]/a^2","A",7,7,8,0.8750,1,"{4634, 4720, 4636, 4406, 12, 3299, 4642}"
64,1,51,0,0.0828363,"\int \frac{1}{\cos ^{-1}(a x)^3} \, dx","Int[ArcCos[a*x]^(-3),x]","\frac{\sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}+\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{2 a}+\frac{x}{2 \cos ^{-1}(a x)}","\frac{\sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)^2}+\frac{\text{Si}\left(\cos ^{-1}(a x)\right)}{2 a}+\frac{x}{2 \cos ^{-1}(a x)}",1,"Sqrt[1 - a^2*x^2]/(2*a*ArcCos[a*x]^2) + x/(2*ArcCos[a*x]) + SinIntegral[ArcCos[a*x]]/(2*a)","A",4,4,6,0.6667,1,"{4622, 4720, 4624, 3299}"
65,0,0,0,0.0121795,"\int \frac{1}{x \cos ^{-1}(a x)^3} \, dx","Int[1/(x*ArcCos[a*x]^3),x]","\int \frac{1}{x \cos ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^3), x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0128526,"\int \frac{1}{x^2 \cos ^{-1}(a x)^3} \, dx","Int[1/(x^2*ArcCos[a*x]^3),x]","\int \frac{1}{x^2 \cos ^{-1}(a x)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \cos ^{-1}(a x)^3},x\right)",0,"Defer[Int][1/(x^2*ArcCos[a*x]^3), x]","A",0,0,0,0,-1,"{}"
67,1,158,0,0.3379033,"\int \frac{x^4}{\cos ^{-1}(a x)^4} \, dx","Int[x^4/ArcCos[a*x]^4,x]","\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{48 a^5}+\frac{27 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{96 a^5}-\frac{25 x^4 \sqrt{1-a^2 x^2}}{6 a \cos ^{-1}(a x)}+\frac{x^4 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{2 x^3}{3 a^2 \cos ^{-1}(a x)^2}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{a^3 \cos ^{-1}(a x)}+\frac{5 x^5}{6 \cos ^{-1}(a x)^2}","\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{48 a^5}+\frac{27 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{32 a^5}+\frac{125 \text{CosIntegral}\left(5 \cos ^{-1}(a x)\right)}{96 a^5}-\frac{25 x^4 \sqrt{1-a^2 x^2}}{6 a \cos ^{-1}(a x)}+\frac{x^4 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{2 x^3}{3 a^2 \cos ^{-1}(a x)^2}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{a^3 \cos ^{-1}(a x)}+\frac{5 x^5}{6 \cos ^{-1}(a x)^2}",1,"(x^4*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^3) - (2*x^3)/(3*a^2*ArcCos[a*x]^2) + (5*x^5)/(6*ArcCos[a*x]^2) + (2*x^2*Sqrt[1 - a^2*x^2])/(a^3*ArcCos[a*x]) - (25*x^4*Sqrt[1 - a^2*x^2])/(6*a*ArcCos[a*x]) + CosIntegral[ArcCos[a*x]]/(48*a^5) + (27*CosIntegral[3*ArcCos[a*x]])/(32*a^5) + (125*CosIntegral[5*ArcCos[a*x]])/(96*a^5)","A",12,4,10,0.4000,1,"{4634, 4720, 4632, 3302}"
68,1,143,0,0.290715,"\int \frac{x^3}{\cos ^{-1}(a x)^4} \, dx","Int[x^3/ArcCos[a*x]^4,x]","\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{3 a^4}-\frac{8 x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)}+\frac{x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{x^2}{2 a^2 \cos ^{-1}(a x)^2}+\frac{x \sqrt{1-a^2 x^2}}{a^3 \cos ^{-1}(a x)}+\frac{2 x^4}{3 \cos ^{-1}(a x)^2}","\frac{\text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{3 a^4}+\frac{4 \text{CosIntegral}\left(4 \cos ^{-1}(a x)\right)}{3 a^4}-\frac{8 x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)}+\frac{x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{x^2}{2 a^2 \cos ^{-1}(a x)^2}+\frac{x \sqrt{1-a^2 x^2}}{a^3 \cos ^{-1}(a x)}+\frac{2 x^4}{3 \cos ^{-1}(a x)^2}",1,"(x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^3) - x^2/(2*a^2*ArcCos[a*x]^2) + (2*x^4)/(3*ArcCos[a*x]^2) + (x*Sqrt[1 - a^2*x^2])/(a^3*ArcCos[a*x]) - (8*x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]) + CosIntegral[2*ArcCos[a*x]]/(3*a^4) + (4*CosIntegral[4*ArcCos[a*x]])/(3*a^4)","A",9,4,10,0.4000,1,"{4634, 4720, 4632, 3302}"
69,1,141,0,0.3120279,"\int \frac{x^2}{\cos ^{-1}(a x)^4} \, dx","Int[x^2/ArcCos[a*x]^4,x]","\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{8 a^3}-\frac{3 x^2 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)}+\frac{x^2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}+\frac{\sqrt{1-a^2 x^2}}{3 a^3 \cos ^{-1}(a x)}-\frac{x}{3 a^2 \cos ^{-1}(a x)^2}+\frac{x^3}{2 \cos ^{-1}(a x)^2}","\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{24 a^3}+\frac{9 \text{CosIntegral}\left(3 \cos ^{-1}(a x)\right)}{8 a^3}-\frac{3 x^2 \sqrt{1-a^2 x^2}}{2 a \cos ^{-1}(a x)}+\frac{x^2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}+\frac{\sqrt{1-a^2 x^2}}{3 a^3 \cos ^{-1}(a x)}-\frac{x}{3 a^2 \cos ^{-1}(a x)^2}+\frac{x^3}{2 \cos ^{-1}(a x)^2}",1,"(x^2*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^3) - x/(3*a^2*ArcCos[a*x]^2) + x^3/(2*ArcCos[a*x]^2) + Sqrt[1 - a^2*x^2]/(3*a^3*ArcCos[a*x]) - (3*x^2*Sqrt[1 - a^2*x^2])/(2*a*ArcCos[a*x]) + CosIntegral[ArcCos[a*x]]/(24*a^3) + (9*CosIntegral[3*ArcCos[a*x]])/(8*a^3)","A",10,6,10,0.6000,1,"{4634, 4720, 4632, 3302, 4622, 4724}"
70,1,97,0,0.1661155,"\int \frac{x}{\cos ^{-1}(a x)^4} \, dx","Int[x/ArcCos[a*x]^4,x]","\frac{2 \text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{3 a^2}-\frac{2 x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)}+\frac{x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{1}{6 a^2 \cos ^{-1}(a x)^2}+\frac{x^2}{3 \cos ^{-1}(a x)^2}","\frac{2 \text{CosIntegral}\left(2 \cos ^{-1}(a x)\right)}{3 a^2}-\frac{2 x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)}+\frac{x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}-\frac{1}{6 a^2 \cos ^{-1}(a x)^2}+\frac{x^2}{3 \cos ^{-1}(a x)^2}",1,"(x*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^3) - 1/(6*a^2*ArcCos[a*x]^2) + x^2/(3*ArcCos[a*x]^2) - (2*x*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]) + (2*CosIntegral[2*ArcCos[a*x]])/(3*a^2)","A",5,5,8,0.6250,1,"{4634, 4720, 4632, 3302, 4642}"
71,1,78,0,0.1564354,"\int \frac{1}{\cos ^{-1}(a x)^4} \, dx","Int[ArcCos[a*x]^(-4),x]","-\frac{\sqrt{1-a^2 x^2}}{6 a \cos ^{-1}(a x)}+\frac{\sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}+\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{6 a}+\frac{x}{6 \cos ^{-1}(a x)^2}","-\frac{\sqrt{1-a^2 x^2}}{6 a \cos ^{-1}(a x)}+\frac{\sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^3}+\frac{\text{CosIntegral}\left(\cos ^{-1}(a x)\right)}{6 a}+\frac{x}{6 \cos ^{-1}(a x)^2}",1,"Sqrt[1 - a^2*x^2]/(3*a*ArcCos[a*x]^3) + x/(6*ArcCos[a*x]^2) - Sqrt[1 - a^2*x^2]/(6*a*ArcCos[a*x]) + CosIntegral[ArcCos[a*x]]/(6*a)","A",5,4,6,0.6667,1,"{4622, 4720, 4724, 3302}"
72,0,0,0,0.0255599,"\int \frac{1}{x \cos ^{-1}(a x)^4} \, dx","Int[1/(x*ArcCos[a*x]^4),x]","\int \frac{1}{x \cos ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^4), x]","A",0,0,0,0,-1,"{}"
73,0,0,0,0.0155747,"\int \frac{1}{x^2 \cos ^{-1}(a x)^4} \, dx","Int[1/(x^2*ArcCos[a*x]^4),x]","\int \frac{1}{x^2 \cos ^{-1}(a x)^4} \, dx","\text{Int}\left(\frac{1}{x^2 \cos ^{-1}(a x)^4},x\right)",0,"Defer[Int][1/(x^2*ArcCos[a*x]^4), x]","A",0,0,0,0,-1,"{}"
74,1,121,0,0.2812323,"\int x^4 \sqrt{\cos ^{-1}(a x)} \, dx","Int[x^4*Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{80 a^5}+\frac{1}{5} x^5 \sqrt{\cos ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^5}-\frac{\sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{80 a^5}+\frac{1}{5} x^5 \sqrt{\cos ^{-1}(a x)}",1,"(x^5*Sqrt[ArcCos[a*x]])/5 - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^5) - (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^5) - (Sqrt[Pi/10]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(80*a^5)","A",10,5,12,0.4167,1,"{4630, 4724, 3312, 3304, 3352}"
75,1,95,0,0.1946883,"\int x^3 \sqrt{\cos ^{-1}(a x)} \, dx","Int[x^3*Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{64 a^4}-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{16 a^4}-\frac{3 \sqrt{\cos ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\cos ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{64 a^4}-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{16 a^4}-\frac{3 \sqrt{\cos ^{-1}(a x)}}{32 a^4}+\frac{1}{4} x^4 \sqrt{\cos ^{-1}(a x)}",1,"(-3*Sqrt[ArcCos[a*x]])/(32*a^4) + (x^4*Sqrt[ArcCos[a*x]])/4 - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(64*a^4) - (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(16*a^4)","A",8,5,12,0.4167,1,"{4630, 4724, 3312, 3304, 3352}"
76,1,86,0,0.1839382,"\int x^2 \sqrt{\cos ^{-1}(a x)} \, dx","Int[x^2*Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{12 a^3}+\frac{1}{3} x^3 \sqrt{\cos ^{-1}(a x)}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^3}-\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{12 a^3}+\frac{1}{3} x^3 \sqrt{\cos ^{-1}(a x)}",1,"(x^3*Sqrt[ArcCos[a*x]])/3 - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(4*a^3) - (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(12*a^3)","A",8,5,12,0.4167,1,"{4630, 4724, 3312, 3304, 3352}"
77,1,59,0,0.1508721,"\int x \sqrt{\cos ^{-1}(a x)} \, dx","Int[x*Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^2}-\frac{\sqrt{\cos ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\cos ^{-1}(a x)}","-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^2}-\frac{\sqrt{\cos ^{-1}(a x)}}{4 a^2}+\frac{1}{2} x^2 \sqrt{\cos ^{-1}(a x)}",1,"-Sqrt[ArcCos[a*x]]/(4*a^2) + (x^2*Sqrt[ArcCos[a*x]])/2 - (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(8*a^2)","A",6,5,10,0.5000,1,"{4630, 4724, 3312, 3304, 3352}"
78,1,44,0,0.0900672,"\int \sqrt{\cos ^{-1}(a x)} \, dx","Int[Sqrt[ArcCos[a*x]],x]","x \sqrt{\cos ^{-1}(a x)}-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}","x \sqrt{\cos ^{-1}(a x)}-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}",1,"x*Sqrt[ArcCos[a*x]] - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a","A",4,4,8,0.5000,1,"{4620, 4724, 3304, 3352}"
79,0,0,0,0.0123162,"\int \frac{\sqrt{\cos ^{-1}(a x)}}{x} \, dx","Int[Sqrt[ArcCos[a*x]]/x,x]","\int \frac{\sqrt{\cos ^{-1}(a x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\cos ^{-1}(a x)}}{x},x\right)",0,"Defer[Int][Sqrt[ArcCos[a*x]]/x, x]","A",0,0,0,0,-1,"{}"
80,1,282,0,0.5145345,"\int x^4 \cos ^{-1}(a x)^{3/2} \, dx","Int[x^4*ArcCos[a*x]^(3/2),x]","\frac{2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{25 a^5}+\frac{11 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{400 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{800 a^5}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{50 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{800 a^5}-\frac{3 x^4 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{50 a}-\frac{2 x^2 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \cos ^{-1}(a x)^{3/2}","\frac{2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{25 a^5}+\frac{11 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{400 a^5}+\frac{3 \sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{800 a^5}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{50 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{800 a^5}-\frac{3 x^4 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{50 a}-\frac{2 x^2 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{25 a^3}-\frac{4 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{25 a^5}+\frac{1}{5} x^5 \cos ^{-1}(a x)^{3/2}",1,"(-4*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(25*a^5) - (2*x^2*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(25*a^3) - (3*x^4*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(50*a) + (x^5*ArcCos[a*x]^(3/2))/5 + (11*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(400*a^5) + (2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(25*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(50*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(800*a^5) + (3*Sqrt[Pi/10]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(800*a^5)","A",23,8,12,0.6667,1,"{4630, 4708, 4678, 4624, 3305, 3351, 4636, 4406}"
81,1,157,0,0.3677864,"\int x^3 \cos ^{-1}(a x)^{3/2} \, dx","Int[x^3*ArcCos[a*x]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{512 a^4}+\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{64 a^4}-\frac{3 x^3 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{32 a}-\frac{9 x \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{64 a^3}-\frac{3 \cos ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^{3/2}","\frac{3 \sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{512 a^4}+\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{64 a^4}-\frac{3 x^3 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{32 a}-\frac{9 x \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{64 a^3}-\frac{3 \cos ^{-1}(a x)^{3/2}}{32 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^{3/2}",1,"(-9*x*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(64*a^3) - (3*x^3*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(32*a) - (3*ArcCos[a*x]^(3/2))/(32*a^4) + (x^4*ArcCos[a*x]^(3/2))/4 + (3*Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(512*a^4) + (3*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(64*a^4)","A",16,8,12,0.6667,1,"{4630, 4708, 4642, 4636, 4406, 12, 3305, 3351}"
82,1,147,0,0.3024805,"\int x^2 \cos ^{-1}(a x)^{3/2} \, dx","Int[x^2*ArcCos[a*x]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{24 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{6 a}-\frac{\sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \cos ^{-1}(a x)^{3/2}","\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^3}+\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{24 a^3}-\frac{x^2 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{6 a}-\frac{\sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{3 a^3}+\frac{1}{3} x^3 \cos ^{-1}(a x)^{3/2}",1,"-(Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(3*a^3) - (x^2*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(6*a) + (x^3*ArcCos[a*x]^(3/2))/3 + (3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^3) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(24*a^3)","A",13,8,12,0.6667,1,"{4630, 4708, 4678, 4624, 3305, 3351, 4636, 4406}"
