1,1,73,73,0.0429948,"\int x^3 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Integrate[x^3*(a + b*Tan[c + d*x^2]),x]","\frac{a x^4}{4}+\frac{i b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{4 d^2}-\frac{b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{2 d}+\frac{1}{4} i b x^4","\frac{a x^4}{4}+\frac{i b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{4 d^2}-\frac{b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{2 d}+\frac{1}{4} i b x^4",1,"(a*x^4)/4 + (I/4)*b*x^4 - (b*x^2*Log[1 + E^((2*I)*(c + d*x^2))])/(2*d) + ((I/4)*b*PolyLog[2, -E^((2*I)*(c + d*x^2))])/d^2","A",1
2,0,0,26,2.0296645,"\int x^2 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Integrate[x^2*(a + b*Tan[c + d*x^2]),x]","\int x^2 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^2 \tan \left(c+d x^2\right),x\right)+\frac{a x^3}{3}",0,"Integrate[x^2*(a + b*Tan[c + d*x^2]), x]","A",-1
3,1,26,26,0.0278727,"\int x \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Integrate[x*(a + b*Tan[c + d*x^2]),x]","\frac{a x^2}{2}-\frac{b \log \left(\cos \left(c+d x^2\right)\right)}{2 d}","\frac{a x^2}{2}-\frac{b \log \left(\cos \left(c+d x^2\right)\right)}{2 d}",1,"(a*x^2)/2 - (b*Log[Cos[c + d*x^2]])/(2*d)","A",1
4,0,0,17,0.7764398,"\int \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Integrate[a + b*Tan[c + d*x^2],x]","\int \left(a+b \tan \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(\tan \left(c+d x^2\right),x\right)+a x",0,"Integrate[a + b*Tan[c + d*x^2], x]","A",-1
5,0,0,22,1.3583873,"\int \frac{a+b \tan \left(c+d x^2\right)}{x} \, dx","Integrate[(a + b*Tan[c + d*x^2])/x,x]","\int \frac{a+b \tan \left(c+d x^2\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d x^2\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Tan[c + d*x^2])/x, x]","A",-1
6,0,0,24,1.6306903,"\int \frac{a+b \tan \left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Tan[c + d*x^2])/x^2,x]","\int \frac{a+b \tan \left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Tan[c + d*x^2])/x^2, x]","A",-1
7,1,295,126,6.5504817,"\int x^3 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^3*(a + b*Tan[c + d*x^2])^2,x]","\frac{1}{4} x^4 \sec (c) \left(a^2 \cos (c)+2 a b \sin (c)-b^2 \cos (c)\right)-\frac{a b \csc (c) \sec (c) \left(d^2 x^4 e^{-i \tan ^{-1}(\cot (c))}-\frac{\cot (c) \left(i \text{Li}_2\left(e^{2 i \left(d x^2-\tan ^{-1}(\cot (c))\right)}\right)+i d x^2 \left(-2 \tan ^{-1}(\cot (c))-\pi \right)-2 \left(d x^2-\tan ^{-1}(\cot (c))\right) \log \left(1-e^{2 i \left(d x^2-\tan ^{-1}(\cot (c))\right)}\right)-2 \tan ^{-1}(\cot (c)) \log \left(\sin \left(d x^2-\tan ^{-1}(\cot (c))\right)\right)-\pi  \log \left(1+e^{-2 i d x^2}\right)+\pi  \log \left(\cos \left(d x^2\right)\right)\right)}{\sqrt{\cot ^2(c)+1}}\right)}{2 d^2 \sqrt{\csc ^2(c) \left(\sin ^2(c)+\cos ^2(c)\right)}}+\frac{b^2 \sec (c) \left(d x^2 \sin (c)+\cos (c) \log \left(\cos (c) \cos \left(d x^2\right)-\sin (c) \sin \left(d x^2\right)\right)\right)}{2 d^2 \left(\sin ^2(c)+\cos ^2(c)\right)}+\frac{b^2 x^2 \sec (c) \sin \left(d x^2\right) \sec \left(c+d x^2\right)}{2 d}","\frac{a^2 x^4}{4}+\frac{i a b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{2 d^2}-\frac{a b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{d}+\frac{1}{2} i a b x^4+\frac{b^2 \log \left(\cos \left(c+d x^2\right)\right)}{2 d^2}+\frac{b^2 x^2 \tan \left(c+d x^2\right)}{2 d}-\frac{b^2 x^4}{4}",1,"(x^4*Sec[c]*(a^2*Cos[c] - b^2*Cos[c] + 2*a*b*Sin[c]))/4 + (b^2*Sec[c]*(Cos[c]*Log[Cos[c]*Cos[d*x^2] - Sin[c]*Sin[d*x^2]] + d*x^2*Sin[c]))/(2*d^2*(Cos[c]^2 + Sin[c]^2)) - (a*b*Csc[c]*((d^2*x^4)/E^(I*ArcTan[Cot[c]]) - (Cot[c]*(I*d*x^2*(-Pi - 2*ArcTan[Cot[c]]) - Pi*Log[1 + E^((-2*I)*d*x^2)] - 2*(d*x^2 - ArcTan[Cot[c]])*Log[1 - E^((2*I)*(d*x^2 - ArcTan[Cot[c]]))] + Pi*Log[Cos[d*x^2]] - 2*ArcTan[Cot[c]]*Log[Sin[d*x^2 - ArcTan[Cot[c]]]] + I*PolyLog[2, E^((2*I)*(d*x^2 - ArcTan[Cot[c]]))]))/Sqrt[1 + Cot[c]^2])*Sec[c])/(2*d^2*Sqrt[Csc[c]^2*(Cos[c]^2 + Sin[c]^2)]) + (b^2*x^2*Sec[c]*Sec[c + d*x^2]*Sin[d*x^2])/(2*d)","B",0
8,0,0,21,2.6219669,"\int x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^2*(a + b*Tan[c + d*x^2])^2,x]","\int x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[x^2*(a + b*Tan[c + d*x^2])^2, x]","A",-1
9,1,75,51,0.1959596,"\int x \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Integrate[x*(a + b*Tan[c + d*x^2])^2,x]","\frac{2 b^2 \tan \left(c+d x^2\right)-i \left((a+i b)^2 \log \left(-\tan \left(c+d x^2\right)+i\right)-(a-i b)^2 \log \left(\tan \left(c+d x^2\right)+i\right)\right)}{4 d}","\frac{1}{2} x^2 \left(a^2-b^2\right)-\frac{a b \log \left(\cos \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tan \left(c+d x^2\right)}{2 d}",1,"((-I)*((a + I*b)^2*Log[I - Tan[c + d*x^2]] - (a - I*b)^2*Log[I + Tan[c + d*x^2]]) + 2*b^2*Tan[c + d*x^2])/(4*d)","C",1
10,0,0,17,2.0778668,"\int \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Integrate[(a + b*Tan[c + d*x^2])^2,x]","\int \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(\left(a+b \tan \left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[(a + b*Tan[c + d*x^2])^2, x]","A",-1
11,0,0,21,8.1635211,"\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x} \, dx","Integrate[(a + b*Tan[c + d*x^2])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Tan[c + d*x^2])^2/x, x]","A",-1
12,0,0,21,3.7551372,"\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Tan[c + d*x^2])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Tan[c + d*x^2])^2/x^2, x]","A",-1
13,1,110,122,1.8299012,"\int \frac{x^3}{a+b \tan \left(c+d x^2\right)} \, dx","Integrate[x^3/(a + b*Tan[c + d*x^2]),x]","\frac{i b \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(d x^2+c\right)}}{a-i b}\right)+d x^2 \left(2 b \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d x^2\right)}}{a-i b}\right)+d x^2 (a+i b)\right)}{4 d^2 \left(a^2+b^2\right)}","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{4 d^2 \left(a^2+b^2\right)}+\frac{b x^2 \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}",1,"(d*x^2*((a + I*b)*d*x^2 + 2*b*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^2)))]) + I*b*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^2)))])/(4*(a^2 + b^2)*d^2)","A",1
14,0,0,21,3.1228287,"\int \frac{x^2}{a+b \tan \left(c+d x^2\right)} \, dx","Integrate[x^2/(a + b*Tan[c + d*x^2]),x]","\int \frac{x^2}{a+b \tan \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \tan \left(c+d x^2\right)},x\right)",0,"Integrate[x^2/(a + b*Tan[c + d*x^2]), x]","A",-1
15,1,82,57,0.1651945,"\int \frac{x}{a+b \tan \left(c+d x^2\right)} \, dx","Integrate[x/(a + b*Tan[c + d*x^2]),x]","\frac{(-b-i a) \log \left(-\tan \left(c+d x^2\right)+i\right)+i (a+i b) \log \left(\tan \left(c+d x^2\right)+i\right)+2 b \log \left(a+b \tan \left(c+d x^2\right)\right)}{4 d \left(a^2+b^2\right)}","\frac{b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{2 d \left(a^2+b^2\right)}+\frac{a x^2}{2 \left(a^2+b^2\right)}",1,"(((-I)*a - b)*Log[I - Tan[c + d*x^2]] + I*(a + I*b)*Log[I + Tan[c + d*x^2]] + 2*b*Log[a + b*Tan[c + d*x^2]])/(4*(a^2 + b^2)*d)","C",1
16,0,0,17,1.2186295,"\int \frac{1}{a+b \tan \left(c+d x^2\right)} \, dx","Integrate[(a + b*Tan[c + d*x^2])^(-1),x]","\int \frac{1}{a+b \tan \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{1}{a+b \tan \left(c+d x^2\right)},x\right)",0,"Integrate[(a + b*Tan[c + d*x^2])^(-1), x]","A",-1
17,0,0,21,0.861381,"\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","Integrate[1/(x*(a + b*Tan[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*x^2])), x]","A",-1
18,0,0,21,2.5424737,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*x^2])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*x^2])), x]","A",-1
19,1,703,202,6.8129444,"\int \frac{x^3}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[x^3/(a + b*Tan[c + d*x^2])^2,x]","-\frac{\sec ^2\left(c+d x^2\right) \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)^2 \left(\frac{a \left(i \text{Li}_2\left(e^{2 i \left(d x^2+c+\tan ^{-1}\left(\frac{a}{b}\right)\right)}\right)+i \left(2 \tan ^{-1}\left(\frac{a}{b}\right)-\pi \right) \left(c+d x^2\right)-2 \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d x^2\right) \log \left(1-e^{2 i \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d x^2\right)}\right)+2 \tan ^{-1}\left(\frac{a}{b}\right) \log \left(\sin \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d x^2\right)\right)-\pi  \log \left(1+e^{-2 i \left(c+d x^2\right)}\right)+\pi  \log \left(\cos \left(c+d x^2\right)\right)\right)}{b \sqrt{\frac{a^2}{b^2}+1}}+e^{i \tan ^{-1}\left(\frac{a}{b}\right)} \left(c+d x^2\right)^2\right)}{2 d^2 (a-i b) (a+i b) \sqrt{\frac{a^2+b^2}{b^2}} \left(a+b \tan \left(c+d x^2\right)\right)^2}-\frac{b c \sec ^2\left(c+d x^2\right) \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)^2 \left(a \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)-b \left(c+d x^2\right)\right)}{d^2 (a-i b) (a+i b) \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)^2}+\frac{b^2 \sec ^2\left(c+d x^2\right) \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)^2 \left(a \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)-b \left(c+d x^2\right)\right)}{2 a d^2 (a-i b) (a+i b) \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)^2}+\frac{\sec ^2\left(c+d x^2\right) \left(b^2 \left(c+d x^2\right) \sin \left(c+d x^2\right)-b^2 c \sin \left(c+d x^2\right)\right) \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{2 a d^2 (a-i b) (a+i b) \left(a+b \tan \left(c+d x^2\right)\right)^2}+\frac{\left(d x^2-c\right) \left(c+d x^2\right) \sec ^2\left(c+d x^2\right) \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)^2}{4 d^2 (a-i b) (a+i b) \left(a+b \tan \left(c+d x^2\right)\right)^2}","-\frac{i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{b \left(2 a d x^2+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{b x^2}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{\left(2 a d x^2+b\right)^2}{8 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x^4}{4 \left(a^2+b^2\right)}",1,"((-c + d*x^2)*(c + d*x^2)*Sec[c + d*x^2]^2*(a*Cos[c + d*x^2] + b*Sin[c + d*x^2])^2)/(4*(a - I*b)*(a + I*b)*d^2*(a + b*Tan[c + d*x^2])^2) + (b^2*(-(b*(c + d*x^2)) + a*Log[a*Cos[c + d*x^2] + b*Sin[c + d*x^2]])*Sec[c + d*x^2]^2*(a*Cos[c + d*x^2] + b*Sin[c + d*x^2])^2)/(2*a*(a - I*b)*(a + I*b)*(a^2 + b^2)*d^2*(a + b*Tan[c + d*x^2])^2) - (b*c*(-(b*(c + d*x^2)) + a*Log[a*Cos[c + d*x^2] + b*Sin[c + d*x^2]])*Sec[c + d*x^2]^2*(a*Cos[c + d*x^2] + b*Sin[c + d*x^2])^2)/((a - I*b)*(a + I*b)*(a^2 + b^2)*d^2*(a + b*Tan[c + d*x^2])^2) - ((E^(I*ArcTan[a/b])*(c + d*x^2)^2 + (a*(I*(c + d*x^2)*(-Pi + 2*ArcTan[a/b]) - Pi*Log[1 + E^((-2*I)*(c + d*x^2))] - 2*(c + d*x^2 + ArcTan[a/b])*Log[1 - E^((2*I)*(c + d*x^2 + ArcTan[a/b]))] + Pi*Log[Cos[c + d*x^2]] + 2*ArcTan[a/b]*Log[Sin[c + d*x^2 + ArcTan[a/b]]] + I*PolyLog[2, E^((2*I)*(c + d*x^2 + ArcTan[a/b]))]))/(Sqrt[1 + a^2/b^2]*b))*Sec[c + d*x^2]^2*(a*Cos[c + d*x^2] + b*Sin[c + d*x^2])^2)/(2*(a - I*b)*(a + I*b)*Sqrt[(a^2 + b^2)/b^2]*d^2*(a + b*Tan[c + d*x^2])^2) + (Sec[c + d*x^2]^2*(a*Cos[c + d*x^2] + b*Sin[c + d*x^2])*(-(b^2*c*Sin[c + d*x^2]) + b^2*(c + d*x^2)*Sin[c + d*x^2]))/(2*a*(a - I*b)*(a + I*b)*d^2*(a + b*Tan[c + d*x^2])^2)","B",0
20,0,0,21,7.2417583,"\int \frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[x^2/(a + b*Tan[c + d*x^2])^2,x]","\int \frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[x^2/(a + b*Tan[c + d*x^2])^2, x]","A",-1
21,1,114,94,1.3037421,"\int \frac{x}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[x/(a + b*Tan[c + d*x^2])^2,x]","\frac{\frac{2 b \left(2 a \log \left(a+b \tan \left(c+d x^2\right)\right)-\frac{a^2+b^2}{a+b \tan \left(c+d x^2\right)}\right)}{\left(a^2+b^2\right)^2}-\frac{i \log \left(-\tan \left(c+d x^2\right)+i\right)}{(a+i b)^2}+\frac{i \log \left(\tan \left(c+d x^2\right)+i\right)}{(a-i b)^2}}{4 d}","-\frac{b}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{a b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{d \left(a^2+b^2\right)^2}+\frac{x^2 \left(a^2-b^2\right)}{2 \left(a^2+b^2\right)^2}",1,"(((-I)*Log[I - Tan[c + d*x^2]])/(a + I*b)^2 + (I*Log[I + Tan[c + d*x^2]])/(a - I*b)^2 + (2*b*(2*a*Log[a + b*Tan[c + d*x^2]] - (a^2 + b^2)/(a + b*Tan[c + d*x^2])))/(a^2 + b^2)^2)/(4*d)","C",1
22,0,0,17,5.9554457,"\int \frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[(a + b*Tan[c + d*x^2])^(-2),x]","\int \frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[(a + b*Tan[c + d*x^2])^(-2), x]","A",-1
23,0,0,21,9.9004104,"\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Tan[c + d*x^2])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*x^2])^2), x]","A",-1
24,0,0,21,7.7812169,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*x^2])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*x^2])^2), x]","A",-1
25,1,261,261,0.0851873,"\int x^3 \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^3*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^4}{4}-\frac{315 i b \text{Li}_8\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{4 d^8}-\frac{315 b \sqrt{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^7}+\frac{315 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}+\frac{105 b x^{3/2} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{105 i b x^2 \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{21 b x^{5/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{7 i b x^3 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{7/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{4} i b x^4","\frac{a x^4}{4}-\frac{315 i b \text{Li}_8\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{4 d^8}-\frac{315 b \sqrt{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^7}+\frac{315 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}+\frac{105 b x^{3/2} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{105 i b x^2 \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{21 b x^{5/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{7 i b x^3 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{7/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{4} i b x^4",1,"(a*x^4)/4 + (I/4)*b*x^4 - (2*b*x^(7/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((7*I)*b*x^3*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (21*b*x^(5/2)*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (((105*I)/2)*b*x^2*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 + (105*b*x^(3/2)*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (((315*I)/2)*b*x*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 - (315*b*Sqrt[x]*PolyLog[7, -E^((2*I)*(c + d*Sqrt[x]))])/(2*d^7) - (((315*I)/4)*b*PolyLog[8, -E^((2*I)*(c + d*Sqrt[x]))])/d^8","A",1
26,1,195,195,0.041977,"\int x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^2*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^3}{3}+\frac{15 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}+\frac{15 b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 i b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{10 b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{5 i b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{3} i b x^3","\frac{a x^3}{3}+\frac{15 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}+\frac{15 b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 i b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{10 b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{5 i b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{3} i b x^3",1,"(a*x^3)/3 + (I/3)*b*x^3 - (2*b*x^(5/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((5*I)*b*x^2*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (10*b*x^(3/2)*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - ((15*I)*b*x*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 + (15*b*Sqrt[x]*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (((15*I)/2)*b*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^6","A",1
27,1,135,135,0.0368403,"\int x \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^2}{2}-\frac{3 i b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{3 b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 i b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{2} i b x^2","\frac{a x^2}{2}-\frac{3 i b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{3 b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 i b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{2} i b x^2",1,"(a*x^2)/2 + (I/2)*b*x^2 - (2*b*x^(3/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((3*I)*b*x*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (3*b*Sqrt[x]*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (((3*I)/2)*b*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4","A",1
28,1,66,66,0.0249753,"\int \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Integrate[a + b*Tan[c + d*Sqrt[x]],x]","a x+\frac{i b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i b x","a x+\frac{i b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i b x",1,"a*x + I*b*x - (2*b*Sqrt[x]*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + (I*b*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2","A",1
29,0,0,24,2.6189782,"\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])/x,x]","\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt{x}\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Tan[c + d*Sqrt[x]])/x, x]","A",-1
30,0,0,26,10.9415368,"\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x^2} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Tan[c + d*Sqrt[x]])/x^2, x]","A",-1
