1,1,670,0,0.7051861,"\int (f+g x)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]),x]","-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^4}+\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}-\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{1-c^2 x^2}}+\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}+\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}-\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}","-\frac{f^2 g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^4}+\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{1-c^2 x^2}}-\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{1-c^2 x^2}}+\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}+\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}-\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{1-c^2 x^2}}-\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{1-c^2 x^2}}",1,"-((b*f^2*g*x*Sqrt[d - c^2*d*x^2])/(c*Sqrt[1 - c^2*x^2])) - (2*b*g^3*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[1 - c^2*x^2]) + (b*c*f^3*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) - (3*b*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[1 - c^2*x^2]) + (b*c*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(3*Sqrt[1 - c^2*x^2]) - (b*g^3*x^3*Sqrt[d - c^2*d*x^2])/(45*c*Sqrt[1 - c^2*x^2]) + (3*b*c*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (b*c*g^3*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/2 - (3*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(8*c^2) + (3*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/4 - (f^2*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/c^2 - (g^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*c^4) + (g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*c^4) - (f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2]) - (3*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",16,12,31,0.3871,1,"{4778, 4764, 4648, 4642, 30, 4678, 4698, 4708, 266, 43, 4690, 12}"
2,1,450,0,0.5297491,"\int (f+g x)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]),x]","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}+\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{1-c^2 x^2}}+\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}+\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{1-c^2 x^2}}",1,"(-2*b*f*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[1 - c^2*x^2]) + (b*c*f^2*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) - (b*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[1 - c^2*x^2]) + (2*b*c*f*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) + (b*c*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/2 - (g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(8*c^2) + (g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/4 - (2*f*g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*c^2) - (f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2]) - (g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*c^3*Sqrt[1 - c^2*x^2])","A",13,8,31,0.2581,1,"{4778, 4764, 4648, 4642, 30, 4678, 4698, 4708}"
3,1,238,0,0.251246,"\int (f+g x) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]),x]","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^2}+\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c \sqrt{1-c^2 x^2}}-\frac{g \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 c^2}+\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{1-c^2 x^2}}+\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{1-c^2 x^2}}-\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{1-c^2 x^2}}",1,"-(b*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[1 - c^2*x^2]) + (b*c*f*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[1 - c^2*x^2]) + (b*c*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[1 - c^2*x^2]) + (f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/2 - (g*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*c^2) - (f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*c*Sqrt[1 - c^2*x^2])","A",8,6,29,0.2069,1,"{4778, 4764, 4648, 4642, 30, 4678}"
4,1,725,0,1.8589081,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{f+g x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(f + g*x),x]","-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{1-c^2 x^2} (f+g x)}-\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c (f+g x)}-\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g \sqrt{1-c^2 x^2}}-\frac{a \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tan ^{-1}\left(\frac{c^2 f x+g}{\sqrt{1-c^2 x^2} \sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{a \sqrt{d-c^2 d x^2}}{g}-\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cos ^{-1}(c x) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cos ^{-1}(c x) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g}","-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{1-c^2 x^2} (f+g x)}-\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c (f+g x)}-\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g \sqrt{1-c^2 x^2}}-\frac{a \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tan ^{-1}\left(\frac{c^2 f x+g}{\sqrt{1-c^2 x^2} \sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{a \sqrt{d-c^2 d x^2}}{g}-\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cos ^{-1}(c x) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{i b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cos ^{-1}(c x) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{1-c^2 x^2}}+\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{1-c^2 x^2}}+\frac{b \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g}",1,"(a*Sqrt[d - c^2*d*x^2])/g + (b*c*x*Sqrt[d - c^2*d*x^2])/(g*Sqrt[1 - c^2*x^2]) + (b*Sqrt[d - c^2*d*x^2]*ArcCos[c*x])/g - (c*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*g*Sqrt[1 - c^2*x^2]) + ((1 - (c^2*f^2)/g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*(f + g*x)*Sqrt[1 - c^2*x^2]) - (Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*(f + g*x)) - (a*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (I*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) + (I*b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[1 - c^2*x^2]) - (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[1 - c^2*x^2]) + (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[1 - c^2*x^2])","A",22,19,31,0.6129,1,"{4778, 4766, 683, 4758, 6742, 725, 204, 1654, 12, 4800, 4798, 4678, 8, 4774, 3321, 2264, 2190, 2279, 2391}"
5,1,851,0,2.6936658,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{(f+g x)^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(f + g*x)^2,x]","\frac{b f^2 \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}-\frac{a f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}+\frac{a f \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{i b f \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{i b f \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}-\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b (f+g x)^2 c}-\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) (f+g x)^2 \sqrt{1-c^2 x^2} c}","\frac{b f^2 \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}-\frac{a f^2 \sqrt{d-c^2 d x^2} \sin ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{1-c^2 x^2}}+\frac{a f \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{i b f \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{i b f \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{1-c^2 x^2}}-\frac{b \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}-\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b (f+g x)^2 c}-\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) (f+g x)^2 \sqrt{1-c^2 x^2} c}",1,"-((a*Sqrt[d - c^2*d*x^2])/(g*(f + g*x))) - (b*Sqrt[d - c^2*d*x^2]*ArcCos[c*x])/(g*(f + g*x)) + (b*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]^2)/(2*g^2*(c^2*f^2 - g^2)*Sqrt[1 - c^2*x^2]) - ((g + c^2*f*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*(c^2*f^2 - g^2)*(f + g*x)^2*Sqrt[1 - c^2*x^2]) - (Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*(f + g*x)^2) - (a*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcSin[c*x])/(g^2*(c^2*f^2 - g^2)*Sqrt[1 - c^2*x^2]) + (a*c^2*f*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) + (I*b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) - (I*b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) - (b*c*Sqrt[d - c^2*d*x^2]*Log[f + g*x])/(g^2*Sqrt[1 - c^2*x^2]) + (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2]) - (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])","A",35,22,31,0.7097,1,"{4778, 4766, 37, 4756, 12, 1651, 844, 216, 725, 204, 4800, 4798, 4642, 4774, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
6,1,959,0,0.9617503,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCos[c*x]),x]","-\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{1-c^2 x^2}}+\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{1-c^2 x^2}}-\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{1-c^2 x^2}}+\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3-\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{1-c^2 x^2}}+\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{1-c^2 x^2}}+\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{1-c^2 x^2}}-\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}-\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{1-c^2 x^2}}-\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}","-\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{1-c^2 x^2}}+\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{1-c^2 x^2}}-\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{1-c^2 x^2}}+\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{1-c^2 x^2}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3-\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{1-c^2 x^2}}+\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{1-c^2 x^2}}+\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{1-c^2 x^2}}-\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{1-c^2 x^2}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{1-c^2 x^2}}-\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{1-c^2 x^2}}-\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}+\frac{d g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^4}-\frac{3 d f^2 g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}",1,"(-3*b*d*f^2*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) - (2*b*d*g^3*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[1 - c^2*x^2]) + (5*b*c*d*f^3*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (3*b*d*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[1 - c^2*x^2]) + (2*b*c*d*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(5*Sqrt[1 - c^2*x^2]) - (b*d*g^3*x^3*Sqrt[d - c^2*d*x^2])/(105*c*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f^3*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (7*b*c*d*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(32*Sqrt[1 - c^2*x^2]) - (3*b*c^3*d*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (8*b*c*d*g^3*x^5*Sqrt[d - c^2*d*x^2])/(175*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(12*Sqrt[1 - c^2*x^2]) - (b*c^3*d*g^3*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) + (3*d*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 - (3*d*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(16*c^2) + (3*d*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 + (d*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/4 + (d*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/2 - (3*d*f^2*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*c^2) - (d*g^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*c^4) + (d*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(7*c^4) - (3*d*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2]) - (3*d*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(32*b*c^3*Sqrt[1 - c^2*x^2])","A",24,17,31,0.5484,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 4678, 194, 4700, 4698, 4708, 266, 43, 4690, 12, 373}"