83,1,89,0,0.1786101,"\int x \cos ^{-1}(a x)^{3/2} \, dx","Int[x*ArcCos[a*x]^(3/2),x]","\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{8 a}-\frac{\cos ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^{3/2}","\frac{3 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{32 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{8 a}-\frac{\cos ^{-1}(a x)^{3/2}}{4 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^{3/2}",1,"(-3*x*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(8*a) - ArcCos[a*x]^(3/2)/(4*a^2) + (x^2*ArcCos[a*x]^(3/2))/2 + (3*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(32*a^2)","A",8,8,10,0.8000,1,"{4630, 4708, 4642, 4636, 4406, 12, 3305, 3351}"
84,1,75,0,0.1008885,"\int \cos ^{-1}(a x)^{3/2} \, dx","Int[ArcCos[a*x]^(3/2),x]","-\frac{3 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{2 a}+\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a}+x \cos ^{-1}(a x)^{3/2}","-\frac{3 \sqrt{1-a^2 x^2} \sqrt{\cos ^{-1}(a x)}}{2 a}+\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a}+x \cos ^{-1}(a x)^{3/2}",1,"(-3*Sqrt[1 - a^2*x^2]*Sqrt[ArcCos[a*x]])/(2*a) + x*ArcCos[a*x]^(3/2) + (3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(2*a)","A",5,5,8,0.6250,1,"{4620, 4678, 4624, 3305, 3351}"
85,0,0,0,0.0134277,"\int \frac{\cos ^{-1}(a x)^{3/2}}{x} \, dx","Int[ArcCos[a*x]^(3/2)/x,x]","\int \frac{\cos ^{-1}(a x)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^{3/2}}{x},x\right)",0,"Defer[Int][ArcCos[a*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
86,1,298,0,0.7897014,"\int x^4 \cos ^{-1}(a x)^{5/2} \, dx","Int[x^4*ArcCos[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{320 a^5}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{60 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{1600 a^5}-\frac{x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\cos ^{-1}(a x)}}{15 a^2}-\frac{2 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{15 a^3}-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{15 a^5}-\frac{2 x \sqrt{\cos ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^{5/2}-\frac{3}{100} x^5 \sqrt{\cos ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{32 a^5}+\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{320 a^5}+\frac{\sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{60 a^5}+\frac{3 \sqrt{\frac{\pi }{10}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{1600 a^5}-\frac{x^4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{10 a}-\frac{x^3 \sqrt{\cos ^{-1}(a x)}}{15 a^2}-\frac{2 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{15 a^3}-\frac{4 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{15 a^5}-\frac{2 x \sqrt{\cos ^{-1}(a x)}}{5 a^4}+\frac{1}{5} x^5 \cos ^{-1}(a x)^{5/2}-\frac{3}{100} x^5 \sqrt{\cos ^{-1}(a x)}",1,"(-2*x*Sqrt[ArcCos[a*x]])/(5*a^4) - (x^3*Sqrt[ArcCos[a*x]])/(15*a^2) - (3*x^5*Sqrt[ArcCos[a*x]])/100 - (4*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(15*a^5) - (2*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(15*a^3) - (x^4*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(10*a) + (x^5*ArcCos[a*x]^(5/2))/5 + (15*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(32*a^5) + (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(60*a^5) + (Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(320*a^5) + (3*Sqrt[Pi/10]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(1600*a^5)","A",26,8,12,0.6667,1,"{4630, 4708, 4678, 4620, 4724, 3304, 3352, 3312}"
87,1,205,0,0.5893103,"\int x^3 \cos ^{-1}(a x)^{5/2} \, dx","Int[x^3*ArcCos[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4096 a^4}+\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{256 a^4}-\frac{5 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\cos ^{-1}(a x)}}{256 a^2}-\frac{15 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \cos ^{-1}(a x)^{5/2}}{32 a^4}+\frac{225 \sqrt{\cos ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^{5/2}-\frac{15}{256} x^4 \sqrt{\cos ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4096 a^4}+\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{256 a^4}-\frac{5 x^3 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{32 a}-\frac{45 x^2 \sqrt{\cos ^{-1}(a x)}}{256 a^2}-\frac{15 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{64 a^3}-\frac{3 \cos ^{-1}(a x)^{5/2}}{32 a^4}+\frac{225 \sqrt{\cos ^{-1}(a x)}}{2048 a^4}+\frac{1}{4} x^4 \cos ^{-1}(a x)^{5/2}-\frac{15}{256} x^4 \sqrt{\cos ^{-1}(a x)}",1,"(225*Sqrt[ArcCos[a*x]])/(2048*a^4) - (45*x^2*Sqrt[ArcCos[a*x]])/(256*a^2) - (15*x^4*Sqrt[ArcCos[a*x]])/256 - (15*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(64*a^3) - (5*x^3*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(32*a) - (3*ArcCos[a*x]^(5/2))/(32*a^4) + (x^4*ArcCos[a*x]^(5/2))/4 + (15*Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(4096*a^4) + (15*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(256*a^4)","A",18,7,12,0.5833,1,"{4630, 4708, 4642, 4724, 3312, 3304, 3352}"
88,1,178,0,0.4566781,"\int x^2 \cos ^{-1}(a x)^{5/2} \, dx","Int[x^2*ArcCos[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^3}+\frac{5 \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{144 a^3}-\frac{5 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{18 a}-\frac{5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\cos ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^{5/2}-\frac{5}{36} x^3 \sqrt{\cos ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^3}+\frac{5 \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{144 a^3}-\frac{5 x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{18 a}-\frac{5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{9 a^3}-\frac{5 x \sqrt{\cos ^{-1}(a x)}}{6 a^2}+\frac{1}{3} x^3 \cos ^{-1}(a x)^{5/2}-\frac{5}{36} x^3 \sqrt{\cos ^{-1}(a x)}",1,"(-5*x*Sqrt[ArcCos[a*x]])/(6*a^2) - (5*x^3*Sqrt[ArcCos[a*x]])/36 - (5*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(9*a^3) - (5*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(18*a) + (x^3*ArcCos[a*x]^(5/2))/3 + (15*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^3) + (5*Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(144*a^3)","A",15,8,12,0.6667,1,"{4630, 4708, 4678, 4620, 4724, 3304, 3352, 3312}"
89,1,119,0,0.2873168,"\int x \cos ^{-1}(a x)^{5/2} \, dx","Int[x*ArcCos[a*x]^(5/2),x]","\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a^2}-\frac{5 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{8 a}-\frac{\cos ^{-1}(a x)^{5/2}}{4 a^2}+\frac{15 \sqrt{\cos ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^{5/2}-\frac{15}{32} x^2 \sqrt{\cos ^{-1}(a x)}","\frac{15 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{128 a^2}-\frac{5 x \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{8 a}-\frac{\cos ^{-1}(a x)^{5/2}}{4 a^2}+\frac{15 \sqrt{\cos ^{-1}(a x)}}{64 a^2}+\frac{1}{2} x^2 \cos ^{-1}(a x)^{5/2}-\frac{15}{32} x^2 \sqrt{\cos ^{-1}(a x)}",1,"(15*Sqrt[ArcCos[a*x]])/(64*a^2) - (15*x^2*Sqrt[ArcCos[a*x]])/32 - (5*x*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(8*a) - ArcCos[a*x]^(5/2)/(4*a^2) + (x^2*ArcCos[a*x]^(5/2))/2 + (15*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(128*a^2)","A",9,7,10,0.7000,1,"{4630, 4708, 4642, 4724, 3312, 3304, 3352}"
90,1,88,0,0.1601964,"\int \cos ^{-1}(a x)^{5/2} \, dx","Int[ArcCos[a*x]^(5/2),x]","-\frac{5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{2 a}+\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a}+x \cos ^{-1}(a x)^{5/2}-\frac{15}{4} x \sqrt{\cos ^{-1}(a x)}","-\frac{5 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)^{3/2}}{2 a}+\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a}+x \cos ^{-1}(a x)^{5/2}-\frac{15}{4} x \sqrt{\cos ^{-1}(a x)}",1,"(-15*x*Sqrt[ArcCos[a*x]])/4 - (5*Sqrt[1 - a^2*x^2]*ArcCos[a*x]^(3/2))/(2*a) + x*ArcCos[a*x]^(5/2) + (15*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(4*a)","A",6,5,8,0.6250,1,"{4620, 4678, 4724, 3304, 3352}"
91,0,0,0,0.0123123,"\int \frac{\cos ^{-1}(a x)^{5/2}}{x} \, dx","Int[ArcCos[a*x]^(5/2)/x,x]","\int \frac{\cos ^{-1}(a x)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^{5/2}}{x},x\right)",0,"Defer[Int][ArcCos[a*x]^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
92,1,106,0,0.1048412,"\int \frac{x^4}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[x^4/Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}-\frac{\sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{3 \pi }{2}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}-\frac{\sqrt{\frac{\pi }{10}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^5}",1,"-(Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(4*a^5) - (Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^5) - (Sqrt[Pi/10]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^5)","A",9,4,12,0.3333,1,"{4636, 4406, 3305, 3351}"
93,1,65,0,0.0777967,"\int \frac{x^3}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[x^3/Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^4}-\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{4 a^4}","-\frac{\sqrt{\frac{\pi }{2}} S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^4}-\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{4 a^4}",1,"-(Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^4) - (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(4*a^4)","A",7,4,12,0.3333,1,"{4636, 4406, 3305, 3351}"
94,1,71,0,0.079498,"\int \frac{x^2}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[x^2/Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^3}","-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^3}-\frac{\sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^3}",1,"-(Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(2*a^3) - (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(2*a^3)","A",7,4,12,0.3333,1,"{4636, 4406, 3305, 3351}"
95,1,28,0,0.0402895,"\int \frac{x}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[x/Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a^2}","-\frac{\sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{2 a^2}",1,"-(Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(2*a^2)","A",5,5,10,0.5000,1,"{4636, 4406, 12, 3305, 3351}"
96,1,31,0,0.022666,"\int \frac{1}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[1/Sqrt[ArcCos[a*x]],x]","-\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}","-\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}",1,"-((Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a)","A",3,3,8,0.3750,1,"{4624, 3305, 3351}"
97,0,0,0,0.0126049,"\int \frac{1}{x \sqrt{\cos ^{-1}(a x)}} \, dx","Int[1/(x*Sqrt[ArcCos[a*x]]),x]","\int \frac{1}{x \sqrt{\cos ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\cos ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[ArcCos[a*x]]), x]","A",0,0,0,0,-1,"{}"
98,0,0,0,0.0130397,"\int \frac{1}{x^2 \sqrt{\cos ^{-1}(a x)}} \, dx","Int[1/(x^2*Sqrt[ArcCos[a*x]]),x]","\int \frac{1}{x^2 \sqrt{\cos ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{\cos ^{-1}(a x)}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[ArcCos[a*x]]), x]","A",0,0,0,0,-1,"{}"
99,1,171,0,0.1459148,"\int \frac{x^6}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x^6/ArcCos[a*x]^(3/2),x]","-\frac{5 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{9 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{\sqrt{\frac{7 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{14}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}+\frac{2 x^6 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}","-\frac{5 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{9 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}-\frac{\sqrt{\frac{7 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{14}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{16 a^7}+\frac{2 x^6 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^6*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (5*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^7) - (9*Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^7) - (5*Sqrt[(5*Pi)/2]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^7) - (Sqrt[(7*Pi)/2]*FresnelC[Sqrt[14/Pi]*Sqrt[ArcCos[a*x]]])/(16*a^7)","A",10,3,12,0.2500,1,"{4632, 3304, 3352}"
100,1,127,0,0.103803,"\int \frac{x^5}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x^5/ArcCos[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^6}-\frac{\sqrt{3 \pi } \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^6}-\frac{5 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^6}+\frac{2 x^5 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^6}-\frac{\sqrt{3 \pi } \text{FresnelC}\left(2 \sqrt{\frac{3}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{8 a^6}-\frac{5 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{8 a^6}+\frac{2 x^5 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^5*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a^6 - (Sqrt[3*Pi]*FresnelC[2*Sqrt[3/Pi]*Sqrt[ArcCos[a*x]]])/(8*a^6) - (5*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(8*a^6)","A",8,3,12,0.2500,1,"{4632, 3304, 3352}"