31,1,379,402,3.667759,"\int x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^2*(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{1}{3} \left(x^3 \left(a^2+2 a b \tan (c)-b^2\right)+b \left(-\frac{30 \left(2 a d x^{3/2}-3 b x\right) \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{30 i \left(a d x^2-2 b x^{3/2}\right) \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{45 i a \text{Li}_6\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{90 a \sqrt{x} \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{90 i a x \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{12 a x^{5/2} \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d}-\frac{4 i a x^3}{1+e^{2 i c}}-\frac{45 b \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{90 i b \sqrt{x} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{30 b x^2 \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{12 i b x^{5/2}}{d+e^{2 i c} d}\right)+\frac{6 b^2 x^{5/2} \sec (c) \sin \left(d \sqrt{x}\right) \sec \left(c+d \sqrt{x}\right)}{d}\right)","\frac{a^2 x^3}{3}+\frac{15 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{30 a b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{30 i a b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{20 a b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{10 i a b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 a b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3-\frac{15 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{30 i b^2 \sqrt{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{30 b^2 x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{20 i b^2 x^{3/2} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{10 b^2 x^2 \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{5/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{5/2}}{d}-\frac{b^2 x^3}{3}",1,"(b*(((12*I)*b*x^(5/2))/(d + d*E^((2*I)*c)) - ((4*I)*a*x^3)/(1 + E^((2*I)*c)) + (30*b*x^2*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))])/d^2 - (12*a*x^(5/2)*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))])/d - ((30*I)*(-2*b*x^(3/2) + a*d*x^2)*PolyLog[2, -E^((-2*I)*(c + d*Sqrt[x]))])/d^3 - (30*(-3*b*x + 2*a*d*x^(3/2))*PolyLog[3, -E^((-2*I)*(c + d*Sqrt[x]))])/d^4 - ((90*I)*b*Sqrt[x]*PolyLog[4, -E^((-2*I)*(c + d*Sqrt[x]))])/d^5 + ((90*I)*a*x*PolyLog[4, -E^((-2*I)*(c + d*Sqrt[x]))])/d^4 - (45*b*PolyLog[5, -E^((-2*I)*(c + d*Sqrt[x]))])/d^6 + (90*a*Sqrt[x]*PolyLog[5, -E^((-2*I)*(c + d*Sqrt[x]))])/d^5 - ((45*I)*a*PolyLog[6, -E^((-2*I)*(c + d*Sqrt[x]))])/d^6) + (6*b^2*x^(5/2)*Sec[c]*Sec[c + d*Sqrt[x]]*Sin[d*Sqrt[x]])/d + x^3*(a^2 - b^2 + 2*a*b*Tan[c]))/3","A",1
32,1,365,274,2.3216308,"\int x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x*(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{1}{2} x^2 \left(a^2+2 a b \tan (c)-b^2\right)+\frac{b \left(-6 i \left(1+e^{2 i c}\right) d \sqrt{x} \left(a d \sqrt{x}-b\right) \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)+3 \left(1+e^{2 i c}\right) \left(b-2 a d \sqrt{x}\right) \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)-4 a e^{2 i c} d^3 x^{3/2} \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)-4 a d^3 x^{3/2} \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)+3 i a e^{2 i c} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)+3 i a \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt{x}\right)}\right)-2 i a d^4 x^2+6 b e^{2 i c} d^2 x \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)+6 b d^2 x \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)+4 i b d^3 x^{3/2}\right)}{\left(1+e^{2 i c}\right) d^4}+\frac{2 b^2 x^{3/2} \sec (c) \sin \left(d \sqrt{x}\right) \sec \left(c+d \sqrt{x}\right)}{d}","\frac{a^2 x^2}{2}-\frac{3 i a b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{6 a b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{6 i a b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 a b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i a b x^2+\frac{3 b^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{6 b^2 x \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{3/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{3/2}}{d}-\frac{1}{2} b^2 x^2",1,"(b*((4*I)*b*d^3*x^(3/2) - (2*I)*a*d^4*x^2 + 6*b*d^2*x*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))] + 6*b*d^2*E^((2*I)*c)*x*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))] - 4*a*d^3*x^(3/2)*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))] - 4*a*d^3*E^((2*I)*c)*x^(3/2)*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))] - (6*I)*d*(1 + E^((2*I)*c))*(-b + a*d*Sqrt[x])*Sqrt[x]*PolyLog[2, -E^((-2*I)*(c + d*Sqrt[x]))] + 3*(1 + E^((2*I)*c))*(b - 2*a*d*Sqrt[x])*PolyLog[3, -E^((-2*I)*(c + d*Sqrt[x]))] + (3*I)*a*PolyLog[4, -E^((-2*I)*(c + d*Sqrt[x]))] + (3*I)*a*E^((2*I)*c)*PolyLog[4, -E^((-2*I)*(c + d*Sqrt[x]))]))/(d^4*(1 + E^((2*I)*c))) + (2*b^2*x^(3/2)*Sec[c]*Sec[c + d*Sqrt[x]]*Sin[d*Sqrt[x]])/d + (x^2*(a^2 - b^2 + 2*a*b*Tan[c]))/2","A",1
33,1,308,119,6.334806,"\int \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])^2,x]","x \sec (c) \left(a^2 \cos (c)+2 a b \sin (c)-b^2 \cos (c)\right)-\frac{2 a b \csc (c) \sec (c) \left(d^2 x e^{-i \tan ^{-1}(\cot (c))}-\frac{\cot (c) \left(i \text{Li}_2\left(e^{2 i \left(d \sqrt{x}-\tan ^{-1}(\cot (c))\right)}\right)+i d \sqrt{x} \left(-2 \tan ^{-1}(\cot (c))-\pi \right)-2 \left(d \sqrt{x}-\tan ^{-1}(\cot (c))\right) \log \left(1-e^{2 i \left(d \sqrt{x}-\tan ^{-1}(\cot (c))\right)}\right)-2 \tan ^{-1}(\cot (c)) \log \left(\sin \left(d \sqrt{x}-\tan ^{-1}(\cot (c))\right)\right)-\pi  \log \left(1+e^{-2 i d \sqrt{x}}\right)+\pi  \log \left(\cos \left(d \sqrt{x}\right)\right)\right)}{\sqrt{\cot ^2(c)+1}}\right)}{d^2 \sqrt{\csc ^2(c) \left(\sin ^2(c)+\cos ^2(c)\right)}}+\frac{2 b^2 \sec (c) \left(d \sqrt{x} \sin (c)+\cos (c) \log \left(\cos (c) \cos \left(d \sqrt{x}\right)-\sin (c) \sin \left(d \sqrt{x}\right)\right)\right)}{d^2 \left(\sin ^2(c)+\cos ^2(c)\right)}+\frac{2 b^2 \sqrt{x} \sec (c) \sin \left(d \sqrt{x}\right) \sec \left(c+d \sqrt{x}\right)}{d}","a^2 x+\frac{2 i a b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 a b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+2 i a b x+\frac{2 b^2 \log \left(\cos \left(c+d \sqrt{x}\right)\right)}{d^2}+\frac{2 b^2 \sqrt{x} \tan \left(c+d \sqrt{x}\right)}{d}-b^2 x",1,"x*Sec[c]*(a^2*Cos[c] - b^2*Cos[c] + 2*a*b*Sin[c]) + (2*b^2*Sec[c]*(Cos[c]*Log[Cos[c]*Cos[d*Sqrt[x]] - Sin[c]*Sin[d*Sqrt[x]]] + d*Sqrt[x]*Sin[c]))/(d^2*(Cos[c]^2 + Sin[c]^2)) - (2*a*b*Csc[c]*((d^2*x)/E^(I*ArcTan[Cot[c]]) - (Cot[c]*(I*d*Sqrt[x]*(-Pi - 2*ArcTan[Cot[c]]) - Pi*Log[1 + E^((-2*I)*d*Sqrt[x])] - 2*(d*Sqrt[x] - ArcTan[Cot[c]])*Log[1 - E^((2*I)*(d*Sqrt[x] - ArcTan[Cot[c]]))] + Pi*Log[Cos[d*Sqrt[x]]] - 2*ArcTan[Cot[c]]*Log[Sin[d*Sqrt[x] - ArcTan[Cot[c]]]] + I*PolyLog[2, E^((2*I)*(d*Sqrt[x] - ArcTan[Cot[c]]))]))/Sqrt[1 + Cot[c]^2])*Sec[c])/(d^2*Sqrt[Csc[c]^2*(Cos[c]^2 + Sin[c]^2)]) + (2*b^2*Sqrt[x]*Sec[c]*Sec[c + d*Sqrt[x]]*Sin[d*Sqrt[x]])/d","B",0
34,0,0,23,23.123224,"\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Tan[c + d*Sqrt[x]])^2/x, x]","A",-1
35,0,0,23,8.6351333,"\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Tan[c + d*Sqrt[x]])^2/x^2, x]","A",-1
36,1,401,460,1.9760303,"\int \frac{x^3}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Integrate[x^3/(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{8 b d^7 x^{7/2} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+28 i b d^6 x^3 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+84 b d^5 x^{5/2} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-210 i b d^4 x^2 \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-420 b d^3 x^{3/2} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+630 i b d^2 x \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+630 b d \sqrt{x} \text{Li}_7\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-315 i b \text{Li}_8\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+a d^8 x^4+i b d^8 x^4}{4 d^8 \left(a^2+b^2\right)}","\frac{315 i b \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{4 d^8 \left(a^2+b^2\right)}+\frac{315 b \sqrt{x} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^7 \left(a^2+b^2\right)}-\frac{315 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}-\frac{105 b x^{3/2} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}+\frac{105 i b x^2 \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{21 b x^{5/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{7 i b x^3 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b x^{7/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}",1,"(a*d^8*x^4 + I*b*d^8*x^4 + 8*b*d^7*x^(7/2)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (28*I)*b*d^6*x^3*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 84*b*d^5*x^(5/2)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (210*I)*b*d^4*x^2*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - 420*b*d^3*x^(3/2)*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (630*I)*b*d^2*x*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 630*b*d*Sqrt[x]*PolyLog[7, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (315*I)*b*PolyLog[8, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/(4*(a^2 + b^2)*d^8)","A",1