7,1,680,0,0.735067,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCos[c*x]),x]","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}-\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}-\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}+\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{2 d f g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{1-c^2 x^2}}-\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}-\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}-\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{1-c^2 x^2}}+\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{1-c^2 x^2}}",1,"(-2*b*d*f*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) + (5*b*c*d*f^2*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (b*d*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[1 - c^2*x^2]) + (4*b*c*d*f*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (7*b*c*d*g^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (2*b*c^3*d*f*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) - (b*c^3*d*g^2*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[1 - c^2*x^2]) + (3*d*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 - (d*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(16*c^2) + (d*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 + (d*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/4 + (d*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/6 - (2*d*f*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*c^2) - (3*d*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2]) - (d*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(32*b*c^3*Sqrt[1 - c^2*x^2])","A",20,12,31,0.3871,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 4678, 194, 4700, 4698, 4708}"
8,1,370,0,0.334807,"\int (f+g x) \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCos[c*x]),x]","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}-\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}-\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{1}{4} d f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{16 b c \sqrt{1-c^2 x^2}}-\frac{d g \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 c^2}-\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}+\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{1-c^2 x^2}}-\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{1-c^2 x^2}}+\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{1-c^2 x^2}}-\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{1-c^2 x^2}}",1,"-(b*d*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[1 - c^2*x^2]) + (5*b*c*d*f*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) + (2*b*c*d*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[1 - c^2*x^2]) - (b*c^3*d*f*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[1 - c^2*x^2]) - (b*c^3*d*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[1 - c^2*x^2]) + (3*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 + (d*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/4 - (d*g*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*c^2) - (3*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*c*Sqrt[1 - c^2*x^2])","A",12,9,29,0.3103,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 4678, 194}"
9,1,1064,0,2.2800008,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cos ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCos[c*x]))/(f + g*x),x]","-\frac{b d x^3 \sqrt{d-c^2 d x^2} c^3}{9 g \sqrt{1-c^2 x^2}}+\frac{b d f x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{2 g^2}+\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{1-c^2 x^2}}-\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{d-c^2 d x^2} c}{3 g \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g}+\frac{a d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}+\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}","-\frac{b d x^3 \sqrt{d-c^2 d x^2} c^3}{9 g \sqrt{1-c^2 x^2}}+\frac{b d f x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^2 \sqrt{1-c^2 x^2}}+\frac{d f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{2 g^2}+\frac{d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{1-c^2 x^2}}-\frac{d f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) x \sqrt{d-c^2 d x^2} c}{g^3 \sqrt{1-c^2 x^2}}+\frac{b d x \sqrt{d-c^2 d x^2} c}{3 g \sqrt{1-c^2 x^2}}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g^3}+\frac{d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g}+\frac{a d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{i b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{1-c^2 x^2}}+\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{b d \left(c^2 f^2-g^2\right)^{3/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{1-c^2 x^2}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{d (c f-g) (c f+g) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}+\frac{d \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{1-c^2 x^2} c}",1,"-((a*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2])/g^3) + (b*c*d*x*Sqrt[d - c^2*d*x^2])/(3*g*Sqrt[1 - c^2*x^2]) - (b*c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2])/(g^3*Sqrt[1 - c^2*x^2]) + (b*c^3*d*f*x^2*Sqrt[d - c^2*d*x^2])/(4*g^2*Sqrt[1 - c^2*x^2]) - (b*c^3*d*x^3*Sqrt[d - c^2*d*x^2])/(9*g*Sqrt[1 - c^2*x^2]) - (b*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2]*ArcCos[c*x])/g^3 + (c^2*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(2*g^2) + (d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*g) - (c*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*g^2*Sqrt[1 - c^2*x^2]) + (c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*g^3*Sqrt[1 - c^2*x^2]) + (d*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*g^4*(f + g*x)*Sqrt[1 - c^2*x^2]) + (d*(c*f - g)*(c*f + g)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*g^2*(f + g*x)) + (a*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (I*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) - (I*b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[1 - c^2*x^2]) + (b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^4*Sqrt[1 - c^2*x^2]) - (b*d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^4*Sqrt[1 - c^2*x^2])","A",29,23,31,0.7419,1,"{4778, 4768, 4648, 4642, 30, 4678, 4766, 683, 4758, 6742, 725, 204, 1654, 12, 4800, 4798, 8, 4774, 3321, 2264, 2190, 2279, 2391}"
10,1,1281,0,1.1774559,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCos[c*x]),x]","\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{1-c^2 x^2}}+\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}-\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{1-c^2 x^2}}+\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{1-c^2 x^2}}+\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{1-c^2 x^2}}-\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}-\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}+\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3-\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{1-c^2 x^2}}+\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}-\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}-\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}+\frac{d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}","\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{1-c^2 x^2}}+\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}-\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{1-c^2 x^2}}+\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{1-c^2 x^2}}+\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{1-c^2 x^2}}-\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}-\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}+\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{1-c^2 x^2}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3-\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{1-c^2 x^2}}+\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}-\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{1-c^2 x^2}}-\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}+\frac{d^2 g^3 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^4}-\frac{3 d^2 f^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^3 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}",1,"(-3*b*d^2*f^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) - (2*b*d^2*g^3*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[1 - c^2*x^2]) + (25*b*c*d^2*f^3*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (15*b*d^2*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) + (3*b*c*d^2*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) - (b*d^2*g^3*x^3*Sqrt[d - c^2*d*x^2])/(189*c*Sqrt[1 - c^2*x^2]) - (5*b*c^3*d^2*f^3*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (59*b*c*d^2*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(256*Sqrt[1 - c^2*x^2]) - (9*b*c^3*d^2*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) + (b*c*d^2*g^3*x^5*Sqrt[d - c^2*d*x^2])/(21*Sqrt[1 - c^2*x^2]) - (17*b*c^3*d^2*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (3*b*c^5*d^2*f^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - (19*b*c^3*d^2*g^3*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[1 - c^2*x^2]) + (3*b*c^5*d^2*f*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*g^3*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[1 - c^2*x^2]) - (b*d^2*f^3*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/16 - (15*d^2*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(128*c^2) + (15*d^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/64 + (5*d^2*f^3*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/24 + (5*d^2*f*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/16 + (d^2*f^3*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/6 + (3*d^2*f*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 - (3*d^2*f^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(7*c^2) - (d^2*g^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(7*c^4) + (d^2*g^3*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(9*c^4) - (5*d^2*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2]) - (15*d^2*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(256*b*c^3*Sqrt[1 - c^2*x^2])","A",30,18,31,0.5806,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 261, 4678, 194, 4700, 4698, 4708, 266, 43, 4690, 12, 373}"
11,1,940,0,0.95887,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCos[c*x]),x]","\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}+\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{1-c^2 x^2}}-\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}-\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}+\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}-\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}","\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{1-c^2 x^2}}+\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{1-c^2 x^2}}-\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{1-c^2 x^2}}-\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{1-c^2 x^2}}-\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{1-c^2 x^2}}+\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{1-c^2 x^2}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x^3+\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{1-c^2 x^2}}-\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{1-c^2 x^2}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) x-\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{1-c^2 x^2}}-\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{1-c^2 x^2}}-\frac{2 d^2 f g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^2 \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}",1,"(-2*b*d^2*f*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) + (25*b*c*d^2*f^2*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (5*b*d^2*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[1 - c^2*x^2]) + (2*b*c*d^2*f*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) - (5*b*c^3*d^2*f^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (59*b*c*d^2*g^2*x^4*Sqrt[d - c^2*d*x^2])/(768*Sqrt[1 - c^2*x^2]) - (6*b*c^3*d^2*f*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) - (17*b*c^3*d^2*g^2*x^6*Sqrt[d - c^2*d*x^2])/(288*Sqrt[1 - c^2*x^2]) + (2*b*c^5*d^2*f*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[1 - c^2*x^2]) - (b*d^2*f^2*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/16 - (5*d^2*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(128*c^2) + (5*d^2*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/64 + (5*d^2*f^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/24 + (5*d^2*g^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/48 + (d^2*f^2*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/6 + (d^2*g^2*x^3*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/8 - (2*d^2*f*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(7*c^2) - (5*d^2*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2]) - (5*d^2*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(256*b*c^3*Sqrt[1 - c^2*x^2])","A",26,15,31,0.4839,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 261, 4678, 194, 4700, 4698, 4708, 266, 43}"