101,1,136,0,0.0946939,"\int \frac{x^4}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x^4/ArcCos[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^5}-\frac{3 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^5}-\frac{3 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}-\frac{\sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{4 a^5}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^4*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(2*a^5) - (3*Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(4*a^5) - (Sqrt[(5*Pi)/2]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(4*a^5)","A",8,3,12,0.2500,1,"{4632, 3304, 3352}"
102,1,91,0,0.0651208,"\int \frac{x^3}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x^3/ArcCos[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^4}-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^4}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^4}-\frac{\sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^4}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^3*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (Sqrt[Pi/2]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a^4 - (Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/a^4","A",6,3,12,0.2500,1,"{4632, 3304, 3352}"
103,1,97,0,0.0687269,"\int \frac{x^2}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x^2/ArcCos[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}-\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}-\frac{\sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a^3 - (Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/a^3","A",6,3,12,0.2500,1,"{4632, 3304, 3352}"
104,1,55,0,0.0310101,"\int \frac{x}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[x/ArcCos[a*x]^(3/2),x]","\frac{2 x \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}-\frac{2 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^2}","\frac{2 x \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}-\frac{2 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{a^2}",1,"(2*x*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (2*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/a^2","A",3,3,10,0.3000,1,"{4632, 3304, 3352}"
105,1,59,0,0.0867448,"\int \frac{1}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[ArcCos[a*x]^(-3/2),x]","\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}-\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}","\frac{2 \sqrt{1-a^2 x^2}}{a \sqrt{\cos ^{-1}(a x)}}-\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a}",1,"(2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcCos[a*x]]) - (2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a","A",4,4,8,0.5000,1,"{4622, 4724, 3304, 3352}"
106,0,0,0,0.0123989,"\int \frac{1}{x \cos ^{-1}(a x)^{3/2}} \, dx","Int[1/(x*ArcCos[a*x]^(3/2)),x]","\int \frac{1}{x \cos ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
107,1,235,0,0.4095997,"\int \frac{x^4}{\cos ^{-1}(a x)^{5/2}} \, dx","Int[x^4/ArcCos[a*x]^(5/2),x]","-\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{25 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^5}-\frac{4 \sqrt{\frac{2 \pi }{3}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{25 \sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^5}+\frac{5 \sqrt{\frac{5 \pi }{2}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{6 a^5}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{20 x^5}{3 \sqrt{\cos ^{-1}(a x)}}","-\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{25 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^5}-\frac{4 \sqrt{\frac{2 \pi }{3}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{25 \sqrt{\frac{\pi }{6}} S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{2 a^5}+\frac{5 \sqrt{\frac{5 \pi }{2}} S\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{6 a^5}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{16 x^3}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{20 x^5}{3 \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^4*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^(3/2)) - (16*x^3)/(3*a^2*Sqrt[ArcCos[a*x]]) + (20*x^5)/(3*Sqrt[ArcCos[a*x]]) + (25*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(3*a^5) - (4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/a^5 + (25*Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(2*a^5) - (4*Sqrt[(2*Pi)/3]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/a^5 + (5*Sqrt[(5*Pi)/2]*FresnelS[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(6*a^5)","A",19,6,12,0.5000,1,"{4634, 4720, 4636, 4406, 3305, 3351}"
108,1,126,0,0.3250115,"\int \frac{x^3}{\cos ^{-1}(a x)^{5/2}} \, dx","Int[x^3/ArcCos[a*x]^(5/2),x]","\frac{4 \sqrt{2 \pi } S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^4}+\frac{4 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^4}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{16 x^4}{3 \sqrt{\cos ^{-1}(a x)}}","\frac{4 \sqrt{2 \pi } S\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^4}+\frac{4 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^4}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{4 x^2}{a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{16 x^4}{3 \sqrt{\cos ^{-1}(a x)}}",1,"(2*x^3*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^(3/2)) - (4*x^2)/(a^2*Sqrt[ArcCos[a*x]]) + (16*x^4)/(3*Sqrt[ArcCos[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(3*a^4) + (4*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(3*a^4)","A",15,7,12,0.5833,1,"{4634, 4720, 4636, 4406, 3305, 3351, 12}"
109,1,125,0,0.2864321,"\int \frac{x^2}{\cos ^{-1}(a x)^{5/2}} \, dx","Int[x^2/ArcCos[a*x]^(5/2),x]","\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^3}+\frac{\sqrt{6 \pi } S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{8 x}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{4 x^3}{\sqrt{\cos ^{-1}(a x)}}","\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^3}+\frac{\sqrt{6 \pi } S\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^3}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{8 x}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{4 x^3}{\sqrt{\cos ^{-1}(a x)}}",1,"(2*x^2*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^(3/2)) - (8*x)/(3*a^2*Sqrt[ArcCos[a*x]]) + (4*x^3)/Sqrt[ArcCos[a*x]] + (Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(3*a^3) + (Sqrt[6*Pi]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/a^3","A",13,7,12,0.5833,1,"{4634, 4720, 4636, 4406, 3305, 3351, 4624}"
110,1,89,0,0.1727518,"\int \frac{x}{\cos ^{-1}(a x)^{5/2}} \, dx","Int[x/ArcCos[a*x]^(5/2),x]","\frac{8 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^2}+\frac{2 x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{4}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{8 x^2}{3 \sqrt{\cos ^{-1}(a x)}}","\frac{8 \sqrt{\pi } S\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{3 a^2}+\frac{2 x \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}-\frac{4}{3 a^2 \sqrt{\cos ^{-1}(a x)}}+\frac{8 x^2}{3 \sqrt{\cos ^{-1}(a x)}}",1,"(2*x*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^(3/2)) - 4/(3*a^2*Sqrt[ArcCos[a*x]]) + (8*x^2)/(3*Sqrt[ArcCos[a*x]]) + (8*Sqrt[Pi]*FresnelS[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(3*a^2)","A",8,8,10,0.8000,1,"{4634, 4720, 4636, 4406, 12, 3305, 3351, 4642}"
111,1,76,0,0.0929396,"\int \frac{1}{\cos ^{-1}(a x)^{5/2}} \, dx","Int[ArcCos[a*x]^(-5/2),x]","\frac{2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}+\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a}+\frac{4 x}{3 \sqrt{\cos ^{-1}(a x)}}","\frac{2 \sqrt{1-a^2 x^2}}{3 a \cos ^{-1}(a x)^{3/2}}+\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a}+\frac{4 x}{3 \sqrt{\cos ^{-1}(a x)}}",1,"(2*Sqrt[1 - a^2*x^2])/(3*a*ArcCos[a*x]^(3/2)) + (4*x)/(3*Sqrt[ArcCos[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(3*a)","A",5,5,8,0.6250,1,"{4622, 4720, 4624, 3305, 3351}"
112,0,0,0,0.0125784,"\int \frac{1}{x \cos ^{-1}(a x)^{5/2}} \, dx","Int[1/(x*ArcCos[a*x]^(5/2)),x]","\int \frac{1}{x \cos ^{-1}(a x)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^{5/2}},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^(5/2)), x]","A",0,0,0,0,-1,"{}"
113,1,264,0,0.3829396,"\int \frac{x^4}{\cos ^{-1}(a x)^{7/2}} \, dx","Int[x^4/ArcCos[a*x]^(7/2),x]","\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^5}-\frac{8 \sqrt{6 \pi } \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{5 a^5}+\frac{5 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^5}-\frac{40 x^4 \sqrt{1-a^2 x^2}}{3 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{16 x^3}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{32 x^2 \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\cos ^{-1}(a x)}}+\frac{4 x^5}{3 \cos ^{-1}(a x)^{3/2}}","\frac{\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^5}-\frac{8 \sqrt{6 \pi } \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{5 a^5}+\frac{5 \sqrt{\frac{3 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{a^5}+\frac{5 \sqrt{\frac{5 \pi }{2}} \text{FresnelC}\left(\sqrt{\frac{10}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{3 a^5}-\frac{40 x^4 \sqrt{1-a^2 x^2}}{3 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^4 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{16 x^3}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{32 x^2 \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\cos ^{-1}(a x)}}+\frac{4 x^5}{3 \cos ^{-1}(a x)^{3/2}}",1,"(2*x^4*Sqrt[1 - a^2*x^2])/(5*a*ArcCos[a*x]^(5/2)) - (16*x^3)/(15*a^2*ArcCos[a*x]^(3/2)) + (4*x^5)/(3*ArcCos[a*x]^(3/2)) + (32*x^2*Sqrt[1 - a^2*x^2])/(5*a^3*Sqrt[ArcCos[a*x]]) - (40*x^4*Sqrt[1 - a^2*x^2])/(3*a*Sqrt[ArcCos[a*x]]) + (Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(15*a^5) + (5*Sqrt[(3*Pi)/2]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/a^5 - (8*Sqrt[6*Pi]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(5*a^5) + (5*Sqrt[(5*Pi)/2]*FresnelC[Sqrt[10/Pi]*Sqrt[ArcCos[a*x]]])/(3*a^5)","A",17,5,12,0.4167,1,"{4634, 4720, 4632, 3304, 3352}"
114,1,190,0,0.3230889,"\int \frac{x^3}{\cos ^{-1}(a x)^{7/2}} \, dx","Int[x^3/ArcCos[a*x]^(7/2),x]","\frac{32 \sqrt{2 \pi } \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^4}-\frac{128 x^3 \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{4 x^2}{5 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{16 x \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\cos ^{-1}(a x)}}+\frac{16 x^4}{15 \cos ^{-1}(a x)^{3/2}}","\frac{32 \sqrt{2 \pi } \text{FresnelC}\left(2 \sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^4}+\frac{16 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^4}-\frac{128 x^3 \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^3 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{4 x^2}{5 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{16 x \sqrt{1-a^2 x^2}}{5 a^3 \sqrt{\cos ^{-1}(a x)}}+\frac{16 x^4}{15 \cos ^{-1}(a x)^{3/2}}",1,"(2*x^3*Sqrt[1 - a^2*x^2])/(5*a*ArcCos[a*x]^(5/2)) - (4*x^2)/(5*a^2*ArcCos[a*x]^(3/2)) + (16*x^4)/(15*ArcCos[a*x]^(3/2)) + (16*x*Sqrt[1 - a^2*x^2])/(5*a^3*Sqrt[ArcCos[a*x]]) - (128*x^3*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcCos[a*x]]) + (32*Sqrt[2*Pi]*FresnelC[2*Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(15*a^4) + (16*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(15*a^4)","A",12,5,12,0.4167,1,"{4634, 4720, 4632, 3304, 3352}"
115,1,191,0,0.3407628,"\int \frac{x^2}{\cos ^{-1}(a x)^{7/2}} \, dx","Int[x^2/ArcCos[a*x]^(7/2),x]","\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^3}+\frac{6 \sqrt{6 \pi } \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{5 a^3}-\frac{24 x^2 \sqrt{1-a^2 x^2}}{5 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}+\frac{16 \sqrt{1-a^2 x^2}}{15 a^3 \sqrt{\cos ^{-1}(a x)}}-\frac{8 x}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{4 x^3}{5 \cos ^{-1}(a x)^{3/2}}","\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a^3}+\frac{6 \sqrt{6 \pi } \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{5 a^3}-\frac{24 x^2 \sqrt{1-a^2 x^2}}{5 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x^2 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}+\frac{16 \sqrt{1-a^2 x^2}}{15 a^3 \sqrt{\cos ^{-1}(a x)}}-\frac{8 x}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{4 x^3}{5 \cos ^{-1}(a x)^{3/2}}",1,"(2*x^2*Sqrt[1 - a^2*x^2])/(5*a*ArcCos[a*x]^(5/2)) - (8*x)/(15*a^2*ArcCos[a*x]^(3/2)) + (4*x^3)/(5*ArcCos[a*x]^(3/2)) + (16*Sqrt[1 - a^2*x^2])/(15*a^3*Sqrt[ArcCos[a*x]]) - (24*x^2*Sqrt[1 - a^2*x^2])/(5*a*Sqrt[ArcCos[a*x]]) + (2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(15*a^3) + (6*Sqrt[6*Pi]*FresnelC[Sqrt[6/Pi]*Sqrt[ArcCos[a*x]]])/(5*a^3)","A",13,7,12,0.5833,1,"{4634, 4720, 4632, 3304, 3352, 4622, 4724}"
116,1,119,0,0.1724765,"\int \frac{x}{\cos ^{-1}(a x)^{7/2}} \, dx","Int[x/ArcCos[a*x]^(7/2),x]","\frac{32 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^2}-\frac{32 x \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{4}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{8 x^2}{15 \cos ^{-1}(a x)^{3/2}}","\frac{32 \sqrt{\pi } \text{FresnelC}\left(\frac{2 \sqrt{\cos ^{-1}(a x)}}{\sqrt{\pi }}\right)}{15 a^2}-\frac{32 x \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 x \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}-\frac{4}{15 a^2 \cos ^{-1}(a x)^{3/2}}+\frac{8 x^2}{15 \cos ^{-1}(a x)^{3/2}}",1,"(2*x*Sqrt[1 - a^2*x^2])/(5*a*ArcCos[a*x]^(5/2)) - 4/(15*a^2*ArcCos[a*x]^(3/2)) + (8*x^2)/(15*ArcCos[a*x]^(3/2)) - (32*x*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcCos[a*x]]) + (32*Sqrt[Pi]*FresnelC[(2*Sqrt[ArcCos[a*x]])/Sqrt[Pi]])/(15*a^2)","A",6,6,10,0.6000,1,"{4634, 4720, 4632, 3304, 3352, 4642}"