37,1,308,344,1.5043036,"\int \frac{x^2}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Integrate[x^2/(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{12 b d^5 x^{5/2} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+30 i b d^4 x^2 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+60 b d^3 x^{3/2} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-90 i b d^2 x \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-90 b d \sqrt{x} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+45 i b \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+2 a d^6 x^3+2 i b d^6 x^3}{6 d^6 \left(a^2+b^2\right)}","-\frac{15 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}-\frac{15 b \sqrt{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}+\frac{15 i b x \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}+\frac{10 b x^{3/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{5 i b x^2 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b x^{5/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}",1,"(2*a*d^6*x^3 + (2*I)*b*d^6*x^3 + 12*b*d^5*x^(5/2)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (30*I)*b*d^4*x^2*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 60*b*d^3*x^(3/2)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (90*I)*b*d^2*x*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - 90*b*d*Sqrt[x]*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (45*I)*b*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/(6*(a^2 + b^2)*d^6)","A",1
38,1,213,234,1.2833822,"\int \frac{x}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Integrate[x/(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{4 b d^3 x^{3/2} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+6 i b d^2 x \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+6 b d \sqrt{x} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-3 i b \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+a d^4 x^2+i b d^4 x^2}{2 d^4 \left(a^2+b^2\right)}","\frac{3 i b \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{3 b \sqrt{x} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{3 i b x \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b x^{3/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}",1,"(a*d^4*x^2 + I*b*d^4*x^2 + 4*b*d^3*x^(3/2)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (6*I)*b*d^2*x*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 6*b*d*Sqrt[x]*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (3*I)*b*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/(2*(a^2 + b^2)*d^4)","A",1
39,1,111,119,0.2577244,"\int \frac{1}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])^(-1),x]","\frac{i b \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+2 b d \sqrt{x} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)+d^2 x (a+i b)}{d^2 \left(a^2+b^2\right)}","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b \sqrt{x} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}",1,"((a + I*b)*d^2*x + 2*b*d*Sqrt[x]*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + I*b*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/((a^2 + b^2)*d^2)","A",1
40,0,0,23,11.3653689,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x*(a + b*Tan[c + d*Sqrt[x]])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*Sqrt[x]])), x]","A",-1
41,0,0,23,12.1855544,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])), x]","A",-1
42,1,816,1147,6.1088195,"\int \frac{x^2}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^2/(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{\frac{(a \cos (c)-b \sin (c)) x^3}{a \cos (c)+b \sin (c)}+\frac{6 b^2 \sin \left(d \sqrt{x}\right) x^{5/2}}{d (a \cos (c)+b \sin (c)) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)}+\frac{b \left(\frac{4 a d x^3}{a-i b}+\frac{12 b x^{5/2}}{a-i b}+\frac{12 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(\frac{e^{-2 i \left(c+d \sqrt{x}\right)} (a+i b)}{a-i b}+1\right) x^{5/2}}{(a+i b) (i a+b)}+\frac{30 b \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(\frac{e^{-2 i \left(c+d \sqrt{x}\right)} (a+i b)}{a-i b}+1\right) x^2}{(a+i b) (i a+b) d}+\frac{15 b \left(b \left(-1+e^{2 i c}\right)+i a \left(1+e^{2 i c}\right)\right) \left(-4 i x^{3/2} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d^3-6 x \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d^2+6 i \sqrt{x} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d+3 \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) d^5}+\frac{15 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(2 x^2 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d^4-4 i x^{3/2} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d^3-6 x \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d^2+6 i \sqrt{x} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right) d+3 \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) d^5}\right)}{d \left(-e^{2 i c} b+b-i a \left(1+e^{2 i c}\right)\right)}}{3 \left(a^2+b^2\right)}","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{4 b \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{(a-i b)^2 (a+i b) d}-\frac{4 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{\left(a^2+b^2\right)^2 d}-\frac{4 i b^2 x^{5/2}}{\left(a^2+b^2\right)^2 d}+\frac{4 b^2 x^{5/2}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt{x}\right)}-b\right)}+\frac{10 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^2}{\left(a^2+b^2\right)^2 d^2}+\frac{10 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{(i a-b) (a-i b)^2 d^2}-\frac{10 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^2}-\frac{20 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{20 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{(a-i b)^2 (a+i b) d^3}-\frac{20 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{30 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}-\frac{30 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^4}+\frac{30 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}+\frac{30 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{30 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{(a-i b)^2 (a+i b) d^5}+\frac{30 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{15 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}+\frac{15 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{(i a-b) (a-i b)^2 d^6}-\frac{15 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}",1,"((b*((12*b*x^(5/2))/(a - I*b) + (4*a*d*x^3)/(a - I*b) + (30*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^2*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/((a + I*b)*(I*a + b)*d) + (12*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(5/2)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/((a + I*b)*(I*a + b)) + (15*b*(b*(-1 + E^((2*I)*c)) + I*a*(1 + E^((2*I)*c)))*((-4*I)*d^3*x^(3/2)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - 6*d^2*x*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (6*I)*d*Sqrt[x]*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 3*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))]))/((a^2 + b^2)*d^5) + (15*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*(2*d^4*x^2*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (4*I)*d^3*x^(3/2)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - 6*d^2*x*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + (6*I)*d*Sqrt[x]*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] + 3*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))]))/((a^2 + b^2)*d^5)))/(d*(b - b*E^((2*I)*c) - I*a*(1 + E^((2*I)*c)))) + (x^3*(a*Cos[c] - b*Sin[c]))/(a*Cos[c] + b*Sin[c]) + (6*b^2*x^(5/2)*Sin[d*Sqrt[x]])/(d*(a*Cos[c] + b*Sin[c])*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])))/(3*(a^2 + b^2))","A",1
43,1,633,787,4.5200226,"\int \frac{x}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x/(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{\frac{2 b \left(\frac{3 b \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(2 d \sqrt{x} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-i \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(2 d^2 x \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-2 i d \sqrt{x} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)-\text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)\right)}{d^3 \left(a^2+b^2\right)}+\frac{4 a x^{3/2} \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)}{(a+i b) (b+i a)}+\frac{6 b x \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt{x}\right)}}{a-i b}\right)}{d (a+i b) (b+i a)}+\frac{2 a d x^2}{a-i b}+\frac{4 b x^{3/2}}{a-i b}\right)}{d \left(-i a \left(1+e^{2 i c}\right)+b \left(-e^{2 i c}\right)+b\right)}+\frac{4 b^2 x^{3/2} \sin \left(d \sqrt{x}\right)}{d (a \cos (c)+b \sin (c)) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)}+\frac{x^2 (a \cos (c)-b \sin (c))}{a \cos (c)+b \sin (c)}}{2 \left(a^2+b^2\right)}","\frac{3 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}+\frac{3 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{6 b^2 x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{6 b^2 x \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2}}{d \left(a^2+b^2\right)^2}-\frac{2 b^2 x^2}{\left(a^2+b^2\right)^2}+\frac{4 b^2 x^{3/2}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt{x}\right)}+i a-b\right)}-\frac{3 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 (-b+i a) (a-i b)^2}+\frac{6 b \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}+\frac{6 b x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{4 b x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{2 b x^2}{(-b+i a) (a-i b)^2}+\frac{x^2}{2 (a-i b)^2}",1,"((2*b*((4*b*x^(3/2))/(a - I*b) + (2*a*d*x^2)/(a - I*b) + (6*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/((a + I*b)*(I*a + b)*d) + (4*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(3/2)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))])/((a + I*b)*(I*a + b)) + (3*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*(2*d*Sqrt[x]*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - I*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))]))/((a^2 + b^2)*d^3) + (3*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*(2*d^2*x*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - (2*I)*d*Sqrt[x]*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))] - PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))]))/((a^2 + b^2)*d^3)))/(d*(b - b*E^((2*I)*c) - I*a*(1 + E^((2*I)*c)))) + (x^2*(a*Cos[c] - b*Sin[c]))/(a*Cos[c] + b*Sin[c]) + (4*b^2*x^(3/2)*Sin[d*Sqrt[x]])/(d*(a*Cos[c] + b*Sin[c])*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])))/(2*(a^2 + b^2))","A",1