12,1,517,0,0.4029642,"\int (f+g x) \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cos ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCos[c*x]),x]","\frac{1}{6} d^2 f x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}+\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}-\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}+\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}-\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}","\frac{1}{6} d^2 f x \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)-\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{32 b c \sqrt{1-c^2 x^2}}-\frac{d^2 g \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{7 c^2}-\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}+\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{1-c^2 x^2}}-\frac{b d^2 f \left(1-c^2 x^2\right)^{5/2} \sqrt{d-c^2 d x^2}}{36 c}+\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{1-c^2 x^2}}-\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{1-c^2 x^2}}+\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{1-c^2 x^2}}-\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{1-c^2 x^2}}",1,"-(b*d^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[1 - c^2*x^2]) + (25*b*c*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) + (b*c*d^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[1 - c^2*x^2]) - (5*b*c^3*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[1 - c^2*x^2]) - (3*b*c^3*d^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[1 - c^2*x^2]) - (b*d^2*f*(1 - c^2*x^2)^(5/2)*Sqrt[d - c^2*d*x^2])/(36*c) + (5*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/16 + (5*d^2*f*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/24 + (d^2*f*x*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/6 - (d^2*g*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(7*c^2) - (5*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(32*b*c*Sqrt[1 - c^2*x^2])","A",14,10,29,0.3448,1,"{4778, 4764, 4650, 4648, 4642, 30, 14, 261, 4678, 194}"
13,1,1637,0,2.7299979,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cos ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCos[c*x]))/(f + g*x),x]","\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^4}{4 g^2}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{1-c^2 x^2}}-\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{1-c^2 x^2}}-\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{8 g^2}+\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{1-c^2 x^2}}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{1-c^2 x^2}}+\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{1-c^2 x^2}}-\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g^5}+\frac{d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 g}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}-\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}","\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{1-c^2 x^2}}-\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^4}{4 g^2}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{1-c^2 x^2}}-\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{1-c^2 x^2}}-\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{1-c^2 x^2}}+\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{1-c^2 x^2}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right) c^2}{8 g^2}+\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{1-c^2 x^2}}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{1-c^2 x^2}}+\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{1-c^2 x^2}}-\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \cos ^{-1}(c x)}{g^5}+\frac{d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{5 g}-\frac{d^2 \left(c^2 f^2-2 g^2\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{1-c^2 x^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{i b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cos ^{-1}(c x) \log \left(\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{1-c^2 x^2}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{i \cos ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{1-c^2 x^2}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2}}{g^5}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}-\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{1-c^2 x^2} c}",1,"(a*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2])/g^5 - (2*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*g*Sqrt[1 - c^2*x^2]) - (b*c*d^2*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2])/(3*g^3*Sqrt[1 - c^2*x^2]) + (b*c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2])/(g^5*Sqrt[1 - c^2*x^2]) + (b*c^3*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*f*(c^2*f^2 - 2*g^2)*x^2*Sqrt[d - c^2*d*x^2])/(4*g^4*Sqrt[1 - c^2*x^2]) - (b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2])/(45*g*Sqrt[1 - c^2*x^2]) + (b*c^3*d^2*(c^2*f^2 - 2*g^2)*x^3*Sqrt[d - c^2*d*x^2])/(9*g^3*Sqrt[1 - c^2*x^2]) - (b*c^5*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[1 - c^2*x^2]) + (b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2])/(25*g*Sqrt[1 - c^2*x^2]) + (b*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*ArcCos[c*x])/g^5 + (c^2*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(8*g^2) - (c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(2*g^4) - (c^4*d^2*f*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(4*g^2) - (d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*g) - (d^2*(c^2*f^2 - 2*g^2)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(3*g^3) + (d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x]))/(5*g) + (c*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(16*b*g^2*Sqrt[1 - c^2*x^2]) + (c*d^2*f*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*g^4*Sqrt[1 - c^2*x^2]) - (c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*g^5*Sqrt[1 - c^2*x^2]) - (d^2*(c^2*f^2 - g^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*g^6*(f + g*x)*Sqrt[1 - c^2*x^2]) - (d^2*(c^2*f^2 - g^2)^2*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*g^4*(f + g*x)) - (a*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcTan[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[1 - c^2*x^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (I*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) + (I*b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcCos[c*x]*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[1 - c^2*x^2]) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^6*Sqrt[1 - c^2*x^2]) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^6*Sqrt[1 - c^2*x^2])","A",37,28,31,0.9032,1,"{4778, 4768, 4648, 4642, 30, 4678, 4698, 4708, 266, 43, 4690, 12, 4766, 683, 4758, 6742, 725, 204, 1654, 4800, 4798, 8, 4774, 3321, 2264, 2190, 2279, 2391}"
14,1,450,0,0.5852733,"\int \frac{(f+g x)^3 \left(a+b \cos ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^3*(a + b*ArcCos[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b f^2 g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}-\frac{b g^3 x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b g^3 x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{3 f^2 g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{f^3 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b f^2 g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{3 b f g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}-\frac{b g^3 x^3 \sqrt{1-c^2 x^2}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b g^3 x \sqrt{1-c^2 x^2}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(-3*b*f^2*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) - (2*b*g^3*x*Sqrt[1 - c^2*x^2])/(3*c^3*Sqrt[d - c^2*d*x^2]) - (3*b*f*g^2*x^2*Sqrt[1 - c^2*x^2])/(4*c*Sqrt[d - c^2*d*x^2]) - (b*g^3*x^3*Sqrt[1 - c^2*x^2])/(9*c*Sqrt[d - c^2*d*x^2]) - (3*f^2*g*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (2*g^3*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(3*c^4*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*x*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) - (g^3*x^2*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(3*c^2*Sqrt[d - c^2*d*x^2]) - (f^3*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",13,7,31,0.2258,1,"{4778, 4764, 4642, 4678, 8, 4708, 30}"
15,1,270,0,0.4361498,"\int \frac{(f+g x)^2 \left(a+b \cos ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^2*(a + b*ArcCos[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b f g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{b g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}","-\frac{f^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b f g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}-\frac{b g^2 x^2 \sqrt{1-c^2 x^2}}{4 c \sqrt{d-c^2 d x^2}}",1,"(-2*b*f*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2]) - (b*g^2*x^2*Sqrt[1 - c^2*x^2])/(4*c*Sqrt[d - c^2*d*x^2]) - (2*f*g*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (g^2*x*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) - (f^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) - (g^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",9,7,31,0.2258,1,"{4778, 4764, 4642, 4678, 8, 4708, 30}"
16,1,127,0,0.2233339,"\int \frac{(f+g x) \left(a+b \cos ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)*(a + b*ArcCos[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}","-\frac{f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \sqrt{1-c^2 x^2}}{c \sqrt{d-c^2 d x^2}}",1,"-((b*g*x*Sqrt[1 - c^2*x^2])/(c*Sqrt[d - c^2*d*x^2])) - (g*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (f*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2])","A",6,5,29,0.1724,1,"{4778, 4764, 4642, 4678, 8}"
17,1,370,0,0.6060067,"\int \frac{a+b \cos ^{-1}(c x)}{(f+g x) \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCos[c*x])/((f + g*x)*Sqrt[d - c^2*d*x^2]),x]","\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}","\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{b \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{i \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{i \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}",1,"(I*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (I*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[1 - c^2*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[1 - c^2*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2])","A",10,7,31,0.2258,1,"{4778, 4774, 3321, 2264, 2190, 2279, 2391}"
18,1,496,0,0.7215454,"\int \frac{a+b \cos ^{-1}(c x)}{(f+g x)^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCos[c*x])/((f + g*x)^2*Sqrt[d - c^2*d*x^2]),x]","\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c \sqrt{1-c^2 x^2} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}","\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g \left(1-c^2 x^2\right) \left(a+b \cos ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}+\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{i c^2 f \sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right) \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c \sqrt{1-c^2 x^2} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}",1,"(g*(1 - c^2*x^2)*(a + b*ArcCos[c*x]))/((c^2*f^2 - g^2)*(f + g*x)*Sqrt[d - c^2*d*x^2]) + (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (I*c^2*f*Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[1 - c^2*x^2]*Log[f + g*x])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) + (b*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (b*c^2*f*Sqrt[1 - c^2*x^2]*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2])","A",13,10,31,0.3226,1,"{4778, 4774, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
19,0,0,0,0.1921772,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCos[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \cos ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}},x\right)",0,"Defer[Int][((a + b*ArcCos[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2], x]","A",0,0,0,0,-1,"{}"
