1,1,87,0,0.1336978,"\int \tan (c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{(a C+b B) \tan ^2(c+d x)}{2 d}+\frac{(a B-b C) \tan (c+d x)}{d}+\frac{(a C+b B) \log (\cos (c+d x))}{d}-x (a B-b C)+\frac{b C \tan ^3(c+d x)}{3 d}","\frac{(a C+b B) \tan ^2(c+d x)}{2 d}+\frac{(a B-b C) \tan (c+d x)}{d}+\frac{(a C+b B) \log (\cos (c+d x))}{d}-x (a B-b C)+\frac{b C \tan ^3(c+d x)}{3 d}",1,"-((a*B - b*C)*x) + ((b*B + a*C)*Log[Cos[c + d*x]])/d + ((a*B - b*C)*Tan[c + d*x])/d + ((b*B + a*C)*Tan[c + d*x]^2)/(2*d) + (b*C*Tan[c + d*x]^3)/(3*d)","A",5,5,36,0.1389,1,"{3632, 3592, 3528, 3525, 3475}"
2,1,66,0,0.0458897,"\int (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{(a B-b C) \log (\cos (c+d x))}{d}-x (a C+b B)+\frac{C (a+b \tan (c+d x))^2}{2 b d}+\frac{b B \tan (c+d x)}{d}","-\frac{(a B-b C) \log (\cos (c+d x))}{d}-x (a C+b B)+\frac{C (a+b \tan (c+d x))^2}{2 b d}+\frac{b B \tan (c+d x)}{d}",1,"-((b*B + a*C)*x) - ((a*B - b*C)*Log[Cos[c + d*x]])/d + (b*B*Tan[c + d*x])/d + (C*(a + b*Tan[c + d*x])^2)/(2*b*d)","A",3,3,30,0.1000,1,"{3630, 3525, 3475}"
3,1,42,0,0.0604294,"\int \cot (c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{(a C+b B) \log (\cos (c+d x))}{d}+x (a B-b C)+\frac{b C \tan (c+d x)}{d}","-\frac{(a C+b B) \log (\cos (c+d x))}{d}+x (a B-b C)+\frac{b C \tan (c+d x)}{d}",1,"(a*B - b*C)*x - ((b*B + a*C)*Log[Cos[c + d*x]])/d + (b*C*Tan[c + d*x])/d","A",3,3,36,0.08333,1,"{3632, 3525, 3475}"
4,1,37,0,0.1096054,"\int \cot ^2(c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","x (a C+b B)+\frac{a B \log (\sin (c+d x))}{d}-\frac{b C \log (\cos (c+d x))}{d}","x (a C+b B)+\frac{a B \log (\sin (c+d x))}{d}-\frac{b C \log (\cos (c+d x))}{d}",1,"(b*B + a*C)*x - (b*C*Log[Cos[c + d*x]])/d + (a*B*Log[Sin[c + d*x]])/d","A",5,4,38,0.1053,1,"{3632, 3589, 3475, 3531}"
5,1,43,0,0.1239537,"\int \cot ^3(c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{(a C+b B) \log (\sin (c+d x))}{d}+x (-(a B-b C))-\frac{a B \cot (c+d x)}{d}","\frac{(a C+b B) \log (\sin (c+d x))}{d}+x (-(a B-b C))-\frac{a B \cot (c+d x)}{d}",1,"-((a*B - b*C)*x) - (a*B*Cot[c + d*x])/d + ((b*B + a*C)*Log[Sin[c + d*x]])/d","A",4,4,38,0.1053,1,"{3632, 3591, 3531, 3475}"
6,1,66,0,0.1593873,"\int \cot ^4(c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{(a C+b B) \cot (c+d x)}{d}-\frac{(a B-b C) \log (\sin (c+d x))}{d}-x (a C+b B)-\frac{a B \cot ^2(c+d x)}{2 d}","-\frac{(a C+b B) \cot (c+d x)}{d}-\frac{(a B-b C) \log (\sin (c+d x))}{d}-x (a C+b B)-\frac{a B \cot ^2(c+d x)}{2 d}",1,"-((b*B + a*C)*x) - ((b*B + a*C)*Cot[c + d*x])/d - (a*B*Cot[c + d*x]^2)/(2*d) - ((a*B - b*C)*Log[Sin[c + d*x]])/d","A",5,5,38,0.1316,1,"{3632, 3591, 3529, 3531, 3475}"
7,1,87,0,0.1929295,"\int \cot ^5(c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{(a C+b B) \cot ^2(c+d x)}{2 d}+\frac{(a B-b C) \cot (c+d x)}{d}-\frac{(a C+b B) \log (\sin (c+d x))}{d}+x (a B-b C)-\frac{a B \cot ^3(c+d x)}{3 d}","-\frac{(a C+b B) \cot ^2(c+d x)}{2 d}+\frac{(a B-b C) \cot (c+d x)}{d}-\frac{(a C+b B) \log (\sin (c+d x))}{d}+x (a B-b C)-\frac{a B \cot ^3(c+d x)}{3 d}",1,"(a*B - b*C)*x + ((a*B - b*C)*Cot[c + d*x])/d - ((b*B + a*C)*Cot[c + d*x]^2)/(2*d) - (a*B*Cot[c + d*x]^3)/(3*d) - ((b*B + a*C)*Log[Sin[c + d*x]])/d","A",6,5,38,0.1316,1,"{3632, 3591, 3529, 3531, 3475}"
8,1,108,0,0.2261938,"\int \cot ^6(c+d x) (a+b \tan (c+d x)) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{(a C+b B) \cot ^3(c+d x)}{3 d}+\frac{(a B-b C) \cot ^2(c+d x)}{2 d}+\frac{(a C+b B) \cot (c+d x)}{d}+\frac{(a B-b C) \log (\sin (c+d x))}{d}+x (a C+b B)-\frac{a B \cot ^4(c+d x)}{4 d}","-\frac{(a C+b B) \cot ^3(c+d x)}{3 d}+\frac{(a B-b C) \cot ^2(c+d x)}{2 d}+\frac{(a C+b B) \cot (c+d x)}{d}+\frac{(a B-b C) \log (\sin (c+d x))}{d}+x (a C+b B)-\frac{a B \cot ^4(c+d x)}{4 d}",1,"(b*B + a*C)*x + ((b*B + a*C)*Cot[c + d*x])/d + ((a*B - b*C)*Cot[c + d*x]^2)/(2*d) - ((b*B + a*C)*Cot[c + d*x]^3)/(3*d) - (a*B*Cot[c + d*x]^4)/(4*d) + ((a*B - b*C)*Log[Sin[c + d*x]])/d","A",7,5,38,0.1316,1,"{3632, 3591, 3529, 3531, 3475}"
9,1,148,0,0.301735,"\int \tan (c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{\left(a^2 C+2 a b B-b^2 C\right) \log (\cos (c+d x))}{d}-x \left(a^2 B-2 a b C-b^2 B\right)+\frac{(4 b B-a C) (a+b \tan (c+d x))^3}{12 b^2 d}-\frac{b (a C+b B) \tan (c+d x)}{d}+\frac{C \tan (c+d x) (a+b \tan (c+d x))^3}{4 b d}-\frac{C (a+b \tan (c+d x))^2}{2 d}","\frac{\left(a^2 C+2 a b B-b^2 C\right) \log (\cos (c+d x))}{d}-x \left(a^2 B-2 a b C-b^2 B\right)+\frac{(4 b B-a C) (a+b \tan (c+d x))^3}{12 b^2 d}-\frac{b (a C+b B) \tan (c+d x)}{d}+\frac{C \tan (c+d x) (a+b \tan (c+d x))^3}{4 b d}-\frac{C (a+b \tan (c+d x))^2}{2 d}",1,"-((a^2*B - b^2*B - 2*a*b*C)*x) + ((2*a*b*B + a^2*C - b^2*C)*Log[Cos[c + d*x]])/d - (b*(b*B + a*C)*Tan[c + d*x])/d - (C*(a + b*Tan[c + d*x])^2)/(2*d) + ((4*b*B - a*C)*(a + b*Tan[c + d*x])^3)/(12*b^2*d) + (C*Tan[c + d*x]*(a + b*Tan[c + d*x])^3)/(4*b*d)","A",6,6,38,0.1579,1,"{3632, 3607, 3630, 3528, 3525, 3475}"
10,1,112,0,0.1116642,"\int (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(a^2 C+2 a b B-b^2 C\right)+\frac{b (a B-b C) \tan (c+d x)}{d}+\frac{B (a+b \tan (c+d x))^2}{2 d}+\frac{C (a+b \tan (c+d x))^3}{3 b d}","-\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(a^2 C+2 a b B-b^2 C\right)+\frac{b (a B-b C) \tan (c+d x)}{d}+\frac{B (a+b \tan (c+d x))^2}{2 d}+\frac{C (a+b \tan (c+d x))^3}{3 b d}",1,"-((2*a*b*B + a^2*C - b^2*C)*x) - ((a^2*B - b^2*B - 2*a*b*C)*Log[Cos[c + d*x]])/d + (b*(a*B - b*C)*Tan[c + d*x])/d + (B*(a + b*Tan[c + d*x])^2)/(2*d) + (C*(a + b*Tan[c + d*x])^3)/(3*b*d)","A",4,4,32,0.1250,1,"{3630, 3528, 3525, 3475}"
11,1,87,0,0.1353114,"\int \cot (c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{\left(a^2 C+2 a b B-b^2 C\right) \log (\cos (c+d x))}{d}+x \left(a^2 B-2 a b C-b^2 B\right)+\frac{b (a C+b B) \tan (c+d x)}{d}+\frac{C (a+b \tan (c+d x))^2}{2 d}","-\frac{\left(a^2 C+2 a b B-b^2 C\right) \log (\cos (c+d x))}{d}+x \left(a^2 B-2 a b C-b^2 B\right)+\frac{b (a C+b B) \tan (c+d x)}{d}+\frac{C (a+b \tan (c+d x))^2}{2 d}",1,"(a^2*B - b^2*B - 2*a*b*C)*x - ((2*a*b*B + a^2*C - b^2*C)*Log[Cos[c + d*x]])/d + (b*(b*B + a*C)*Tan[c + d*x])/d + (C*(a + b*Tan[c + d*x])^2)/(2*d)","A",4,4,38,0.1053,1,"{3632, 3528, 3525, 3475}"
12,1,70,0,0.1846833,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","x \left(a^2 C+2 a b B-b^2 C\right)+\frac{a^2 B \log (\sin (c+d x))}{d}-\frac{b (2 a C+b B) \log (\cos (c+d x))}{d}+\frac{b^2 C \tan (c+d x)}{d}","x \left(a^2 C+2 a b B-b^2 C\right)+\frac{a^2 B \log (\sin (c+d x))}{d}-\frac{b (2 a C+b B) \log (\cos (c+d x))}{d}+\frac{b^2 C \tan (c+d x)}{d}",1,"(2*a*b*B + a^2*C - b^2*C)*x - (b*(b*B + 2*a*C)*Log[Cos[c + d*x]])/d + (a^2*B*Log[Sin[c + d*x]])/d + (b^2*C*Tan[c + d*x])/d","A",5,4,40,0.1000,1,"{3632, 3606, 3624, 3475}"
13,1,72,0,0.2066256,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-x \left(a^2 B-2 a b C-b^2 B\right)-\frac{a^2 B \cot (c+d x)}{d}+\frac{a (a C+2 b B) \log (\sin (c+d x))}{d}-\frac{b^2 C \log (\cos (c+d x))}{d}","-x \left(a^2 B-2 a b C-b^2 B\right)-\frac{a^2 B \cot (c+d x)}{d}+\frac{a (a C+2 b B) \log (\sin (c+d x))}{d}-\frac{b^2 C \log (\cos (c+d x))}{d}",1,"-((a^2*B - b^2*B - 2*a*b*C)*x) - (a^2*B*Cot[c + d*x])/d - (b^2*C*Log[Cos[c + d*x]])/d + (a*(2*b*B + a*C)*Log[Sin[c + d*x]])/d","A",5,4,40,0.1000,1,"{3632, 3604, 3624, 3475}"
14,1,88,0,0.2634715,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\sin (c+d x))}{d}-\frac{a^2 B \cot ^2(c+d x)}{2 d}+x \left(b^2 C-a (a C+2 b B)\right)-\frac{a (a C+2 b B) \cot (c+d x)}{d}","-\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\sin (c+d x))}{d}-\frac{a^2 B \cot ^2(c+d x)}{2 d}+x \left(b^2 C-a (a C+2 b B)\right)-\frac{a (a C+2 b B) \cot (c+d x)}{d}",1,"(b^2*C - a*(2*b*B + a*C))*x - (a*(2*b*B + a*C)*Cot[c + d*x])/d - (a^2*B*Cot[c + d*x]^2)/(2*d) - ((a^2*B - b^2*B - 2*a*b*C)*Log[Sin[c + d*x]])/d","A",5,5,40,0.1250,1,"{3632, 3604, 3628, 3531, 3475}"
15,1,118,0,0.3110199,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{\left(a^2 B-2 a b C-b^2 B\right) \cot (c+d x)}{d}+x \left(a^2 B-2 a b C-b^2 B\right)-\frac{a^2 B \cot ^3(c+d x)}{3 d}+\frac{\left(b^2 C-a (a C+2 b B)\right) \log (\sin (c+d x))}{d}-\frac{a (a C+2 b B) \cot ^2(c+d x)}{2 d}","\frac{\left(a^2 B-2 a b C-b^2 B\right) \cot (c+d x)}{d}+x \left(a^2 B-2 a b C-b^2 B\right)-\frac{a^2 B \cot ^3(c+d x)}{3 d}+\frac{\left(b^2 C-a (a C+2 b B)\right) \log (\sin (c+d x))}{d}-\frac{a (a C+2 b B) \cot ^2(c+d x)}{2 d}",1,"(a^2*B - b^2*B - 2*a*b*C)*x + ((a^2*B - b^2*B - 2*a*b*C)*Cot[c + d*x])/d - (a*(2*b*B + a*C)*Cot[c + d*x]^2)/(2*d) - (a^2*B*Cot[c + d*x]^3)/(3*d) + ((b^2*C - a*(2*b*B + a*C))*Log[Sin[c + d*x]])/d","A",6,6,40,0.1500,1,"{3632, 3604, 3628, 3529, 3531, 3475}"
16,1,151,0,0.3693969,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^2 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{\left(a^2 B-2 a b C-b^2 B\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\sin (c+d x))}{d}+x \left(a^2 C+2 a b B-b^2 C\right)-\frac{a^2 B \cot ^4(c+d x)}{4 d}-\frac{\left(b^2 C-a (a C+2 b B)\right) \cot (c+d x)}{d}-\frac{a (a C+2 b B) \cot ^3(c+d x)}{3 d}","\frac{\left(a^2 B-2 a b C-b^2 B\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2 B-2 a b C-b^2 B\right) \log (\sin (c+d x))}{d}+x \left(a^2 C+2 a b B-b^2 C\right)-\frac{a^2 B \cot ^4(c+d x)}{4 d}-\frac{\left(b^2 C-a (a C+2 b B)\right) \cot (c+d x)}{d}-\frac{a (a C+2 b B) \cot ^3(c+d x)}{3 d}",1,"(2*a*b*B + a^2*C - b^2*C)*x - ((b^2*C - a*(2*b*B + a*C))*Cot[c + d*x])/d + ((a^2*B - b^2*B - 2*a*b*C)*Cot[c + d*x]^2)/(2*d) - (a*(2*b*B + a*C)*Cot[c + d*x]^3)/(3*d) - (a^2*B*Cot[c + d*x]^4)/(4*d) + ((a^2*B - b^2*B - 2*a*b*C)*Log[Sin[c + d*x]])/d","A",7,6,40,0.1500,1,"{3632, 3604, 3628, 3529, 3531, 3475}"
17,1,165,0,0.1769735,"\int (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{b \left(a^2 B-2 a b C-b^2 B\right) \tan (c+d x)}{d}-\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \log (\cos (c+d x))}{d}-x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)+\frac{(a B-b C) (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 d}+\frac{C (a+b \tan (c+d x))^4}{4 b d}","\frac{b \left(a^2 B-2 a b C-b^2 B\right) \tan (c+d x)}{d}-\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \log (\cos (c+d x))}{d}-x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)+\frac{(a B-b C) (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 d}+\frac{C (a+b \tan (c+d x))^4}{4 b d}",1,"-((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*x) - ((a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*Log[Cos[c + d*x]])/d + (b*(a^2*B - b^2*B - 2*a*b*C)*Tan[c + d*x])/d + ((a*B - b*C)*(a + b*Tan[c + d*x])^2)/(2*d) + (B*(a + b*Tan[c + d*x])^3)/(3*d) + (C*(a + b*Tan[c + d*x])^4)/(4*b*d)","A",5,4,32,0.1250,1,"{3630, 3528, 3525, 3475}"
18,1,140,0,0.2078813,"\int \cot (c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{b \left(a^2 C+2 a b B-b^2 C\right) \tan (c+d x)}{d}-\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\cos (c+d x))}{d}+x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)+\frac{(a C+b B) (a+b \tan (c+d x))^2}{2 d}+\frac{C (a+b \tan (c+d x))^3}{3 d}","\frac{b \left(a^2 C+2 a b B-b^2 C\right) \tan (c+d x)}{d}-\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\cos (c+d x))}{d}+x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)+\frac{(a C+b B) (a+b \tan (c+d x))^2}{2 d}+\frac{C (a+b \tan (c+d x))^3}{3 d}",1,"(a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*x - ((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*Log[Cos[c + d*x]])/d + (b*(2*a*b*B + a^2*C - b^2*C)*Tan[c + d*x])/d + ((b*B + a*C)*(a + b*Tan[c + d*x])^2)/(2*d) + (C*(a + b*Tan[c + d*x])^3)/(3*d)","A",5,4,38,0.1053,1,"{3632, 3528, 3525, 3475}"