44,1,772,204,6.5934398,"\int \frac{1}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[(a + b*Tan[c + d*Sqrt[x]])^(-2),x]","-\frac{2 \sec ^2\left(c+d \sqrt{x}\right) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)^2 \left(\frac{a \left(i \text{Li}_2\left(e^{2 i \left(c+\tan ^{-1}\left(\frac{a}{b}\right)+d \sqrt{x}\right)}\right)+i \left(2 \tan ^{-1}\left(\frac{a}{b}\right)-\pi \right) \left(c+d \sqrt{x}\right)-2 \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d \sqrt{x}\right) \log \left(1-e^{2 i \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d \sqrt{x}\right)}\right)+2 \tan ^{-1}\left(\frac{a}{b}\right) \log \left(\sin \left(\tan ^{-1}\left(\frac{a}{b}\right)+c+d \sqrt{x}\right)\right)-\pi  \log \left(1+e^{-2 i \left(c+d \sqrt{x}\right)}\right)+\pi  \log \left(\cos \left(c+d \sqrt{x}\right)\right)\right)}{b \sqrt{\frac{a^2}{b^2}+1}}+e^{i \tan ^{-1}\left(\frac{a}{b}\right)} \left(c+d \sqrt{x}\right)^2\right)}{d^2 (a-i b) (a+i b) \sqrt{\frac{a^2+b^2}{b^2}} \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}-\frac{4 b c \sec ^2\left(c+d \sqrt{x}\right) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)^2 \left(a \log \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)-b \left(c+d \sqrt{x}\right)\right)}{d^2 (a-i b) (a+i b) \left(a^2+b^2\right) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}+\frac{2 b^2 \sec ^2\left(c+d \sqrt{x}\right) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)^2 \left(a \log \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)-b \left(c+d \sqrt{x}\right)\right)}{a d^2 (a-i b) (a+i b) \left(a^2+b^2\right) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}+\frac{2 \sec ^2\left(c+d \sqrt{x}\right) \left(b^2 \left(c+d \sqrt{x}\right) \sin \left(c+d \sqrt{x}\right)-b^2 c \sin \left(c+d \sqrt{x}\right)\right) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)}{a d^2 (a-i b) (a+i b) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}+\frac{\left(d \sqrt{x}-c\right) \left(c+d \sqrt{x}\right) \sec ^2\left(c+d \sqrt{x}\right) \left(a \cos \left(c+d \sqrt{x}\right)+b \sin \left(c+d \sqrt{x}\right)\right)^2}{d^2 (a-i b) (a+i b) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}","-\frac{2 i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{2 b \left(2 a d \sqrt{x}+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{2 b \sqrt{x}}{d \left(a^2+b^2\right) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)}+\frac{\left(2 a d \sqrt{x}+b\right)^2}{2 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x}{a^2+b^2}",1,"((-c + d*Sqrt[x])*(c + d*Sqrt[x])*Sec[c + d*Sqrt[x]]^2*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])^2)/((a - I*b)*(a + I*b)*d^2*(a + b*Tan[c + d*Sqrt[x]])^2) + (2*b^2*(-(b*(c + d*Sqrt[x])) + a*Log[a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]]])*Sec[c + d*Sqrt[x]]^2*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])^2)/(a*(a - I*b)*(a + I*b)*(a^2 + b^2)*d^2*(a + b*Tan[c + d*Sqrt[x]])^2) - (4*b*c*(-(b*(c + d*Sqrt[x])) + a*Log[a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]]])*Sec[c + d*Sqrt[x]]^2*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])^2)/((a - I*b)*(a + I*b)*(a^2 + b^2)*d^2*(a + b*Tan[c + d*Sqrt[x]])^2) - (2*(E^(I*ArcTan[a/b])*(c + d*Sqrt[x])^2 + (a*(I*(c + d*Sqrt[x])*(-Pi + 2*ArcTan[a/b]) - Pi*Log[1 + E^((-2*I)*(c + d*Sqrt[x]))] - 2*(c + d*Sqrt[x] + ArcTan[a/b])*Log[1 - E^((2*I)*(c + d*Sqrt[x] + ArcTan[a/b]))] + Pi*Log[Cos[c + d*Sqrt[x]]] + 2*ArcTan[a/b]*Log[Sin[c + d*Sqrt[x] + ArcTan[a/b]]] + I*PolyLog[2, E^((2*I)*(c + d*Sqrt[x] + ArcTan[a/b]))]))/(Sqrt[1 + a^2/b^2]*b))*Sec[c + d*Sqrt[x]]^2*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])^2)/((a - I*b)*(a + I*b)*Sqrt[(a^2 + b^2)/b^2]*d^2*(a + b*Tan[c + d*Sqrt[x]])^2) + (2*Sec[c + d*Sqrt[x]]^2*(a*Cos[c + d*Sqrt[x]] + b*Sin[c + d*Sqrt[x]])*(-(b^2*c*Sin[c + d*Sqrt[x]]) + b^2*(c + d*Sqrt[x])*Sin[c + d*Sqrt[x]]))/(a*(a - I*b)*(a + I*b)*d^2*(a + b*Tan[c + d*Sqrt[x]])^2)","B",0
45,0,0,23,46.8291826,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Tan[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*Sqrt[x]])^2), x]","A",-1
46,0,0,23,21.1612994,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])^2), x]","A",-1
47,1,287,287,0.1337955,"\int x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Integrate[x^2*(a + b*Tan[c + d*x^(1/3)]),x]","\frac{a x^3}{3}+\frac{945 b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^9}-\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}-\frac{945 b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{630 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{315 b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{126 i b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{42 b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{12 i b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{3} i b x^3","\frac{a x^3}{3}+\frac{945 b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^9}-\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}-\frac{945 b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{630 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{315 b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{126 i b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{42 b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{12 i b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{3} i b x^3",1,"(a*x^3)/3 + (I/3)*b*x^3 - (3*b*x^(8/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + ((12*I)*b*x^(7/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (42*b*x^2*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 - ((126*I)*b*x^(5/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 + (315*b*x^(4/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/d^5 + ((630*I)*b*x*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6 - (945*b*x^(2/3)*PolyLog[7, -E^((2*I)*(c + d*x^(1/3)))])/d^7 - ((945*I)*b*x^(1/3)*PolyLog[8, -E^((2*I)*(c + d*x^(1/3)))])/d^8 + (945*b*PolyLog[9, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^9)","A",1
48,1,203,203,0.0435283,"\int x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Integrate[x*(a + b*Tan[c + d*x^(1/3)]),x]","\frac{a x^2}{2}+\frac{45 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{4 d^6}+\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^5}-\frac{45 i b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^4}-\frac{15 b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{15 i b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^2}-\frac{3 b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{2} i b x^2","\frac{a x^2}{2}+\frac{45 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{4 d^6}+\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^5}-\frac{45 i b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^4}-\frac{15 b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{15 i b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^2}-\frac{3 b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{2} i b x^2",1,"(a*x^2)/2 + (I/2)*b*x^2 - (3*b*x^(5/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + (((15*I)/2)*b*x^(4/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (15*b*x*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 - (((45*I)/2)*b*x^(2/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 + (45*b*x^(1/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^5) + (((45*I)/4)*b*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6","A",1
49,1,98,98,0.0306182,"\int \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Integrate[a + b*Tan[c + d*x^(1/3)],x]","a x-\frac{3 b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^3}+\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i b x","a x-\frac{3 b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^3}+\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i b x",1,"a*x + I*b*x - (3*b*x^(2/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + ((3*I)*b*x^(1/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (3*b*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^3)","A",1