20,1,496,0,0.7914638,"\int \frac{\left(a+b \cos ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCos[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{2 b m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{2 b m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{2 i b^2 m \text{PolyLog}\left(4,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{2 i b^2 m \text{PolyLog}\left(4,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^4}{12 b^2 c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^3 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{3 b c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^3 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{3 b c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}","-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{2 b m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{2 b m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{2 i b^2 m \text{PolyLog}\left(4,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{2 i b^2 m \text{PolyLog}\left(4,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^4}{12 b^2 c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^3 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{3 b c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^3 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{3 b c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}",1,"((-I/12)*m*(a + b*ArcCos[c*x])^4)/(b^2*c) + (m*(a + b*ArcCos[c*x])^3*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(3*b*c) + (m*(a + b*ArcCos[c*x])^3*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(3*b*c) - ((a + b*ArcCos[c*x])^3*Log[h*(f + g*x)^m])/(3*b*c) - (I*m*(a + b*ArcCos[c*x])^2*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/c - (I*m*(a + b*ArcCos[c*x])^2*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/c + (2*b*m*(a + b*ArcCos[c*x])*PolyLog[3, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/c + (2*b*m*(a + b*ArcCos[c*x])*PolyLog[3, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/c + ((2*I)*b^2*m*PolyLog[4, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/c + ((2*I)*b^2*m*PolyLog[4, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/c","A",13,9,35,0.2571,1,"{4642, 4780, 4742, 4520, 2190, 2531, 6609, 2282, 6589}"
21,1,374,0,0.6112721,"\int \frac{\left(a+b \cos ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCos[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","-\frac{i m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^3}{6 b^2 c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^2 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{2 b c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^2 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{2 b c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}","-\frac{i m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{i m \left(a+b \cos ^{-1}(c x)\right)^3}{6 b^2 c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^2 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{2 b c}+\frac{m \left(a+b \cos ^{-1}(c x)\right)^2 \log \left(1+\frac{g e^{i \cos ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{2 b c}-\frac{\left(a+b \cos ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}",1,"((-I/6)*m*(a + b*ArcCos[c*x])^3)/(b^2*c) + (m*(a + b*ArcCos[c*x])^2*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(2*b*c) + (m*(a + b*ArcCos[c*x])^2*Log[1 + (E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(2*b*c) - ((a + b*ArcCos[c*x])^2*Log[h*(f + g*x)^m])/(2*b*c) - (I*m*(a + b*ArcCos[c*x])*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/c - (I*m*(a + b*ArcCos[c*x])*PolyLog[2, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/c + (b*m*PolyLog[3, -((E^(I*ArcCos[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/c + (b*m*PolyLog[3, -((E^(I*ArcCos[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/c","A",11,8,33,0.2424,1,"{4642, 4780, 4742, 4520, 2190, 2531, 2282, 6589}"
22,1,237,0,0.338099,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[Log[h*(f + g*x)^m]/Sqrt[1 - c^2*x^2],x]","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}",1,"((I/2)*m*ArcSin[c*x]^2)/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c + (ArcSin[c*x]*Log[h*(f + g*x)^m])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",9,7,25,0.2800,1,"{216, 2404, 4741, 4519, 2190, 2279, 2391}"
23,0,0,0,0.2001234,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)} \, dx","Int[Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])),x]","\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cos ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcCos[c*x])), x]","A",0,0,0,0,-1,"{}"
24,1,137,0,0.1940063,"\int x^3 \cos ^{-1}(a+b x) \, dx","Int[x^3*ArcCos[a + b*x],x]","\frac{\left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right) \sqrt{1-(a+b x)^2}}{96 b^4}+\frac{\left(8 a^4+24 a^2+3\right) \sin ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{1-(a+b x)^2}}{48 b^2}-\frac{x^3 \sqrt{1-(a+b x)^2}}{16 b}+\frac{1}{4} x^4 \cos ^{-1}(a+b x)","\frac{\left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right) \sqrt{1-(a+b x)^2}}{96 b^4}+\frac{\left(8 a^4+24 a^2+3\right) \sin ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{1-(a+b x)^2}}{48 b^2}-\frac{x^3 \sqrt{1-(a+b x)^2}}{16 b}+\frac{1}{4} x^4 \cos ^{-1}(a+b x)",1,"(7*a*x^2*Sqrt[1 - (a + b*x)^2])/(48*b^2) - (x^3*Sqrt[1 - (a + b*x)^2])/(16*b) + ((4*a*(16 + 19*a^2) - (9 + 26*a^2)*(a + b*x))*Sqrt[1 - (a + b*x)^2])/(96*b^4) + (x^4*ArcCos[a + b*x])/4 + ((3 + 24*a^2 + 8*a^4)*ArcSin[a + b*x])/(32*b^4)","A",6,6,10,0.6000,1,"{4806, 4744, 743, 833, 780, 216}"
25,1,94,0,0.114887,"\int x^2 \cos ^{-1}(a+b x) \, dx","Int[x^2*ArcCos[a + b*x],x]","-\frac{\left(11 a^2-5 a b x+4\right) \sqrt{1-(a+b x)^2}}{18 b^3}-\frac{a \left(2 a^2+3\right) \sin ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{1-(a+b x)^2}}{9 b}+\frac{1}{3} x^3 \cos ^{-1}(a+b x)","-\frac{\left(11 a^2-5 a b x+4\right) \sqrt{1-(a+b x)^2}}{18 b^3}-\frac{a \left(2 a^2+3\right) \sin ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{1-(a+b x)^2}}{9 b}+\frac{1}{3} x^3 \cos ^{-1}(a+b x)",1,"-(x^2*Sqrt[1 - (a + b*x)^2])/(9*b) - ((4 + 11*a^2 - 5*a*b*x)*Sqrt[1 - (a + b*x)^2])/(18*b^3) + (x^3*ArcCos[a + b*x])/3 - (a*(3 + 2*a^2)*ArcSin[a + b*x])/(6*b^3)","A",5,5,10,0.5000,1,"{4806, 4744, 743, 780, 216}"
26,1,80,0,0.0731415,"\int x \cos ^{-1}(a+b x) \, dx","Int[x*ArcCos[a + b*x],x]","\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{1-(a+b x)^2}}{4 b^2}+\frac{1}{2} x^2 \cos ^{-1}(a+b x)-\frac{x \sqrt{1-(a+b x)^2}}{4 b}","\frac{\left(2 a^2+1\right) \sin ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{1-(a+b x)^2}}{4 b^2}+\frac{1}{2} x^2 \cos ^{-1}(a+b x)-\frac{x \sqrt{1-(a+b x)^2}}{4 b}",1,"(3*a*Sqrt[1 - (a + b*x)^2])/(4*b^2) - (x*Sqrt[1 - (a + b*x)^2])/(4*b) + (x^2*ArcCos[a + b*x])/2 + ((1 + 2*a^2)*ArcSin[a + b*x])/(4*b^2)","A",5,5,8,0.6250,1,"{4806, 4744, 743, 641, 216}"
27,1,36,0,0.0168144,"\int \cos ^{-1}(a+b x) \, dx","Int[ArcCos[a + b*x],x]","\frac{(a+b x) \cos ^{-1}(a+b x)}{b}-\frac{\sqrt{1-(a+b x)^2}}{b}","\frac{(a+b x) \cos ^{-1}(a+b x)}{b}-\frac{\sqrt{1-(a+b x)^2}}{b}",1,"-(Sqrt[1 - (a + b*x)^2]/b) + ((a + b*x)*ArcCos[a + b*x])/b","A",3,3,6,0.5000,1,"{4804, 4620, 261}"
28,1,177,0,0.2763206,"\int \frac{\cos ^{-1}(a+b x)}{x} \, dx","Int[ArcCos[a + b*x]/x,x]","-i \text{PolyLog}\left(2,\frac{e^{i \cos ^{-1}(a+b x)}}{a-i \sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,\frac{e^{i \cos ^{-1}(a+b x)}}{a+i \sqrt{1-a^2}}\right)+\cos ^{-1}(a+b x) \log \left(1-\frac{e^{i \cos ^{-1}(a+b x)}}{a-i \sqrt{1-a^2}}\right)+\cos ^{-1}(a+b x) \log \left(1-\frac{e^{i \cos ^{-1}(a+b x)}}{a+i \sqrt{1-a^2}}\right)-\frac{1}{2} i \cos ^{-1}(a+b x)^2","-i \text{PolyLog}\left(2,\frac{e^{i \cos ^{-1}(a+b x)}}{a-i \sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,\frac{e^{i \cos ^{-1}(a+b x)}}{a+i \sqrt{1-a^2}}\right)+\cos ^{-1}(a+b x) \log \left(1-\frac{e^{i \cos ^{-1}(a+b x)}}{a-i \sqrt{1-a^2}}\right)+\cos ^{-1}(a+b x) \log \left(1-\frac{e^{i \cos ^{-1}(a+b x)}}{a+i \sqrt{1-a^2}}\right)-\frac{1}{2} i \cos ^{-1}(a+b x)^2",1,"(-I/2)*ArcCos[a + b*x]^2 + ArcCos[a + b*x]*Log[1 - E^(I*ArcCos[a + b*x])/(a - I*Sqrt[1 - a^2])] + ArcCos[a + b*x]*Log[1 - E^(I*ArcCos[a + b*x])/(a + I*Sqrt[1 - a^2])] - I*PolyLog[2, E^(I*ArcCos[a + b*x])/(a - I*Sqrt[1 - a^2])] - I*PolyLog[2, E^(I*ArcCos[a + b*x])/(a + I*Sqrt[1 - a^2])]","A",9,6,10,0.6000,1,"{4806, 4742, 4522, 2190, 2279, 2391}"
29,1,63,0,0.075788,"\int \frac{\cos ^{-1}(a+b x)}{x^2} \, dx","Int[ArcCos[a + b*x]/x^2,x]","\frac{b \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{\sqrt{1-a^2}}-\frac{\cos ^{-1}(a+b x)}{x}","\frac{b \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{\sqrt{1-a^2}}-\frac{\cos ^{-1}(a+b x)}{x}",1,"-(ArcCos[a + b*x]/x) + (b*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/Sqrt[1 - a^2]","A",4,4,10,0.4000,1,"{4806, 4744, 725, 206}"
30,1,103,0,0.1110941,"\int \frac{\cos ^{-1}(a+b x)}{x^3} \, dx","Int[ArcCos[a + b*x]/x^3,x]","\frac{a b^2 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{2 \left(1-a^2\right)^{3/2}}+\frac{b \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right) x}-\frac{\cos ^{-1}(a+b x)}{2 x^2}","\frac{a b^2 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{2 \left(1-a^2\right)^{3/2}}+\frac{b \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right) x}-\frac{\cos ^{-1}(a+b x)}{2 x^2}",1,"(b*Sqrt[1 - (a + b*x)^2])/(2*(1 - a^2)*x) - ArcCos[a + b*x]/(2*x^2) + (a*b^2*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/(2*(1 - a^2)^(3/2))","A",5,5,10,0.5000,1,"{4806, 4744, 731, 725, 206}"
31,1,144,0,0.1792908,"\int \frac{\cos ^{-1}(a+b x)}{x^4} \, dx","Int[ArcCos[a + b*x]/x^4,x]","\frac{a b^2 \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right)^2 x}+\frac{\left(2 a^2+1\right) b^3 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{6 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{1-(a+b x)^2}}{6 \left(1-a^2\right) x^2}-\frac{\cos ^{-1}(a+b x)}{3 x^3}","\frac{a b^2 \sqrt{1-(a+b x)^2}}{2 \left(1-a^2\right)^2 x}+\frac{\left(2 a^2+1\right) b^3 \tanh ^{-1}\left(\frac{1-a (a+b x)}{\sqrt{1-a^2} \sqrt{1-(a+b x)^2}}\right)}{6 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{1-(a+b x)^2}}{6 \left(1-a^2\right) x^2}-\frac{\cos ^{-1}(a+b x)}{3 x^3}",1,"(b*Sqrt[1 - (a + b*x)^2])/(6*(1 - a^2)*x^2) + (a*b^2*Sqrt[1 - (a + b*x)^2])/(2*(1 - a^2)^2*x) - ArcCos[a + b*x]/(3*x^3) + ((1 + 2*a^2)*b^3*ArcTanh[(1 - a*(a + b*x))/(Sqrt[1 - a^2]*Sqrt[1 - (a + b*x)^2])])/(6*(1 - a^2)^(5/2))","A",6,6,10,0.6000,1,"{4806, 4744, 745, 807, 725, 206}"
32,1,82,0,0.0820063,"\int \cos ^{-1}(a+b x)^3 \, dx","Int[ArcCos[a + b*x]^3,x]","\frac{6 \sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \cos ^{-1}(a+b x)^3}{b}-\frac{3 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)^2}{b}-\frac{6 (a+b x) \cos ^{-1}(a+b x)}{b}","\frac{6 \sqrt{1-(a+b x)^2}}{b}+\frac{(a+b x) \cos ^{-1}(a+b x)^3}{b}-\frac{3 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)^2}{b}-\frac{6 (a+b x) \cos ^{-1}(a+b x)}{b}",1,"(6*Sqrt[1 - (a + b*x)^2])/b - (6*(a + b*x)*ArcCos[a + b*x])/b - (3*Sqrt[1 - (a + b*x)^2]*ArcCos[a + b*x]^2)/b + ((a + b*x)*ArcCos[a + b*x]^3)/b","A",5,4,8,0.5000,1,"{4804, 4620, 4678, 261}"
33,1,47,0,0.0544189,"\int \cos ^{-1}(a+b x)^2 \, dx","Int[ArcCos[a + b*x]^2,x]","\frac{(a+b x) \cos ^{-1}(a+b x)^2}{b}-\frac{2 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)}{b}-2 x","\frac{(a+b x) \cos ^{-1}(a+b x)^2}{b}-\frac{2 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)}{b}-2 x",1,"-2*x - (2*Sqrt[1 - (a + b*x)^2]*ArcCos[a + b*x])/b + ((a + b*x)*ArcCos[a + b*x]^2)/b","A",4,4,8,0.5000,1,"{4804, 4620, 4678, 8}"
34,1,12,0,0.0215678,"\int \frac{1}{\cos ^{-1}(a+b x)} \, dx","Int[ArcCos[a + b*x]^(-1),x]","-\frac{\text{Si}\left(\cos ^{-1}(a+b x)\right)}{b}","-\frac{\text{Si}\left(\cos ^{-1}(a+b x)\right)}{b}",1,"-(SinIntegral[ArcCos[a + b*x]]/b)","A",3,3,8,0.3750,1,"{4804, 4624, 3299}"
35,1,40,0,0.0784772,"\int \frac{1}{\cos ^{-1}(a+b x)^2} \, dx","Int[ArcCos[a + b*x]^(-2),x]","\frac{\sqrt{1-(a+b x)^2}}{b \cos ^{-1}(a+b x)}-\frac{\text{CosIntegral}\left(\cos ^{-1}(a+b x)\right)}{b}","\frac{\sqrt{1-(a+b x)^2}}{b \cos ^{-1}(a+b x)}-\frac{\text{CosIntegral}\left(\cos ^{-1}(a+b x)\right)}{b}",1,"Sqrt[1 - (a + b*x)^2]/(b*ArcCos[a + b*x]) - CosIntegral[ArcCos[a + b*x]]/b","A",4,4,8,0.5000,1,"{4804, 4622, 4724, 3302}"
36,1,65,0,0.08065,"\int \frac{1}{\cos ^{-1}(a+b x)^3} \, dx","Int[ArcCos[a + b*x]^(-3),x]","\frac{\text{Si}\left(\cos ^{-1}(a+b x)\right)}{2 b}+\frac{a+b x}{2 b \cos ^{-1}(a+b x)}+\frac{\sqrt{1-(a+b x)^2}}{2 b \cos ^{-1}(a+b x)^2}","\frac{\text{Si}\left(\cos ^{-1}(a+b x)\right)}{2 b}+\frac{a+b x}{2 b \cos ^{-1}(a+b x)}+\frac{\sqrt{1-(a+b x)^2}}{2 b \cos ^{-1}(a+b x)^2}",1,"Sqrt[1 - (a + b*x)^2]/(2*b*ArcCos[a + b*x]^2) + (a + b*x)/(2*b*ArcCos[a + b*x]) + SinIntegral[ArcCos[a + b*x]]/(2*b)","A",5,5,8,0.6250,1,"{4804, 4622, 4720, 4624, 3299}"
37,1,111,0,0.1473595,"\int \cos ^{-1}(a+b x)^{5/2} \, dx","Int[ArcCos[a + b*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{4 b}+\frac{(a+b x) \cos ^{-1}(a+b x)^{5/2}}{b}-\frac{5 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)^{3/2}}{2 b}-\frac{15 (a+b x) \sqrt{\cos ^{-1}(a+b x)}}{4 b}","\frac{15 \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{4 b}+\frac{(a+b x) \cos ^{-1}(a+b x)^{5/2}}{b}-\frac{5 \sqrt{1-(a+b x)^2} \cos ^{-1}(a+b x)^{3/2}}{2 b}-\frac{15 (a+b x) \sqrt{\cos ^{-1}(a+b x)}}{4 b}",1,"(-15*(a + b*x)*Sqrt[ArcCos[a + b*x]])/(4*b) - (5*Sqrt[1 - (a + b*x)^2]*ArcCos[a + b*x]^(3/2))/(2*b) + ((a + b*x)*ArcCos[a + b*x]^(5/2))/b + (15*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/(4*b)","A",7,6,10,0.6000,1,"{4804, 4620, 4678, 4724, 3304, 3352}"