117,1,105,0,0.1655029,"\int \frac{1}{\cos ^{-1}(a x)^{7/2}} \, dx","Int[ArcCos[a*x]^(-7/2),x]","-\frac{8 \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}+\frac{8 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a}+\frac{4 x}{15 \cos ^{-1}(a x)^{3/2}}","-\frac{8 \sqrt{1-a^2 x^2}}{15 a \sqrt{\cos ^{-1}(a x)}}+\frac{2 \sqrt{1-a^2 x^2}}{5 a \cos ^{-1}(a x)^{5/2}}+\frac{8 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a x)}\right)}{15 a}+\frac{4 x}{15 \cos ^{-1}(a x)^{3/2}}",1,"(2*Sqrt[1 - a^2*x^2])/(5*a*ArcCos[a*x]^(5/2)) + (4*x)/(15*ArcCos[a*x]^(3/2)) - (8*Sqrt[1 - a^2*x^2])/(15*a*Sqrt[ArcCos[a*x]]) + (8*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a*x]]])/(15*a)","A",6,5,8,0.6250,1,"{4622, 4720, 4724, 3304, 3352}"
118,0,0,0,0.0128925,"\int \frac{1}{x \cos ^{-1}(a x)^{7/2}} \, dx","Int[1/(x*ArcCos[a*x]^(7/2)),x]","\int \frac{1}{x \cos ^{-1}(a x)^{7/2}} \, dx","\text{Int}\left(\frac{1}{x \cos ^{-1}(a x)^{7/2}},x\right)",0,"Defer[Int][1/(x*ArcCos[a*x]^(7/2)), x]","A",0,0,0,0,-1,"{}"
119,0,0,0,0.1167918,"\int (b x)^m \cos ^{-1}(a x)^4 \, dx","Int[(b*x)^m*ArcCos[a*x]^4,x]","\int (b x)^m \cos ^{-1}(a x)^4 \, dx","\frac{4 a \text{Int}\left(\frac{\cos ^{-1}(a x)^3 (b x)^{m+1}}{\sqrt{1-a^2 x^2}},x\right)}{b (m+1)}+\frac{\cos ^{-1}(a x)^4 (b x)^{m+1}}{b (m+1)}",0,"((b*x)^(1 + m)*ArcCos[a*x]^4)/(b*(1 + m)) + (4*a*Defer[Int][((b*x)^(1 + m)*ArcCos[a*x]^3)/Sqrt[1 - a^2*x^2], x])/(b*(1 + m))","A",0,0,0,0,-1,"{}"
120,0,0,0,0.1144619,"\int (b x)^m \cos ^{-1}(a x)^3 \, dx","Int[(b*x)^m*ArcCos[a*x]^3,x]","\int (b x)^m \cos ^{-1}(a x)^3 \, dx","\frac{3 a \text{Int}\left(\frac{\cos ^{-1}(a x)^2 (b x)^{m+1}}{\sqrt{1-a^2 x^2}},x\right)}{b (m+1)}+\frac{\cos ^{-1}(a x)^3 (b x)^{m+1}}{b (m+1)}",0,"((b*x)^(1 + m)*ArcCos[a*x]^3)/(b*(1 + m)) + (3*a*Defer[Int][((b*x)^(1 + m)*ArcCos[a*x]^2)/Sqrt[1 - a^2*x^2], x])/(b*(1 + m))","A",0,0,0,0,-1,"{}"
121,1,150,0,0.1074213,"\int (b x)^m \cos ^{-1}(a x)^2 \, dx","Int[(b*x)^m*ArcCos[a*x]^2,x]","\frac{2 a^2 (b x)^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)}{b^3 (m+1) (m+2) (m+3)}+\frac{2 a \cos ^{-1}(a x) (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}+\frac{\cos ^{-1}(a x)^2 (b x)^{m+1}}{b (m+1)}","\frac{2 a^2 (b x)^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};a^2 x^2\right)}{b^3 (m+1) (m+2) (m+3)}+\frac{2 a \cos ^{-1}(a x) (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}+\frac{\cos ^{-1}(a x)^2 (b x)^{m+1}}{b (m+1)}",1,"((b*x)^(1 + m)*ArcCos[a*x]^2)/(b*(1 + m)) + (2*a*(b*x)^(2 + m)*ArcCos[a*x]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(b^2*(1 + m)*(2 + m)) + (2*a^2*(b*x)^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, a^2*x^2])/(b^3*(1 + m)*(2 + m)*(3 + m))","A",2,2,12,0.1667,1,"{4628, 4712}"
122,1,68,0,0.0256728,"\int (b x)^m \cos ^{-1}(a x) \, dx","Int[(b*x)^m*ArcCos[a*x],x]","\frac{a (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}+\frac{\cos ^{-1}(a x) (b x)^{m+1}}{b (m+1)}","\frac{a (b x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{b^2 (m+1) (m+2)}+\frac{\cos ^{-1}(a x) (b x)^{m+1}}{b (m+1)}",1,"((b*x)^(1 + m)*ArcCos[a*x])/(b*(1 + m)) + (a*(b*x)^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(b^2*(1 + m)*(2 + m))","A",2,2,10,0.2000,1,"{4628, 364}"
123,0,0,0,0.0172439,"\int \frac{(b x)^m}{\cos ^{-1}(a x)} \, dx","Int[(b*x)^m/ArcCos[a*x],x]","\int \frac{(b x)^m}{\cos ^{-1}(a x)} \, dx","\text{Int}\left(\frac{(b x)^m}{\cos ^{-1}(a x)},x\right)",0,"Defer[Int][(b*x)^m/ArcCos[a*x], x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0151697,"\int \frac{(b x)^m}{\cos ^{-1}(a x)^2} \, dx","Int[(b*x)^m/ArcCos[a*x]^2,x]","\int \frac{(b x)^m}{\cos ^{-1}(a x)^2} \, dx","\text{Int}\left(\frac{(b x)^m}{\cos ^{-1}(a x)^2},x\right)",0,"Defer[Int][(b*x)^m/ArcCos[a*x]^2, x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.0154452,"\int (b x)^m \cos ^{-1}(a x)^{3/2} \, dx","Int[(b*x)^m*ArcCos[a*x]^(3/2),x]","\int (b x)^m \cos ^{-1}(a x)^{3/2} \, dx","\text{Int}\left(\cos ^{-1}(a x)^{3/2} (b x)^m,x\right)",0,"Defer[Int][(b*x)^m*ArcCos[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
126,0,0,0,0.0160559,"\int (b x)^m \sqrt{\cos ^{-1}(a x)} \, dx","Int[(b*x)^m*Sqrt[ArcCos[a*x]],x]","\int (b x)^m \sqrt{\cos ^{-1}(a x)} \, dx","\text{Int}\left(\sqrt{\cos ^{-1}(a x)} (b x)^m,x\right)",0,"Defer[Int][(b*x)^m*Sqrt[ArcCos[a*x]], x]","A",0,0,0,0,-1,"{}"
127,0,0,0,0.0158808,"\int \frac{(b x)^m}{\sqrt{\cos ^{-1}(a x)}} \, dx","Int[(b*x)^m/Sqrt[ArcCos[a*x]],x]","\int \frac{(b x)^m}{\sqrt{\cos ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{(b x)^m}{\sqrt{\cos ^{-1}(a x)}},x\right)",0,"Defer[Int][(b*x)^m/Sqrt[ArcCos[a*x]], x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.0150363,"\int \frac{(b x)^m}{\cos ^{-1}(a x)^{3/2}} \, dx","Int[(b*x)^m/ArcCos[a*x]^(3/2),x]","\int \frac{(b x)^m}{\cos ^{-1}(a x)^{3/2}} \, dx","\text{Int}\left(\frac{(b x)^m}{\cos ^{-1}(a x)^{3/2}},x\right)",0,"Defer[Int][(b*x)^m/ArcCos[a*x]^(3/2), x]","A",0,0,0,0,-1,"{}"
129,0,0,0,0.016163,"\int (b x)^m \cos ^{-1}(a x)^n \, dx","Int[(b*x)^m*ArcCos[a*x]^n,x]","\int (b x)^m \cos ^{-1}(a x)^n \, dx","\text{Int}\left((b x)^m \cos ^{-1}(a x)^n,x\right)",0,"Defer[Int][(b*x)^m*ArcCos[a*x]^n, x]","A",0,0,0,0,-1,"{}"
130,1,165,0,0.1756243,"\int x^3 \cos ^{-1}(a x)^n \, dx","Int[x^3*ArcCos[a*x]^n,x]","\frac{2^{-n-4} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,4 i \cos ^{-1}(a x)\right)}{a^4}","\frac{2^{-n-4} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-4 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-n-4} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \cos ^{-1}(a x)\right)}{a^4}+\frac{2^{-2 (n+3)} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,4 i \cos ^{-1}(a x)\right)}{a^4}",1,"(2^(-4 - n)*ArcCos[a*x]^n*Gamma[1 + n, (-2*I)*ArcCos[a*x]])/(a^4*((-I)*ArcCos[a*x])^n) + (2^(-4 - n)*ArcCos[a*x]^n*Gamma[1 + n, (2*I)*ArcCos[a*x]])/(a^4*(I*ArcCos[a*x])^n) + (ArcCos[a*x]^n*Gamma[1 + n, (-4*I)*ArcCos[a*x]])/(2^(2*(3 + n))*a^4*((-I)*ArcCos[a*x])^n) + (ArcCos[a*x]^n*Gamma[1 + n, (4*I)*ArcCos[a*x]])/(2^(2*(3 + n))*a^4*(I*ArcCos[a*x])^n)","A",9,4,10,0.4000,1,"{4636, 4406, 3308, 2181}"
131,1,163,0,0.1489597,"\int x^2 \cos ^{-1}(a x)^n \, dx","Int[x^2*ArcCos[a*x]^n,x]","\frac{\cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{\left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,3 i \cos ^{-1}(a x)\right)}{8 a^3}","\frac{\cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{\left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,i \cos ^{-1}(a x)\right)}{8 a^3}+\frac{3^{-n-1} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,3 i \cos ^{-1}(a x)\right)}{8 a^3}",1,"(ArcCos[a*x]^n*Gamma[1 + n, (-I)*ArcCos[a*x]])/(8*a^3*((-I)*ArcCos[a*x])^n) + (ArcCos[a*x]^n*Gamma[1 + n, I*ArcCos[a*x]])/(8*a^3*(I*ArcCos[a*x])^n) + (3^(-1 - n)*ArcCos[a*x]^n*Gamma[1 + n, (-3*I)*ArcCos[a*x]])/(8*a^3*((-I)*ArcCos[a*x])^n) + (3^(-1 - n)*ArcCos[a*x]^n*Gamma[1 + n, (3*I)*ArcCos[a*x]])/(8*a^3*(I*ArcCos[a*x])^n)","A",9,4,10,0.4000,1,"{4636, 4406, 3308, 2181}"
132,1,83,0,0.0827482,"\int x \cos ^{-1}(a x)^n \, dx","Int[x*ArcCos[a*x]^n,x]","\frac{2^{-n-3} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \cos ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \cos ^{-1}(a x)\right)}{a^2}","\frac{2^{-n-3} \cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 i \cos ^{-1}(a x)\right)}{a^2}+\frac{2^{-n-3} \left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,2 i \cos ^{-1}(a x)\right)}{a^2}",1,"(2^(-3 - n)*ArcCos[a*x]^n*Gamma[1 + n, (-2*I)*ArcCos[a*x]])/(a^2*((-I)*ArcCos[a*x])^n) + (2^(-3 - n)*ArcCos[a*x]^n*Gamma[1 + n, (2*I)*ArcCos[a*x]])/(a^2*(I*ArcCos[a*x])^n)","A",6,5,8,0.6250,1,"{4636, 4406, 12, 3308, 2181}"
133,1,75,0,0.0493503,"\int \cos ^{-1}(a x)^n \, dx","Int[ArcCos[a*x]^n,x]","\frac{\cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \cos ^{-1}(a x)\right)}{2 a}+\frac{\left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,i \cos ^{-1}(a x)\right)}{2 a}","\frac{\cos ^{-1}(a x)^n \left(-i \cos ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-i \cos ^{-1}(a x)\right)}{2 a}+\frac{\left(i \cos ^{-1}(a x)\right)^{-n} \cos ^{-1}(a x)^n \text{Gamma}\left(n+1,i \cos ^{-1}(a x)\right)}{2 a}",1,"(ArcCos[a*x]^n*Gamma[1 + n, (-I)*ArcCos[a*x]])/(2*a*((-I)*ArcCos[a*x])^n) + (ArcCos[a*x]^n*Gamma[1 + n, I*ArcCos[a*x]])/(2*a*(I*ArcCos[a*x])^n)","A",4,3,6,0.5000,1,"{4624, 3308, 2181}"
134,0,0,0,0.0151887,"\int \frac{\cos ^{-1}(a x)^n}{x} \, dx","Int[ArcCos[a*x]^n/x,x]","\int \frac{\cos ^{-1}(a x)^n}{x} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^n}{x},x\right)",0,"Defer[Int][ArcCos[a*x]^n/x, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.0152596,"\int \frac{\cos ^{-1}(a x)^n}{x^2} \, dx","Int[ArcCos[a*x]^n/x^2,x]","\int \frac{\cos ^{-1}(a x)^n}{x^2} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^n}{x^2},x\right)",0,"Defer[Int][ArcCos[a*x]^n/x^2, x]","A",0,0,0,0,-1,"{}"
136,0,0,0,0.0205362,"\int (b x)^{3/2} \cos ^{-1}(a x)^n \, dx","Int[(b*x)^(3/2)*ArcCos[a*x]^n,x]","\int (b x)^{3/2} \cos ^{-1}(a x)^n \, dx","\text{Int}\left((b x)^{3/2} \cos ^{-1}(a x)^n,x\right)",0,"Defer[Int][(b*x)^(3/2)*ArcCos[a*x]^n, x]","A",0,0,0,0,-1,"{}"
137,0,0,0,0.0181128,"\int \sqrt{b x} \cos ^{-1}(a x)^n \, dx","Int[Sqrt[b*x]*ArcCos[a*x]^n,x]","\int \sqrt{b x} \cos ^{-1}(a x)^n \, dx","\text{Int}\left(\sqrt{b x} \cos ^{-1}(a x)^n,x\right)",0,"Defer[Int][Sqrt[b*x]*ArcCos[a*x]^n, x]","A",0,0,0,0,-1,"{}"
138,0,0,0,0.0189931,"\int \frac{\cos ^{-1}(a x)^n}{\sqrt{b x}} \, dx","Int[ArcCos[a*x]^n/Sqrt[b*x],x]","\int \frac{\cos ^{-1}(a x)^n}{\sqrt{b x}} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^n}{\sqrt{b x}},x\right)",0,"Defer[Int][ArcCos[a*x]^n/Sqrt[b*x], x]","A",0,0,0,0,-1,"{}"
139,0,0,0,0.0220214,"\int \frac{\cos ^{-1}(a x)^n}{(b x)^{3/2}} \, dx","Int[ArcCos[a*x]^n/(b*x)^(3/2),x]","\int \frac{\cos ^{-1}(a x)^n}{(b x)^{3/2}} \, dx","\text{Int}\left(\frac{\cos ^{-1}(a x)^n}{(b x)^{3/2}},x\right)",0,"Defer[Int][ArcCos[a*x]^n/(b*x)^(3/2), x]","A",0,0,0,0,-1,"{}"
140,1,76,0,0.0355778,"\int x^3 \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcCos[c*x]),x]","\frac{1}{4} x^4 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x^3 \sqrt{1-c^2 x^2}}{16 c}-\frac{3 b x \sqrt{1-c^2 x^2}}{32 c^3}+\frac{3 b \sin ^{-1}(c x)}{32 c^4}","\frac{1}{4} x^4 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x^3 \sqrt{1-c^2 x^2}}{16 c}-\frac{3 b x \sqrt{1-c^2 x^2}}{32 c^3}+\frac{3 b \sin ^{-1}(c x)}{32 c^4}",1,"(-3*b*x*Sqrt[1 - c^2*x^2])/(32*c^3) - (b*x^3*Sqrt[1 - c^2*x^2])/(16*c) + (x^4*(a + b*ArcCos[c*x]))/4 + (3*b*ArcSin[c*x])/(32*c^4)","A",4,3,12,0.2500,1,"{4628, 321, 216}"
141,1,60,0,0.0418091,"\int x^2 \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcCos[c*x]),x]","\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^3}-\frac{b \sqrt{1-c^2 x^2}}{3 c^3}","\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^{3/2}}{9 c^3}-\frac{b \sqrt{1-c^2 x^2}}{3 c^3}",1,"-(b*Sqrt[1 - c^2*x^2])/(3*c^3) + (b*(1 - c^2*x^2)^(3/2))/(9*c^3) + (x^3*(a + b*ArcCos[c*x]))/3","A",4,3,12,0.2500,1,"{4628, 266, 43}"
142,1,51,0,0.0191739,"\int x \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcCos[c*x]),x]","\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x \sqrt{1-c^2 x^2}}{4 c}+\frac{b \sin ^{-1}(c x)}{4 c^2}","\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x \sqrt{1-c^2 x^2}}{4 c}+\frac{b \sin ^{-1}(c x)}{4 c^2}",1,"-(b*x*Sqrt[1 - c^2*x^2])/(4*c) + (x^2*(a + b*ArcCos[c*x]))/2 + (b*ArcSin[c*x])/(4*c^2)","A",3,3,10,0.3000,1,"{4628, 321, 216}"
143,1,31,0,0.019312,"\int \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[a + b*ArcCos[c*x],x]","a x-\frac{b \sqrt{1-c^2 x^2}}{c}+b x \cos ^{-1}(c x)","a x-\frac{b \sqrt{1-c^2 x^2}}{c}+b x \cos ^{-1}(c x)",1,"a*x - (b*Sqrt[1 - c^2*x^2])/c + b*x*ArcCos[c*x]","A",3,2,8,0.2500,1,"{4620, 261}"
144,1,63,0,0.0716771,"\int \frac{a+b \cos ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcCos[c*x])/x,x]","-\frac{1}{2} i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^2}{2 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)","-\frac{1}{2} i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^2}{2 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)",1,"((-I/2)*(a + b*ArcCos[c*x])^2)/b + (a + b*ArcCos[c*x])*Log[1 + E^((2*I)*ArcCos[c*x])] - (I/2)*b*PolyLog[2, -E^((2*I)*ArcCos[c*x])]","A",5,5,12,0.4167,1,"{4626, 3719, 2190, 2279, 2391}"
145,1,32,0,0.0281992,"\int \frac{a+b \cos ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcCos[c*x])/x^2,x]","b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{a+b \cos ^{-1}(c x)}{x}","b c \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)-\frac{a+b \cos ^{-1}(c x)}{x}",1,"-((a + b*ArcCos[c*x])/x) + b*c*ArcTanh[Sqrt[1 - c^2*x^2]]","A",4,4,12,0.3333,1,"{4628, 266, 63, 208}"
146,1,39,0,0.0194112,"\int \frac{a+b \cos ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcCos[c*x])/x^3,x]","\frac{b c \sqrt{1-c^2 x^2}}{2 x}-\frac{a+b \cos ^{-1}(c x)}{2 x^2}","\frac{b c \sqrt{1-c^2 x^2}}{2 x}-\frac{a+b \cos ^{-1}(c x)}{2 x^2}",1,"(b*c*Sqrt[1 - c^2*x^2])/(2*x) - (a + b*ArcCos[c*x])/(2*x^2)","A",2,2,12,0.1667,1,"{4628, 264}"