50,0,0,24,2.6902879,"\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])/x,x]","\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt[3]{x}\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Tan[c + d*x^(1/3)])/x, x]","A",-1
51,0,0,26,4.9399408,"\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x^2} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])/x^2,x]","\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt[3]{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Tan[c + d*x^(1/3)])/x^2, x]","A",-1
52,1,599,597,4.8892927,"\int x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Integrate[x^2*(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{1}{3} \left(x^3 \left(a^2+2 a b \tan (c)-b^2\right)+b \left(\frac{9 a \left(-8 i d^7 x^{7/3} \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-28 d^6 x^2 \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+84 i d^5 x^{5/3} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+105 \left(2 d^4 x^{4/3} \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-4 i d^3 x \text{Li}_6\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-6 d^2 x^{2/3} \text{Li}_7\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+6 i d \sqrt[3]{x} \text{Li}_8\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+3 \text{Li}_9\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)\right)\right)}{d^9}-\frac{18 a x^{8/3} \log \left(1+e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}-\frac{4 i a x^3}{1+e^{2 i c}}+\frac{72 b x^{7/3} \log \left(1+e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{63 b \left(4 i d^6 x^2 \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+12 d^5 x^{5/3} \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-15 i \left(2 d^4 x^{4/3} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-4 i d^3 x \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-6 d^2 x^{2/3} \text{Li}_6\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+6 i d \sqrt[3]{x} \text{Li}_7\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+3 \text{Li}_8\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)\right)\right)}{d^9}+\frac{18 i b x^{8/3}}{d+e^{2 i c} d}\right)+\frac{9 b^2 x^{8/3} \sec (c) \sin \left(d \sqrt[3]{x}\right) \sec \left(c+d \sqrt[3]{x}\right)}{d}\right)","\frac{a^2 x^3}{3}+\frac{945 a b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}-\frac{1890 i a b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}-\frac{1890 a b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{1260 i a b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{630 a b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{252 i a b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{84 a b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{24 i a b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{6 a b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3+\frac{945 i b^2 \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}+\frac{1890 b^2 \sqrt[3]{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}-\frac{1890 i b^2 x^{2/3} \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}-\frac{1260 b^2 x \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{630 i b^2 x^{4/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{252 b^2 x^{5/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{84 i b^2 x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{24 b^2 x^{7/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{8/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{8/3}}{d}-\frac{b^2 x^3}{3}",1,"(b*(((18*I)*b*x^(8/3))/(d + d*E^((2*I)*c)) - ((4*I)*a*x^3)/(1 + E^((2*I)*c)) + (72*b*x^(7/3)*Log[1 + E^((-2*I)*(c + d*x^(1/3)))])/d^2 - (18*a*x^(8/3)*Log[1 + E^((-2*I)*(c + d*x^(1/3)))])/d + (63*b*((4*I)*d^6*x^2*PolyLog[2, -E^((-2*I)*(c + d*x^(1/3)))] + 12*d^5*x^(5/3)*PolyLog[3, -E^((-2*I)*(c + d*x^(1/3)))] - (15*I)*(2*d^4*x^(4/3)*PolyLog[4, -E^((-2*I)*(c + d*x^(1/3)))] - (4*I)*d^3*x*PolyLog[5, -E^((-2*I)*(c + d*x^(1/3)))] - 6*d^2*x^(2/3)*PolyLog[6, -E^((-2*I)*(c + d*x^(1/3)))] + (6*I)*d*x^(1/3)*PolyLog[7, -E^((-2*I)*(c + d*x^(1/3)))] + 3*PolyLog[8, -E^((-2*I)*(c + d*x^(1/3)))])))/d^9 + (9*a*((-8*I)*d^7*x^(7/3)*PolyLog[2, -E^((-2*I)*(c + d*x^(1/3)))] - 28*d^6*x^2*PolyLog[3, -E^((-2*I)*(c + d*x^(1/3)))] + (84*I)*d^5*x^(5/3)*PolyLog[4, -E^((-2*I)*(c + d*x^(1/3)))] + 105*(2*d^4*x^(4/3)*PolyLog[5, -E^((-2*I)*(c + d*x^(1/3)))] - (4*I)*d^3*x*PolyLog[6, -E^((-2*I)*(c + d*x^(1/3)))] - 6*d^2*x^(2/3)*PolyLog[7, -E^((-2*I)*(c + d*x^(1/3)))] + (6*I)*d*x^(1/3)*PolyLog[8, -E^((-2*I)*(c + d*x^(1/3)))] + 3*PolyLog[9, -E^((-2*I)*(c + d*x^(1/3)))])))/d^9) + (9*b^2*x^(8/3)*Sec[c]*Sec[c + d*x^(1/3)]*Sin[d*x^(1/3)])/d + x^3*(a^2 - b^2 + 2*a*b*Tan[c]))/3","A",1
53,1,383,408,3.4740312,"\int x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Integrate[x*(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{1}{2} \left(x^2 \left(a^2+2 a b \tan (c)-b^2\right)+b \left(-\frac{30 \left(2 a d x-3 b x^{2/3}\right) \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 i \left(a d x^{4/3}-2 b x\right) \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{45 i a \text{Li}_6\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{90 a \sqrt[3]{x} \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{90 i a x^{2/3} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{12 a x^{5/3} \log \left(1+e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}-\frac{4 i a x^2}{1+e^{2 i c}}-\frac{45 b \text{Li}_5\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}-\frac{90 i b \sqrt[3]{x} \text{Li}_4\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{30 b x^{4/3} \log \left(1+e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{12 i b x^{5/3}}{d+e^{2 i c} d}\right)+\frac{6 b^2 x^{5/3} \sec (c) \sin \left(d \sqrt[3]{x}\right) \sec \left(c+d \sqrt[3]{x}\right)}{d}\right)","\frac{a^2 x^2}{2}+\frac{45 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}+\frac{45 a b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{45 i a b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 a b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{15 i a b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{6 a b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i a b x^2-\frac{45 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}+\frac{45 i b^2 \sqrt[3]{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{45 b^2 x^{2/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 i b^2 x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{15 b^2 x^{4/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{5/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{5/3}}{d}-\frac{1}{2} b^2 x^2",1,"(b*(((12*I)*b*x^(5/3))/(d + d*E^((2*I)*c)) - ((4*I)*a*x^2)/(1 + E^((2*I)*c)) + (30*b*x^(4/3)*Log[1 + E^((-2*I)*(c + d*x^(1/3)))])/d^2 - (12*a*x^(5/3)*Log[1 + E^((-2*I)*(c + d*x^(1/3)))])/d - ((30*I)*(-2*b*x + a*d*x^(4/3))*PolyLog[2, -E^((-2*I)*(c + d*x^(1/3)))])/d^3 - (30*(-3*b*x^(2/3) + 2*a*d*x)*PolyLog[3, -E^((-2*I)*(c + d*x^(1/3)))])/d^4 - ((90*I)*b*x^(1/3)*PolyLog[4, -E^((-2*I)*(c + d*x^(1/3)))])/d^5 + ((90*I)*a*x^(2/3)*PolyLog[4, -E^((-2*I)*(c + d*x^(1/3)))])/d^4 - (45*b*PolyLog[5, -E^((-2*I)*(c + d*x^(1/3)))])/d^6 + (90*a*x^(1/3)*PolyLog[5, -E^((-2*I)*(c + d*x^(1/3)))])/d^5 - ((45*I)*a*PolyLog[6, -E^((-2*I)*(c + d*x^(1/3)))])/d^6) + (6*b^2*x^(5/3)*Sec[c]*Sec[c + d*x^(1/3)]*Sin[d*x^(1/3)])/d + x^2*(a^2 - b^2 + 2*a*b*Tan[c]))/2","A",1
54,1,185,206,2.1347214,"\int \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])^2,x]","x \left(a^2+2 a b \tan (c)-b^2\right)+\frac{b \left(\frac{6 i b d^2 x^{2/3}-4 i a d^3 x}{1+e^{2 i c}}+3 i \left(b-2 a d \sqrt[3]{x}\right) \text{Li}_2\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)+6 d \sqrt[3]{x} \left(b-a d \sqrt[3]{x}\right) \log \left(1+e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)-3 a \text{Li}_3\left(-e^{-2 i \left(c+d \sqrt[3]{x}\right)}\right)\right)}{d^3}+\frac{3 b^2 x^{2/3} \sec (c) \sin \left(d \sqrt[3]{x}\right) \sec \left(c+d \sqrt[3]{x}\right)}{d}","a^2 x-\frac{3 a b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{6 i a b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{6 a b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+2 i a b x-\frac{3 i b^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{2/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{2/3}}{d}-b^2 x",1,"(b*(((6*I)*b*d^2*x^(2/3) - (4*I)*a*d^3*x)/(1 + E^((2*I)*c)) + 6*d*(b - a*d*x^(1/3))*x^(1/3)*Log[1 + E^((-2*I)*(c + d*x^(1/3)))] + (3*I)*(b - 2*a*d*x^(1/3))*PolyLog[2, -E^((-2*I)*(c + d*x^(1/3)))] - 3*a*PolyLog[3, -E^((-2*I)*(c + d*x^(1/3)))]))/d^3 + (3*b^2*x^(2/3)*Sec[c]*Sec[c + d*x^(1/3)]*Sin[d*x^(1/3)])/d + x*(a^2 - b^2 + 2*a*b*Tan[c])","A",1
55,0,0,23,17.9369562,"\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Tan[c + d*x^(1/3)])^2/x, x]","A",-1
56,0,0,23,8.8048628,"\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Tan[c + d*x^(1/3)])^2/x^2, x]","A",-1