38,1,89,0,0.09211,"\int \cos ^{-1}(a+b x)^{3/2} \, dx","Int[ArcCos[a + b*x]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \cos ^{-1}(a+b x)^{3/2}}{b}-\frac{3 \sqrt{1-(a+b x)^2} \sqrt{\cos ^{-1}(a+b x)}}{2 b}","\frac{3 \sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \cos ^{-1}(a+b x)^{3/2}}{b}-\frac{3 \sqrt{1-(a+b x)^2} \sqrt{\cos ^{-1}(a+b x)}}{2 b}",1,"(-3*Sqrt[1 - (a + b*x)^2]*Sqrt[ArcCos[a + b*x]])/(2*b) + ((a + b*x)*ArcCos[a + b*x]^(3/2))/b + (3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/(2*b)","A",6,6,10,0.6000,1,"{4804, 4620, 4678, 4624, 3305, 3351}"
39,1,55,0,0.0806047,"\int \sqrt{\cos ^{-1}(a+b x)} \, dx","Int[Sqrt[ArcCos[a + b*x]],x]","\frac{(a+b x) \sqrt{\cos ^{-1}(a+b x)}}{b}-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}","\frac{(a+b x) \sqrt{\cos ^{-1}(a+b x)}}{b}-\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*Sqrt[ArcCos[a + b*x]])/b - (Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/b","A",5,5,10,0.5000,1,"{4804, 4620, 4724, 3304, 3352}"
40,1,33,0,0.0297642,"\int \frac{1}{\sqrt{\cos ^{-1}(a+b x)}} \, dx","Int[1/Sqrt[ArcCos[a + b*x]],x]","-\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}","-\frac{\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}",1,"-((Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/b)","A",4,4,10,0.4000,1,"{4804, 4624, 3305, 3351}"
41,1,64,0,0.0860013,"\int \frac{1}{\cos ^{-1}(a+b x)^{3/2}} \, dx","Int[ArcCos[a + b*x]^(-3/2),x]","\frac{2 \sqrt{1-(a+b x)^2}}{b \sqrt{\cos ^{-1}(a+b x)}}-\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}","\frac{2 \sqrt{1-(a+b x)^2}}{b \sqrt{\cos ^{-1}(a+b x)}}-\frac{2 \sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{b}",1,"(2*Sqrt[1 - (a + b*x)^2])/(b*Sqrt[ArcCos[a + b*x]]) - (2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/b","A",5,5,10,0.5000,1,"{4804, 4622, 4724, 3304, 3352}"
42,1,90,0,0.0920133,"\int \frac{1}{\cos ^{-1}(a+b x)^{5/2}} \, dx","Int[ArcCos[a + b*x]^(-5/2),x]","\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{3 b}+\frac{4 (a+b x)}{3 b \sqrt{\cos ^{-1}(a+b x)}}+\frac{2 \sqrt{1-(a+b x)^2}}{3 b \cos ^{-1}(a+b x)^{3/2}}","\frac{4 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(a+b x)}\right)}{3 b}+\frac{4 (a+b x)}{3 b \sqrt{\cos ^{-1}(a+b x)}}+\frac{2 \sqrt{1-(a+b x)^2}}{3 b \cos ^{-1}(a+b x)^{3/2}}",1,"(2*Sqrt[1 - (a + b*x)^2])/(3*b*ArcCos[a + b*x]^(3/2)) + (4*(a + b*x))/(3*b*Sqrt[ArcCos[a + b*x]]) + (4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/(3*b)","A",6,6,10,0.6000,1,"{4804, 4622, 4720, 4624, 3305, 3351}"
43,1,106,0,0.1304236,"\int \frac{1}{\sqrt{a+b \cos ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcCos[c + d*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+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}","\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a+b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"-((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d)) + (Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d)","A",7,7,14,0.5000,1,"{4804, 4624, 3306, 3305, 3351, 3304, 3352}"
44,1,108,0,0.115801,"\int \frac{1}{\sqrt{a-b \cos ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a - b*ArcCos[c + d*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+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a-b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}","\frac{\sqrt{2 \pi } \sin \left(\frac{a}{b}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a-b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}-\frac{\sqrt{2 \pi } \cos \left(\frac{a}{b}\right) S\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{a-b \cos ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"-((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a - b*ArcCos[c + d*x]])/Sqrt[b]])/(Sqrt[b]*d)) + (Sqrt[2*Pi]*FresnelC[(Sqrt[2/Pi]*Sqrt[a - b*ArcCos[c + d*x]])/Sqrt[b]]*Sin[a/b])/(Sqrt[b]*d)","A",7,7,15,0.4667,1,"{4804, 4624, 3306, 3305, 3351, 3304, 3352}"
45,1,68,0,0.0813552,"\int \frac{\cos ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcCos[a + b*x]/((a*d)/b + d*x),x]","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a+b x)}\right)}{2 d}-\frac{i \cos ^{-1}(a+b x)^2}{2 d}+\frac{\cos ^{-1}(a+b x) \log \left(1+e^{2 i \cos ^{-1}(a+b x)}\right)}{d}","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}(a+b x)}\right)}{2 d}-\frac{i \cos ^{-1}(a+b x)^2}{2 d}+\frac{\cos ^{-1}(a+b x) \log \left(1+e^{2 i \cos ^{-1}(a+b x)}\right)}{d}",1,"((-I/2)*ArcCos[a + b*x]^2)/d + (ArcCos[a + b*x]*Log[1 + E^((2*I)*ArcCos[a + b*x])])/d - ((I/2)*PolyLog[2, -E^((2*I)*ArcCos[a + b*x])])/d","A",7,7,19,0.3684,1,"{4806, 12, 4626, 3719, 2190, 2279, 2391}"
46,1,34,0,0.0297441,"\int \sqrt{1-x^2} \cos ^{-1}(x) \, dx","Int[Sqrt[1 - x^2]*ArcCos[x],x]","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2","\frac{x^2}{4}+\frac{1}{2} \sqrt{1-x^2} x \cos ^{-1}(x)-\frac{1}{4} \cos ^{-1}(x)^2",1,"x^2/4 + (x*Sqrt[1 - x^2]*ArcCos[x])/2 - ArcCos[x]^2/4","A",3,3,14,0.2143,1,"{4648, 4642, 30}"
47,1,51,0,0.0385854,"\int x^3 \cos ^{-1}\left(a x^2\right) \, dx","Int[x^3*ArcCos[a*x^2],x]","-\frac{x^2 \sqrt{1-a^2 x^4}}{8 a}+\frac{\sin ^{-1}\left(a x^2\right)}{8 a^2}+\frac{1}{4} x^4 \cos ^{-1}\left(a x^2\right)","-\frac{x^2 \sqrt{1-a^2 x^4}}{8 a}+\frac{\sin ^{-1}\left(a x^2\right)}{8 a^2}+\frac{1}{4} x^4 \cos ^{-1}\left(a x^2\right)",1,"-(x^2*Sqrt[1 - a^2*x^4])/(8*a) + (x^4*ArcCos[a*x^2])/4 + ArcSin[a*x^2]/(8*a^2)","A",5,5,10,0.5000,1,"{4843, 12, 275, 321, 216}"
48,1,55,0,0.0284355,"\int x^2 \cos ^{-1}\left(a x^2\right) \, dx","Int[x^2*ArcCos[a*x^2],x]","-\frac{2 x \sqrt{1-a^2 x^4}}{9 a}+\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{9 a^{3/2}}+\frac{1}{3} x^3 \cos ^{-1}\left(a x^2\right)","-\frac{2 x \sqrt{1-a^2 x^4}}{9 a}+\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{9 a^{3/2}}+\frac{1}{3} x^3 \cos ^{-1}\left(a x^2\right)",1,"(-2*x*Sqrt[1 - a^2*x^4])/(9*a) + (x^3*ArcCos[a*x^2])/3 + (2*EllipticF[ArcSin[Sqrt[a]*x], -1])/(9*a^(3/2))","A",4,4,10,0.4000,1,"{4843, 12, 321, 221}"
49,1,35,0,0.0236618,"\int x \cos ^{-1}\left(a x^2\right) \, dx","Int[x*ArcCos[a*x^2],x]","\frac{1}{2} x^2 \cos ^{-1}\left(a x^2\right)-\frac{\sqrt{1-a^2 x^4}}{2 a}","\frac{1}{2} x^2 \cos ^{-1}\left(a x^2\right)-\frac{\sqrt{1-a^2 x^4}}{2 a}",1,"-Sqrt[1 - a^2*x^4]/(2*a) + (x^2*ArcCos[a*x^2])/2","A",3,3,8,0.3750,1,"{6715, 4620, 261}"
50,1,43,0,0.0324736,"\int \cos ^{-1}\left(a x^2\right) \, dx","Int[ArcCos[a*x^2],x]","x \cos ^{-1}\left(a x^2\right)-\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}+\frac{2 E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}","x \cos ^{-1}\left(a x^2\right)-\frac{2 F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}+\frac{2 E\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)}{\sqrt{a}}",1,"x*ArcCos[a*x^2] + (2*EllipticE[ArcSin[Sqrt[a]*x], -1])/Sqrt[a] - (2*EllipticF[ArcSin[Sqrt[a]*x], -1])/Sqrt[a]","A",6,6,6,1.000,1,"{4841, 12, 307, 221, 1199, 424}"
51,1,62,0,0.0584569,"\int \frac{\cos ^{-1}\left(a x^2\right)}{x} \, dx","Int[ArcCos[a*x^2]/x,x]","-\frac{1}{4} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^2\right)}\right)-\frac{1}{4} i \cos ^{-1}\left(a x^2\right)^2+\frac{1}{2} \cos ^{-1}\left(a x^2\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^2\right)}\right)","-\frac{1}{4} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^2\right)}\right)-\frac{1}{4} i \cos ^{-1}\left(a x^2\right)^2+\frac{1}{2} \cos ^{-1}\left(a x^2\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^2\right)}\right)",1,"(-I/4)*ArcCos[a*x^2]^2 + (ArcCos[a*x^2]*Log[1 + E^((2*I)*ArcCos[a*x^2])])/2 - (I/4)*PolyLog[2, -E^((2*I)*ArcCos[a*x^2])]","A",5,5,10,0.5000,1,"{4831, 3719, 2190, 2279, 2391}"
52,1,29,0,0.014442,"\int \frac{\cos ^{-1}\left(a x^2\right)}{x^2} \, dx","Int[ArcCos[a*x^2]/x^2,x]","-\frac{\cos ^{-1}\left(a x^2\right)}{x}-2 \sqrt{a} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)","-\frac{\cos ^{-1}\left(a x^2\right)}{x}-2 \sqrt{a} F\left(\left.\sin ^{-1}\left(\sqrt{a} x\right)\right|-1\right)",1,"-(ArcCos[a*x^2]/x) - 2*Sqrt[a]*EllipticF[ArcSin[Sqrt[a]*x], -1]","A",3,3,10,0.3000,1,"{4843, 12, 221}"
53,1,58,0,0.036197,"\int x^2 \cos ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x^2*ArcCos[a/x],x]","-\frac{1}{6} a x^2 \sqrt{1-\frac{a^2}{x^2}}-\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-\frac{a^2}{x^2}}\right)+\frac{1}{3} x^3 \sec ^{-1}\left(\frac{x}{a}\right)","-\frac{1}{6} a x^2 \sqrt{1-\frac{a^2}{x^2}}-\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{1-\frac{a^2}{x^2}}\right)+\frac{1}{3} x^3 \sec ^{-1}\left(\frac{x}{a}\right)",1,"-(a*Sqrt[1 - a^2/x^2]*x^2)/6 + (x^3*ArcSec[x/a])/3 - (a^3*ArcTanh[Sqrt[1 - a^2/x^2]])/6","A",6,6,10,0.6000,1,"{4833, 5220, 266, 51, 63, 208}"
54,1,34,0,0.0165922,"\int x \cos ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x*ArcCos[a/x],x]","\frac{1}{2} x^2 \sec ^{-1}\left(\frac{x}{a}\right)-\frac{1}{2} a x \sqrt{1-\frac{a^2}{x^2}}","\frac{1}{2} x^2 \sec ^{-1}\left(\frac{x}{a}\right)-\frac{1}{2} a x \sqrt{1-\frac{a^2}{x^2}}",1,"-(a*Sqrt[1 - a^2/x^2]*x)/2 + (x^2*ArcSec[x/a])/2","A",3,3,8,0.3750,1,"{4833, 5220, 191}"
55,1,27,0,0.0169255,"\int \cos ^{-1}\left(\frac{a}{x}\right) \, dx","Int[ArcCos[a/x],x]","x \sec ^{-1}\left(\frac{x}{a}\right)-a \tanh ^{-1}\left(\sqrt{1-\frac{a^2}{x^2}}\right)","x \sec ^{-1}\left(\frac{x}{a}\right)-a \tanh ^{-1}\left(\sqrt{1-\frac{a^2}{x^2}}\right)",1,"x*ArcSec[x/a] - a*ArcTanh[Sqrt[1 - a^2/x^2]]","A",5,5,6,0.8333,1,"{4833, 5214, 266, 63, 208}"
56,1,60,0,0.0546249,"\int \frac{\cos ^{-1}\left(\frac{a}{x}\right)}{x} \, dx","Int[ArcCos[a/x]/x,x]","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{a}{x}\right)}\right)+\frac{1}{2} i \cos ^{-1}\left(\frac{a}{x}\right)^2-\cos ^{-1}\left(\frac{a}{x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\frac{a}{x}\right)}\right)","\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{a}{x}\right)}\right)+\frac{1}{2} i \cos ^{-1}\left(\frac{a}{x}\right)^2-\cos ^{-1}\left(\frac{a}{x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\frac{a}{x}\right)}\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",5,5,10,0.5000,1,"{4831, 3719, 2190, 2279, 2391}"
57,1,30,0,0.0218937,"\int \frac{\cos ^{-1}\left(\frac{a}{x}\right)}{x^2} \, dx","Int[ArcCos[a/x]/x^2,x]","\frac{\sqrt{1-\frac{a^2}{x^2}}}{a}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{x}","\frac{\sqrt{1-\frac{a^2}{x^2}}}{a}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{x}",1,"Sqrt[1 - a^2/x^2]/a - ArcSec[x/a]/x","A",3,3,10,0.3000,1,"{4833, 5220, 261}"
58,1,51,0,0.0325045,"\int \frac{\cos ^{-1}\left(\frac{a}{x}\right)}{x^3} \, dx","Int[ArcCos[a/x]/x^3,x]","\frac{\sqrt{1-\frac{a^2}{x^2}}}{4 a x}-\frac{\csc ^{-1}\left(\frac{x}{a}\right)}{4 a^2}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{2 x^2}","\frac{\sqrt{1-\frac{a^2}{x^2}}}{4 a x}-\frac{\csc ^{-1}\left(\frac{x}{a}\right)}{4 a^2}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{2 x^2}",1,"Sqrt[1 - a^2/x^2]/(4*a*x) - ArcCsc[x/a]/(4*a^2) - ArcSec[x/a]/(2*x^2)","A",5,5,10,0.5000,1,"{4833, 5220, 335, 321, 216}"
59,1,56,0,0.0383783,"\int \frac{\cos ^{-1}\left(\frac{a}{x}\right)}{x^4} \, dx","Int[ArcCos[a/x]/x^4,x]","-\frac{\left(1-\frac{a^2}{x^2}\right)^{3/2}}{9 a^3}+\frac{\sqrt{1-\frac{a^2}{x^2}}}{3 a^3}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{3 x^3}","-\frac{\left(1-\frac{a^2}{x^2}\right)^{3/2}}{9 a^3}+\frac{\sqrt{1-\frac{a^2}{x^2}}}{3 a^3}-\frac{\sec ^{-1}\left(\frac{x}{a}\right)}{3 x^3}",1,"Sqrt[1 - a^2/x^2]/(3*a^3) - (1 - a^2/x^2)^(3/2)/(9*a^3) - ArcSec[x/a]/(3*x^3)","A",5,4,10,0.4000,1,"{4833, 5220, 266, 43}"
60,1,78,0,0.028212,"\int x^2 \cos ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcCos[Sqrt[x]],x]","-\frac{1}{18} \sqrt{1-x} x^{5/2}-\frac{5}{72} \sqrt{1-x} x^{3/2}+\frac{1}{3} x^3 \cos ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{1-x} \sqrt{x}-\frac{5}{96} \sin ^{-1}(1-2 x)","-\frac{1}{18} \sqrt{1-x} x^{5/2}-\frac{5}{72} \sqrt{1-x} x^{3/2}+\frac{1}{3} x^3 \cos ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{1-x} \sqrt{x}-\frac{5}{96} \sin ^{-1}(1-2 x)",1,"(-5*Sqrt[1 - x]*Sqrt[x])/48 - (5*Sqrt[1 - x]*x^(3/2))/72 - (Sqrt[1 - x]*x^(5/2))/18 + (x^3*ArcCos[Sqrt[x]])/3 - (5*ArcSin[1 - 2*x])/96","A",8,6,10,0.6000,1,"{4843, 12, 50, 53, 619, 216}"