19,1,117,0,0.3355815,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{b \left(3 a^2 C+3 a b B-b^2 C\right) \log (\cos (c+d x))}{d}+x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)+\frac{a^3 B \log (\sin (c+d x))}{d}+\frac{b^2 (2 a C+b B) \tan (c+d x)}{d}+\frac{b C (a+b \tan (c+d x))^2}{2 d}","-\frac{b \left(3 a^2 C+3 a b B-b^2 C\right) \log (\cos (c+d x))}{d}+x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)+\frac{a^3 B \log (\sin (c+d x))}{d}+\frac{b^2 (2 a C+b B) \tan (c+d x)}{d}+\frac{b C (a+b \tan (c+d x))^2}{2 d}",1,"(3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*x - (b*(3*a*b*B + 3*a^2*C - b^2*C)*Log[Cos[c + d*x]])/d + (a^3*B*Log[Sin[c + d*x]])/d + (b^2*(b*B + 2*a*C)*Tan[c + d*x])/d + (b*C*(a + b*Tan[c + d*x])^2)/(2*d)","A",6,5,40,0.1250,1,"{3632, 3607, 3637, 3624, 3475}"
20,1,119,0,0.331394,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)+\frac{a^2 (a C+3 b B) \log (\sin (c+d x))}{d}+\frac{b^2 (a B+b C) \tan (c+d x)}{d}-\frac{b^2 (3 a C+b B) \log (\cos (c+d x))}{d}-\frac{a B \cot (c+d x) (a+b \tan (c+d x))^2}{d}","-x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)+\frac{a^2 (a C+3 b B) \log (\sin (c+d x))}{d}+\frac{b^2 (a B+b C) \tan (c+d x)}{d}-\frac{b^2 (3 a C+b B) \log (\cos (c+d x))}{d}-\frac{a B \cot (c+d x) (a+b \tan (c+d x))^2}{d}",1,"-((a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*x) - (b^2*(b*B + 3*a*C)*Log[Cos[c + d*x]])/d + (a^2*(3*b*B + a*C)*Log[Sin[c + d*x]])/d + (b^2*(a*B + b*C)*Tan[c + d*x])/d - (a*B*Cot[c + d*x]*(a + b*Tan[c + d*x])^2)/d","A",6,5,40,0.1250,1,"{3632, 3605, 3637, 3624, 3475}"
21,1,127,0,0.3549048,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","-\frac{a \left(a^2 B-3 a b C-3 b^2 B\right) \log (\sin (c+d x))}{d}-x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)-\frac{a^2 (a C+2 b B) \cot (c+d x)}{d}-\frac{a B \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 C \log (\cos (c+d x))}{d}","-\frac{a \left(a^2 B-3 a b C-3 b^2 B\right) \log (\sin (c+d x))}{d}-x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)-\frac{a^2 (a C+2 b B) \cot (c+d x)}{d}-\frac{a B \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 C \log (\cos (c+d x))}{d}",1,"-((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*x) - (a^2*(2*b*B + a*C)*Cot[c + d*x])/d - (b^3*C*Log[Cos[c + d*x]])/d - (a*(a^2*B - 3*b^2*B - 3*a*b*C)*Log[Sin[c + d*x]])/d - (a*B*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2)/(2*d)","A",6,5,40,0.1250,1,"{3632, 3605, 3635, 3624, 3475}"
22,1,154,0,0.426631,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{a \left(3 a^2 B-9 a b C-8 b^2 B\right) \cot (c+d x)}{3 d}-\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\sin (c+d x))}{d}+x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)-\frac{a^2 (3 a C+5 b B) \cot ^2(c+d x)}{6 d}-\frac{a B \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}","\frac{a \left(3 a^2 B-9 a b C-8 b^2 B\right) \cot (c+d x)}{3 d}-\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\sin (c+d x))}{d}+x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)-\frac{a^2 (3 a C+5 b B) \cot ^2(c+d x)}{6 d}-\frac{a B \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}",1,"(a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*x + (a*(3*a^2*B - 8*b^2*B - 9*a*b*C)*Cot[c + d*x])/(3*d) - (a^2*(5*b*B + 3*a*C)*Cot[c + d*x]^2)/(6*d) - ((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*Log[Sin[c + d*x]])/d - (a*B*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2)/(3*d)","A",6,6,40,0.1500,1,"{3632, 3605, 3635, 3628, 3531, 3475}"
23,1,191,0,0.5137933,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{a \left(2 a^2 B-6 a b C-5 b^2 B\right) \cot ^2(c+d x)}{4 d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \cot (c+d x)}{d}+\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \log (\sin (c+d x))}{d}+x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)-\frac{a^2 (2 a C+3 b B) \cot ^3(c+d x)}{6 d}-\frac{a B \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}","\frac{a \left(2 a^2 B-6 a b C-5 b^2 B\right) \cot ^2(c+d x)}{4 d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \cot (c+d x)}{d}+\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \log (\sin (c+d x))}{d}+x \left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right)-\frac{a^2 (2 a C+3 b B) \cot ^3(c+d x)}{6 d}-\frac{a B \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}",1,"(3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*x + ((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*Cot[c + d*x])/d + (a*(2*a^2*B - 5*b^2*B - 6*a*b*C)*Cot[c + d*x]^2)/(4*d) - (a^2*(3*b*B + 2*a*C)*Cot[c + d*x]^3)/(6*d) + ((a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*Log[Sin[c + d*x]])/d - (a*B*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2)/(4*d)","A",7,7,40,0.1750,1,"{3632, 3605, 3635, 3628, 3529, 3531, 3475}"
24,1,233,0,0.5582151,"\int \cot ^7(c+d x) (a+b \tan (c+d x))^3 \left(B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Cot[c + d*x]^7*(a + b*Tan[c + d*x])^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{a \left(5 a^2 B-15 a b C-12 b^2 B\right) \cot ^3(c+d x)}{15 d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \cot ^2(c+d x)}{2 d}-\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \cot (c+d x)}{d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\sin (c+d x))}{d}-x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)-\frac{a^2 (5 a C+7 b B) \cot ^4(c+d x)}{20 d}-\frac{a B \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}","\frac{a \left(5 a^2 B-15 a b C-12 b^2 B\right) \cot ^3(c+d x)}{15 d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \cot ^2(c+d x)}{2 d}-\frac{\left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right) \cot (c+d x)}{d}+\frac{\left(3 a^2 b B+a^3 C-3 a b^2 C-b^3 B\right) \log (\sin (c+d x))}{d}-x \left(-3 a^2 b C+a^3 B-3 a b^2 B+b^3 C\right)-\frac{a^2 (5 a C+7 b B) \cot ^4(c+d x)}{20 d}-\frac{a B \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}",1,"-((a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*x) - ((a^3*B - 3*a*b^2*B - 3*a^2*b*C + b^3*C)*Cot[c + d*x])/d + ((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*Cot[c + d*x]^2)/(2*d) + (a*(5*a^2*B - 12*b^2*B - 15*a*b*C)*Cot[c + d*x]^3)/(15*d) - (a^2*(7*b*B + 5*a*C)*Cot[c + d*x]^4)/(20*d) + ((3*a^2*b*B - b^3*B + a^3*C - 3*a*b^2*C)*Log[Sin[c + d*x]])/d - (a*B*Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2)/(5*d)","A",8,7,40,0.1750,1,"{3632, 3605, 3635, 3628, 3529, 3531, 3475}"
25,1,127,0,0.468378,"\int \frac{\tan ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","-\frac{a^3 (b B-a C) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{(a B+b C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (b B-a C)}{a^2+b^2}+\frac{(b B-a C) \tan (c+d x)}{b^2 d}+\frac{C \tan ^2(c+d x)}{2 b d}","-\frac{a^3 (b B-a C) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{(a B+b C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (b B-a C)}{a^2+b^2}+\frac{(b B-a C) \tan (c+d x)}{b^2 d}+\frac{C \tan ^2(c+d x)}{2 b d}",1,"-(((b*B - a*C)*x)/(a^2 + b^2)) + ((a*B + b*C)*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a^3*(b*B - a*C)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)*d) + ((b*B - a*C)*Tan[c + d*x])/(b^2*d) + (C*Tan[c + d*x]^2)/(2*b*d)","A",7,7,40,0.1750,1,"{3632, 3607, 3647, 3626, 3617, 31, 3475}"
26,1,101,0,0.2432847,"\int \frac{\tan (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","\frac{a^2 (b B-a C) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}-\frac{(b B-a C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (a B+b C)}{a^2+b^2}+\frac{C \tan (c+d x)}{b d}","\frac{a^2 (b B-a C) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}-\frac{(b B-a C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (a B+b C)}{a^2+b^2}+\frac{C \tan (c+d x)}{b d}",1,"-(((a*B + b*C)*x)/(a^2 + b^2)) - ((b*B - a*C)*Log[Cos[c + d*x]])/((a^2 + b^2)*d) + (a^2*(b*B - a*C)*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) + (C*Tan[c + d*x])/(b*d)","A",6,6,38,0.1579,1,"{3632, 3606, 3626, 3617, 31, 3475}"
27,1,85,0,0.1627111,"\int \frac{B \tan (c+d x)+C \tan ^2(c+d x)}{a+b \tan (c+d x)} \, dx","Int[(B*Tan[c + d*x] + C*Tan[c + d*x]^2)/(a + b*Tan[c + d*x]),x]","-\frac{a (b B-a C) \log (a+b \tan (c+d x))}{b d \left(a^2+b^2\right)}-\frac{(a B+b C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (b B-a C)}{a^2+b^2}","-\frac{a (b B-a C) \log (a+b \tan (c+d x))}{b d \left(a^2+b^2\right)}-\frac{(a B+b C) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (b B-a C)}{a^2+b^2}",1,"((b*B - a*C)*x)/(a^2 + b^2) - ((a*B + b*C)*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a*(b*B - a*C)*Log[a + b*Tan[c + d*x]])/(b*(a^2 + b^2)*d)","A",6,4,32,0.1250,1,"{1629, 635, 203, 260}"
28,1,58,0,0.1439776,"\int \frac{\cot (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","\frac{(b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (a B+b C)}{a^2+b^2}","\frac{(b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (a B+b C)}{a^2+b^2}",1,"((a*B + b*C)*x)/(a^2 + b^2) + ((b*B - a*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",3,3,38,0.07895,1,"{3632, 3531, 3530}"
29,1,80,0,0.2008353,"\int \frac{\cot ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","-\frac{b (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{x (b B-a C)}{a^2+b^2}+\frac{B \log (\sin (c+d x))}{a d}","-\frac{b (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{x (b B-a C)}{a^2+b^2}+\frac{B \log (\sin (c+d x))}{a d}",1,"-(((b*B - a*C)*x)/(a^2 + b^2)) + (B*Log[Sin[c + d*x]])/(a*d) - (b*(b*B - a*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a*(a^2 + b^2)*d)","A",4,4,40,0.1000,1,"{3632, 3611, 3530, 3475}"
30,1,103,0,0.3422371,"\int \frac{\cot ^3(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","\frac{b^2 (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{x (a B+b C)}{a^2+b^2}-\frac{(b B-a C) \log (\sin (c+d x))}{a^2 d}-\frac{B \cot (c+d x)}{a d}","\frac{b^2 (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{x (a B+b C)}{a^2+b^2}-\frac{(b B-a C) \log (\sin (c+d x))}{a^2 d}-\frac{B \cot (c+d x)}{a d}",1,"-(((a*B + b*C)*x)/(a^2 + b^2)) - (B*Cot[c + d*x])/(a*d) - ((b*B - a*C)*Log[Sin[c + d*x]])/(a^2*d) + (b^2*(b*B - a*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)*d)","A",5,5,40,0.1250,1,"{3632, 3609, 3651, 3530, 3475}"