147,1,62,0,0.0367287,"\int \frac{a+b \cos ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcCos[c*x])/x^4,x]","-\frac{a+b \cos ^{-1}(c x)}{3 x^3}+\frac{b c \sqrt{1-c^2 x^2}}{6 x^2}+\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)","-\frac{a+b \cos ^{-1}(c x)}{3 x^3}+\frac{b c \sqrt{1-c^2 x^2}}{6 x^2}+\frac{1}{6} b c^3 \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)",1,"(b*c*Sqrt[1 - c^2*x^2])/(6*x^2) - (a + b*ArcCos[c*x])/(3*x^3) + (b*c^3*ArcTanh[Sqrt[1 - c^2*x^2]])/6","A",5,5,12,0.4167,1,"{4628, 266, 51, 63, 208}"
148,1,102,0,0.1524401,"\int x^2 \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcCos[c*x])^2,x]","-\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c}-\frac{4 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^2-\frac{4 b^2 x}{9 c^2}-\frac{2}{27} b^2 x^3","-\frac{2 b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c}-\frac{4 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^2-\frac{4 b^2 x}{9 c^2}-\frac{2}{27} b^2 x^3",1,"(-4*b^2*x)/(9*c^2) - (2*b^2*x^3)/27 - (4*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(9*c^3) - (2*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(9*c) + (x^3*(a + b*ArcCos[c*x])^2)/3","A",5,5,14,0.3571,1,"{4628, 4708, 4678, 8, 30}"
149,1,76,0,0.1175887,"\int x \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcCos[c*x])^2,x]","-\frac{b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{2 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^2-\frac{1}{4} b^2 x^2","-\frac{b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{2 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^2-\frac{1}{4} b^2 x^2",1,"-(b^2*x^2)/4 - (b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/(2*c) - (a + b*ArcCos[c*x])^2/(4*c^2) + (x^2*(a + b*ArcCos[c*x])^2)/2","A",4,4,12,0.3333,1,"{4628, 4708, 4642, 30}"
150,1,47,0,0.0578785,"\int \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcCos[c*x])^2,x]","-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{c}+x \left(a+b \cos ^{-1}(c x)\right)^2-2 b^2 x","-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)}{c}+x \left(a+b \cos ^{-1}(c x)\right)^2-2 b^2 x",1,"-2*b^2*x - (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x]))/c + x*(a + b*ArcCos[c*x])^2","A",3,3,10,0.3000,1,"{4620, 4678, 8}"
151,1,92,0,0.1180952,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcCos[c*x])^2/x,x]","-i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^3}{3 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2","-i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^3}{3 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2",1,"((-I/3)*(a + b*ArcCos[c*x])^3)/b + (a + b*ArcCos[c*x])^2*Log[1 + E^((2*I)*ArcCos[c*x])] - I*b*(a + b*ArcCos[c*x])*PolyLog[2, -E^((2*I)*ArcCos[c*x])] + (b^2*PolyLog[3, -E^((2*I)*ArcCos[c*x])])/2","A",6,6,14,0.4286,1,"{4626, 3719, 2190, 2531, 2282, 6589}"
152,1,89,0,0.1275384,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcCos[c*x])^2/x^2,x]","2 i b^2 c \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(c x)}\right)-2 i b^2 c \text{PolyLog}\left(2,i e^{i \cos ^{-1}(c x)}\right)-\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{x}-4 i b c \tan ^{-1}\left(e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)","2 i b^2 c \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(c x)}\right)-2 i b^2 c \text{PolyLog}\left(2,i e^{i \cos ^{-1}(c x)}\right)-\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{x}-4 i b c \tan ^{-1}\left(e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)",1,"-((a + b*ArcCos[c*x])^2/x) - (4*I)*b*c*(a + b*ArcCos[c*x])*ArcTan[E^(I*ArcCos[c*x])] + (2*I)*b^2*c*PolyLog[2, (-I)*E^(I*ArcCos[c*x])] - (2*I)*b^2*c*PolyLog[2, I*E^(I*ArcCos[c*x])]","A",7,5,14,0.3571,1,"{4628, 4710, 4181, 2279, 2391}"
153,1,178,0,0.2953934,"\int x^2 \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcCos[c*x])^3,x]","-\frac{4 a b^2 x}{3 c^2}-\frac{2}{9} b^2 x^3 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 c}-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^3-\frac{2 b^3 \left(1-c^2 x^2\right)^{3/2}}{27 c^3}+\frac{14 b^3 \sqrt{1-c^2 x^2}}{9 c^3}-\frac{4 b^3 x \cos ^{-1}(c x)}{3 c^2}","-\frac{4 a b^2 x}{3 c^2}-\frac{2}{9} b^2 x^3 \left(a+b \cos ^{-1}(c x)\right)-\frac{b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 c}-\frac{2 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^3-\frac{2 b^3 \left(1-c^2 x^2\right)^{3/2}}{27 c^3}+\frac{14 b^3 \sqrt{1-c^2 x^2}}{9 c^3}-\frac{4 b^3 x \cos ^{-1}(c x)}{3 c^2}",1,"(-4*a*b^2*x)/(3*c^2) + (14*b^3*Sqrt[1 - c^2*x^2])/(9*c^3) - (2*b^3*(1 - c^2*x^2)^(3/2))/(27*c^3) - (4*b^3*x*ArcCos[c*x])/(3*c^2) - (2*b^2*x^3*(a + b*ArcCos[c*x]))/9 - (2*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(3*c^3) - (b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(3*c) + (x^3*(a + b*ArcCos[c*x])^3)/3","A",10,7,14,0.5000,1,"{4628, 4708, 4678, 4620, 261, 266, 43}"
154,1,125,0,0.2075121,"\int x \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcCos[c*x])^3,x]","-\frac{3}{4} b^2 x^2 \left(a+b \cos ^{-1}(c x)\right)-\frac{3 b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^3}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^3+\frac{3 b^3 x \sqrt{1-c^2 x^2}}{8 c}-\frac{3 b^3 \sin ^{-1}(c x)}{8 c^2}","-\frac{3}{4} b^2 x^2 \left(a+b \cos ^{-1}(c x)\right)-\frac{3 b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^3}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^3+\frac{3 b^3 x \sqrt{1-c^2 x^2}}{8 c}-\frac{3 b^3 \sin ^{-1}(c x)}{8 c^2}",1,"(3*b^3*x*Sqrt[1 - c^2*x^2])/(8*c) - (3*b^2*x^2*(a + b*ArcCos[c*x]))/4 - (3*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(4*c) - (a + b*ArcCos[c*x])^3/(4*c^2) + (x^2*(a + b*ArcCos[c*x])^3)/2 - (3*b^3*ArcSin[c*x])/(8*c^2)","A",6,5,12,0.4167,1,"{4628, 4708, 4642, 321, 216}"
155,1,82,0,0.1075721,"\int \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcCos[c*x])^3,x]","-6 a b^2 x-\frac{3 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{c}+x \left(a+b \cos ^{-1}(c x)\right)^3+\frac{6 b^3 \sqrt{1-c^2 x^2}}{c}-6 b^3 x \cos ^{-1}(c x)","-6 a b^2 x-\frac{3 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{c}+x \left(a+b \cos ^{-1}(c x)\right)^3+\frac{6 b^3 \sqrt{1-c^2 x^2}}{c}-6 b^3 x \cos ^{-1}(c x)",1,"-6*a*b^2*x + (6*b^3*Sqrt[1 - c^2*x^2])/c - 6*b^3*x*ArcCos[c*x] - (3*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/c + x*(a + b*ArcCos[c*x])^3","A",5,3,10,0.3000,1,"{4620, 4678, 261}"
156,1,127,0,0.1409596,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcCos[c*x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^4}{4 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^3","\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-\frac{3}{2} i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2+\frac{3}{4} i b^3 \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}(c x)}\right)-\frac{i \left(a+b \cos ^{-1}(c x)\right)^4}{4 b}+\log \left(1+e^{2 i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^3",1,"((-I/4)*(a + b*ArcCos[c*x])^4)/b + (a + b*ArcCos[c*x])^3*Log[1 + E^((2*I)*ArcCos[c*x])] - ((3*I)/2)*b*(a + b*ArcCos[c*x])^2*PolyLog[2, -E^((2*I)*ArcCos[c*x])] + (3*b^2*(a + b*ArcCos[c*x])*PolyLog[3, -E^((2*I)*ArcCos[c*x])])/2 + ((3*I)/4)*b^3*PolyLog[4, -E^((2*I)*ArcCos[c*x])]","A",7,7,14,0.5000,1,"{4626, 3719, 2190, 2531, 6609, 2282, 6589}"
157,1,151,0,0.2138953,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcCos[c*x])^3/x^2,x]","6 i b^2 c \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-6 i b^2 c \text{PolyLog}\left(2,i e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-6 b^3 c \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(c x)}\right)+6 b^3 c \text{PolyLog}\left(3,i e^{i \cos ^{-1}(c x)}\right)-\frac{\left(a+b \cos ^{-1}(c x)\right)^3}{x}-6 i b c \tan ^{-1}\left(e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2","6 i b^2 c \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-6 i b^2 c \text{PolyLog}\left(2,i e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)-6 b^3 c \text{PolyLog}\left(3,-i e^{i \cos ^{-1}(c x)}\right)+6 b^3 c \text{PolyLog}\left(3,i e^{i \cos ^{-1}(c x)}\right)-\frac{\left(a+b \cos ^{-1}(c x)\right)^3}{x}-6 i b c \tan ^{-1}\left(e^{i \cos ^{-1}(c x)}\right) \left(a+b \cos ^{-1}(c x)\right)^2",1,"-((a + b*ArcCos[c*x])^3/x) - (6*I)*b*c*(a + b*ArcCos[c*x])^2*ArcTan[E^(I*ArcCos[c*x])] + (6*I)*b^2*c*(a + b*ArcCos[c*x])*PolyLog[2, (-I)*E^(I*ArcCos[c*x])] - (6*I)*b^2*c*(a + b*ArcCos[c*x])*PolyLog[2, I*E^(I*ArcCos[c*x])] - 6*b^3*c*PolyLog[3, (-I)*E^(I*ArcCos[c*x])] + 6*b^3*c*PolyLog[3, I*E^(I*ArcCos[c*x])]","A",9,6,14,0.4286,1,"{4628, 4710, 4181, 2531, 2282, 6589}"
158,1,117,0,0.2156201,"\int \frac{x^2}{a+b \cos ^{-1}(c x)} \, dx","Int[x^2/(a + b*ArcCos[c*x]),x]","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{4 b c^3}+\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{4 b c^3}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{4 b c^3}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{4 b c^3}","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{4 b c^3}+\frac{\sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{4 b c^3}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{\cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{4 b c^3}",1,"(CosIntegral[a/b + ArcCos[c*x]]*Sin[a/b])/(4*b*c^3) + (CosIntegral[(3*a)/b + 3*ArcCos[c*x]]*Sin[(3*a)/b])/(4*b*c^3) - (Cos[a/b]*SinIntegral[a/b + ArcCos[c*x]])/(4*b*c^3) - (Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcCos[c*x]])/(4*b*c^3)","A",9,5,14,0.3571,1,"{4636, 4406, 3303, 3299, 3302}"
159,1,63,0,0.1208682,"\int \frac{x}{a+b \cos ^{-1}(c x)} \, dx","Int[x/(a + b*ArcCos[c*x]),x]","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{2 b c^2}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{2 b c^2}","\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{2 b c^2}-\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{2 b c^2}",1,"(CosIntegral[(2*a)/b + 2*ArcCos[c*x]]*Sin[(2*a)/b])/(2*b*c^2) - (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcCos[c*x]])/(2*b*c^2)","A",6,6,12,0.5000,1,"{4636, 4406, 12, 3303, 3299, 3302}"
160,1,54,0,0.0619756,"\int \frac{1}{a+b \cos ^{-1}(c x)} \, dx","Int[(a + b*ArcCos[c*x])^(-1),x]","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b c}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b c}","\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b c}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b c}",1,"(CosIntegral[(a + b*ArcCos[c*x])/b]*Sin[a/b])/(b*c) - (Cos[a/b]*SinIntegral[(a + b*ArcCos[c*x])/b])/(b*c)","A",4,4,10,0.4000,1,"{4624, 3303, 3299, 3302}"
161,0,0,0,0.0232703,"\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)} \, dx","Int[1/(x*(a + b*ArcCos[c*x])),x]","\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \cos ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCos[c*x])), x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.0244692,"\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(a + b*ArcCos[c*x])),x]","\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*(a + b*ArcCos[c*x])), x]","A",0,0,0,0,-1,"{}"
163,1,151,0,0.1826544,"\int \frac{x^2}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[x^2/(a + b*ArcCos[c*x])^2,x]","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{x^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}+\frac{x^2 \sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}",1,"(x^2*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcCos[c*x])) - (Cos[a/b]*CosIntegral[a/b + ArcCos[c*x]])/(4*b^2*c^3) - (3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcCos[c*x]])/(4*b^2*c^3) - (Sin[a/b]*SinIntegral[a/b + ArcCos[c*x]])/(4*b^2*c^3) - (3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcCos[c*x]])/(4*b^2*c^3)","A",8,4,14,0.2857,1,"{4632, 3303, 3299, 3302}"
164,1,91,0,0.0968336,"\int \frac{x}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[x/(a + b*ArcCos[c*x])^2,x]","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{b^2 c^2}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{b^2 c^2}+\frac{x \sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}","-\frac{\cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{\sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{x \sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}",1,"(x*Sqrt[1 - c^2*x^2])/(b*c*(a + b*ArcCos[c*x])) - (Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcCos[c*x]])/(b^2*c^2) - (Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcCos[c*x]])/(b^2*c^2)","A",4,4,12,0.3333,1,"{4632, 3303, 3299, 3302}"
165,1,82,0,0.1679402,"\int \frac{1}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcCos[c*x])^(-2),x]","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{b^2 c}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{b^2 c}+\frac{\sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}","-\frac{\cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b^2 c}+\frac{\sqrt{1-c^2 x^2}}{b c \left(a+b \cos ^{-1}(c x)\right)}",1,"Sqrt[1 - c^2*x^2]/(b*c*(a + b*ArcCos[c*x])) - (Cos[a/b]*CosIntegral[a/b + ArcCos[c*x]])/(b^2*c) - (Sin[a/b]*SinIntegral[a/b + ArcCos[c*x]])/(b^2*c)","A",5,5,10,0.5000,1,"{4622, 4724, 3303, 3299, 3302}"
166,0,0,0,0.0213703,"\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(a + b*ArcCos[c*x])^2),x]","\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCos[c*x])^2), x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0218532,"\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(a + b*ArcCos[c*x])^2),x]","\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*ArcCos[c*x])^2), x]","A",0,0,0,0,-1,"{}"