61,1,60,0,0.0191523,"\int x \cos ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcCos[Sqrt[x]],x]","-\frac{1}{8} \sqrt{1-x} x^{3/2}+\frac{1}{2} x^2 \cos ^{-1}\left(\sqrt{x}\right)-\frac{3}{16} \sqrt{1-x} \sqrt{x}-\frac{3}{32} \sin ^{-1}(1-2 x)","-\frac{1}{8} \sqrt{1-x} x^{3/2}+\frac{1}{2} x^2 \cos ^{-1}\left(\sqrt{x}\right)-\frac{3}{16} \sqrt{1-x} \sqrt{x}-\frac{3}{32} \sin ^{-1}(1-2 x)",1,"(-3*Sqrt[1 - x]*Sqrt[x])/16 - (Sqrt[1 - x]*x^(3/2))/8 + (x^2*ArcCos[Sqrt[x]])/2 - (3*ArcSin[1 - 2*x])/32","A",7,6,8,0.7500,1,"{4843, 12, 50, 53, 619, 216}"
62,1,37,0,0.0107611,"\int \cos ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcCos[Sqrt[x]],x]","-\frac{1}{2} \sqrt{1-x} \sqrt{x}-\frac{1}{4} \sin ^{-1}(1-2 x)+x \cos ^{-1}\left(\sqrt{x}\right)","-\frac{1}{2} \sqrt{1-x} \sqrt{x}-\frac{1}{4} \sin ^{-1}(1-2 x)+x \cos ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[1 - x]*Sqrt[x])/2 + x*ArcCos[Sqrt[x]] - ArcSin[1 - 2*x]/4","A",6,6,6,1.000,1,"{4841, 12, 50, 53, 619, 216}"
63,1,56,0,0.0558409,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcCos[Sqrt[x]]/x,x]","-i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\sqrt{x}\right)}\right)-i \cos ^{-1}\left(\sqrt{x}\right)^2+2 \cos ^{-1}\left(\sqrt{x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\sqrt{x}\right)}\right)","-i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\sqrt{x}\right)}\right)-i \cos ^{-1}\left(\sqrt{x}\right)^2+2 \cos ^{-1}\left(\sqrt{x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\sqrt{x}\right)}\right)",1,"(-I)*ArcCos[Sqrt[x]]^2 + 2*ArcCos[Sqrt[x]]*Log[1 + E^((2*I)*ArcCos[Sqrt[x]])] - I*PolyLog[2, -E^((2*I)*ArcCos[Sqrt[x]])]","A",5,5,10,0.5000,1,"{4831, 3719, 2190, 2279, 2391}"
64,1,27,0,0.0119337,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcCos[Sqrt[x]]/x^2,x]","\frac{\sqrt{1-x}}{\sqrt{x}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{x}","\frac{\sqrt{1-x}}{\sqrt{x}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{x}",1,"Sqrt[1 - x]/Sqrt[x] - ArcCos[Sqrt[x]]/x","A",3,3,10,0.3000,1,"{4843, 12, 37}"
65,1,50,0,0.0176729,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcCos[Sqrt[x]]/x^3,x]","\frac{\sqrt{1-x}}{6 x^{3/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{1-x}}{3 \sqrt{x}}","\frac{\sqrt{1-x}}{6 x^{3/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{1-x}}{3 \sqrt{x}}",1,"Sqrt[1 - x]/(6*x^(3/2)) + Sqrt[1 - x]/(3*Sqrt[x]) - ArcCos[Sqrt[x]]/(2*x^2)","A",4,4,10,0.4000,1,"{4843, 12, 45, 37}"
66,1,68,0,0.0218177,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcCos[Sqrt[x]]/x^4,x]","\frac{4 \sqrt{1-x}}{45 x^{3/2}}+\frac{\sqrt{1-x}}{15 x^{5/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{8 \sqrt{1-x}}{45 \sqrt{x}}","\frac{4 \sqrt{1-x}}{45 x^{3/2}}+\frac{\sqrt{1-x}}{15 x^{5/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{8 \sqrt{1-x}}{45 \sqrt{x}}",1,"Sqrt[1 - x]/(15*x^(5/2)) + (4*Sqrt[1 - x])/(45*x^(3/2)) + (8*Sqrt[1 - x])/(45*Sqrt[x]) - ArcCos[Sqrt[x]]/(3*x^3)","A",5,4,10,0.4000,1,"{4843, 12, 45, 37}"
67,1,86,0,0.0277524,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{x^5} \, dx","Int[ArcCos[Sqrt[x]]/x^5,x]","\frac{2 \sqrt{1-x}}{35 x^{3/2}}+\frac{3 \sqrt{1-x}}{70 x^{5/2}}+\frac{\sqrt{1-x}}{28 x^{7/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{4 x^4}+\frac{4 \sqrt{1-x}}{35 \sqrt{x}}","\frac{2 \sqrt{1-x}}{35 x^{3/2}}+\frac{3 \sqrt{1-x}}{70 x^{5/2}}+\frac{\sqrt{1-x}}{28 x^{7/2}}-\frac{\cos ^{-1}\left(\sqrt{x}\right)}{4 x^4}+\frac{4 \sqrt{1-x}}{35 \sqrt{x}}",1,"Sqrt[1 - x]/(28*x^(7/2)) + (3*Sqrt[1 - x])/(70*x^(5/2)) + (2*Sqrt[1 - x])/(35*x^(3/2)) + (4*Sqrt[1 - x])/(35*Sqrt[x]) - ArcCos[Sqrt[x]]/(4*x^4)","A",6,4,10,0.4000,1,"{4843, 12, 45, 37}"
68,1,25,0,0.0187569,"\int \frac{\cos ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[ArcCos[Sqrt[x]]/Sqrt[x],x]","2 \sqrt{x} \cos ^{-1}\left(\sqrt{x}\right)-2 \sqrt{1-x}","2 \sqrt{x} \cos ^{-1}\left(\sqrt{x}\right)-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x] + 2*Sqrt[x]*ArcCos[Sqrt[x]]","A",3,3,12,0.2500,1,"{6715, 4620, 261}"
69,1,68,0,0.0614399,"\int \frac{\cos ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcCos[a*x^n]/x,x]","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{i \cos ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\cos ^{-1}\left(a x^n\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^n\right)}\right)}{n}","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{i \cos ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\cos ^{-1}\left(a x^n\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^n\right)}\right)}{n}",1,"((-I/2)*ArcCos[a*x^n]^2)/n + (ArcCos[a*x^n]*Log[1 + E^((2*I)*ArcCos[a*x^n])])/n - ((I/2)*PolyLog[2, -E^((2*I)*ArcCos[a*x^n])])/n","A",5,5,10,0.5000,1,"{4831, 3719, 2190, 2279, 2391}"
70,1,62,0,0.0574571,"\int \frac{\cos ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcCos[a*x^5]/x,x]","-\frac{1}{10} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} i \cos ^{-1}\left(a x^5\right)^2+\frac{1}{5} \cos ^{-1}\left(a x^5\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^5\right)}\right)","-\frac{1}{10} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} i \cos ^{-1}\left(a x^5\right)^2+\frac{1}{5} \cos ^{-1}\left(a x^5\right) \log \left(1+e^{2 i \cos ^{-1}\left(a x^5\right)}\right)",1,"(-I/10)*ArcCos[a*x^5]^2 + (ArcCos[a*x^5]*Log[1 + E^((2*I)*ArcCos[a*x^5])])/5 - (I/10)*PolyLog[2, -E^((2*I)*ArcCos[a*x^5])]","A",5,5,10,0.5000,1,"{4831, 3719, 2190, 2279, 2391}"
71,1,47,0,0.0514806,"\int x^3 \cos ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcCos[a + b*x^4],x]","\frac{\left(a+b x^4\right) \cos ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{1-\left(a+b x^4\right)^2}}{4 b}","\frac{\left(a+b x^4\right) \cos ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{1-\left(a+b x^4\right)^2}}{4 b}",1,"-Sqrt[1 - (a + b*x^4)^2]/(4*b) + ((a + b*x^4)*ArcCos[a + b*x^4])/(4*b)","A",4,4,12,0.3333,1,"{6715, 4804, 4620, 261}"
72,1,48,0,0.0544105,"\int x^{-1+n} \cos ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcCos[a + b*x^n],x]","\frac{\left(a+b x^n\right) \cos ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{1-\left(a+b x^n\right)^2}}{b n}","\frac{\left(a+b x^n\right) \cos ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{1-\left(a+b x^n\right)^2}}{b n}",1,"-(Sqrt[1 - (a + b*x^n)^2]/(b*n)) + ((a + b*x^n)*ArcCos[a + b*x^n])/(b*n)","A",4,4,14,0.2857,1,"{6715, 4804, 4620, 261}"
73,1,127,0,0.0287647,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^4 \, dx","Int[(a + b*ArcCos[1 + d*x^2])^4,x]","\frac{192 b^3 \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}{d x}-48 b^2 x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2-\frac{8 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^3}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x","\frac{192 b^3 \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}{d x}-48 b^2 x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2-\frac{8 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^3}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x",1,"384*b^4*x + (192*b^3*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcCos[1 + d*x^2]))/(d*x) - 48*b^2*x*(a + b*ArcCos[1 + d*x^2])^2 - (8*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcCos[1 + d*x^2])^3)/(d*x) + x*(a + b*ArcCos[1 + d*x^2])^4","A",3,2,14,0.1429,1,"{4815, 8}"
74,1,110,0,0.0571493,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^3 \, dx","Int[(a + b*ArcCos[1 + d*x^2])^3,x]","-24 a b^2 x-\frac{6 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^3+\frac{48 b^3 \sqrt{-d^2 x^4-2 d x^2}}{d x}-24 b^3 x \cos ^{-1}\left(d x^2+1\right)","-24 a b^2 x-\frac{6 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^3+\frac{48 b^3 \sqrt{-d^2 x^4-2 d x^2}}{d x}-24 b^3 x \cos ^{-1}\left(d x^2+1\right)",1,"-24*a*b^2*x + (48*b^3*Sqrt[-2*d*x^2 - d^2*x^4])/(d*x) - 24*b^3*x*ArcCos[1 + d*x^2] - (6*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcCos[1 + d*x^2])^2)/(d*x) + x*(a + b*ArcCos[1 + d*x^2])^3","A",5,4,14,0.2857,1,"{4815, 4841, 12, 1588}"
75,1,63,0,0.0115554,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^2 \, dx","Int[(a + b*ArcCos[1 + d*x^2])^2,x]","-\frac{4 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2-8 b^2 x","-\frac{4 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}{d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2-8 b^2 x",1,"-8*b^2*x - (4*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcCos[1 + d*x^2]))/(d*x) + x*(a + b*ArcCos[1 + d*x^2])^2","A",2,2,14,0.1429,1,"{4815, 8}"
76,1,43,0,0.0371819,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right) \, dx","Int[a + b*ArcCos[1 + d*x^2],x]","a x-\frac{2 b \sqrt{-d^2 x^4-2 d x^2}}{d x}+b x \cos ^{-1}\left(d x^2+1\right)","a x-\frac{2 b \sqrt{-d^2 x^4-2 d x^2}}{d x}+b x \cos ^{-1}\left(d x^2+1\right)",1,"a*x - (2*b*Sqrt[-2*d*x^2 - d^2*x^4])/(d*x) + b*x*ArcCos[1 + d*x^2]","A",4,3,12,0.2500,1,"{4841, 12, 1588}"
77,1,99,0,0.0311988,"\int \frac{1}{a+b \cos ^{-1}\left(1+d x^2\right)} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-1),x]","\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{-d x^2}}+\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{-d x^2}}","\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{-d x^2}}+\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{-d x^2}}",1,"(x*Cos[a/(2*b)]*CosIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[-(d*x^2)]) + (x*Sin[a/(2*b)]*SinIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[-(d*x^2)])","A",1,1,14,0.07143,1,"{4817}"
78,1,151,0,0.0203403,"\int \frac{1}{\left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^2} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-2),x]","\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{-d x^2}}-\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{-d x^2}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{2 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}","\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{-d x^2}}-\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{-d x^2}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{2 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}",1,"Sqrt[-2*d*x^2 - d^2*x^4]/(2*b*d*x*(a + b*ArcCos[1 + d*x^2])) + (x*CosIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)]*Sin[a/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[-(d*x^2)]) - (x*Cos[a/(2*b)]*SinIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[-(d*x^2)])","A",1,1,14,0.07143,1,"{4826}"
79,1,173,0,0.0362387,"\int \frac{1}{\left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^3} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-3),x]","-\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{-d x^2}}-\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{-d x^2}}+\frac{x}{8 b^2 \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{4 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2}","-\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{-d x^2}}-\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{-d x^2}}+\frac{x}{8 b^2 \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{4 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^2}",1,"Sqrt[-2*d*x^2 - d^2*x^4]/(4*b*d*x*(a + b*ArcCos[1 + d*x^2])^2) + x/(8*b^2*(a + b*ArcCos[1 + d*x^2])) - (x*Cos[a/(2*b)]*CosIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[-(d*x^2)]) - (x*Sin[a/(2*b)]*SinIntegral[(a + b*ArcCos[1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[-(d*x^2)])","A",2,2,14,0.1429,1,"{4829, 4817}"
80,1,127,0,0.0283064,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^4 \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^4,x]","\frac{192 b^3 \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}{d x}-48 b^2 x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2-\frac{8 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^3}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^4+384 b^4 x","\frac{192 b^3 \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}{d x}-48 b^2 x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2-\frac{8 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^3}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^4+384 b^4 x",1,"384*b^4*x + (192*b^3*Sqrt[2*d*x^2 - d^2*x^4]*(a + b*ArcCos[-1 + d*x^2]))/(d*x) - 48*b^2*x*(a + b*ArcCos[-1 + d*x^2])^2 - (8*b*Sqrt[2*d*x^2 - d^2*x^4]*(a + b*ArcCos[-1 + d*x^2])^3)/(d*x) + x*(a + b*ArcCos[-1 + d*x^2])^4","A",3,2,14,0.1429,1,"{4815, 8}"