31,1,137,0,0.6816098,"\int \frac{\cot ^4(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^4*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x]),x]","-\frac{\left(a^2 B+a b C-b^2 B\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^3 (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{x (b B-a C)}{a^2+b^2}+\frac{(b B-a C) \cot (c+d x)}{a^2 d}-\frac{B \cot ^2(c+d x)}{2 a d}","-\frac{\left(a^2 B+a b C-b^2 B\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^3 (b B-a C) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{x (b B-a C)}{a^2+b^2}+\frac{(b B-a C) \cot (c+d x)}{a^2 d}-\frac{B \cot ^2(c+d x)}{2 a d}",1,"((b*B - a*C)*x)/(a^2 + b^2) + ((b*B - a*C)*Cot[c + d*x])/(a^2*d) - (B*Cot[c + d*x]^2)/(2*a*d) - ((a^2*B - b^2*B + a*b*C)*Log[Sin[c + d*x]])/(a^3*d) - (b^3*(b*B - a*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)*d)","A",6,6,40,0.1500,1,"{3632, 3609, 3649, 3651, 3530, 3475}"
32,1,208,0,0.532155,"\int \frac{\tan ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^2,x]","\frac{a (b B-a C) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(-2 a^2 C+a b B-b^2 C\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 \left(a^2 b B-2 a^3 C-4 a b^2 C+3 b^3 B\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{\left(a^2 B+2 a b C-b^2 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}","\frac{a (b B-a C) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(-2 a^2 C+a b B-b^2 C\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 \left(a^2 b B-2 a^3 C-4 a b^2 C+3 b^3 B\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{\left(a^2 B+2 a b C-b^2 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}",1,"-(((2*a*b*B - a^2*C + b^2*C)*x)/(a^2 + b^2)^2) + ((a^2*B - b^2*B + 2*a*b*C)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) + (a^2*(a^2*b*B + 3*b^3*B - 2*a^3*C - 4*a*b^2*C)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^2*d) - ((a*b*B - 2*a^2*C - b^2*C)*Tan[c + d*x])/(b^2*(a^2 + b^2)*d) + (a*(b*B - a*C)*Tan[c + d*x]^2)/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",7,7,40,0.1750,1,"{3632, 3605, 3647, 3626, 3617, 31, 3475}"
33,1,157,0,0.3112186,"\int \frac{\tan (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 (b B-a C)}{b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-C)+2 a b B+b^2 C\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2 (b B-a C)}{b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-C)+2 a b B+b^2 C\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}",1,"-(((a^2*B - b^2*B + 2*a*b*C)*x)/(a^2 + b^2)^2) - ((2*a*b*B - a^2*C + b^2*C)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) - (a*(2*b^3*B - a^3*C - 3*a*b^2*C)*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)^2*d) - (a^2*(b*B - a*C))/(b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",6,6,38,0.1579,1,"{3632, 3604, 3626, 3617, 31, 3475}"
34,1,115,0,0.1465698,"\int \frac{B \tan (c+d x)+C \tan ^2(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[(B*Tan[c + d*x] + C*Tan[c + d*x]^2)/(a + b*Tan[c + d*x])^2,x]","\frac{a (b B-a C)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 B+2 a b C-b^2 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}","\frac{a (b B-a C)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 B+2 a b C-b^2 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}",1,"((2*a*b*B - a^2*C + b^2*C)*x)/(a^2 + b^2)^2 - ((a^2*B - b^2*B + 2*a*b*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) + (a*(b*B - a*C))/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,32,0.09375,1,"{3628, 3531, 3530}"
35,1,111,0,0.2076273,"\int \frac{\cot (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^2,x]","-\frac{b B-a C}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (-C)+2 a b B+b^2 C\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}","-\frac{b B-a C}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (-C)+2 a b B+b^2 C\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}",1,"((a^2*B - b^2*B + 2*a*b*C)*x)/(a^2 + b^2)^2 + ((2*a*b*B - a^2*C + b^2*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) - (b*B - a*C)/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",4,4,38,0.1053,1,"{3632, 3529, 3531, 3530}"
36,1,137,0,0.4026812,"\int \frac{\cot ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^2,x]","\frac{b (b B-a C)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b \left(3 a^2 b B-2 a^3 C+b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}+\frac{B \log (\sin (c+d x))}{a^2 d}","\frac{b (b B-a C)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b \left(3 a^2 b B-2 a^3 C+b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-C)+2 a b B+b^2 C\right)}{\left(a^2+b^2\right)^2}+\frac{B \log (\sin (c+d x))}{a^2 d}",1,"-(((2*a*b*B - a^2*C + b^2*C)*x)/(a^2 + b^2)^2) + (B*Log[Sin[c + d*x]])/(a^2*d) - (b*(3*a^2*b*B + b^3*B - 2*a^3*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)^2*d) + (b*(b*B - a*C))/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",5,5,40,0.1250,1,"{3632, 3609, 3651, 3530, 3475}"
37,1,192,0,0.6075645,"\int \frac{\cot ^3(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^2,x]","-\frac{b \left(a^2 B-a b C+2 b^2 B\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b^2 \left(4 a^2 b B-3 a^3 C-a b^2 C+2 b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}-\frac{(2 b B-a C) \log (\sin (c+d x))}{a^3 d}-\frac{B \cot (c+d x)}{a d (a+b \tan (c+d x))}","-\frac{b \left(a^2 B-a b C+2 b^2 B\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b^2 \left(4 a^2 b B-3 a^3 C-a b^2 C+2 b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 B+2 a b C-b^2 B\right)}{\left(a^2+b^2\right)^2}-\frac{(2 b B-a C) \log (\sin (c+d x))}{a^3 d}-\frac{B \cot (c+d x)}{a d (a+b \tan (c+d x))}",1,"-(((a^2*B - b^2*B + 2*a*b*C)*x)/(a^2 + b^2)^2) - ((2*b*B - a*C)*Log[Sin[c + d*x]])/(a^3*d) + (b^2*(4*a^2*b*B + 2*b^3*B - 3*a^3*C - a*b^2*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^2*d) - (b*(a^2*B + 2*b^2*B - a*b*C))/(a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) - (B*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x]))","A",6,6,40,0.1500,1,"{3632, 3609, 3649, 3651, 3530, 3475}"
38,1,331,0,0.8605729,"\int \frac{\tan ^3(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","\frac{a (b B-a C) \tan ^3(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2 b B-3 a^3 C-7 a b^2 C+5 b^3 B\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(-6 a^2 b^2 C+a^3 b B-3 a^4 C+3 a b^3 B-b^4 C\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}+\frac{a^2 \left(3 a^2 b^3 B-9 a^3 b^2 C+a^4 b B-3 a^5 C-10 a b^4 C+6 b^5 B\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}","\frac{a (b B-a C) \tan ^3(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2 b B-3 a^3 C-7 a b^2 C+5 b^3 B\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(-6 a^2 b^2 C+a^3 b B-3 a^4 C+3 a b^3 B-b^4 C\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}+\frac{a^2 \left(3 a^2 b^3 B-9 a^3 b^2 C+a^4 b B-3 a^5 C-10 a b^4 C+6 b^5 B\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*x)/(a^2 + b^2)^3 + ((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a^2*(a^4*b*B + 3*a^2*b^3*B + 6*b^5*B - 3*a^5*C - 9*a^3*b^2*C - 10*a*b^4*C)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^3*d) - ((a^3*b*B + 3*a*b^3*B - 3*a^4*C - 6*a^2*b^2*C - b^4*C)*Tan[c + d*x])/(b^3*(a^2 + b^2)^2*d) + (a*(b*B - a*C)*Tan[c + d*x]^3)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(a^2*b*B + 5*b^3*B - 3*a^3*C - 7*a*b^2*C)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",8,8,40,0.2000,1,"{3632, 3605, 3645, 3647, 3626, 3617, 31, 3475}"
39,1,250,0,0.5813985,"\int \frac{\tan ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","\frac{a (b B-a C) \tan ^2(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a \left(a^2 b^3 B+3 a^3 b^2 C+a^5 C+6 a b^4 C-3 b^5 B\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}","\frac{a (b B-a C) \tan ^2(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a \left(a^2 b^3 B+3 a^3 b^2 C+a^5 C+6 a b^4 C-3 b^5 B\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}",1,"-(((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*x)/(a^2 + b^2)^3) + ((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a*(a^2*b^3*B - 3*b^5*B + a^5*C + 3*a^3*b^2*C + 6*a*b^4*C)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^3*d) + (a*(b*B - a*C)*Tan[c + d*x]^2)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(2*b^3*B - a^3*C - 3*a*b^2*C))/(b^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",7,7,40,0.1750,1,"{3632, 3605, 3635, 3626, 3617, 31, 3475}"
40,1,189,0,0.4274308,"\int \frac{\tan (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 (b B-a C)}{2 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2 (b B-a C)}{2 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^3 (-C)-3 a b^2 C+2 b^3 B\right)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}",1,"-(((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*x)/(a^2 + b^2)^3) - ((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - (a^2*(b*B - a*C))/(2*b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(2*b^3*B - a^3*C - 3*a*b^2*C))/(b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",5,5,38,0.1316,1,"{3632, 3604, 3628, 3531, 3530}"
41,1,179,0,0.2549858,"\int \frac{B \tan (c+d x)+C \tan ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[(B*Tan[c + d*x] + C*Tan[c + d*x]^2)/(a + b*Tan[c + d*x])^3,x]","\frac{a (b B-a C)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2 B+2 a b C-b^2 B}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}","\frac{a (b B-a C)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2 B+2 a b C-b^2 B}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}",1,"((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*x)/(a^2 + b^2)^3 - ((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) + (a*(b*B - a*C))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a^2*B - b^2*B + 2*a*b*C)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,32,0.1250,1,"{3628, 3529, 3531, 3530}"
42,1,175,0,0.3155012,"\int \frac{\cot (c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","-\frac{b B-a C}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 (-C)+2 a b B+b^2 C}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}","-\frac{b B-a C}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 (-C)+2 a b B+b^2 C}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*x)/(a^2 + b^2)^3 + ((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - (b*B - a*C)/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (2*a*b*B - a^2*C + b^2*C)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",5,4,38,0.1053,1,"{3632, 3529, 3531, 3530}"
43,1,215,0,0.6798831,"\int \frac{\cot ^2(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^2*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","\frac{b (b B-a C)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2 b B-2 a^3 C+b^3 B\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2 b^3 B+a^3 b^2 C+6 a^4 b B-3 a^5 C+b^5 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}+\frac{B \log (\sin (c+d x))}{a^3 d}","\frac{b (b B-a C)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2 b B-2 a^3 C+b^3 B\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2 b^3 B+a^3 b^2 C+6 a^4 b B-3 a^5 C+b^5 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b B+a^3 (-C)+3 a b^2 C-b^3 B\right)}{\left(a^2+b^2\right)^3}+\frac{B \log (\sin (c+d x))}{a^3 d}",1,"-(((3*a^2*b*B - b^3*B - a^3*C + 3*a*b^2*C)*x)/(a^2 + b^2)^3) + (B*Log[Sin[c + d*x]])/(a^3*d) - (b*(6*a^4*b*B + 3*a^2*b^3*B + b^5*B - 3*a^5*C + a^3*b^2*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^3*d) + (b*(b*B - a*C))/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b*(3*a^2*b*B + b^3*B - 2*a^3*C))/(a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,6,40,0.1500,1,"{3632, 3609, 3649, 3651, 3530, 3475}"