168,1,246,0,0.5345187,"\int \frac{x^2}{\left(a+b \cos ^{-1}(c x)\right)^3} \, dx","Int[x^2/(a + b*ArcCos[c*x])^3,x]","-\frac{9 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b^3 c^3}-\frac{9 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{9 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\cos ^{-1}(c x)\right)}{8 b^3 c^3}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \cos ^{-1}(c x)\right)}{8 b^3 c^3}-\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{b^3 c^3}-\frac{x}{b^2 c^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{3 x^3}{2 b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x^2 \sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{8 b^3 c^3}-\frac{9 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{8 b^3 c^3}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{8 b^3 c^3}+\frac{9 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{8 b^3 c^3}-\frac{x}{b^2 c^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{3 x^3}{2 b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x^2 \sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}",1,"(x^2*Sqrt[1 - c^2*x^2])/(2*b*c*(a + b*ArcCos[c*x])^2) - x/(b^2*c^2*(a + b*ArcCos[c*x])) + (3*x^3)/(2*b^2*(a + b*ArcCos[c*x])) - (9*CosIntegral[a/b + ArcCos[c*x]]*Sin[a/b])/(8*b^3*c^3) + (CosIntegral[(a + b*ArcCos[c*x])/b]*Sin[a/b])/(b^3*c^3) - (9*CosIntegral[(3*a)/b + 3*ArcCos[c*x]]*Sin[(3*a)/b])/(8*b^3*c^3) + (9*Cos[a/b]*SinIntegral[a/b + ArcCos[c*x]])/(8*b^3*c^3) + (9*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcCos[c*x]])/(8*b^3*c^3) - (Cos[a/b]*SinIntegral[(a + b*ArcCos[c*x])/b])/(b^3*c^3)","A",16,8,14,0.5714,1,"{4634, 4720, 4636, 4406, 3303, 3299, 3302, 4624}"
169,1,130,0,0.3110355,"\int \frac{x}{\left(a+b \cos ^{-1}(c x)\right)^3} \, dx","Int[x/(a + b*ArcCos[c*x])^3,x]","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{b^3 c^2}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \cos ^{-1}(c x)\right)}{b^3 c^2}-\frac{1}{2 b^2 c^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x^2}{b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x \sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}","-\frac{\sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{b^3 c^2}+\frac{\cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{b}\right)}{b^3 c^2}-\frac{1}{2 b^2 c^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x^2}{b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{x \sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}",1,"(x*Sqrt[1 - c^2*x^2])/(2*b*c*(a + b*ArcCos[c*x])^2) - 1/(2*b^2*c^2*(a + b*ArcCos[c*x])) + x^2/(b^2*(a + b*ArcCos[c*x])) - (CosIntegral[(2*a)/b + 2*ArcCos[c*x]]*Sin[(2*a)/b])/(b^3*c^2) + (Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcCos[c*x]])/(b^3*c^2)","A",9,9,12,0.7500,1,"{4634, 4720, 4636, 4406, 12, 3303, 3299, 3302, 4642}"
170,1,111,0,0.165866,"\int \frac{1}{\left(a+b \cos ^{-1}(c x)\right)^3} \, dx","Int[(a + b*ArcCos[c*x])^(-3),x]","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{2 b^3 c}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{2 b^3 c}+\frac{x}{2 b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{\sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}","-\frac{\sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{2 b^3 c}+\frac{\cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}(c x)}{b}\right)}{2 b^3 c}+\frac{x}{2 b^2 \left(a+b \cos ^{-1}(c x)\right)}+\frac{\sqrt{1-c^2 x^2}}{2 b c \left(a+b \cos ^{-1}(c x)\right)^2}",1,"Sqrt[1 - c^2*x^2]/(2*b*c*(a + b*ArcCos[c*x])^2) + x/(2*b^2*(a + b*ArcCos[c*x])) - (CosIntegral[(a + b*ArcCos[c*x])/b]*Sin[a/b])/(2*b^3*c) + (Cos[a/b]*SinIntegral[(a + b*ArcCos[c*x])/b])/(2*b^3*c)","A",6,6,10,0.6000,1,"{4622, 4720, 4624, 3303, 3299, 3302}"
171,0,0,0,0.0226184,"\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^3} \, dx","Int[1/(x*(a + b*ArcCos[c*x])^3),x]","\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCos[c*x])^3), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.0238722,"\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^3} \, dx","Int[1/(x^2*(a + b*ArcCos[c*x])^3),x]","\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][1/(x^2*(a + b*ArcCos[c*x])^3), x]","A",0,0,0,0,-1,"{}"
173,1,242,0,0.7024233,"\int x^2 \sqrt{a+b \cos ^{-1}(c x)} \, dx","Int[x^2*Sqrt[a + b*ArcCos[c*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}+\frac{1}{3} x^3 \sqrt{a+b \cos ^{-1}(c x)}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c^3}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{b} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{12 c^3}+\frac{1}{3} x^3 \sqrt{a+b \cos ^{-1}(c x)}",1,"(x^3*Sqrt[a + b*ArcCos[c*x]])/3 - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(4*c^3) - (Sqrt[b]*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(12*c^3) - (Sqrt[b]*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(4*c^3) - (Sqrt[b]*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(12*c^3)","A",14,8,16,0.5000,1,"{4630, 4724, 3312, 3306, 3305, 3351, 3304, 3352}"
174,1,137,0,0.3996899,"\int x \sqrt{a+b \cos ^{-1}(c x)} \, dx","Int[x*Sqrt[a + b*ArcCos[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 c^2}-\frac{\sqrt{\pi } \sqrt{b} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 c^2}-\frac{\sqrt{a+b \cos ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \cos ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{8 c^2}-\frac{\sqrt{\pi } \sqrt{b} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{8 c^2}-\frac{\sqrt{a+b \cos ^{-1}(c x)}}{4 c^2}+\frac{1}{2} x^2 \sqrt{a+b \cos ^{-1}(c x)}",1,"-Sqrt[a + b*ArcCos[c*x]]/(4*c^2) + (x^2*Sqrt[a + b*ArcCos[c*x]])/2 - (Sqrt[b]*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(8*c^2) - (Sqrt[b]*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(8*c^2)","A",9,8,14,0.5714,1,"{4630, 4724, 3312, 3306, 3305, 3351, 3304, 3352}"
175,1,121,0,0.2783333,"\int \sqrt{a+b \cos ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcCos[c*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+x \sqrt{a+b \cos ^{-1}(c x)}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{c}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{c}+x \sqrt{a+b \cos ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcCos[c*x]] - (Sqrt[b]*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/c - (Sqrt[b]*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/c","A",7,7,12,0.5833,1,"{4620, 4724, 3306, 3305, 3351, 3304, 3352}"
176,0,0,0,0.0341507,"\int \frac{\sqrt{a+b \cos ^{-1}(c x)}}{x} \, dx","Int[Sqrt[a + b*ArcCos[c*x]]/x,x]","\int \frac{\sqrt{a+b \cos ^{-1}(c x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{a+b \cos ^{-1}(c x)}}{x},x\right)",0,"Defer[Int][Sqrt[a + b*ArcCos[c*x]]/x, x]","A",0,0,0,0,-1,"{}"
177,0,0,0,0.0336354,"\int \frac{\sqrt{a+b \cos ^{-1}(c x)}}{x^2} \, dx","Int[Sqrt[a + b*ArcCos[c*x]]/x^2,x]","\int \frac{\sqrt{a+b \cos ^{-1}(c x)}}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \cos ^{-1}(c x)}}{x^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcCos[c*x]]/x^2, x]","A",0,0,0,0,-1,"{}"
178,1,313,0,0.9489778,"\int x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2} \, dx","Int[x^2*(a + b*ArcCos[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{b x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{6 c}-\frac{b \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}+\frac{\sqrt{\frac{\pi }{6}} b^{3/2} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{b x^2 \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{6 c}-\frac{b \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{3 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^{3/2}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcCos[c*x]])/(3*c^3) - (b*x^2*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcCos[c*x]])/(6*c) + (x^3*(a + b*ArcCos[c*x])^(3/2))/3 + (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(8*c^3) + (b^(3/2)*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(24*c^3) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(8*c^3) - (b^(3/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(24*c^3)","A",22,11,16,0.6875,1,"{4630, 4708, 4678, 4624, 3306, 3305, 3351, 3304, 3352, 4636, 4406}"
179,1,172,0,0.4613259,"\int x \left(a+b \cos ^{-1}(c x)\right)^{3/2} \, dx","Int[x*(a + b*ArcCos[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 c^2}+\frac{3 \sqrt{\pi } b^{3/2} \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 c^2}-\frac{3 b x \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{8 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^{3/2} \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{32 c^2}+\frac{3 \sqrt{\pi } b^{3/2} \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{32 c^2}-\frac{3 b x \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{8 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2}",1,"(-3*b*x*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcCos[c*x]])/(8*c) - (a + b*ArcCos[c*x])^(3/2)/(4*c^2) + (x^2*(a + b*ArcCos[c*x])^(3/2))/2 + (3*b^(3/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(32*c^2) - (3*b^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(32*c^2)","A",11,11,14,0.7857,1,"{4630, 4708, 4642, 4636, 4406, 12, 3306, 3305, 3351, 3304, 3352}"
180,1,159,0,0.2372639,"\int \left(a+b \cos ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcCos[c*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 b \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{2 c}+x \left(a+b \cos ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 c}-\frac{3 b \sqrt{1-c^2 x^2} \sqrt{a+b \cos ^{-1}(c x)}}{2 c}+x \left(a+b \cos ^{-1}(c x)\right)^{3/2}",1,"(-3*b*Sqrt[1 - c^2*x^2]*Sqrt[a + b*ArcCos[c*x]])/(2*c) + x*(a + b*ArcCos[c*x])^(3/2) + (3*b^(3/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(2*c) - (3*b^(3/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(2*c)","A",8,8,12,0.6667,1,"{4620, 4678, 4624, 3306, 3305, 3351, 3304, 3352}"
181,0,0,0,0.0391337,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x} \, dx","Int[(a + b*ArcCos[c*x])^(3/2)/x,x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x},x\right)",0,"Defer[Int][(a + b*ArcCos[c*x])^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
182,0,0,0,0.038918,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x^2} \, dx","Int[(a + b*ArcCos[c*x])^(3/2)/x^2,x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^{3/2}}{x^2},x\right)",0,"Defer[Int][(a + b*ArcCos[c*x])^(3/2)/x^2, x]","A",0,0,0,0,-1,"{}"
183,1,358,0,1.3163733,"\int x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2} \, dx","Int[x^2*(a + b*ArcCos[c*x])^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}-\frac{5 b^2 x \sqrt{a+b \cos ^{-1}(c x)}}{6 c^2}-\frac{5}{36} b^2 x^3 \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{18 c}-\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^{5/2}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}+\frac{5 \sqrt{\frac{\pi }{6}} b^{5/2} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{144 c^3}-\frac{5 b^2 x \sqrt{a+b \cos ^{-1}(c x)}}{6 c^2}-\frac{5}{36} b^2 x^3 \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b x^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{18 c}-\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{9 c^3}+\frac{1}{3} x^3 \left(a+b \cos ^{-1}(c x)\right)^{5/2}",1,"(-5*b^2*x*Sqrt[a + b*ArcCos[c*x]])/(6*c^2) - (5*b^2*x^3*Sqrt[a + b*ArcCos[c*x]])/36 - (5*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^(3/2))/(9*c^3) - (5*b*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^(3/2))/(18*c) + (x^3*(a + b*ArcCos[c*x])^(5/2))/3 + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(16*c^3) + (5*b^(5/2)*Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(144*c^3) + (15*b^(5/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(16*c^3) + (5*b^(5/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(144*c^3)","A",24,11,16,0.6875,1,"{4630, 4708, 4678, 4620, 4724, 3306, 3305, 3351, 3304, 3352, 3312}"
184,1,216,0,0.7028729,"\int x \left(a+b \cos ^{-1}(c x)\right)^{5/2} \, dx","Int[x*(a + b*ArcCos[c*x])^(5/2),x]","\frac{15 \sqrt{\pi } b^{5/2} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 c^2}+\frac{15 \sqrt{\pi } b^{5/2} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 c^2}+\frac{15 b^2 \sqrt{a+b \cos ^{-1}(c x)}}{64 c^2}-\frac{15}{32} b^2 x^2 \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{8 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2}","\frac{15 \sqrt{\pi } b^{5/2} \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{128 c^2}+\frac{15 \sqrt{\pi } b^{5/2} \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{128 c^2}+\frac{15 b^2 \sqrt{a+b \cos ^{-1}(c x)}}{64 c^2}-\frac{15}{32} b^2 x^2 \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b x \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{8 c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{4 c^2}+\frac{1}{2} x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2}",1,"(15*b^2*Sqrt[a + b*ArcCos[c*x]])/(64*c^2) - (15*b^2*x^2*Sqrt[a + b*ArcCos[c*x]])/32 - (5*b*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^(3/2))/(8*c) - (a + b*ArcCos[c*x])^(5/2)/(4*c^2) + (x^2*(a + b*ArcCos[c*x])^(5/2))/2 + (15*b^(5/2)*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(128*c^2) + (15*b^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(128*c^2)","A",12,10,14,0.7143,1,"{4630, 4708, 4642, 4724, 3312, 3306, 3305, 3351, 3304, 3352}"