81,1,110,0,0.055042,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^3 \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^3,x]","-24 a b^2 x-\frac{6 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^3+\frac{48 b^3 \sqrt{2 d x^2-d^2 x^4}}{d x}-24 b^3 x \cos ^{-1}\left(d x^2-1\right)","-24 a b^2 x-\frac{6 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^3+\frac{48 b^3 \sqrt{2 d x^2-d^2 x^4}}{d x}-24 b^3 x \cos ^{-1}\left(d x^2-1\right)",1,"-24*a*b^2*x + (48*b^3*Sqrt[2*d*x^2 - d^2*x^4])/(d*x) - 24*b^3*x*ArcCos[-1 + d*x^2] - (6*b*Sqrt[2*d*x^2 - d^2*x^4]*(a + b*ArcCos[-1 + d*x^2])^2)/(d*x) + x*(a + b*ArcCos[-1 + d*x^2])^3","A",5,4,14,0.2857,1,"{4815, 4841, 12, 1588}"
82,1,63,0,0.0115222,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^2 \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^2,x]","-\frac{4 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2-8 b^2 x","-\frac{4 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}{d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2-8 b^2 x",1,"-8*b^2*x - (4*b*Sqrt[2*d*x^2 - d^2*x^4]*(a + b*ArcCos[-1 + d*x^2]))/(d*x) + x*(a + b*ArcCos[-1 + d*x^2])^2","A",2,2,14,0.1429,1,"{4815, 8}"
83,1,43,0,0.0357681,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right) \, dx","Int[a + b*ArcCos[-1 + d*x^2],x]","a x-\frac{2 b \sqrt{2 d x^2-d^2 x^4}}{d x}+b x \cos ^{-1}\left(d x^2-1\right)","a x-\frac{2 b \sqrt{2 d x^2-d^2 x^4}}{d x}+b x \cos ^{-1}\left(d x^2-1\right)",1,"a*x - (2*b*Sqrt[2*d*x^2 - d^2*x^4])/(d*x) + b*x*ArcCos[-1 + d*x^2]","A",4,3,12,0.2500,1,"{4841, 12, 1588}"
84,1,98,0,0.0133217,"\int \frac{1}{a+b \cos ^{-1}\left(-1+d x^2\right)} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-1),x]","\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}","\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}",1,"(x*CosIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)]*Sin[a/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2]) - (x*Cos[a/(2*b)]*SinIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{4818}"
85,1,149,0,0.0176495,"\int \frac{1}{\left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^2} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-2),x]","-\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{2 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}","-\frac{x \cos \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{x \sin \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{2 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}",1,"Sqrt[2*d*x^2 - d^2*x^4]/(2*b*d*x*(a + b*ArcCos[-1 + d*x^2])) - (x*Cos[a/(2*b)]*CosIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2]) - (x*Sin[a/(2*b)]*SinIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{4827}"
86,1,171,0,0.0328004,"\int \frac{1}{\left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^3} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-3),x]","-\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x}{8 b^2 \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}+\frac{\sqrt{2 d x^2-d^2 x^4}}{4 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2}","-\frac{x \sin \left(\frac{a}{2 b}\right) \text{CosIntegral}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x \cos \left(\frac{a}{2 b}\right) \text{Si}\left(\frac{a+b \cos ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x}{8 b^2 \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)}+\frac{\sqrt{2 d x^2-d^2 x^4}}{4 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^2}",1,"Sqrt[2*d*x^2 - d^2*x^4]/(4*b*d*x*(a + b*ArcCos[-1 + d*x^2])^2) + x/(8*b^2*(a + b*ArcCos[-1 + d*x^2])) - (x*CosIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)]*Sin[a/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2]) + (x*Cos[a/(2*b)]*SinIntegral[(a + b*ArcCos[-1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2])","A",2,2,14,0.1429,1,"{4829, 4818}"
87,1,249,0,0.0949448,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^{5/2} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(5/2),x]","\frac{30 b^2 \sin ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}-\frac{5 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}{d x}+\frac{30 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}-\frac{30 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{5/2}","\frac{30 b^2 \sin ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}-\frac{5 b \sqrt{-d^2 x^4-2 d x^2} \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}{d x}+\frac{30 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}-\frac{30 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{5/2}",1,"(-5*b*Sqrt[-2*d*x^2 - d^2*x^4]*(a + b*ArcCos[1 + d*x^2])^(3/2))/(d*x) + x*(a + b*ArcCos[1 + d*x^2])^(5/2) - (30*Sqrt[Pi]*Cos[a/(2*b)]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/((b^(-1))^(5/2)*d*x) + (30*Sqrt[Pi]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/((b^(-1))^(5/2)*d*x) + (30*b^2*Sqrt[a + b*ArcCos[1 + d*x^2]]*Sin[ArcCos[1 + d*x^2]/2]^2)/(d*x)","A",2,2,16,0.1250,1,"{4815, 4812}"
88,1,207,0,0.0663642,"\int \left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^{3/2} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(3/2),x]","-\frac{3 b \sqrt{-d^2 x^4-2 d x^2} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}+\frac{6 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+\frac{6 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}","-\frac{3 b \sqrt{-d^2 x^4-2 d x^2} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}+\frac{6 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+\frac{6 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}",1,"(-3*b*Sqrt[-2*d*x^2 - d^2*x^4]*Sqrt[a + b*ArcCos[1 + d*x^2]])/(d*x) + x*(a + b*ArcCos[1 + d*x^2])^(3/2) + (6*Sqrt[Pi]*Cos[a/(2*b)]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/((b^(-1))^(3/2)*d*x) + (6*Sqrt[Pi]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/((b^(-1))^(3/2)*d*x)","A",2,2,16,0.1250,1,"{4815, 4820}"
89,1,184,0,0.0215428,"\int \sqrt{a+b \cos ^{-1}\left(1+d x^2\right)} \, dx","Int[Sqrt[a + b*ArcCos[1 + d*x^2]],x]","-\frac{2 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}+\frac{2 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}-\frac{2 \sin ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}","-\frac{2 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}+\frac{2 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}-\frac{2 \sin ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{d x}",1,"(2*Sqrt[Pi]*Cos[a/(2*b)]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/(Sqrt[b^(-1)]*d*x) - (2*Sqrt[Pi]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/(Sqrt[b^(-1)]*d*x) - (2*Sqrt[a + b*ArcCos[1 + d*x^2]]*Sin[ArcCos[1 + d*x^2]/2]^2)/(d*x)","A",1,1,16,0.06250,1,"{4812}"
90,1,145,0,0.0175331,"\int \frac{1}{\sqrt{a+b \cos ^{-1}\left(1+d x^2\right)}} \, dx","Int[1/Sqrt[a + b*ArcCos[1 + d*x^2]],x]","-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}","-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}",1,"(-2*Sqrt[b^(-1)]*Sqrt[Pi]*Cos[a/(2*b)]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/(d*x) - (2*Sqrt[b^(-1)]*Sqrt[Pi]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/(d*x)","A",1,1,16,0.06250,1,"{4820}"
91,1,190,0,0.0293162,"\int \frac{1}{\left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^{3/2}} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-3/2),x]","\frac{\sqrt{-d^2 x^4-2 d x^2}}{b d x \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}","\frac{\sqrt{-d^2 x^4-2 d x^2}}{b d x \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{d x}",1,"Sqrt[-2*d*x^2 - d^2*x^4]/(b*d*x*Sqrt[a + b*ArcCos[1 + d*x^2]]) + (2*(b^(-1))^(3/2)*Sqrt[Pi]*Cos[a/(2*b)]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/(d*x) - (2*(b^(-1))^(3/2)*Sqrt[Pi]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/(d*x)","A",1,1,16,0.06250,1,"{4823}"
92,1,221,0,0.0500054,"\int \frac{1}{\left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^{5/2}} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-5/2),x]","\frac{x}{3 b^2 \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{3 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{3 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{3 d x}","\frac{x}{3 b^2 \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{3 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{3 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{3 d x}",1,"Sqrt[-2*d*x^2 - d^2*x^4]/(3*b*d*x*(a + b*ArcCos[1 + d*x^2])^(3/2)) + x/(3*b^2*Sqrt[a + b*ArcCos[1 + d*x^2]]) + (2*(b^(-1))^(5/2)*Sqrt[Pi]*Cos[a/(2*b)]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/(3*d*x) + (2*(b^(-1))^(5/2)*Sqrt[Pi]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/(3*d*x)","A",2,2,16,0.1250,1,"{4829, 4820}"
93,1,269,0,0.060164,"\int \frac{1}{\left(a+b \cos ^{-1}\left(1+d x^2\right)\right)^{7/2}} \, dx","Int[(a + b*ArcCos[1 + d*x^2])^(-7/2),x]","-\frac{\sqrt{-d^2 x^4-2 d x^2}}{15 b^3 d x \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}+\frac{x}{15 b^2 \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{5 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{5/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 d x}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 d x}","-\frac{\sqrt{-d^2 x^4-2 d x^2}}{15 b^3 d x \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}+\frac{x}{15 b^2 \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{3/2}}+\frac{\sqrt{-d^2 x^4-2 d x^2}}{5 b d x \left(a+b \cos ^{-1}\left(d x^2+1\right)\right)^{5/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \sin \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 d x}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \cos \left(\frac{a}{2 b}\right) \sin \left(\frac{1}{2} \cos ^{-1}\left(d x^2+1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 d x}",1,"Sqrt[-2*d*x^2 - d^2*x^4]/(5*b*d*x*(a + b*ArcCos[1 + d*x^2])^(5/2)) + x/(15*b^2*(a + b*ArcCos[1 + d*x^2])^(3/2)) - Sqrt[-2*d*x^2 - d^2*x^4]/(15*b^3*d*x*Sqrt[a + b*ArcCos[1 + d*x^2]]) - (2*(b^(-1))^(7/2)*Sqrt[Pi]*Cos[a/(2*b)]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[ArcCos[1 + d*x^2]/2])/(15*d*x) + (2*(b^(-1))^(7/2)*Sqrt[Pi]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)]*Sin[ArcCos[1 + d*x^2]/2])/(15*d*x)","A",2,2,16,0.1250,1,"{4829, 4823}"
94,1,249,0,0.0552374,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^{5/2} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(5/2),x]","-\frac{30 b^2 \cos ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}-\frac{5 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}{d x}+\frac{30 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+\frac{30 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{5/2}","-\frac{30 b^2 \cos ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}-\frac{5 b \sqrt{2 d x^2-d^2 x^4} \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}{d x}+\frac{30 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+\frac{30 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{5/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{5/2}",1,"(-5*b*Sqrt[2*d*x^2 - d^2*x^4]*(a + b*ArcCos[-1 + d*x^2])^(3/2))/(d*x) + x*(a + b*ArcCos[-1 + d*x^2])^(5/2) - (30*b^2*Sqrt[a + b*ArcCos[-1 + d*x^2]]*Cos[ArcCos[-1 + d*x^2]/2]^2)/(d*x) + (30*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/((b^(-1))^(5/2)*d*x) + (30*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/((b^(-1))^(5/2)*d*x)","A",2,2,16,0.1250,1,"{4815, 4813}"
95,1,207,0,0.0440606,"\int \left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^{3/2} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(3/2),x]","-\frac{3 b \sqrt{2 d x^2-d^2 x^4} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}-\frac{6 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+\frac{6 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}","-\frac{3 b \sqrt{2 d x^2-d^2 x^4} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}-\frac{6 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+\frac{6 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\left(\frac{1}{b}\right)^{3/2} d x}+x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}",1,"(-3*b*Sqrt[2*d*x^2 - d^2*x^4]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/(d*x) + x*(a + b*ArcCos[-1 + d*x^2])^(3/2) + (6*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/((b^(-1))^(3/2)*d*x) - (6*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/((b^(-1))^(3/2)*d*x)","A",2,2,16,0.1250,1,"{4815, 4821}"
96,1,184,0,0.0202655,"\int \sqrt{a+b \cos ^{-1}\left(-1+d x^2\right)} \, dx","Int[Sqrt[a + b*ArcCos[-1 + d*x^2]],x]","-\frac{2 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}-\frac{2 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}+\frac{2 \cos ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}","-\frac{2 \sqrt{\pi } \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}-\frac{2 \sqrt{\pi } \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{1}{b}} d x}+\frac{2 \cos ^2\left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{d x}",1,"(2*Sqrt[a + b*ArcCos[-1 + d*x^2]]*Cos[ArcCos[-1 + d*x^2]/2]^2)/(d*x) - (2*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/(Sqrt[b^(-1)]*d*x) - (2*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/(Sqrt[b^(-1)]*d*x)","A",1,1,16,0.06250,1,"{4813}"