44,1,287,0,0.9411998,"\int \frac{\cot ^3(c+d x) \left(B \tan (c+d x)+C \tan ^2(c+d x)\right)}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^3*(B*Tan[c + d*x] + C*Tan[c + d*x]^2))/(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(6 a^2 b^2 B-3 a^3 b C+a^4 B-a b^3 C+3 b^4 B\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(2 a^2 B-a b C+3 b^2 B\right)}{2 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b^2 \left(9 a^2 b^3 B-3 a^3 b^2 C+10 a^4 b B-6 a^5 C-a b^4 C+3 b^5 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}-\frac{(3 b B-a C) \log (\sin (c+d x))}{a^4 d}-\frac{B \cot (c+d x)}{a d (a+b \tan (c+d x))^2}","-\frac{b \left(6 a^2 b^2 B-3 a^3 b C+a^4 B-a b^3 C+3 b^4 B\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(2 a^2 B-a b C+3 b^2 B\right)}{2 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b^2 \left(9 a^2 b^3 B-3 a^3 b^2 C+10 a^4 b B-6 a^5 C-a b^4 C+3 b^5 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 b C+a^3 B-3 a b^2 B-b^3 C\right)}{\left(a^2+b^2\right)^3}-\frac{(3 b B-a C) \log (\sin (c+d x))}{a^4 d}-\frac{B \cot (c+d x)}{a d (a+b \tan (c+d x))^2}",1,"-(((a^3*B - 3*a*b^2*B + 3*a^2*b*C - b^3*C)*x)/(a^2 + b^2)^3) - ((3*b*B - a*C)*Log[Sin[c + d*x]])/(a^4*d) + (b^2*(10*a^4*b*B + 9*a^2*b^3*B + 3*b^5*B - 6*a^5*C - 3*a^3*b^2*C - a*b^4*C)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^3*d) - (b*(2*a^2*B + 3*b^2*B - a*b*C))/(2*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (B*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x])^2) - (b*(a^4*B + 6*a^2*b^2*B + 3*b^4*B - 3*a^3*b*C - a*b^3*C))/(a^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",7,6,40,0.1500,1,"{3632, 3609, 3649, 3651, 3530, 3475}"
45,1,132,0,0.1553608,"\int \tan ^2(c+d x) (b \tan (c+d x))^n \left(A+B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Tan[c + d*x]^2*(b*Tan[c + d*x])^n*(A + B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{(A-C) (b \tan (c+d x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\tan ^2(c+d x)\right)}{b^3 d (n+3)}+\frac{B (b \tan (c+d x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\tan ^2(c+d x)\right)}{b^4 d (n+4)}+\frac{C (b \tan (c+d x))^{n+3}}{b^3 d (n+3)}","\frac{(A-C) (b \tan (c+d x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\tan ^2(c+d x)\right)}{b^3 d (n+3)}+\frac{B (b \tan (c+d x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\tan ^2(c+d x)\right)}{b^4 d (n+4)}+\frac{C (b \tan (c+d x))^{n+3}}{b^3 d (n+3)}",1,"(C*(b*Tan[c + d*x])^(3 + n))/(b^3*d*(3 + n)) + ((A - C)*Hypergeometric2F1[1, (3 + n)/2, (5 + n)/2, -Tan[c + d*x]^2]*(b*Tan[c + d*x])^(3 + n))/(b^3*d*(3 + n)) + (B*Hypergeometric2F1[1, (4 + n)/2, (6 + n)/2, -Tan[c + d*x]^2]*(b*Tan[c + d*x])^(4 + n))/(b^4*d*(4 + n))","A",7,5,39,0.1282,1,"{16, 3630, 3538, 3476, 364}"
46,1,154,0,0.1377754,"\int \tan ^m(c+d x) (b \tan (c+d x))^n \left(A+B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Tan[c + d*x]^m*(b*Tan[c + d*x])^n*(A + B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{(A-C) \tan ^{m+1}(c+d x) (b \tan (c+d x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\tan ^2(c+d x)\right)}{d (m+n+1)}+\frac{B \tan ^{m+2}(c+d x) (b \tan (c+d x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);-\tan ^2(c+d x)\right)}{d (m+n+2)}+\frac{C \tan ^{m+1}(c+d x) (b \tan (c+d x))^n}{d (m+n+1)}","\frac{(A-C) \tan ^{m+1}(c+d x) (b \tan (c+d x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);-\tan ^2(c+d x)\right)}{d (m+n+1)}+\frac{B \tan ^{m+2}(c+d x) (b \tan (c+d x))^n \, _2F_1\left(1,\frac{1}{2} (m+n+2);\frac{1}{2} (m+n+4);-\tan ^2(c+d x)\right)}{d (m+n+2)}+\frac{C \tan ^{m+1}(c+d x) (b \tan (c+d x))^n}{d (m+n+1)}",1,"(C*Tan[c + d*x]^(1 + m)*(b*Tan[c + d*x])^n)/(d*(1 + m + n)) + ((A - C)*Hypergeometric2F1[1, (1 + m + n)/2, (3 + m + n)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m)*(b*Tan[c + d*x])^n)/(d*(1 + m + n)) + (B*Hypergeometric2F1[1, (2 + m + n)/2, (4 + m + n)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m)*(b*Tan[c + d*x])^n)/(d*(2 + m + n))","A",7,5,39,0.1282,1,"{20, 3630, 3538, 3476, 364}"
47,1,170,0,0.1435554,"\int \tan ^m(c+d x) \sqrt{b \tan (c+d x)} \left(A+B \tan (c+d x)+C \tan ^2(c+d x)\right) \, dx","Int[Tan[c + d*x]^m*Sqrt[b*Tan[c + d*x]]*(A + B*Tan[c + d*x] + C*Tan[c + d*x]^2),x]","\frac{2 (A-C) \sqrt{b \tan (c+d x)} \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);-\tan ^2(c+d x)\right)}{d (2 m+3)}+\frac{2 B \sqrt{b \tan (c+d x)} \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+5);\frac{1}{4} (2 m+9);-\tan ^2(c+d x)\right)}{d (2 m+5)}+\frac{2 C \sqrt{b \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3)}","\frac{2 (A-C) \sqrt{b \tan (c+d x)} \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);-\tan ^2(c+d x)\right)}{d (2 m+3)}+\frac{2 B \sqrt{b \tan (c+d x)} \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+5);\frac{1}{4} (2 m+9);-\tan ^2(c+d x)\right)}{d (2 m+5)}+\frac{2 C \sqrt{b \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3)}",1,"(2*C*Tan[c + d*x]^(1 + m)*Sqrt[b*Tan[c + d*x]])/(d*(3 + 2*m)) + (2*(A - C)*Hypergeometric2F1[1, (3 + 2*m)/4, (7 + 2*m)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m)*Sqrt[b*Tan[c + d*x]])/(d*(3 + 2*m)) + (2*B*Hypergeometric2F1[1, (5 + 2*m)/4, (9 + 2*m)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m)*Sqrt[b*Tan[c + d*x]])/(d*(5 + 2*m))","A",7,5,41,0.1220,1,"{20, 3630, 3538, 3476, 364}"
48,1,170,0,0.1365347,"\int \frac{\tan ^m(c+d x) \left(A+B \tan (c+d x)+C \tan ^2(c+d x)\right)}{\sqrt{b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x] + C*Tan[c + d*x]^2))/Sqrt[b*Tan[c + d*x]],x]","\frac{2 (A-C) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+1);\frac{1}{4} (2 m+5);-\tan ^2(c+d x)\right)}{d (2 m+1) \sqrt{b \tan (c+d x)}}+\frac{2 B \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);-\tan ^2(c+d x)\right)}{d (2 m+3) \sqrt{b \tan (c+d x)}}+\frac{2 C \tan ^{m+1}(c+d x)}{d (2 m+1) \sqrt{b \tan (c+d x)}}","\frac{2 (A-C) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+1);\frac{1}{4} (2 m+5);-\tan ^2(c+d x)\right)}{d (2 m+1) \sqrt{b \tan (c+d x)}}+\frac{2 B \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2 m+3);\frac{1}{4} (2 m+7);-\tan ^2(c+d x)\right)}{d (2 m+3) \sqrt{b \tan (c+d x)}}+\frac{2 C \tan ^{m+1}(c+d x)}{d (2 m+1) \sqrt{b \tan (c+d x)}}",1,"(2*C*Tan[c + d*x]^(1 + m))/(d*(1 + 2*m)*Sqrt[b*Tan[c + d*x]]) + (2*(A - C)*Hypergeometric2F1[1, (1 + 2*m)/4, (5 + 2*m)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(d*(1 + 2*m)*Sqrt[b*Tan[c + d*x]]) + (2*B*Hypergeometric2F1[1, (3 + 2*m)/4, (7 + 2*m)/4, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(d*(3 + 2*m)*Sqrt[b*Tan[c + d*x]])","A",7,5,41,0.1220,1,"{20, 3630, 3538, 3476, 364}"
49,1,328,0,1.5608618,"\int \frac{\tan ^m(c+d x) \left(A+B \tan (c+d x)+C \tan ^2(c+d x)\right)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x] + C*Tan[c + d*x]^2))/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{\left(\sqrt{-b^2} (A-C)+b B\right) \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} F_1\left(\frac{1}{2};1,-m;\frac{3}{2};\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{b \tan (c+d x)}{a}+1\right)}{b d \left(a-\sqrt{-b^2}\right)}-\frac{\left(b B-\sqrt{-b^2} (A-C)\right) \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} F_1\left(\frac{1}{2};1,-m;\frac{3}{2};\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}},\frac{b \tan (c+d x)}{a}+1\right)}{b d \left(a+\sqrt{-b^2}\right)}+\frac{2 C \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b \tan (c+d x)}{a}+1\right)}{b d}","-\frac{\left(\sqrt{-b^2} (A-C)+b B\right) \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} F_1\left(\frac{1}{2};1,-m;\frac{3}{2};\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}},\frac{b \tan (c+d x)}{a}+1\right)}{b d \left(a-\sqrt{-b^2}\right)}-\frac{\left(b B-\sqrt{-b^2} (A-C)\right) \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} F_1\left(\frac{1}{2};1,-m;\frac{3}{2};\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}},\frac{b \tan (c+d x)}{a}+1\right)}{b d \left(a+\sqrt{-b^2}\right)}+\frac{2 C \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \left(-\frac{b \tan (c+d x)}{a}\right)^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};\frac{b \tan (c+d x)}{a}+1\right)}{b d}",1,"-(((b*B + Sqrt[-b^2]*(A - C))*AppellF1[1/2, 1, -m, 3/2, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2]), 1 + (b*Tan[c + d*x])/a]*Tan[c + d*x]^m*Sqrt[a + b*Tan[c + d*x]])/(b*(a - Sqrt[-b^2])*d*(-((b*Tan[c + d*x])/a))^m)) - ((b*B - Sqrt[-b^2]*(A - C))*AppellF1[1/2, 1, -m, 3/2, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2]), 1 + (b*Tan[c + d*x])/a]*Tan[c + d*x]^m*Sqrt[a + b*Tan[c + d*x]])/(b*(a + Sqrt[-b^2])*d*(-((b*Tan[c + d*x])/a))^m) + (2*C*Hypergeometric2F1[1/2, -m, 3/2, 1 + (b*Tan[c + d*x])/a]*Tan[c + d*x]^m*Sqrt[a + b*Tan[c + d*x]])/(b*d*(-((b*Tan[c + d*x])/a))^m)","A",13,7,43,0.1628,1,"{3655, 6720, 1692, 246, 245, 430, 429}"
50,1,353,0,0.7853039,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{b \tan (e+f x) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{\log (\cos (e+f x)) \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+x \left(-3 a^2 b (d (A-C)+B c)+a^3 (A c-B d-c C)-3 a b^2 (A c-B d-c C)+b^3 (d (A-C)+B c)\right)+\frac{(d (A-C)+B c) (a+b \tan (e+f x))^3}{3 f}+\frac{(a+b \tan (e+f x))^2 (a A d+a B c-a C d+A b c-b B d-b c C)}{2 f}-\frac{(a C d-5 b (B d+c C)) (a+b \tan (e+f x))^4}{20 b^2 f}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^4}{5 b f}","\frac{b \tan (e+f x) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{\log (\cos (e+f x)) \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+x \left(-3 a^2 b (d (A-C)+B c)+a^3 (A c-B d-c C)-3 a b^2 (A c-B d-c C)+b^3 (d (A-C)+B c)\right)+\frac{(d (A-C)+B c) (a+b \tan (e+f x))^3}{3 f}+\frac{(a+b \tan (e+f x))^2 (a A d+a B c-a C d+A b c-b B d-b c C)}{2 f}-\frac{(a C d-5 b (B d+c C)) (a+b \tan (e+f x))^4}{20 b^2 f}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^4}{5 b f}",1,"(a^3*(A*c - c*C - B*d) - 3*a*b^2*(A*c - c*C - B*d) - 3*a^2*b*(B*c + (A - C)*d) + b^3*(B*c + (A - C)*d))*x - ((3*a^2*b*(A*c - c*C - B*d) - b^3*(A*c - c*C - B*d) + a^3*(B*c + (A - C)*d) - 3*a*b^2*(B*c + (A - C)*d))*Log[Cos[e + f*x]])/f + (b*(2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*Tan[e + f*x])/f + ((A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*(a + b*Tan[e + f*x])^2)/(2*f) + ((B*c + (A - C)*d)*(a + b*Tan[e + f*x])^3)/(3*f) - ((a*C*d - 5*b*(c*C + B*d))*(a + b*Tan[e + f*x])^4)/(20*b^2*f) + (C*d*Tan[e + f*x]*(a + b*Tan[e + f*x])^4)/(5*b*f)","A",6,5,43,0.1163,1,"{3637, 3630, 3528, 3525, 3475}"