57,1,451,511,2.1361195,"\int \frac{x^2}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Integrate[x^2/(a + b*Tan[c + d*x^(1/3)]),x]","\frac{18 b d^8 x^{8/3} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+72 i b d^7 x^{7/3} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+252 b d^6 x^2 \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-756 i b d^5 x^{5/3} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-1890 b d^4 x^{4/3} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+3780 i b d^3 x \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+5670 b d^2 x^{2/3} \text{Li}_7\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-5670 i b d \sqrt[3]{x} \text{Li}_8\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-2835 b \text{Li}_9\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+2 a d^9 x^3+2 i b d^9 x^3}{6 d^9 \left(a^2+b^2\right)}","-\frac{945 b \text{Li}_9\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^9 \left(a^2+b^2\right)}+\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^8 \left(a^2+b^2\right)}+\frac{945 b x^{2/3} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^7 \left(a^2+b^2\right)}-\frac{630 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^6 \left(a^2+b^2\right)}-\frac{315 b x^{4/3} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}+\frac{126 i b x^{5/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}+\frac{42 b x^2 \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{12 i b x^{7/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b x^{8/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}",1,"(2*a*d^9*x^3 + (2*I)*b*d^9*x^3 + 18*b*d^8*x^(8/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (72*I)*b*d^7*x^(7/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 252*b*d^6*x^2*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (756*I)*b*d^5*x^(5/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 1890*b*d^4*x^(4/3)*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (3780*I)*b*d^3*x*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 5670*b*d^2*x^(2/3)*PolyLog[7, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (5670*I)*b*d*x^(1/3)*PolyLog[8, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 2835*b*PolyLog[9, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/(6*(a^2 + b^2)*d^9)","A",1
58,1,310,352,1.3819708,"\int \frac{x}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Integrate[x/(a + b*Tan[c + d*x^(1/3)]),x]","\frac{12 b d^5 x^{5/3} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+30 i b d^4 x^{4/3} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+60 b d^3 x \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-90 i b d^2 x^{2/3} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-90 b d \sqrt[3]{x} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+45 i b \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+2 a d^6 x^2+2 i b d^6 x^2}{4 d^6 \left(a^2+b^2\right)}","-\frac{45 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{4 d^6 \left(a^2+b^2\right)}-\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^5 \left(a^2+b^2\right)}+\frac{45 i b x^{2/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{15 b x \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{15 i b x^{4/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{3 b x^{5/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}",1,"(2*a*d^6*x^2 + (2*I)*b*d^6*x^2 + 12*b*d^5*x^(5/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (30*I)*b*d^4*x^(4/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 60*b*d^3*x*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (90*I)*b*d^2*x^(2/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 90*b*d*x^(1/3)*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (45*I)*b*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/(4*(a^2 + b^2)*d^6)","A",1
59,1,165,176,1.0171594,"\int \frac{1}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])^(-1),x]","\frac{6 b d^2 x^{2/3} \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+6 i b d \sqrt[3]{x} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+3 b \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)+2 a d^3 x+2 i b d^3 x}{2 d^3 \left(a^2+b^2\right)}","\frac{3 b \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^3 \left(a^2+b^2\right)}-\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b x^{2/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}",1,"(2*a*d^3*x + (2*I)*b*d^3*x + 6*b*d^2*x^(2/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (6*I)*b*d*x^(1/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 3*b*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/(2*(a^2 + b^2)*d^3)","A",1
60,0,0,23,10.9196836,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","Integrate[1/(x*(a + b*Tan[c + d*x^(1/3)])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*x^(1/3)])), x]","A",-1
61,0,0,23,8.511953,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*x^(1/3)])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*x^(1/3)])), x]","A",-1
62,1,1136,1691,5.7365338,"\int \frac{x^2}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Integrate[x^2/(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{\frac{(a-i b)^2 (a+i b) (a \cos (c)-b \sin (c)) x^3}{a \cos (c)+b \sin (c)}+\frac{9 (a-i b)^2 (a+i b) b^2 \sin \left(d \sqrt[3]{x}\right) x^{8/3}}{d (a \cos (c)+b \sin (c)) \left(a \cos \left(c+d \sqrt[3]{x}\right)+b \sin \left(c+d \sqrt[3]{x}\right)\right)}-\frac{i b \left(4 a (a+i b) (i a+b) x^3 d^9+18 (a+i b) b (i a+b) x^{8/3} d^8+18 a (a-i b) \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) x^{8/3} \log \left(\frac{e^{-2 i \left(c+d \sqrt[3]{x}\right)} (a+i b)}{a-i b}+1\right) d^8+72 (a-i b) b \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) x^{7/3} \log \left(\frac{e^{-2 i \left(c+d \sqrt[3]{x}\right)} (a+i b)}{a-i b}+1\right) d^7+63 b (i a+b) \left(b \left(-1+e^{2 i c}\right)+i a \left(1+e^{2 i c}\right)\right) \left(-4 i x^2 \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^6-12 x^{5/3} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^5+15 i \left(2 x^{4/3} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^4-4 i x \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^3-6 x^{2/3} \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^2+6 i \sqrt[3]{x} \text{Li}_7\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d+3 \text{Li}_8\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)\right)\right)+9 a (a-i b) \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(8 i x^{7/3} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^7+28 x^2 \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^6-84 i x^{5/3} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^5-105 \left(2 x^{4/3} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^4-4 i x \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^3-6 x^{2/3} \text{Li}_7\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^2+6 i \sqrt[3]{x} \text{Li}_8\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d+3 \text{Li}_9\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)\right)\right)\right)}{d^9 \left(-e^{2 i c} b+b-i a \left(1+e^{2 i c}\right)\right)}}{3 (a-i b)^3 (a+i b)^2}","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{6 b \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{(a-i b)^2 (a+i b) d}-\frac{6 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{\left(a^2+b^2\right)^2 d}-\frac{6 i b^2 x^{8/3}}{\left(a^2+b^2\right)^2 d}+\frac{6 b^2 x^{8/3}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}+\frac{24 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}+\frac{24 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{(i a-b) (a-i b)^2 d^2}-\frac{24 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}-\frac{84 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{84 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{(a-i b)^2 (a+i b) d^3}-\frac{84 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{252 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}-\frac{252 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{(i a-b) (a-i b)^2 d^4}+\frac{252 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}+\frac{630 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{630 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{(a-i b)^2 (a+i b) d^5}+\frac{630 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{1260 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}+\frac{1260 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^6}-\frac{1260 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}-\frac{1890 i b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{(a-i b)^2 (a+i b) d^7}-\frac{1890 i b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}-\frac{1890 b \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{(i a-b) (a-i b)^2 d^8}+\frac{1890 b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}+\frac{945 i b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}-\frac{945 b \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{(a-i b)^2 (a+i b) d^9}+\frac{945 i b^2 \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}",1,"(((-I)*b*(18*(a + I*b)*b*(I*a + b)*d^8*x^(8/3) + 4*a*(a + I*b)*(I*a + b)*d^9*x^3 + 72*(a - I*b)*b*d^7*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(7/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 18*a*(a - I*b)*d^8*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(8/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 63*b*(I*a + b)*(b*(-1 + E^((2*I)*c)) + I*a*(1 + E^((2*I)*c)))*((-4*I)*d^6*x^2*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 12*d^5*x^(5/3)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (15*I)*(2*d^4*x^(4/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (4*I)*d^3*x*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 6*d^2*x^(2/3)*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (6*I)*d*x^(1/3)*PolyLog[7, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 3*PolyLog[8, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])) + 9*a*(a - I*b)*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*((8*I)*d^7*x^(7/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 28*d^6*x^2*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (84*I)*d^5*x^(5/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 105*(2*d^4*x^(4/3)*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (4*I)*d^3*x*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 6*d^2*x^(2/3)*PolyLog[7, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (6*I)*d*x^(1/3)*PolyLog[8, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 3*PolyLog[9, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))]))))/(d^9*(b - b*E^((2*I)*c) - I*a*(1 + E^((2*I)*c)))) + ((a - I*b)^2*(a + I*b)*x^3*(a*Cos[c] - b*Sin[c]))/(a*Cos[c] + b*Sin[c]) + (9*(a - I*b)^2*(a + I*b)*b^2*x^(8/3)*Sin[d*x^(1/3)])/(d*(a*Cos[c] + b*Sin[c])*(a*Cos[c + d*x^(1/3)] + b*Sin[c + d*x^(1/3)])))/(3*(a - I*b)^3*(a + I*b)^2)","A",1
63,1,820,1155,5.9850631,"\int \frac{x}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Integrate[x/(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{\frac{6 x^{5/3} \sin \left(d \sqrt[3]{x}\right) b^2}{d (a \cos (c)+b \sin (c)) \left(a \cos \left(c+d \sqrt[3]{x}\right)+b \sin \left(c+d \sqrt[3]{x}\right)\right)}+\frac{\left(\frac{4 a d x^2}{a-i b}+\frac{12 b x^{5/3}}{a-i b}+\frac{12 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(\frac{e^{-2 i \left(c+d \sqrt[3]{x}\right)} (a+i b)}{a-i b}+1\right) x^{5/3}}{(a+i b) (i a+b)}+\frac{30 b \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(\frac{e^{-2 i \left(c+d \sqrt[3]{x}\right)} (a+i b)}{a-i b}+1\right) x^{4/3}}{(a+i b) (i a+b) d}+\frac{15 b \left(b \left(-1+e^{2 i c}\right)+i a \left(1+e^{2 i c}\right)\right) \left(-4 i x \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^3-6 x^{2/3} \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^2+6 i \sqrt[3]{x} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d+3 \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) d^5}+\frac{15 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(2 x^{4/3} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^4-4 i x \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^3-6 x^{2/3} \text{Li}_4\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d^2+6 i \sqrt[3]{x} \text{Li}_5\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right) d+3 \text{Li}_6\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)\right)}{\left(a^2+b^2\right) d^5}\right) b}{d \left(-e^{2 i c} b+b-i a \left(1+e^{2 i c}\right)\right)}+\frac{x^2 (a \cos (c)-b \sin (c))}{a \cos (c)+b \sin (c)}}{2 \left(a^2+b^2\right)}","-\frac{2 x^2 b^2}{\left(a^2+b^2\right)^2}-\frac{6 i x^{5/3} b^2}{\left(a^2+b^2\right)^2 d}+\frac{6 x^{5/3} b^2}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}-\frac{6 i x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d}+\frac{15 x^{4/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{30 i x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{30 i x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}+\frac{45 x^{2/3} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 i \sqrt[3]{x} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}+\frac{45 i \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}-\frac{45 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}-\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}+\frac{2 x^2 b}{(i a-b) (a-i b)^2}+\frac{6 x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b}{(a-i b)^2 (a+i b) d}+\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^2}+\frac{30 x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^3}-\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^4}-\frac{45 \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^5}+\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{2 (i a-b) (a-i b)^2 d^6}+\frac{x^2}{2 (a-i b)^2}",1,"((b*((12*b*x^(5/3))/(a - I*b) + (4*a*d*x^2)/(a - I*b) + (30*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(4/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/((a + I*b)*(I*a + b)*d) + (12*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(5/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/((a + I*b)*(I*a + b)) + (15*b*(b*(-1 + E^((2*I)*c)) + I*a*(1 + E^((2*I)*c)))*((-4*I)*d^3*x*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 6*d^2*x^(2/3)*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (6*I)*d*x^(1/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 3*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))]))/((a^2 + b^2)*d^5) + (15*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*(2*d^4*x^(4/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - (4*I)*d^3*x*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - 6*d^2*x^(2/3)*PolyLog[4, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + (6*I)*d*x^(1/3)*PolyLog[5, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] + 3*PolyLog[6, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))]))/((a^2 + b^2)*d^5)))/(d*(b - b*E^((2*I)*c) - I*a*(1 + E^((2*I)*c)))) + (x^2*(a*Cos[c] - b*Sin[c]))/(a*Cos[c] + b*Sin[c]) + (6*b^2*x^(5/3)*Sin[d*x^(1/3)])/(d*(a*Cos[c] + b*Sin[c])*(a*Cos[c + d*x^(1/3)] + b*Sin[c + d*x^(1/3)])))/(2*(a^2 + b^2))","A",1
64,1,538,610,3.8760219,"\int \frac{1}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Integrate[(a + b*Tan[c + d*x^(1/3)])^(-2),x]","\frac{\frac{b \left(\frac{3 b \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 a \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \left(2 d \sqrt[3]{x} \text{Li}_2\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)-i \text{Li}_3\left(\frac{(-a-i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)\right)}{d^2 \left(a^2+b^2\right)}+\frac{6 a x^{2/3} \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)}{(a+i b) (b+i a)}+\frac{6 b \sqrt[3]{x} \left(a \left(1+e^{2 i c}\right)-i b \left(-1+e^{2 i c}\right)\right) \log \left(1+\frac{(a+i b) e^{-2 i \left(c+d \sqrt[3]{x}\right)}}{a-i b}\right)}{d (a+i b) (b+i a)}+\frac{4 a d x}{a-i b}+\frac{6 b x^{2/3}}{a-i b}\right)}{d \left(-i a \left(1+e^{2 i c}\right)+b \left(-e^{2 i c}\right)+b\right)}+\frac{3 b^2 x^{2/3} \sin \left(d \sqrt[3]{x}\right)}{d (a \cos (c)+b \sin (c)) \left(a \cos \left(c+d \sqrt[3]{x}\right)+b \sin \left(c+d \sqrt[3]{x}\right)\right)}+\frac{x (a \cos (c)-b \sin (c))}{a \cos (c)+b \sin (c)}}{a^2+b^2}","-\frac{3 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{3 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{6 b^2 \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3}}{d \left(a^2+b^2\right)^2}-\frac{4 b^2 x}{\left(a^2+b^2\right)^2}+\frac{6 b^2 x^{2/3}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt[3]{x}\right)}+i a-b\right)}+\frac{3 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}+\frac{6 b \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{6 b x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{4 b x}{(-b+i a) (a-i b)^2}+\frac{x}{(a-i b)^2}",1,"((b*((6*b*x^(2/3))/(a - I*b) + (4*a*d*x)/(a - I*b) + (6*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(1/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/((a + I*b)*(I*a + b)*d) + (6*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*x^(2/3)*Log[1 + (a + I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/((a + I*b)*(I*a + b)) + (3*b*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))])/((a^2 + b^2)*d^2) + (3*a*((-I)*b*(-1 + E^((2*I)*c)) + a*(1 + E^((2*I)*c)))*(2*d*x^(1/3)*PolyLog[2, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))] - I*PolyLog[3, (-a - I*b)/((a - I*b)*E^((2*I)*(c + d*x^(1/3))))]))/((a^2 + b^2)*d^2)))/(d*(b - b*E^((2*I)*c) - I*a*(1 + E^((2*I)*c)))) + (x*(a*Cos[c] - b*Sin[c]))/(a*Cos[c] + b*Sin[c]) + (3*b^2*x^(2/3)*Sin[d*x^(1/3)])/(d*(a*Cos[c] + b*Sin[c])*(a*Cos[c + d*x^(1/3)] + b*Sin[c + d*x^(1/3)])))/(a^2 + b^2)","A",1
65,0,0,23,39.9599352,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Tan[c + d*x^(1/3)])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Tan[c + d*x^(1/3)])^2), x]","A",-1
66,0,0,23,32.0499826,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Tan[c + d*x^(1/3)])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Tan[c + d*x^(1/3)])^2), x]","A",-1