97,1,145,0,0.0172358,"\int \frac{1}{\sqrt{a+b \cos ^{-1}\left(-1+d x^2\right)}} \, dx","Int[1/Sqrt[a + b*ArcCos[-1 + d*x^2]],x]","\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}","\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \sqrt{\frac{1}{b}} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}",1,"(-2*Sqrt[b^(-1)]*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/(d*x) + (2*Sqrt[b^(-1)]*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/(d*x)","A",1,1,16,0.06250,1,"{4821}"
98,1,190,0,0.0239368,"\int \frac{1}{\left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^{3/2}} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-3/2),x]","\frac{\sqrt{2 d x^2-d^2 x^4}}{b d x \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}","\frac{\sqrt{2 d x^2-d^2 x^4}}{b d x \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{3/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{d x}",1,"Sqrt[2*d*x^2 - d^2*x^4]/(b*d*x*Sqrt[a + b*ArcCos[-1 + d*x^2]]) - (2*(b^(-1))^(3/2)*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/(d*x) - (2*(b^(-1))^(3/2)*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/(d*x)","A",1,1,16,0.06250,1,"{4824}"
99,1,221,0,0.0434584,"\int \frac{1}{\left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^{5/2}} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-5/2),x]","\frac{x}{3 b^2 \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{3 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{3 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{3 d x}","\frac{x}{3 b^2 \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{3 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}-\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{3 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{5/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{3 d x}",1,"Sqrt[2*d*x^2 - d^2*x^4]/(3*b*d*x*(a + b*ArcCos[-1 + d*x^2])^(3/2)) + x/(3*b^2*Sqrt[a + b*ArcCos[-1 + d*x^2]]) + (2*(b^(-1))^(5/2)*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/(3*d*x) - (2*(b^(-1))^(5/2)*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/(3*d*x)","A",2,2,16,0.1250,1,"{4829, 4821}"
100,1,269,0,0.0500292,"\int \frac{1}{\left(a+b \cos ^{-1}\left(-1+d x^2\right)\right)^{7/2}} \, dx","Int[(a + b*ArcCos[-1 + d*x^2])^(-7/2),x]","-\frac{\sqrt{2 d x^2-d^2 x^4}}{15 b^3 d x \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}+\frac{x}{15 b^2 \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{5 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{5/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{15 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{15 d x}","-\frac{\sqrt{2 d x^2-d^2 x^4}}{15 b^3 d x \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}+\frac{x}{15 b^2 \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{3/2}}+\frac{\sqrt{2 d x^2-d^2 x^4}}{5 b d x \left(a+b \cos ^{-1}\left(d x^2-1\right)\right)^{5/2}}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \cos \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{15 d x}+\frac{2 \sqrt{\pi } \left(\frac{1}{b}\right)^{7/2} \sin \left(\frac{a}{2 b}\right) \cos \left(\frac{1}{2} \cos ^{-1}\left(d x^2-1\right)\right) S\left(\frac{\sqrt{\frac{1}{b}} \sqrt{a+b \cos ^{-1}\left(d x^2-1\right)}}{\sqrt{\pi }}\right)}{15 d x}",1,"Sqrt[2*d*x^2 - d^2*x^4]/(5*b*d*x*(a + b*ArcCos[-1 + d*x^2])^(5/2)) + x/(15*b^2*(a + b*ArcCos[-1 + d*x^2])^(3/2)) - Sqrt[2*d*x^2 - d^2*x^4]/(15*b^3*d*x*Sqrt[a + b*ArcCos[-1 + d*x^2]]) + (2*(b^(-1))^(7/2)*Sqrt[Pi]*Cos[a/(2*b)]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelC[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]])/(15*d*x) + (2*(b^(-1))^(7/2)*Sqrt[Pi]*Cos[ArcCos[-1 + d*x^2]/2]*FresnelS[(Sqrt[b^(-1)]*Sqrt[a + b*ArcCos[-1 + d*x^2]])/Sqrt[Pi]]*Sin[a/(2*b)])/(15*d*x)","A",2,2,16,0.1250,1,"{4829, 4824}"
101,0,0,0,0.0437305,"\int \frac{\left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
102,1,279,0,0.2071581,"\int \frac{\left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"((I/4)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4)/(b*c) - ((a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*Log[1 + E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (((3*I)/2)*b*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (3*b^2*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) - (((3*I)/4)*b^3*PolyLog[4, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c","A",8,8,40,0.2000,1,"{6681, 4626, 3719, 2190, 2531, 6609, 2282, 6589}"
103,1,207,0,0.1743583,"\int \frac{\left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"((I/3)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3)/(b*c) - ((a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*Log[1 + E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (I*b*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b^2*PolyLog[3, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",7,7,40,0.1750,1,"{6681, 4626, 3719, 2190, 2531, 2282, 6589}"
104,1,141,0,0.1043117,"\int \frac{a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","\frac{i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}","\frac{i b \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{i \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1+e^{2 i \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}",1,"((I/2)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2)/(b*c) - ((a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*Log[1 + E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c","A",6,7,38,0.1842,1,"{206, 6681, 4626, 3719, 2190, 2279, 2391}"
105,0,0,0,0.0420346,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
106,0,0,0,0.040541,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cos ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCos[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
107,1,84,0,0.0663046,"\int \cos ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcCos[c*E^(a + b*x)],x]","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{i \cos ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\cos ^{-1}\left(c e^{a+b x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(c e^{a+b x}\right)}\right)}{b}","-\frac{i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{i \cos ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\cos ^{-1}\left(c e^{a+b x}\right) \log \left(1+e^{2 i \cos ^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"((-I/2)*ArcCos[c*E^(a + b*x)]^2)/b + (ArcCos[c*E^(a + b*x)]*Log[1 + E^((2*I)*ArcCos[c*E^(a + b*x)])])/b - ((I/2)*PolyLog[2, -E^((2*I)*ArcCos[c*E^(a + b*x)])])/b","A",6,6,10,0.6000,1,"{2282, 4626, 3719, 2190, 2279, 2391}"
108,1,81,0,0.0643541,"\int e^{\cos ^{-1}(a x)} x^3 \, dx","Int[E^ArcCos[a*x]*x^3,x]","\frac{e^{\cos ^{-1}(a x)} \cos \left(2 \cos ^{-1}(a x)\right)}{10 a^4}+\frac{e^{\cos ^{-1}(a x)} \cos \left(4 \cos ^{-1}(a x)\right)}{34 a^4}-\frac{e^{\cos ^{-1}(a x)} \sin \left(2 \cos ^{-1}(a x)\right)}{20 a^4}-\frac{e^{\cos ^{-1}(a x)} \sin \left(4 \cos ^{-1}(a x)\right)}{136 a^4}","\frac{e^{\cos ^{-1}(a x)} \cos \left(2 \cos ^{-1}(a x)\right)}{10 a^4}+\frac{e^{\cos ^{-1}(a x)} \cos \left(4 \cos ^{-1}(a x)\right)}{34 a^4}-\frac{e^{\cos ^{-1}(a x)} \sin \left(2 \cos ^{-1}(a x)\right)}{20 a^4}-\frac{e^{\cos ^{-1}(a x)} \sin \left(4 \cos ^{-1}(a x)\right)}{136 a^4}",1,"(E^ArcCos[a*x]*Cos[2*ArcCos[a*x]])/(10*a^4) + (E^ArcCos[a*x]*Cos[4*ArcCos[a*x]])/(34*a^4) - (E^ArcCos[a*x]*Sin[2*ArcCos[a*x]])/(20*a^4) - (E^ArcCos[a*x]*Sin[4*ArcCos[a*x]])/(136*a^4)","A",6,4,10,0.4000,1,"{4837, 12, 4469, 4432}"
109,1,82,0,0.0613399,"\int e^{\cos ^{-1}(a x)} x^2 \, dx","Int[E^ArcCos[a*x]*x^2,x]","-\frac{\sqrt{1-a^2 x^2} e^{\cos ^{-1}(a x)}}{8 a^3}+\frac{x e^{\cos ^{-1}(a x)}}{8 a^2}+\frac{3 e^{\cos ^{-1}(a x)} \cos \left(3 \cos ^{-1}(a x)\right)}{40 a^3}-\frac{e^{\cos ^{-1}(a x)} \sin \left(3 \cos ^{-1}(a x)\right)}{40 a^3}","-\frac{\sqrt{1-a^2 x^2} e^{\cos ^{-1}(a x)}}{8 a^3}+\frac{x e^{\cos ^{-1}(a x)}}{8 a^2}+\frac{3 e^{\cos ^{-1}(a x)} \cos \left(3 \cos ^{-1}(a x)\right)}{40 a^3}-\frac{e^{\cos ^{-1}(a x)} \sin \left(3 \cos ^{-1}(a x)\right)}{40 a^3}",1,"(E^ArcCos[a*x]*x)/(8*a^2) - (E^ArcCos[a*x]*Sqrt[1 - a^2*x^2])/(8*a^3) + (3*E^ArcCos[a*x]*Cos[3*ArcCos[a*x]])/(40*a^3) - (E^ArcCos[a*x]*Sin[3*ArcCos[a*x]])/(40*a^3)","A",6,4,10,0.4000,1,"{4837, 12, 4469, 4432}"
110,1,41,0,0.0340067,"\int e^{\cos ^{-1}(a x)} x \, dx","Int[E^ArcCos[a*x]*x,x]","\frac{e^{\cos ^{-1}(a x)} \cos \left(2 \cos ^{-1}(a x)\right)}{5 a^2}-\frac{e^{\cos ^{-1}(a x)} \sin \left(2 \cos ^{-1}(a x)\right)}{10 a^2}","\frac{e^{\cos ^{-1}(a x)} \cos \left(2 \cos ^{-1}(a x)\right)}{5 a^2}-\frac{e^{\cos ^{-1}(a x)} \sin \left(2 \cos ^{-1}(a x)\right)}{10 a^2}",1,"(E^ArcCos[a*x]*Cos[2*ArcCos[a*x]])/(5*a^2) - (E^ArcCos[a*x]*Sin[2*ArcCos[a*x]])/(10*a^2)","A",5,4,8,0.5000,1,"{4837, 12, 4469, 4432}"
111,1,39,0,0.0140558,"\int e^{\cos ^{-1}(a x)} \, dx","Int[E^ArcCos[a*x],x]","\frac{1}{2} x e^{\cos ^{-1}(a x)}-\frac{\sqrt{1-a^2 x^2} e^{\cos ^{-1}(a x)}}{2 a}","\frac{1}{2} x e^{\cos ^{-1}(a x)}-\frac{\sqrt{1-a^2 x^2} e^{\cos ^{-1}(a x)}}{2 a}",1,"(E^ArcCos[a*x]*x)/2 - (E^ArcCos[a*x]*Sqrt[1 - a^2*x^2])/(2*a)","A",2,2,6,0.3333,1,"{4837, 4432}"
112,1,45,0,0.0543512,"\int \frac{e^{\cos ^{-1}(a x)}}{x} \, dx","Int[E^ArcCos[a*x]/x,x]","i e^{\cos ^{-1}(a x)}-2 i e^{\cos ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)","i e^{\cos ^{-1}(a x)}-2 i e^{\cos ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)",1,"I*E^ArcCos[a*x] - (2*I)*E^ArcCos[a*x]*Hypergeometric2F1[-I/2, 1, 1 - I/2, -E^((2*I)*ArcCos[a*x])]","A",6,5,10,0.5000,1,"{4837, 12, 4442, 2194, 2251}"
113,1,87,0,0.1058515,"\int \frac{e^{\cos ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcCos[a*x]/x^2,x]","(1+i) a e^{(1+i) \cos ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)-(2+2 i) a e^{(1+i) \cos ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)","(1+i) a e^{(1+i) \cos ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)-(2+2 i) a e^{(1+i) \cos ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};-e^{2 i \cos ^{-1}(a x)}\right)",1,"(1 + I)*a*E^((1 + I)*ArcCos[a*x])*Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, -E^((2*I)*ArcCos[a*x])] - (2 + 2*I)*a*E^((1 + I)*ArcCos[a*x])*Hypergeometric2F1[1/2 - I/2, 2, 3/2 - I/2, -E^((2*I)*ArcCos[a*x])]","A",6,4,10,0.4000,1,"{4837, 12, 4471, 2251}"
114,1,48,0,0.0328311,"\int \cos ^{-1}\left(\frac{c}{a+b x}\right) \, dx","Int[ArcCos[c/(a + b*x)],x]","\frac{(a+b x) \sec ^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{(a+b x)^2}}\right)}{b}","\frac{(a+b x) \sec ^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}-\frac{c \tanh ^{-1}\left(\sqrt{1-\frac{c^2}{(a+b x)^2}}\right)}{b}",1,"((a + b*x)*ArcSec[a/c + (b*x)/c])/b - (c*ArcTanh[Sqrt[1 - c^2/(a + b*x)^2]])/b","A",6,6,10,0.6000,1,"{4833, 5250, 372, 266, 63, 206}"
115,1,26,0,0.0706919,"\int \frac{x}{\sqrt{1-x^2} \sqrt{\cos ^{-1}(x)}} \, dx","Int[x/(Sqrt[1 - x^2]*Sqrt[ArcCos[x]]),x]","-\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(x)}\right)","-\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{\cos ^{-1}(x)}\right)",1,"-(Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[ArcCos[x]]])","A",3,3,19,0.1579,1,"{4724, 3304, 3352}"
116,1,5,0,0.0608316,"\int \frac{x}{\sqrt{1-x^2} \cos ^{-1}(x)} \, dx","Int[x/(Sqrt[1 - x^2]*ArcCos[x]),x]","-\text{CosIntegral}\left(\cos ^{-1}(x)\right)","-\text{CosIntegral}\left(\cos ^{-1}(x)\right)",1,"-CosIntegral[ArcCos[x]]","A",2,2,17,0.1176,1,"{4724, 3302}"
117,1,39,0,0.0653671,"\int \frac{\cos ^{-1}\left(\sqrt{1+b x^2}\right)^n}{\sqrt{1+b x^2}} \, dx","Int[ArcCos[Sqrt[1 + b*x^2]]^n/Sqrt[1 + b*x^2],x]","-\frac{\sqrt{-b x^2} \cos ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}","-\frac{\sqrt{-b x^2} \cos ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}",1,"-((Sqrt[-(b*x^2)]*ArcCos[Sqrt[1 + b*x^2]]^(1 + n))/(b*(1 + n)*x))","A",2,2,26,0.07692,1,"{4835, 4642}"
118,1,31,0,0.0608216,"\int \frac{1}{\sqrt{1+b x^2} \cos ^{-1}\left(\sqrt{1+b x^2}\right)} \, dx","Int[1/(Sqrt[1 + b*x^2]*ArcCos[Sqrt[1 + b*x^2]]),x]","-\frac{\sqrt{-b x^2} \log \left(\cos ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}","-\frac{\sqrt{-b x^2} \log \left(\cos ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}",1,"-((Sqrt[-(b*x^2)]*Log[ArcCos[Sqrt[1 + b*x^2]]])/(b*x))","A",2,2,26,0.07692,1,"{4835, 4640}"