51,1,248,0,0.4512637,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\log (\cos (e+f x)) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}+x \left(a^2 (A c-B d-c C)-2 a b (d (A-C)+B c)-b^2 (A c-B d-c C)\right)+\frac{(d (A-C)+B c) (a+b \tan (e+f x))^2}{2 f}+\frac{b \tan (e+f x) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(a C d-4 b (B d+c C)) (a+b \tan (e+f x))^3}{12 b^2 f}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^3}{4 b f}","-\frac{\log (\cos (e+f x)) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}+x \left(a^2 (A c-B d-c C)-2 a b (d (A-C)+B c)-b^2 (A c-B d-c C)\right)+\frac{(d (A-C)+B c) (a+b \tan (e+f x))^2}{2 f}+\frac{b \tan (e+f x) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(a C d-4 b (B d+c C)) (a+b \tan (e+f x))^3}{12 b^2 f}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^3}{4 b f}",1,"(a^2*(A*c - c*C - B*d) - b^2*(A*c - c*C - B*d) - 2*a*b*(B*c + (A - C)*d))*x - ((2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*Log[Cos[e + f*x]])/f + (b*(A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*Tan[e + f*x])/f + ((B*c + (A - C)*d)*(a + b*Tan[e + f*x])^2)/(2*f) - ((a*C*d - 4*b*(c*C + B*d))*(a + b*Tan[e + f*x])^3)/(12*b^2*f) + (C*d*Tan[e + f*x]*(a + b*Tan[e + f*x])^3)/(4*b*f)","A",5,5,43,0.1163,1,"{3637, 3630, 3528, 3525, 3475}"
52,1,161,0,0.2413941,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\log (\cos (e+f x)) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-x (-a (A c-B d-c C)+b d (A-C)+b B c)+\frac{d \tan (e+f x) (a B+A b-b C)}{f}-\frac{(-3 a C d-3 b B d+b c C) (c+d \tan (e+f x))^2}{6 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^2}{3 d f}","-\frac{\log (\cos (e+f x)) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}+x (a (A c-B d-c C)-b (d (A-C)+B c))+\frac{d \tan (e+f x) (a B+A b-b C)}{f}-\frac{(-3 a C d-3 b B d+b c C) (c+d \tan (e+f x))^2}{6 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^2}{3 d f}",1,"-((b*B*c + b*(A - C)*d - a*(A*c - c*C - B*d))*x) - ((A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*Log[Cos[e + f*x]])/f + ((A*b + a*B - b*C)*d*Tan[e + f*x])/f - ((b*c*C - 3*b*B*d - 3*a*C*d)*(c + d*Tan[e + f*x])^2)/(6*d^2*f) + (b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^2)/(3*d*f)","A",4,4,41,0.09756,1,"{3637, 3630, 3525, 3475}"
53,1,73,0,0.0606425,"\int (c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{(d (A-C)+B c) \log (\cos (e+f x))}{f}+x (A c-B d-c C)+\frac{B d \tan (e+f x)}{f}+\frac{C (c+d \tan (e+f x))^2}{2 d f}","-\frac{(d (A-C)+B c) \log (\cos (e+f x))}{f}+x (A c-B d-c C)+\frac{B d \tan (e+f x)}{f}+\frac{C (c+d \tan (e+f x))^2}{2 d f}",1,"(A*c - c*C - B*d)*x - ((B*c + (A - C)*d)*Log[Cos[e + f*x]])/f + (B*d*Tan[e + f*x])/f + (C*(c + d*Tan[e + f*x])^2)/(2*d*f)","A",3,3,31,0.09677,1,"{3630, 3525, 3475}"
54,1,155,0,0.3494314,"\int \frac{(c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[((c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","\frac{(b c-a d) \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)}+\frac{\log (\cos (e+f x)) (-a A d-a B c+a C d+A b c-b B d-b c C)}{f \left(a^2+b^2\right)}+\frac{x (a (A c-B d-c C)+b d (A-C)+b B c)}{a^2+b^2}+\frac{C d \tan (e+f x)}{b f}","\frac{(b c-a d) \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)}+\frac{\log (\cos (e+f x)) (-a A d-a B c+a C d+A b c-b B d-b c C)}{f \left(a^2+b^2\right)}+\frac{x (a (A c-B d-c C)+b (d (A-C)+B c))}{a^2+b^2}+\frac{C d \tan (e+f x)}{b f}",1,"((b*B*c + b*(A - C)*d + a*(A*c - c*C - B*d))*x)/(a^2 + b^2) + ((A*b*c - a*B*c - b*c*C - a*A*d - b*B*d + a*C*d)*Log[Cos[e + f*x]])/((a^2 + b^2)*f) + ((A*b^2 - a*(b*B - a*C))*(b*c - a*d)*Log[a + b*Tan[e + f*x]])/(b^2*(a^2 + b^2)*f) + (C*d*Tan[e + f*x])/(b*f)","A",5,5,43,0.1163,1,"{3637, 3626, 3617, 31, 3475}"
55,1,265,0,0.4735465,"\int \frac{(c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[((c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","-\frac{(b c-a d) \left(A b^2-a (b B-a C)\right)}{b^2 f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right) \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)^2}+\frac{\log (\cos (e+f x)) \left(a^2 (-(d (A-C)+B c))+2 a b (A c-B d-c C)+b^2 (d (A-C)+B c)\right)}{f \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (A c-B d-c C)+2 a b (d (A-C)+B c)-b^2 (A c-B d-c C)\right)}{\left(a^2+b^2\right)^2}","-\frac{(b c-a d) \left(A b^2-a (b B-a C)\right)}{b^2 f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right) \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)^2}+\frac{\log (\cos (e+f x)) \left(a^2 (-(d (A-C)+B c))+2 a b (A c-B d-c C)+b^2 (d (A-C)+B c)\right)}{f \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (A c-B d-c C)+2 a b (d (A-C)+B c)-b^2 (A c-B d-c C)\right)}{\left(a^2+b^2\right)^2}",1,"((a^2*(A*c - c*C - B*d) - b^2*(A*c - c*C - B*d) + 2*a*b*(B*c + (A - C)*d))*x)/(a^2 + b^2)^2 + ((2*a*b*(A*c - c*C - B*d) - a^2*(B*c + (A - C)*d) + b^2*(B*c + (A - C)*d))*Log[Cos[e + f*x]])/((a^2 + b^2)^2*f) + ((a^4*C*d + b^4*(B*c + A*d) + 2*a*b^3*(A*c - c*C - B*d) - a^2*b^2*(B*c + (A - 3*C)*d))*Log[a + b*Tan[e + f*x]])/(b^2*(a^2 + b^2)^2*f) - ((A*b^2 - a*(b*B - a*C))*(b*c - a*d))/(b^2*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",5,5,43,0.1163,1,"{3635, 3626, 3617, 31, 3475}"
56,1,320,0,0.7032365,"\int \frac{(c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[((c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","-\frac{(b c-a d) \left(A b^2-a (b B-a C)\right)}{2 b^2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)}{b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}+\frac{\left(3 a^2 b (A c-B d-c C)+a^3 (-(d (A-C)+B c))+3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b (d (A-C)+B c)+a^3 (A c-B d-c C)-3 a b^2 (A c-B d-c C)-b^3 (d (A-C)+B c)\right)}{\left(a^2+b^2\right)^3}","-\frac{(b c-a d) \left(A b^2-a (b B-a C)\right)}{2 b^2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)}{b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}+\frac{\left(3 a^2 b (A c-B d-c C)+a^3 (-(d (A-C)+B c))+3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b (d (A-C)+B c)+a^3 (A c-B d-c C)-3 a b^2 (A c-B d-c C)-b^3 (d (A-C)+B c)\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*(A*c - c*C - B*d) - 3*a*b^2*(A*c - c*C - B*d) + 3*a^2*b*(B*c + (A - C)*d) - b^3*(B*c + (A - C)*d))*x)/(a^2 + b^2)^3 + ((3*a^2*b*(A*c - c*C - B*d) - b^3*(A*c - c*C - B*d) - a^3*(B*c + (A - C)*d) + 3*a*b^2*(B*c + (A - C)*d))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*f) - ((A*b^2 - a*(b*B - a*C))*(b*c - a*d))/(2*b^2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (a^4*C*d + b^4*(B*c + A*d) + 2*a*b^3*(A*c - c*C - B*d) - a^2*b^2*(B*c + (A - 3*C)*d))/(b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",4,4,43,0.09302,1,"{3635, 3628, 3531, 3530}"
57,1,661,0,2.3835904,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(c+d \tan (e+f x))^3 \left(-3 a^2 b d^2 (3 c C-16 B d)+4 a^3 C d^3+3 a b^2 d \left(20 d^2 (A-C)-5 B c d+2 c^2 C\right)+b^3 \left(-\left(5 c d^2 (A-C)-2 B c^2 d+20 B d^3+c^3 C\right)\right)\right)}{60 d^4 f}+\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+a^3 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+3 a b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{f}-x \left(3 a^2 b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+\frac{\left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+\frac{b \tan (e+f x) (c+d \tan (e+f x))^3 \left(5 b d^2 (a B+A b-b C)+(b c-a d) (-a C d-2 b B d+b c C)\right)}{20 d^3 f}-\frac{(-a C d-2 b B d+b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3}{10 d^2 f}+\frac{C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^3}{6 d f}","\frac{(c+d \tan (e+f x))^3 \left(-3 a^2 b d^2 (3 c C-16 B d)+4 a^3 C d^3+3 a b^2 d \left(20 d^2 (A-C)-5 B c d+2 c^2 C\right)+b^3 \left(-\left(5 c d^2 (A-C)-2 B c^2 d+20 B d^3+c^3 C\right)\right)\right)}{60 d^4 f}+\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+a^3 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+3 a b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{f}-x \left(3 a^2 b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+\frac{\left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+\frac{b \tan (e+f x) (c+d \tan (e+f x))^3 \left(5 b d^2 (a B+A b-b C)+(b c-a d) (-a C d-2 b B d+b c C)\right)}{20 d^3 f}-\frac{(-a C d-2 b B d+b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3}{10 d^2 f}+\frac{C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^3}{6 d f}",1,"-((a^3*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a*b^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + 3*a^2*b*(2*c*(A - C)*d + B*(c^2 - d^2)) - b^3*(2*c*(A - C)*d + B*(c^2 - d^2)))*x) + ((3*a^2*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^3*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - a^3*(2*c*(A - C)*d + B*(c^2 - d^2)) + 3*a*b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Log[Cos[e + f*x]])/f + (d*(3*a^2*b*(A*c - c*C - B*d) - b^3*(A*c - c*C - B*d) + a^3*(B*c + (A - C)*d) - 3*a*b^2*(B*c + (A - C)*d))*Tan[e + f*x])/f + ((a^3*B - 3*a*b^2*B + 3*a^2*b*(A - C) - b^3*(A - C))*(c + d*Tan[e + f*x])^2)/(2*f) + ((4*a^3*C*d^3 - 3*a^2*b*d^2*(3*c*C - 16*B*d) + 3*a*b^2*d*(2*c^2*C - 5*B*c*d + 20*(A - C)*d^2) - b^3*(c^3*C - 2*B*c^2*d + 5*c*(A - C)*d^2 + 20*B*d^3))*(c + d*Tan[e + f*x])^3)/(60*d^4*f) + (b*(5*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(b*c*C - 2*b*B*d - a*C*d))*Tan[e + f*x]*(c + d*Tan[e + f*x])^3)/(20*d^3*f) - ((b*c*C - 2*b*B*d - a*C*d)*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3)/(10*d^2*f) + (C*(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^3)/(6*d*f)","A",7,6,45,0.1333,1,"{3647, 3637, 3630, 3528, 3525, 3475}"
58,1,443,0,1.2781172,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(c+d \tan (e+f x))^3 \left(8 a^2 C d^2-10 a b d (c C-4 B d)+b^2 \left(20 d^2 (A-C)-5 B c d+2 c^2 C\right)\right)}{60 d^3 f}+\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}-x \left(a^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+2 a b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)+\frac{\left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{b \tan (e+f x) (-2 a C d-5 b B d+2 b c C) (c+d \tan (e+f x))^3}{20 d^2 f}+\frac{C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3}{5 d f}","\frac{(c+d \tan (e+f x))^3 \left(8 a^2 C d^2-10 a b d (c C-4 B d)+b^2 \left(20 d^2 (A-C)-5 B c d+2 c^2 C\right)\right)}{60 d^3 f}+\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}-x \left(a^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+2 a b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)+\frac{\left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{b \tan (e+f x) (-2 a C d-5 b B d+2 b c C) (c+d \tan (e+f x))^3}{20 d^2 f}+\frac{C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3}{5 d f}",1,"-((a^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + 2*a*b*(2*c*(A - C)*d + B*(c^2 - d^2)))*x) + ((2*a*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - a^2*(2*c*(A - C)*d + B*(c^2 - d^2)) + b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Log[Cos[e + f*x]])/f + (d*(2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*Tan[e + f*x])/f + ((a^2*B - b^2*B + 2*a*b*(A - C))*(c + d*Tan[e + f*x])^2)/(2*f) + ((8*a^2*C*d^2 - 10*a*b*d*(c*C - 4*B*d) + b^2*(2*c^2*C - 5*B*c*d + 20*(A - C)*d^2))*(c + d*Tan[e + f*x])^3)/(60*d^3*f) - (b*(2*b*c*C - 5*b*B*d - 2*a*C*d)*Tan[e + f*x]*(c + d*Tan[e + f*x])^3)/(20*d^2*f) + (C*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3)/(5*d*f)","A",6,6,45,0.1333,1,"{3647, 3637, 3630, 3528, 3525, 3475}"