185,1,179,0,0.4283013,"\int \left(a+b \cos ^{-1}(c x)\right)^{5/2} \, dx","Int[(a + b*ArcCos[c*x])^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{15}{4} b^2 x \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \cos ^{-1}(c x)\right)^{5/2}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{15}{4} b^2 x \sqrt{a+b \cos ^{-1}(c x)}-\frac{5 b \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^{3/2}}{2 c}+x \left(a+b \cos ^{-1}(c x)\right)^{5/2}",1,"(-15*b^2*x*Sqrt[a + b*ArcCos[c*x]])/4 - (5*b*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^(3/2))/(2*c) + x*(a + b*ArcCos[c*x])^(5/2) + (15*b^(5/2)*Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(4*c) + (15*b^(5/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(4*c)","A",9,8,12,0.6667,1,"{4620, 4678, 4724, 3306, 3305, 3351, 3304, 3352}"
186,0,0,0,0.0411428,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x} \, dx","Int[(a + b*ArcCos[c*x])^(5/2)/x,x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x},x\right)",0,"Defer[Int][(a + b*ArcCos[c*x])^(5/2)/x, x]","A",0,0,0,0,-1,"{}"
187,0,0,0,0.040121,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x^2} \, dx","Int[(a + b*ArcCos[c*x])^(5/2)/x^2,x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^{5/2}}{x^2},x\right)",0,"Defer[Int][(a + b*ArcCos[c*x])^(5/2)/x^2, x]","A",0,0,0,0,-1,"{}"
188,1,223,0,0.3706958,"\int \frac{x^2}{\sqrt{a+b \cos ^{-1}(c x)}} \, dx","Int[x^2/Sqrt[a + b*ArcCos[c*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{6}} \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{6}} \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{6}} \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c^3}",1,"-(Sqrt[Pi/2]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) - (Sqrt[Pi/6]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(2*Sqrt[b]*c^3) + (Sqrt[Pi/2]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(2*Sqrt[b]*c^3) + (Sqrt[Pi/6]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(2*Sqrt[b]*c^3)","A",13,7,16,0.4375,1,"{4636, 4406, 3306, 3305, 3351, 3304, 3352}"
189,1,99,0,0.17077,"\int \frac{x}{\sqrt{a+b \cos ^{-1}(c x)}} \, dx","Int[x/Sqrt[a + b*ArcCos[c*x]],x]","\frac{\sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} c^2}-\frac{\sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} c^2}","\frac{\sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{2 \sqrt{b} c^2}-\frac{\sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{2 \sqrt{b} c^2}",1,"-(Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(2*Sqrt[b]*c^2) + (Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(2*Sqrt[b]*c^2)","A",8,8,14,0.5714,1,"{4636, 4406, 12, 3306, 3305, 3351, 3304, 3352}"
190,1,102,0,0.0901623,"\int \frac{1}{\sqrt{a+b \cos ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcCos[c*x]],x]","\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}","\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{\sqrt{b} c}",1,"-((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(Sqrt[b]*c)) + (Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*c)","A",6,6,12,0.5000,1,"{4624, 3306, 3305, 3351, 3304, 3352}"
191,0,0,0,0.0355121,"\int \frac{1}{x \sqrt{a+b \cos ^{-1}(c x)}} \, dx","Int[1/(x*Sqrt[a + b*ArcCos[c*x]]),x]","\int \frac{1}{x \sqrt{a+b \cos ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a+b \cos ^{-1}(c x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[a + b*ArcCos[c*x]]), x]","A",0,0,0,0,-1,"{}"
192,0,0,0,0.0354743,"\int \frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}} \, dx","Int[1/(x^2*Sqrt[a + b*ArcCos[c*x]]),x]","\int \frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a+b \cos ^{-1}(c x)}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[a + b*ArcCos[c*x]]), x]","A",0,0,0,0,-1,"{}"
193,1,252,0,0.3879832,"\int \frac{x^2}{\left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","Int[x^2/(a + b*ArcCos[c*x])^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{2 x^2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}","-\frac{\sqrt{\frac{\pi }{2}} \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} \cos \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}-\frac{\sqrt{\frac{3 \pi }{2}} \sin \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c^3}+\frac{2 x^2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}",1,"(2*x^2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcCos[c*x]]) - (Sqrt[Pi/2]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) - (Sqrt[(3*Pi)/2]*Cos[(3*a)/b]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(b^(3/2)*c^3) - (Sqrt[Pi/2]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c^3) - (Sqrt[(3*Pi)/2]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(3/2)*c^3)","A",12,6,16,0.3750,1,"{4632, 3306, 3305, 3351, 3304, 3352}"
194,1,130,0,0.1535515,"\int \frac{x}{\left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcCos[c*x])^(3/2),x]","-\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}+\frac{2 x \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}","-\frac{2 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{b^{3/2} c^2}-\frac{2 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{b^{3/2} c^2}+\frac{2 x \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}",1,"(2*x*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcCos[c*x]]) - (2*Sqrt[Pi]*Cos[(2*a)/b]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(b^(3/2)*c^2) - (2*Sqrt[Pi]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(b^(3/2)*c^2)","A",6,6,14,0.4286,1,"{4632, 3306, 3305, 3351, 3304, 3352}"
195,1,137,0,0.2659893,"\int \frac{1}{\left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcCos[c*x])^(-3/2),x]","-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}","-\frac{2 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{2 \sqrt{1-c^2 x^2}}{b c \sqrt{a+b \cos ^{-1}(c x)}}",1,"(2*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[a + b*ArcCos[c*x]]) - (2*Sqrt[2*Pi]*Cos[a/b]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(b^(3/2)*c) - (2*Sqrt[2*Pi]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(b^(3/2)*c)","A",7,7,12,0.5833,1,"{4622, 4724, 3306, 3305, 3351, 3304, 3352}"
196,0,0,0,0.0429365,"\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/(x*(a + b*ArcCos[c*x])^(3/2)),x]","\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCos[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
197,0,0,0,0.0409574,"\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*ArcCos[c*x])^(3/2)),x]","\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/(x^2*(a + b*ArcCos[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
198,1,292,0,0.9453429,"\int \frac{x^2}{\left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","Int[x^2/(a + b*ArcCos[c*x])^(5/2),x]","-\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}-\frac{\sqrt{6 \pi } \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}+\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}+\frac{\sqrt{6 \pi } \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}-\frac{8 x}{3 b^2 c^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{4 x^3}{b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 x^2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}","-\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}-\frac{\sqrt{6 \pi } \sin \left(\frac{3 a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}+\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c^3}+\frac{\sqrt{6 \pi } \cos \left(\frac{3 a}{b}\right) S\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{5/2} c^3}-\frac{8 x}{3 b^2 c^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{4 x^3}{b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 x^2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}",1,"(2*x^2*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcCos[c*x])^(3/2)) - (8*x)/(3*b^2*c^2*Sqrt[a + b*ArcCos[c*x]]) + (4*x^3)/(b^2*Sqrt[a + b*ArcCos[c*x]]) + (Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(3*b^(5/2)*c^3) + (Sqrt[6*Pi]*Cos[(3*a)/b]*FresnelS[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(b^(5/2)*c^3) - (Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*c^3) - (Sqrt[6*Pi]*FresnelC[(Sqrt[6/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[(3*a)/b])/(b^(5/2)*c^3)","A",22,10,16,0.6250,1,"{4634, 4720, 4636, 4406, 3306, 3305, 3351, 3304, 3352, 4624}"
199,1,180,0,0.4872701,"\int \frac{x}{\left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcCos[c*x])^(5/2),x]","-\frac{8 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{8 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} c^2}-\frac{4}{3 b^2 c^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{8 x^2}{3 b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 x \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}","-\frac{8 \sqrt{\pi } \sin \left(\frac{2 a}{b}\right) \text{FresnelC}\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{\pi } \sqrt{b}}\right)}{3 b^{5/2} c^2}+\frac{8 \sqrt{\pi } \cos \left(\frac{2 a}{b}\right) S\left(\frac{2 \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b} \sqrt{\pi }}\right)}{3 b^{5/2} c^2}-\frac{4}{3 b^2 c^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{8 x^2}{3 b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 x \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}",1,"(2*x*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcCos[c*x])^(3/2)) - 4/(3*b^2*c^2*Sqrt[a + b*ArcCos[c*x]]) + (8*x^2)/(3*b^2*Sqrt[a + b*ArcCos[c*x]]) + (8*Sqrt[Pi]*Cos[(2*a)/b]*FresnelS[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])])/(3*b^(5/2)*c^2) - (8*Sqrt[Pi]*FresnelC[(2*Sqrt[a + b*ArcCos[c*x]])/(Sqrt[b]*Sqrt[Pi])]*Sin[(2*a)/b])/(3*b^(5/2)*c^2)","A",11,11,14,0.7857,1,"{4634, 4720, 4636, 4406, 12, 3306, 3305, 3351, 3304, 3352, 4642}"
200,1,163,0,0.2586316,"\int \frac{1}{\left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","Int[(a + b*ArcCos[c*x])^(-5/2),x]","-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{4 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{4 x}{3 b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}","-\frac{4 \sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{4 \sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c x)}}{\sqrt{b}}\right)}{3 b^{5/2} c}+\frac{4 x}{3 b^2 \sqrt{a+b \cos ^{-1}(c x)}}+\frac{2 \sqrt{1-c^2 x^2}}{3 b c \left(a+b \cos ^{-1}(c x)\right)^{3/2}}",1,"(2*Sqrt[1 - c^2*x^2])/(3*b*c*(a + b*ArcCos[c*x])^(3/2)) + (4*x)/(3*b^2*Sqrt[a + b*ArcCos[c*x]]) + (4*Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]])/(3*b^(5/2)*c) - (4*Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c*x]])/Sqrt[b]]*Sin[a/b])/(3*b^(5/2)*c)","A",8,8,12,0.6667,1,"{4622, 4720, 4624, 3306, 3305, 3351, 3304, 3352}"
201,0,0,0,0.0406992,"\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","Int[1/(x*(a + b*ArcCos[c*x])^(5/2)),x]","\int \frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \cos ^{-1}(c x)\right)^{5/2}},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCos[c*x])^(5/2)), x]","A",0,0,0,0,-1,"{}"
202,0,0,0,0.0405848,"\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","Int[1/(x^2*(a + b*ArcCos[c*x])^(5/2)),x]","\int \frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2}} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \cos ^{-1}(c x)\right)^{5/2}},x\right)",0,"Defer[Int][1/(x^2*(a + b*ArcCos[c*x])^(5/2)), x]","A",0,0,0,0,-1,"{}"
203,1,120,0,0.0669195,"\int (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(d*x)^(5/2)*(a + b*ArcCos[c*x]),x]","\frac{2 (d x)^{7/2} \left(a+b \cos ^{-1}(c x)\right)}{7 d}-\frac{20 b d^2 \sqrt{1-c^2 x^2} \sqrt{d x}}{147 c^3}+\frac{20 b d^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{147 c^{7/2}}-\frac{4 b \sqrt{1-c^2 x^2} (d x)^{5/2}}{49 c}","\frac{2 (d x)^{7/2} \left(a+b \cos ^{-1}(c x)\right)}{7 d}-\frac{20 b d^2 \sqrt{1-c^2 x^2} \sqrt{d x}}{147 c^3}+\frac{20 b d^{5/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{147 c^{7/2}}-\frac{4 b \sqrt{1-c^2 x^2} (d x)^{5/2}}{49 c}",1,"(-20*b*d^2*Sqrt[d*x]*Sqrt[1 - c^2*x^2])/(147*c^3) - (4*b*(d*x)^(5/2)*Sqrt[1 - c^2*x^2])/(49*c) + (2*(d*x)^(7/2)*(a + b*ArcCos[c*x]))/(7*d) + (20*b*d^(5/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(147*c^(7/2))","A",5,4,16,0.2500,1,"{4628, 321, 329, 221}"
204,1,124,0,0.0912919,"\int (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(d*x)^(3/2)*(a + b*ArcCos[c*x]),x]","\frac{2 (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)}{5 d}-\frac{12 b d^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}+\frac{12 b d^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}-\frac{4 b \sqrt{1-c^2 x^2} (d x)^{3/2}}{25 c}","\frac{2 (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)}{5 d}-\frac{12 b d^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}+\frac{12 b d^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{25 c^{5/2}}-\frac{4 b \sqrt{1-c^2 x^2} (d x)^{3/2}}{25 c}",1,"(-4*b*(d*x)^(3/2)*Sqrt[1 - c^2*x^2])/(25*c) + (2*(d*x)^(5/2)*(a + b*ArcCos[c*x]))/(5*d) + (12*b*d^(3/2)*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(25*c^(5/2)) - (12*b*d^(3/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(25*c^(5/2))","A",7,7,16,0.4375,1,"{4628, 321, 329, 307, 221, 1199, 424}"