59,1,264,0,0.4722022,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\log (\cos (e+f x)) \left(2 a A c d+a B \left(c^2-d^2\right)-2 a c C d+A b \left(c^2-d^2\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}-x \left(a \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+\frac{(a B+A b-b C) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(-4 a C d-4 b B d+b c C) (c+d \tan (e+f x))^3}{12 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^3}{4 d f}","-\frac{\log (\cos (e+f x)) \left(A \left(2 a c d+b \left(c^2-d^2\right)\right)+a \left(B c^2-B d^2-2 c C d\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}-x \left(a \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+\frac{(a B+A b-b C) (c+d \tan (e+f x))^2}{2 f}+\frac{d \tan (e+f x) (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(-4 a C d-4 b B d+b c C) (c+d \tan (e+f x))^3}{12 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^3}{4 d f}",1,"-((a*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + b*(2*c*(A - C)*d + B*(c^2 - d^2)))*x) - ((2*a*A*c*d - 2*a*c*C*d + A*b*(c^2 - d^2) + a*B*(c^2 - d^2) - b*(c^2*C + 2*B*c*d - C*d^2))*Log[Cos[e + f*x]])/f + (d*(A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*Tan[e + f*x])/f + ((A*b + a*B - b*C)*(c + d*Tan[e + f*x])^2)/(2*f) - ((b*c*C - 4*b*B*d - 4*a*C*d)*(c + d*Tan[e + f*x])^3)/(12*d^2*f) + (b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^3)/(4*d*f)","A",5,5,43,0.1163,1,"{3637, 3630, 3528, 3525, 3475}"
60,1,131,0,0.1550124,"\int (c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\left(2 c d (A-C)+B \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+\frac{d \tan (e+f x) (d (A-C)+B c)}{f}+\frac{B (c+d \tan (e+f x))^2}{2 f}+\frac{C (c+d \tan (e+f x))^3}{3 d f}","-\frac{\left(2 c d (A-C)+B \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+\frac{d \tan (e+f x) (d (A-C)+B c)}{f}+\frac{B (c+d \tan (e+f x))^2}{2 f}+\frac{C (c+d \tan (e+f x))^3}{3 d f}",1,"-((c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2))*x) - ((2*c*(A - C)*d + B*(c^2 - d^2))*Log[Cos[e + f*x]])/f + (d*(B*c + (A - C)*d)*Tan[e + f*x])/f + (B*(c + d*Tan[e + f*x])^2)/(2*f) + (C*(c + d*Tan[e + f*x])^3)/(3*d*f)","A",4,4,33,0.1212,1,"{3630, 3528, 3525, 3475}"
61,1,252,0,0.8273201,"\int \frac{(c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[((c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","-\frac{\log (\cos (e+f x)) \left(2 a A c d+a B \left(c^2-d^2\right)-2 a c C d-A b \left(c^2-d^2\right)+b \left(2 B c d+c^2 C-C d^2\right)\right)}{f \left(a^2+b^2\right)}-\frac{x \left(a \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{a^2+b^2}+\frac{(b c-a d)^2 \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)}+\frac{d \tan (e+f x) (-a C d+b B d+b c C)}{b^2 f}+\frac{C (c+d \tan (e+f x))^2}{2 b f}","-\frac{\log (\cos (e+f x)) \left(A \left(2 a c d-b \left(c^2-d^2\right)\right)+a \left(B c^2-B d^2-2 c C d\right)+b \left(2 B c d+c^2 C-C d^2\right)\right)}{f \left(a^2+b^2\right)}-\frac{x \left(a \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{a^2+b^2}+\frac{(b c-a d)^2 \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)}+\frac{d \tan (e+f x) (-a C d+b B d+b c C)}{b^2 f}+\frac{C (c+d \tan (e+f x))^2}{2 b f}",1,"-(((a*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b*(2*c*(A - C)*d + B*(c^2 - d^2)))*x)/(a^2 + b^2)) - ((2*a*A*c*d - 2*a*c*C*d - A*b*(c^2 - d^2) + a*B*(c^2 - d^2) + b*(c^2*C + 2*B*c*d - C*d^2))*Log[Cos[e + f*x]])/((a^2 + b^2)*f) + ((A*b^2 - a*(b*B - a*C))*(b*c - a*d)^2*Log[a + b*Tan[e + f*x]])/(b^3*(a^2 + b^2)*f) + (d*(b*c*C + b*B*d - a*C*d)*Tan[e + f*x])/(b^2*f) + (C*(c + d*Tan[e + f*x])^2)/(2*b*f)","A",6,6,45,0.1333,1,"{3647, 3637, 3626, 3617, 31, 3475}"
62,1,415,0,1.0528517,"\int \frac{(c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[((c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","-\frac{\log (\cos (e+f x)) \left(a^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-2 a b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^2}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{(b c-a d) \left(a^2 b^2 (B c-4 C d)+a^3 b B d-2 a^4 C d-a b^3 (2 A c-3 B d-2 c C)-b^4 (2 A d+B c)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)^2}+\frac{d^2 \tan (e+f x) \left(2 a^2 C-a b B+A b^2+b^2 C\right)}{b^2 f \left(a^2+b^2\right)}","-\frac{\log (\cos (e+f x)) \left(a^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-2 a b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^2}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{(b c-a d) \left(a^2 b^2 (B c-4 C d)+a^3 b B d-2 a^4 C d-a b^3 (2 A c-3 B d-2 c C)-b^4 (2 A d+B c)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)^2}+\frac{d^2 \tan (e+f x) \left(2 a^2 C-a b B+A b^2+b^2 C\right)}{b^2 f \left(a^2+b^2\right)}",1,"-(((a^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 2*a*b*(2*c*(A - C)*d + B*(c^2 - d^2)))*x)/(a^2 + b^2)^2) - ((2*a*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + a^2*(2*c*(A - C)*d + B*(c^2 - d^2)) - b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Log[Cos[e + f*x]])/((a^2 + b^2)^2*f) - ((b*c - a*d)*(a^3*b*B*d - 2*a^4*C*d - b^4*(B*c + 2*A*d) - a*b^3*(2*A*c - 2*c*C - 3*B*d) + a^2*b^2*(B*c - 4*C*d))*Log[a + b*Tan[e + f*x]])/(b^3*(a^2 + b^2)^2*f) + ((A*b^2 - a*b*B + 2*a^2*C + b^2*C)*d^2*Tan[e + f*x])/(b^2*(a^2 + b^2)*f) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^2)/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",6,6,45,0.1333,1,"{3645, 3637, 3626, 3617, 31, 3475}"
63,1,597,0,1.2900347,"\int \frac{(c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[((c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","\frac{\left(-a^3 b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-2 C d^2\right)+3 a^4 b^2 C d^2+a^6 C d^2+3 a b^5 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+b^6 \left(c (2 B d+c C)-A \left(c^2-d^2\right)\right)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)^3}-\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+a^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{f \left(a^2+b^2\right)^3}-\frac{x \left(-3 a^2 b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{\left(a^2+b^2\right)^3}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^2}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(b c-a d) \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{b^3 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}","\frac{\left(-a^3 b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-2 C d^2\right)+3 a^4 b^2 C d^2+a^6 C d^2+3 a b^5 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+b^6 \left(c (2 B d+c C)-A \left(c^2-d^2\right)\right)\right) \log (a+b \tan (e+f x))}{b^3 f \left(a^2+b^2\right)^3}-\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+a^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)\right)}{f \left(a^2+b^2\right)^3}-\frac{x \left(-3 a^2 b \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{\left(a^2+b^2\right)^3}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^2}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(b c-a d) \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{b^3 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}",1,"-(((a^3*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a*b^2*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a^2*b*(2*c*(A - C)*d + B*(c^2 - d^2)) + b^3*(2*c*(A - C)*d + B*(c^2 - d^2)))*x)/(a^2 + b^2)^3) - ((3*a^2*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^3*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + a^3*(2*c*(A - C)*d + B*(c^2 - d^2)) - 3*a*b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Log[Cos[e + f*x]])/((a^2 + b^2)^3*f) + ((a^6*C*d^2 + 3*a^4*b^2*C*d^2 - 3*a^2*b^4*(c^2*C + 2*B*c*d - 2*C*d^2 - A*(c^2 - d^2)) + b^6*(c*(c*C + 2*B*d) - A*(c^2 - d^2)) - a^3*b^3*(2*c*(A - C)*d + B*(c^2 - d^2)) + 3*a*b^5*(2*c*(A - C)*d + B*(c^2 - d^2)))*Log[a + b*Tan[e + f*x]])/(b^3*(a^2 + b^2)^3*f) - ((b*c - a*d)*(a^4*C*d + b^4*(B*c + A*d) + 2*a*b^3*(A*c - c*C - B*d) - a^2*b^2*(B*c + (A - 3*C)*d)))/(b^3*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^2)/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2)","A",6,6,45,0.1333,1,"{3645, 3635, 3626, 3617, 31, 3475}"
64,1,603,0,1.532786,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(c+d \tan (e+f x))^4 \left(5 a^2 C d^2-6 a b d (c C-5 B d)+b^2 \left(15 d^2 (A-C)-3 B c d+c^2 C\right)\right)}{60 d^3 f}-\frac{d \tan (e+f x) \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}+\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{f}+x \left(a^2 \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)+b^2 \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)+\frac{\left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^3}{3 f}+\frac{(c+d \tan (e+f x))^2 \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{2 f}-\frac{b \tan (e+f x) (-a C d-3 b B d+b c C) (c+d \tan (e+f x))^4}{15 d^2 f}+\frac{C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^4}{6 d f}","\frac{(c+d \tan (e+f x))^4 \left(5 a^2 C d^2-6 a b d (c C-5 B d)+b^2 \left(15 d^2 (A-C)-3 B c d+c^2 C\right)\right)}{60 d^3 f}-\frac{d \tan (e+f x) \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}+\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{f}+x \left(a^2 \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)+b^2 \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)+\frac{\left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^3}{3 f}+\frac{(c+d \tan (e+f x))^2 \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{2 f}-\frac{b \tan (e+f x) (-a C d-3 b B d+b c C) (c+d \tan (e+f x))^4}{15 d^2 f}+\frac{C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^4}{6 d f}",1,"(a^2*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3) + b^2*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) - 2*a*b*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*x + ((2*a*b*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) - a^2*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)) + b^2*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/f - (d*(2*a*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - a^2*(2*c*(A - C)*d + B*(c^2 - d^2)) + b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Tan[e + f*x])/f + ((2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*(c + d*Tan[e + f*x])^2)/(2*f) + ((a^2*B - b^2*B + 2*a*b*(A - C))*(c + d*Tan[e + f*x])^3)/(3*f) + ((5*a^2*C*d^2 - 6*a*b*d*(c*C - 5*B*d) + b^2*(c^2*C - 3*B*c*d + 15*(A - C)*d^2))*(c + d*Tan[e + f*x])^4)/(60*d^3*f) - (b*(b*c*C - 3*b*B*d - a*C*d)*Tan[e + f*x]*(c + d*Tan[e + f*x])^4)/(15*d^2*f) + (C*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^4)/(6*d*f)","A",7,6,45,0.1333,1,"{3647, 3637, 3630, 3528, 3525, 3475}"
65,1,387,0,0.7050246,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{d \tan (e+f x) \left(2 a A c d+a B \left(c^2-d^2\right)-2 a c C d+A b \left(c^2-d^2\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}-\frac{\log (\cos (e+f x)) \left(A \left(3 a c^2 d-a d^3+b c^3-3 b c d^2\right)+a \left(B c^3-3 B c d^2-3 c^2 C d+C d^3\right)-b \left(3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)}{f}-x \left(-a \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)+b d (A-C) \left(3 c^2-d^2\right)+b B \left(c^3-3 c d^2\right)\right)+\frac{(a B+A b-b C) (c+d \tan (e+f x))^3}{3 f}+\frac{(c+d \tan (e+f x))^2 (a A d+a B c-a C d+A b c-b B d-b c C)}{2 f}-\frac{(-5 a C d-5 b B d+b c C) (c+d \tan (e+f x))^4}{20 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^4}{5 d f}","\frac{d \tan (e+f x) \left(A \left(2 a c d+b \left(c^2-d^2\right)\right)+a \left(B c^2-B d^2-2 c C d\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}-\frac{\log (\cos (e+f x)) \left(A \left(3 a c^2 d-a d^3+b c^3-3 b c d^2\right)+a \left(B c^3-3 B c d^2-3 c^2 C d+C d^3\right)-b \left(3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)}{f}+x \left(a \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)-b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)+\frac{(a B+A b-b C) (c+d \tan (e+f x))^3}{3 f}+\frac{(c+d \tan (e+f x))^2 (a A d+a B c-a C d+A b c-b B d-b c C)}{2 f}-\frac{(-5 a C d-5 b B d+b c C) (c+d \tan (e+f x))^4}{20 d^2 f}+\frac{b C \tan (e+f x) (c+d \tan (e+f x))^4}{5 d f}",1,"-((b*(A - C)*d*(3*c^2 - d^2) + b*B*(c^3 - 3*c*d^2) - a*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3))*x) - ((A*(b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3) - b*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3) + a*(B*c^3 - 3*c^2*C*d - 3*B*c*d^2 + C*d^3))*Log[Cos[e + f*x]])/f + (d*(2*a*A*c*d - 2*a*c*C*d + A*b*(c^2 - d^2) + a*B*(c^2 - d^2) - b*(c^2*C + 2*B*c*d - C*d^2))*Tan[e + f*x])/f + ((A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*(c + d*Tan[e + f*x])^2)/(2*f) + ((A*b + a*B - b*C)*(c + d*Tan[e + f*x])^3)/(3*f) - ((b*c*C - 5*b*B*d - 5*a*C*d)*(c + d*Tan[e + f*x])^4)/(20*d^2*f) + (b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^4)/(5*d*f)","A",6,5,43,0.1163,1,"{3637, 3630, 3528, 3525, 3475}"
66,1,191,0,0.2438652,"\int (c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{d \tan (e+f x) \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)}{f}-\frac{\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)+\frac{(d (A-C)+B c) (c+d \tan (e+f x))^2}{2 f}+\frac{B (c+d \tan (e+f x))^3}{3 f}+\frac{C (c+d \tan (e+f x))^4}{4 d f}","\frac{d \tan (e+f x) \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)}{f}-\frac{\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)+\frac{(d (A-C)+B c) (c+d \tan (e+f x))^2}{2 f}+\frac{B (c+d \tan (e+f x))^3}{3 f}+\frac{C (c+d \tan (e+f x))^4}{4 d f}",1,"-((c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2))*x) - (((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2))*Log[Cos[e + f*x]])/f + (d*(2*c*(A - C)*d + B*(c^2 - d^2))*Tan[e + f*x])/f + ((B*c + (A - C)*d)*(c + d*Tan[e + f*x])^2)/(2*f) + (B*(c + d*Tan[e + f*x])^3)/(3*f) + (C*(c + d*Tan[e + f*x])^4)/(4*d*f)","A",5,4,33,0.1212,1,"{3630, 3528, 3525, 3475}"
67,1,363,0,1.5116551,"\int \frac{(c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[((c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","-\frac{\log (\cos (e+f x)) \left(A \left(a d \left(3 c^2-d^2\right)-b \left(c^3-3 c d^2\right)\right)+a \left(B c^3-3 B c d^2-3 c^2 C d+C d^3\right)+b \left(3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)}{f \left(a^2+b^2\right)}-\frac{x \left(a \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)-b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{a^2+b^2}+\frac{(b c-a d)^3 \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^4 f \left(a^2+b^2\right)}+\frac{d \tan (e+f x) \left((b c-a d) (-a C d+b B d+b c C)+b^2 d (d (A-C)+B c)\right)}{b^3 f}+\frac{(-a C d+b B d+b c C) (c+d \tan (e+f x))^2}{2 b^2 f}+\frac{C (c+d \tan (e+f x))^3}{3 b f}","-\frac{\log (\cos (e+f x)) \left(A \left(a d \left(3 c^2-d^2\right)-b \left(c^3-3 c d^2\right)\right)+a \left(B c^3-3 B c d^2-3 c^2 C d+C d^3\right)+b \left(3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)\right)}{f \left(a^2+b^2\right)}-\frac{x \left(a \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)-b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{a^2+b^2}+\frac{(b c-a d)^3 \left(A b^2-a (b B-a C)\right) \log (a+b \tan (e+f x))}{b^4 f \left(a^2+b^2\right)}+\frac{d \tan (e+f x) \left((b c-a d) (-a C d+b B d+b c C)+b^2 d (d (A-C)+B c)\right)}{b^3 f}+\frac{(-a C d+b B d+b c C) (c+d \tan (e+f x))^2}{2 b^2 f}+\frac{C (c+d \tan (e+f x))^3}{3 b f}",1,"-(((a*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) - b*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*x)/(a^2 + b^2)) - ((b*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3) + a*(B*c^3 - 3*c^2*C*d - 3*B*c*d^2 + C*d^3) + A*(a*d*(3*c^2 - d^2) - b*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/((a^2 + b^2)*f) + ((A*b^2 - a*(b*B - a*C))*(b*c - a*d)^3*Log[a + b*Tan[e + f*x]])/(b^4*(a^2 + b^2)*f) + (d*(b^2*d*(B*c + (A - C)*d) + (b*c - a*d)*(b*c*C + b*B*d - a*C*d))*Tan[e + f*x])/(b^3*f) + ((b*c*C + b*B*d - a*C*d)*(c + d*Tan[e + f*x])^2)/(2*b^2*f) + (C*(c + d*Tan[e + f*x])^3)/(3*b*f)","A",7,6,45,0.1333,1,"{3647, 3637, 3626, 3617, 31, 3475}"
68,1,574,0,2.321417,"\int \frac{(c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[((c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)+b^2 \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{d^2 \tan (e+f x) \left(-a^2 b (2 B d+3 c C)+3 a^3 C d-A b^2 (b c-a d)+a b^2 (B c+2 C d)-b^3 (B d+2 c C)\right)}{b^3 f \left(a^2+b^2\right)}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^3}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(3 a^2 C-2 a b B+2 A b^2+b^2 C\right) (c+d \tan (e+f x))^2}{2 b^2 f \left(a^2+b^2\right)}-\frac{(b c-a d)^2 \left(a^2 b^2 (B c-d (A+5 C))+2 a^3 b B d-3 a^4 C d-2 a b^3 (A c-2 B d-c C)-b^4 (3 A d+B c)\right) \log (a+b \tan (e+f x))}{b^4 f \left(a^2+b^2\right)^2}","\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right)}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^3-3 c d^2\right)+3 B c^2 d-B d^3+c^3 C-3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)+b^2 \left(A c^3-3 A c d^2-3 B c^2 d+B d^3-c^3 C+3 c C d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{d^2 \tan (e+f x) \left(-a^2 b (2 B d+3 c C)+3 a^3 C d-A b^2 (b c-a d)+a b^2 (B c+2 C d)-b^3 (B d+2 c C)\right)}{b^3 f \left(a^2+b^2\right)}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^3}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(3 a^2 C-2 a b B+2 A b^2+b^2 C\right) (c+d \tan (e+f x))^2}{2 b^2 f \left(a^2+b^2\right)}-\frac{(b c-a d)^2 \left(a^2 b^2 (B c-d (A+5 C))+2 a^3 b B d-3 a^4 C d-2 a b^3 (A c-2 B d-c C)-b^4 (3 A d+B c)\right) \log (a+b \tan (e+f x))}{b^4 f \left(a^2+b^2\right)^2}",1,"-(((b^2*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3) + a^2*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) - 2*a*b*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*x)/(a^2 + b^2)^2) + ((2*a*b*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3) - a^2*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)) + b^2*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/((a^2 + b^2)^2*f) - ((b*c - a*d)^2*(2*a^3*b*B*d - 3*a^4*C*d - b^4*(B*c + 3*A*d) - 2*a*b^3*(A*c - c*C - 2*B*d) + a^2*b^2*(B*c - (A + 5*C)*d))*Log[a + b*Tan[e + f*x]])/(b^4*(a^2 + b^2)^2*f) - (d^2*(3*a^3*C*d - A*b^2*(b*c - a*d) - b^3*(2*c*C + B*d) - a^2*b*(3*c*C + 2*B*d) + a*b^2*(B*c + 2*C*d))*Tan[e + f*x])/(b^3*(a^2 + b^2)*f) + ((2*A*b^2 - 2*a*b*B + 3*a^2*C + b^2*C)*d*(c + d*Tan[e + f*x])^2)/(2*b^2*(a^2 + b^2)*f) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^3)/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",7,7,45,0.1556,1,"{3645, 3647, 3637, 3626, 3617, 31, 3475}"
69,1,798,0,2.8388431,"\int \frac{(c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[((c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^3}{2 b \left(a^2+b^2\right) f (a+b \tan (e+f x))^2}+\frac{\left(-3 C d a^4+b B d a^3+b^2 (2 B c+(A-7 C) d) a^2-b^3 (4 A c-4 C c-5 B d) a-b^4 (2 B c+3 A d)\right) (c+d \tan (e+f x))^2}{2 b^2 \left(a^2+b^2\right)^2 f (a+b \tan (e+f x))}-\frac{\left(\left(C c^3+3 B d c^2-3 C d^2 c-B d^3-A \left(c^3-3 c d^2\right)\right) a^3-3 b \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a^2+3 b^2 \left(A c^3-C c^3-3 B d c^2-3 A d^2 c+3 C d^2 c+B d^3\right) a+b^3 \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right) x}{\left(a^2+b^2\right)^3}-\frac{\left(\left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a^3+3 b \left(C c^3+3 B d c^2-3 C d^2 c-B d^3-A \left(c^3-3 c d^2\right)\right) a^2-3 b^2 \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a+b^3 \left(A c^3-C c^3-3 B d c^2-3 A d^2 c+3 C d^2 c+B d^3\right)\right) \log (\cos (e+f x))}{\left(a^2+b^2\right)^3 f}-\frac{(b c-a d) \left(-3 C d^2 a^6+b B d^2 a^5+b^2 d (B c-9 C d) a^4+b^3 B \left(c^2+3 d^2\right) a^3+b^4 \left(3 C c^2+6 B d c-10 C d^2-A \left(3 c^2-d^2\right)\right) a^2-b^5 \left(8 c (A-C) d+3 B \left(c^2-2 d^2\right)\right) a-b^6 \left(c (c C+3 B d)-A \left(c^2-3 d^2\right)\right)\right) \log (a+b \tan (e+f x))}{b^4 \left(a^2+b^2\right)^3 f}-\frac{d^2 \left(-3 C d a^4+b B d a^3+b^2 (B c-6 C d) a^2-b^3 (2 A c-2 C c-3 B d) a-b^4 (B c+(2 A+C) d)\right) \tan (e+f x)}{b^3 \left(a^2+b^2\right)^2 f}","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^3}{2 b \left(a^2+b^2\right) f (a+b \tan (e+f x))^2}+\frac{\left(-3 C d a^4+b B d a^3+b^2 (2 B c+(A-7 C) d) a^2-b^3 (4 A c-4 C c-5 B d) a-b^4 (2 B c+3 A d)\right) (c+d \tan (e+f x))^2}{2 b^2 \left(a^2+b^2\right)^2 f (a+b \tan (e+f x))}-\frac{\left(\left(C c^3+3 B d c^2-3 C d^2 c-B d^3-A \left(c^3-3 c d^2\right)\right) a^3-3 b \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a^2+3 b^2 \left(A c^3-C c^3-3 B d c^2-3 A d^2 c+3 C d^2 c+B d^3\right) a+b^3 \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right)\right) x}{\left(a^2+b^2\right)^3}-\frac{\left(\left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a^3+3 b \left(C c^3+3 B d c^2-3 C d^2 c-B d^3-A \left(c^3-3 c d^2\right)\right) a^2-3 b^2 \left((A-C) d \left(3 c^2-d^2\right)+B \left(c^3-3 c d^2\right)\right) a+b^3 \left(A c^3-C c^3-3 B d c^2-3 A d^2 c+3 C d^2 c+B d^3\right)\right) \log (\cos (e+f x))}{\left(a^2+b^2\right)^3 f}-\frac{(b c-a d) \left(-3 C d^2 a^6+b B d^2 a^5+b^2 d (B c-9 C d) a^4+b^3 B \left(c^2+3 d^2\right) a^3+b^4 \left(3 C c^2+6 B d c-10 C d^2-A \left(3 c^2-d^2\right)\right) a^2-b^5 \left(8 c (A-C) d+3 B \left(c^2-2 d^2\right)\right) a-b^6 \left(c (c C+3 B d)-A \left(c^2-3 d^2\right)\right)\right) \log (a+b \tan (e+f x))}{b^4 \left(a^2+b^2\right)^3 f}-\frac{d^2 \left(-3 C d a^4+b B d a^3+b^2 (B c-6 C d) a^2-b^3 (2 A c-2 C c-3 B d) a-b^4 (B c+(2 A+C) d)\right) \tan (e+f x)}{b^3 \left(a^2+b^2\right)^2 f}",1,"-(((3*a*b^2*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3) + a^3*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) - 3*a^2*b*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)) + b^3*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*x)/(a^2 + b^2)^3) - ((b^3*(A*c^3 - c^3*C - 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 + B*d^3) + 3*a^2*b*(c^3*C + 3*B*c^2*d - 3*c*C*d^2 - B*d^3 - A*(c^3 - 3*c*d^2)) + a^3*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)) - 3*a*b^2*((A - C)*d*(3*c^2 - d^2) + B*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/((a^2 + b^2)^3*f) - ((b*c - a*d)*(a^5*b*B*d^2 - 3*a^6*C*d^2 + a^4*b^2*d*(B*c - 9*C*d) + a^3*b^3*B*(c^2 + 3*d^2) - b^6*(c*(c*C + 3*B*d) - A*(c^2 - 3*d^2)) - a*b^5*(8*c*(A - C)*d + 3*B*(c^2 - 2*d^2)) + a^2*b^4*(3*c^2*C + 6*B*c*d - 10*C*d^2 - A*(3*c^2 - d^2)))*Log[a + b*Tan[e + f*x]])/(b^4*(a^2 + b^2)^3*f) - (d^2*(a^3*b*B*d - 3*a^4*C*d - a*b^3*(2*A*c - 2*c*C - 3*B*d) + a^2*b^2*(B*c - 6*C*d) - b^4*(B*c + (2*A + C)*d))*Tan[e + f*x])/(b^3*(a^2 + b^2)^2*f) + ((a^3*b*B*d - 3*a^4*C*d - b^4*(2*B*c + 3*A*d) - a*b^3*(4*A*c - 4*c*C - 5*B*d) + a^2*b^2*(2*B*c + (A - 7*C)*d))*(c + d*Tan[e + f*x])^2)/(2*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^3)/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2)","A",7,6,45,0.1333,1,"{3645, 3637, 3626, 3617, 31, 3475}"