205,1,88,0,0.0456004,"\int \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[Sqrt[d*x]*(a + b*ArcCos[c*x]),x]","\frac{2 (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)}{3 d}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d x}}{9 c}+\frac{4 b \sqrt{d} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{9 c^{3/2}}","\frac{2 (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)}{3 d}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d x}}{9 c}+\frac{4 b \sqrt{d} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{9 c^{3/2}}",1,"(-4*b*Sqrt[d*x]*Sqrt[1 - c^2*x^2])/(9*c) + (2*(d*x)^(3/2)*(a + b*ArcCos[c*x]))/(3*d) + (4*b*Sqrt[d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(9*c^(3/2))","A",4,4,16,0.2500,1,"{4628, 321, 329, 221}"
206,1,89,0,0.0739902,"\int \frac{a+b \cos ^{-1}(c x)}{\sqrt{d x}} \, dx","Int[(a + b*ArcCos[c*x])/Sqrt[d*x],x]","\frac{2 \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)}{d}-\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}+\frac{4 b E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}","\frac{2 \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)}{d}-\frac{4 b F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}+\frac{4 b E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{\sqrt{c} \sqrt{d}}",1,"(2*Sqrt[d*x]*(a + b*ArcCos[c*x]))/d + (4*b*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(Sqrt[c]*Sqrt[d]) - (4*b*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(Sqrt[c]*Sqrt[d])","A",6,6,16,0.3750,1,"{4628, 329, 307, 221, 1199, 424}"
207,1,55,0,0.0340409,"\int \frac{a+b \cos ^{-1}(c x)}{(d x)^{3/2}} \, dx","Int[(a + b*ArcCos[c*x])/(d*x)^(3/2),x]","-\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{d \sqrt{d x}}-\frac{4 b \sqrt{c} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{d^{3/2}}","-\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{d \sqrt{d x}}-\frac{4 b \sqrt{c} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{d^{3/2}}",1,"(-2*(a + b*ArcCos[c*x]))/(d*Sqrt[d*x]) - (4*b*Sqrt[c]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/d^(3/2)","A",3,3,16,0.1875,1,"{4628, 329, 221}"
208,1,125,0,0.0915139,"\int \frac{a+b \cos ^{-1}(c x)}{(d x)^{5/2}} \, dx","Int[(a + b*ArcCos[c*x])/(d*x)^(5/2),x]","-\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{3 d (d x)^{3/2}}+\frac{4 b c \sqrt{1-c^2 x^2}}{3 d^2 \sqrt{d x}}-\frac{4 b c^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}+\frac{4 b c^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}","-\frac{2 \left(a+b \cos ^{-1}(c x)\right)}{3 d (d x)^{3/2}}+\frac{4 b c \sqrt{1-c^2 x^2}}{3 d^2 \sqrt{d x}}-\frac{4 b c^{3/2} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}+\frac{4 b c^{3/2} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{d x}}{\sqrt{d}}\right)\right|-1\right)}{3 d^{5/2}}",1,"(4*b*c*Sqrt[1 - c^2*x^2])/(3*d^2*Sqrt[d*x]) - (2*(a + b*ArcCos[c*x]))/(3*d*(d*x)^(3/2)) + (4*b*c^(3/2)*EllipticE[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(3*d^(5/2)) - (4*b*c^(3/2)*EllipticF[ArcSin[(Sqrt[c]*Sqrt[d*x])/Sqrt[d]], -1])/(3*d^(5/2))","A",7,7,16,0.4375,1,"{4628, 325, 329, 307, 221, 1199, 424}"
209,1,109,0,0.1390399,"\int (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^(5/2)*(a + b*ArcCos[c*x])^2,x]","\frac{16 b^2 c^2 (d x)^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};c^2 x^2\right)}{693 d^3}+\frac{8 b c (d x)^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{63 d^2}+\frac{2 (d x)^{7/2} \left(a+b \cos ^{-1}(c x)\right)^2}{7 d}","\frac{16 b^2 c^2 (d x)^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};c^2 x^2\right)}{693 d^3}+\frac{8 b c (d x)^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{63 d^2}+\frac{2 (d x)^{7/2} \left(a+b \cos ^{-1}(c x)\right)^2}{7 d}",1,"(2*(d*x)^(7/2)*(a + b*ArcCos[c*x])^2)/(7*d) + (8*b*c*(d*x)^(9/2)*(a + b*ArcCos[c*x])*Hypergeometric2F1[1/2, 9/4, 13/4, c^2*x^2])/(63*d^2) + (16*b^2*c^2*(d*x)^(11/2)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, c^2*x^2])/(693*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
210,1,109,0,0.140138,"\int (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^(3/2)*(a + b*ArcCos[c*x])^2,x]","\frac{16 b^2 c^2 (d x)^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};c^2 x^2\right)}{315 d^3}+\frac{8 b c (d x)^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{35 d^2}+\frac{2 (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)^2}{5 d}","\frac{16 b^2 c^2 (d x)^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};c^2 x^2\right)}{315 d^3}+\frac{8 b c (d x)^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{35 d^2}+\frac{2 (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)^2}{5 d}",1,"(2*(d*x)^(5/2)*(a + b*ArcCos[c*x])^2)/(5*d) + (8*b*c*(d*x)^(7/2)*(a + b*ArcCos[c*x])*Hypergeometric2F1[1/2, 7/4, 11/4, c^2*x^2])/(35*d^2) + (16*b^2*c^2*(d*x)^(9/2)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, c^2*x^2])/(315*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
211,1,109,0,0.1340419,"\int \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d*x]*(a + b*ArcCos[c*x])^2,x]","\frac{16 b^2 c^2 (d x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{105 d^3}+\frac{8 b c (d x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{15 d^2}+\frac{2 (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 d}","\frac{16 b^2 c^2 (d x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{105 d^3}+\frac{8 b c (d x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{15 d^2}+\frac{2 (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2}{3 d}",1,"(2*(d*x)^(3/2)*(a + b*ArcCos[c*x])^2)/(3*d) + (8*b*c*(d*x)^(5/2)*(a + b*ArcCos[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(15*d^2) + (16*b^2*c^2*(d*x)^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(105*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
212,1,107,0,0.1245879,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{d x}} \, dx","Int[(a + b*ArcCos[c*x])^2/Sqrt[d*x],x]","\frac{16 b^2 c^2 (d x)^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};c^2 x^2\right)}{15 d^3}+\frac{8 b c (d x)^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 d^2}+\frac{2 \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2}{d}","\frac{16 b^2 c^2 (d x)^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};c^2 x^2\right)}{15 d^3}+\frac{8 b c (d x)^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 d^2}+\frac{2 \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2}{d}",1,"(2*Sqrt[d*x]*(a + b*ArcCos[c*x])^2)/d + (8*b*c*(d*x)^(3/2)*(a + b*ArcCos[c*x])*Hypergeometric2F1[1/2, 3/4, 7/4, c^2*x^2])/(3*d^2) + (16*b^2*c^2*(d*x)^(5/2)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, c^2*x^2])/(15*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
213,1,105,0,0.1301466,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2}{(d x)^{3/2}} \, dx","Int[(a + b*ArcCos[c*x])^2/(d*x)^(3/2),x]","-\frac{16 b^2 c^2 (d x)^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};c^2 x^2\right)}{3 d^3}-\frac{8 b c \sqrt{d x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{d^2}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^2}{d \sqrt{d x}}","-\frac{16 b^2 c^2 (d x)^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};c^2 x^2\right)}{3 d^3}-\frac{8 b c \sqrt{d x} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{d^2}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^2}{d \sqrt{d x}}",1,"(-2*(a + b*ArcCos[c*x])^2)/(d*Sqrt[d*x]) - (8*b*c*Sqrt[d*x]*(a + b*ArcCos[c*x])*Hypergeometric2F1[1/4, 1/2, 5/4, c^2*x^2])/d^2 - (16*b^2*c^2*(d*x)^(3/2)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, c^2*x^2])/(3*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
214,1,109,0,0.1417377,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2}{(d x)^{5/2}} \, dx","Int[(a + b*ArcCos[c*x])^2/(d*x)^(5/2),x]","\frac{16 b^2 c^2 \sqrt{d x} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};c^2 x^2\right)}{3 d^3}+\frac{8 b c \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 d^2 \sqrt{d x}}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^2}{3 d (d x)^{3/2}}","\frac{16 b^2 c^2 \sqrt{d x} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};c^2 x^2\right)}{3 d^3}+\frac{8 b c \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 d^2 \sqrt{d x}}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^2}{3 d (d x)^{3/2}}",1,"(-2*(a + b*ArcCos[c*x])^2)/(3*d*(d*x)^(3/2)) + (8*b*c*(a + b*ArcCos[c*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, c^2*x^2])/(3*d^2*Sqrt[d*x]) + (16*b^2*c^2*Sqrt[d*x]*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, c^2*x^2])/(3*d^3)","A",2,2,18,0.1111,1,"{4628, 4712}"
215,0,0,0,0.1643838,"\int (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","Int[(d*x)^(3/2)*(a + b*ArcCos[c*x])^3,x]","\int (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","\frac{6 b c \text{Int}\left(\frac{(d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{5 d}+\frac{2 (d x)^{5/2} \left(a+b \cos ^{-1}(c x)\right)^3}{5 d}",0,"(2*(d*x)^(5/2)*(a + b*ArcCos[c*x])^3)/(5*d) + (6*b*c*Defer[Int][((d*x)^(5/2)*(a + b*ArcCos[c*x])^2)/Sqrt[1 - c^2*x^2], x])/(5*d)","A",0,0,0,0,-1,"{}"
216,0,0,0,0.1665529,"\int \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","Int[Sqrt[d*x]*(a + b*ArcCos[c*x])^3,x]","\int \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^3 \, dx","\frac{2 b c \text{Int}\left(\frac{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{d}+\frac{2 (d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^3}{3 d}",0,"(2*(d*x)^(3/2)*(a + b*ArcCos[c*x])^3)/(3*d) + (2*b*c*Defer[Int][((d*x)^(3/2)*(a + b*ArcCos[c*x])^2)/Sqrt[1 - c^2*x^2], x])/d","A",0,0,0,0,-1,"{}"
217,0,0,0,0.1465736,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{\sqrt{d x}} \, dx","Int[(a + b*ArcCos[c*x])^3/Sqrt[d*x],x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{\sqrt{d x}} \, dx","\frac{6 b c \text{Int}\left(\frac{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2}},x\right)}{d}+\frac{2 \sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^3}{d}",0,"(2*Sqrt[d*x]*(a + b*ArcCos[c*x])^3)/d + (6*b*c*Defer[Int][(Sqrt[d*x]*(a + b*ArcCos[c*x])^2)/Sqrt[1 - c^2*x^2], x])/d","A",0,0,0,0,-1,"{}"
218,0,0,0,0.1575221,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{(d x)^{3/2}} \, dx","Int[(a + b*ArcCos[c*x])^3/(d*x)^(3/2),x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{(d x)^{3/2}} \, dx","-\frac{6 b c \text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2} \sqrt{d x}},x\right)}{d}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^3}{d \sqrt{d x}}",0,"(-2*(a + b*ArcCos[c*x])^3)/(d*Sqrt[d*x]) - (6*b*c*Defer[Int][(a + b*ArcCos[c*x])^2/(Sqrt[d*x]*Sqrt[1 - c^2*x^2]), x])/d","A",0,0,0,0,-1,"{}"
219,0,0,0,0.1671259,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{(d x)^{5/2}} \, dx","Int[(a + b*ArcCos[c*x])^3/(d*x)^(5/2),x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^3}{(d x)^{5/2}} \, dx","-\frac{2 b c \text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^2}{\sqrt{1-c^2 x^2} (d x)^{3/2}},x\right)}{d}-\frac{2 \left(a+b \cos ^{-1}(c x)\right)^3}{3 d (d x)^{3/2}}",0,"(-2*(a + b*ArcCos[c*x])^3)/(3*d*(d*x)^(3/2)) - (2*b*c*Defer[Int][(a + b*ArcCos[c*x])^2/((d*x)^(3/2)*Sqrt[1 - c^2*x^2]), x])/d","A",0,0,0,0,-1,"{}"
220,0,0,0,0.0282532,"\int \frac{(d x)^{3/2}}{a+b \cos ^{-1}(c x)} \, dx","Int[(d*x)^(3/2)/(a + b*ArcCos[c*x]),x]","\int \frac{(d x)^{3/2}}{a+b \cos ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^{3/2}}{a+b \cos ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^(3/2)/(a + b*ArcCos[c*x]), x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.0250688,"\int \frac{\sqrt{d x}}{a+b \cos ^{-1}(c x)} \, dx","Int[Sqrt[d*x]/(a + b*ArcCos[c*x]),x]","\int \frac{\sqrt{d x}}{a+b \cos ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{d x}}{a+b \cos ^{-1}(c x)},x\right)",0,"Defer[Int][Sqrt[d*x]/(a + b*ArcCos[c*x]), x]","A",0,0,0,0,-1,"{}"
222,0,0,0,0.02601,"\int \frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[d*x]*(a + b*ArcCos[c*x])),x]","\int \frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(Sqrt[d*x]*(a + b*ArcCos[c*x])), x]","A",0,0,0,0,-1,"{}"
223,0,0,0,0.0290772,"\int \frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)} \, dx","Int[1/((d*x)^(3/2)*(a + b*ArcCos[c*x])),x]","\int \frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d*x)^(3/2)*(a + b*ArcCos[c*x])), x]","A",0,0,0,0,-1,"{}"
224,0,0,0,0.0269893,"\int \frac{(d x)^{3/2}}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[(d*x)^(3/2)/(a + b*ArcCos[c*x])^2,x]","\int \frac{(d x)^{3/2}}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^{3/2}}{\left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^(3/2)/(a + b*ArcCos[c*x])^2, x]","A",0,0,0,0,-1,"{}"
225,0,0,0,0.0233537,"\int \frac{\sqrt{d x}}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[d*x]/(a + b*ArcCos[c*x])^2,x]","\int \frac{\sqrt{d x}}{\left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{d x}}{\left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[d*x]/(a + b*ArcCos[c*x])^2, x]","A",0,0,0,0,-1,"{}"
226,0,0,0,0.0240853,"\int \frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[d*x]*(a + b*ArcCos[c*x])^2),x]","\int \frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{d x} \left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(Sqrt[d*x]*(a + b*ArcCos[c*x])^2), x]","A",0,0,0,0,-1,"{}"
227,0,0,0,0.0285917,"\int \frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","Int[1/((d*x)^(3/2)*(a + b*ArcCos[c*x])^2),x]","\int \frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d x)^{3/2} \left(a+b \cos ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d*x)^(3/2)*(a + b*ArcCos[c*x])^2), x]","A",0,0,0,0,-1,"{}"