70,1,337,0,1.5876934,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{c+d \tan (e+f x)} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x]),x]","-\frac{\log (\cos (e+f x)) \left(3 a^2 b (A c+B d-c C)+a^3 (B c-d (A-C))-3 a b^2 (B c-d (A-C))-b^3 (A c+B d-c C)\right)}{f \left(c^2+d^2\right)}+\frac{x \left(-3 a^2 b (B c-d (A-C))+a^3 (A c+B d-c C)-3 a b^2 (A c+B d-c C)+b^3 (B c-d (A-C))\right)}{c^2+d^2}-\frac{(b c-a d)^3 \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^4 f \left(c^2+d^2\right)}+\frac{b \tan (e+f x) \left(b d^2 (a B+A b-b C)+(b c-a d) (-a C d-b B d+b c C)\right)}{d^3 f}-\frac{(-a C d-b B d+b c C) (a+b \tan (e+f x))^2}{2 d^2 f}+\frac{C (a+b \tan (e+f x))^3}{3 d f}","-\frac{\log (\cos (e+f x)) \left(3 a^2 b (A c+B d-c C)+a^3 (B c-d (A-C))-3 a b^2 (B c-d (A-C))-b^3 (A c+B d-c C)\right)}{f \left(c^2+d^2\right)}+\frac{x \left(-3 a^2 b (B c-d (A-C))+a^3 (A c+B d-c C)-3 a b^2 (A c+B d-c C)+b^3 (B c-d (A-C))\right)}{c^2+d^2}-\frac{(b c-a d)^3 \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^4 f \left(c^2+d^2\right)}+\frac{b \tan (e+f x) \left(b d^2 (a B+A b-b C)+(b c-a d) (-a C d-b B d+b c C)\right)}{d^3 f}-\frac{(-a C d-b B d+b c C) (a+b \tan (e+f x))^2}{2 d^2 f}+\frac{C (a+b \tan (e+f x))^3}{3 d f}",1,"((a^3*(A*c - c*C + B*d) - 3*a*b^2*(A*c - c*C + B*d) - 3*a^2*b*(B*c - (A - C)*d) + b^3*(B*c - (A - C)*d))*x)/(c^2 + d^2) - ((3*a^2*b*(A*c - c*C + B*d) - b^3*(A*c - c*C + B*d) + a^3*(B*c - (A - C)*d) - 3*a*b^2*(B*c - (A - C)*d))*Log[Cos[e + f*x]])/((c^2 + d^2)*f) - ((b*c - a*d)^3*(c^2*C - B*c*d + A*d^2)*Log[c + d*Tan[e + f*x]])/(d^4*(c^2 + d^2)*f) + (b*(b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(b*c*C - b*B*d - a*C*d))*Tan[e + f*x])/(d^3*f) - ((b*c*C - b*B*d - a*C*d)*(a + b*Tan[e + f*x])^2)/(2*d^2*f) + (C*(a + b*Tan[e + f*x])^3)/(3*d*f)","A",7,6,45,0.1333,1,"{3647, 3637, 3626, 3617, 31, 3475}"
71,1,236,0,0.8040349,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{c+d \tan (e+f x)} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x]),x]","-\frac{\log (\cos (e+f x)) \left(a^2 (B c-d (A-C))+2 a b (A c+B d-c C)-b^2 (B c-d (A-C))\right)}{f \left(c^2+d^2\right)}+\frac{x \left(a^2 (A c+B d-c C)-2 a b (B c-d (A-C))-b^2 (A c+B d-c C)\right)}{c^2+d^2}+\frac{(b c-a d)^2 \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)}-\frac{b \tan (e+f x) (-a C d-b B d+b c C)}{d^2 f}+\frac{C (a+b \tan (e+f x))^2}{2 d f}","-\frac{\log (\cos (e+f x)) \left(a^2 (B c-d (A-C))+2 a b (A c+B d-c C)-b^2 (B c-d (A-C))\right)}{f \left(c^2+d^2\right)}+\frac{x \left(a^2 (A c+B d-c C)-2 a b (B c-d (A-C))-b^2 (A c+B d-c C)\right)}{c^2+d^2}+\frac{(b c-a d)^2 \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)}-\frac{b \tan (e+f x) (-a C d-b B d+b c C)}{d^2 f}+\frac{C (a+b \tan (e+f x))^2}{2 d f}",1,"((a^2*(A*c - c*C + B*d) - b^2*(A*c - c*C + B*d) - 2*a*b*(B*c - (A - C)*d))*x)/(c^2 + d^2) - ((2*a*b*(A*c - c*C + B*d) + a^2*(B*c - (A - C)*d) - b^2*(B*c - (A - C)*d))*Log[Cos[e + f*x]])/((c^2 + d^2)*f) + ((b*c - a*d)^2*(c^2*C - B*c*d + A*d^2)*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)*f) - (b*(b*c*C - b*B*d - a*C*d)*Tan[e + f*x])/(d^2*f) + (C*(a + b*Tan[e + f*x])^2)/(2*d*f)","A",6,6,45,0.1333,1,"{3647, 3637, 3626, 3617, 31, 3475}"
72,1,156,0,0.3415205,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{c+d \tan (e+f x)} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x]),x]","-\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)}-\frac{\log (\cos (e+f x)) (-a A d+a B c+a C d+A b c+b B d-b c C)}{f \left(c^2+d^2\right)}+\frac{x (a (A c+B d-c C)-b (B c-d (A-C)))}{c^2+d^2}+\frac{b C \tan (e+f x)}{d f}","-\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)}-\frac{\log (\cos (e+f x)) (-a A d+a B c+a C d+A b c+b B d-b c C)}{f \left(c^2+d^2\right)}+\frac{x (a (A c+B d-c C)-b (B c-d (A-C)))}{c^2+d^2}+\frac{b C \tan (e+f x)}{d f}",1,"((a*(A*c - c*C + B*d) - b*(B*c - (A - C)*d))*x)/(c^2 + d^2) - ((A*b*c + a*B*c - b*c*C - a*A*d + b*B*d + a*C*d)*Log[Cos[e + f*x]])/((c^2 + d^2)*f) - ((b*c - a*d)*(c^2*C - B*c*d + A*d^2)*Log[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)*f) + (b*C*Tan[e + f*x])/(d*f)","A",5,5,43,0.1163,1,"{3637, 3626, 3617, 31, 3475}"
73,1,99,0,0.097683,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{c+d \tan (e+f x)} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(c + d*Tan[e + f*x]),x]","\frac{\left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d f \left(c^2+d^2\right)}-\frac{(B c-d (A-C)) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x (A c+B d-c C)}{c^2+d^2}","\frac{\left(A d^2-B c d+c^2 C\right) \log (c+d \tan (e+f x))}{d f \left(c^2+d^2\right)}-\frac{(B c-d (A-C)) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x (A c+B d-c C)}{c^2+d^2}",1,"((A*c - c*C + B*d)*x)/(c^2 + d^2) - ((B*c - (A - C)*d)*Log[Cos[e + f*x]])/((c^2 + d^2)*f) + ((c^2*C - B*c*d + A*d^2)*Log[c + d*Tan[e + f*x]])/(d*(c^2 + d^2)*f)","A",4,4,33,0.1212,1,"{3626, 3617, 31, 3475}"
74,1,164,0,0.2563642,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])),x]","\frac{x (a (A c+B d-c C)-b d (A-C)+b B c)}{\left(a^2+b^2\right) \left(c^2+d^2\right)}+\frac{\left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)}-\frac{\left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)}","\frac{x (a (A c+B d-c C)+b (B c-d (A-C)))}{\left(a^2+b^2\right) \left(c^2+d^2\right)}+\frac{\left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)}-\frac{\left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)}",1,"((b*B*c - b*(A - C)*d + a*(A*c - c*C + B*d))*x)/((a^2 + b^2)*(c^2 + d^2)) + ((A*b^2 - a*(b*B - a*C))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f) - ((c^2*C - B*c*d + A*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)*(c^2 + d^2)*f)","A",3,2,45,0.04444,1,"{3651, 3530}"
75,1,281,0,0.7952119,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])),x]","\frac{x \left(a^2 (A c+B d-c C)+2 a b (B c-d (A-C))-b^2 (A c+B d-c C)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}+\frac{\left(-a^2 b^2 (3 A d+B c-C d)+2 a^3 b B d+a^4 (-C) d+2 a b^3 c (A-C)+b^4 (B c-A d)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^2}+\frac{d \left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^2}","\frac{x \left(a^2 (A c+B d-c C)+2 a b (B c-d (A-C))-b^2 (A c+B d-c C)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}+\frac{\left(-a^2 b^2 (3 A d+B c-C d)+2 a^3 b B d+a^4 (-C) d+2 a b^3 c (A-C)+b^4 (B c-A d)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^2}+\frac{d \left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^2}",1,"((a^2*(A*c - c*C + B*d) - b^2*(A*c - c*C + B*d) + 2*a*b*(B*c - (A - C)*d))*x)/((a^2 + b^2)^2*(c^2 + d^2)) + ((2*a*b^3*c*(A - C) + 2*a^3*b*B*d - a^4*C*d + b^4*(B*c - A*d) - a^2*b^2*(B*c + 3*A*d - C*d))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^2*f) + (d*(c^2*C - B*c*d + A*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^2*(c^2 + d^2)*f) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",4,3,45,0.06667,1,"{3649, 3651, 3530}"
76,1,477,0,1.7858409,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])),x]","\frac{\left(-a^3 b^3 \left(8 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(c (2 B d+c C)-A \left(c^2+d^2\right)\right)+3 a^4 b^2 d (2 A d+B c-C d)-3 a^5 b B d^2+a^6 C d^2+3 a b^5 B c^2+b^6 \left(c (c C-B d)-A \left(c^2-d^2\right)\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^3}+\frac{x \left(3 a^2 b (B c-d (A-C))+a^3 (A c+B d-c C)-3 a b^2 (A c+B d-c C)-b^3 (B c-d (A-C))\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)}-\frac{-a^2 b^2 (3 A d+B c-C d)+2 a^3 b B d+a^4 (-C) d+2 a b^3 c (A-C)+b^4 (B c-A d)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x))}-\frac{A b^2-a (b B-a C)}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2}-\frac{d^2 \left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^3}","\frac{\left(-a^3 b^3 \left(8 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(c (2 B d+c C)-A \left(c^2+d^2\right)\right)+3 a^4 b^2 d (2 A d+B c-C d)-3 a^5 b B d^2+a^6 C d^2+3 a b^5 B c^2+b^6 \left(c (c C-B d)-A \left(c^2-d^2\right)\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^3}+\frac{x \left(3 a^2 b (B c-d (A-C))+a^3 (A c+B d-c C)-3 a b^2 (A c+B d-c C)-b^3 (B c-d (A-C))\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)}-\frac{-a^2 b^2 (3 A d+B c-C d)+2 a^3 b B d+a^4 (-C) d+2 a b^3 c (A-C)+b^4 (B c-A d)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x))}-\frac{A b^2-a (b B-a C)}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2}-\frac{d^2 \left(A d^2-B c d+c^2 C\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^3}",1,"((a^3*(A*c - c*C + B*d) - 3*a*b^2*(A*c - c*C + B*d) + 3*a^2*b*(B*c - (A - C)*d) - b^3*(B*c - (A - C)*d))*x)/((a^2 + b^2)^3*(c^2 + d^2)) + ((3*a*b^5*B*c^2 - 3*a^5*b*B*d^2 + a^6*C*d^2 + 3*a^4*b^2*d*(B*c + 2*A*d - C*d) + b^6*(c*(c*C - B*d) - A*(c^2 - d^2)) - a^3*b^3*(8*c*(A - C)*d + B*(c^2 - d^2)) - 3*a^2*b^4*(c*(c*C + 2*B*d) - A*(c^2 + d^2)))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*(b*c - a*d)^3*f) - (d^2*(c^2*C - B*c*d + A*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)*f) - (A*b^2 - a*(b*B - a*C))/(2*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2) - (2*a*b^3*c*(A - C) + 2*a^3*b*B*d - a^4*C*d + b^4*(B*c - A*d) - a^2*b^2*(B*c + 3*A*d - C*d))/((a^2 + b^2)^2*(b*c - a*d)^2*f*(a + b*Tan[e + f*x]))","A",5,3,45,0.06667,1,"{3649, 3651, 3530}"
77,1,579,0,2.1338156,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^2} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^2,x]","\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+a^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-3 a b^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(-3 a^2 b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+b^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(c^2+d^2\right)^2}+\frac{b^2 \tan (e+f x) \left(a d \left(d^2 (A+2 C)-B c d+3 c^2 C\right)-b \left(c d^2 (A+2 C)-2 B c^2 d-B d^3+3 c^3 C\right)\right)}{d^3 f \left(c^2+d^2\right)}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{b \left(d^2 (2 A+C)-2 B c d+3 c^2 C\right) (a+b \tan (e+f x))^2}{2 d^2 f \left(c^2+d^2\right)}+\frac{(b c-a d)^2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(c^2 d^2 (A+5 C)+3 A d^4-2 B c^3 d-4 B c d^3+3 c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^4 f \left(c^2+d^2\right)^2}","\frac{\log (\cos (e+f x)) \left(3 a^2 b \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+a^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-3 a b^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^3 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(-3 a^2 b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+a^3 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-3 a b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+b^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(c^2+d^2\right)^2}+\frac{b^2 \tan (e+f x) \left(a d \left(d^2 (A+2 C)-B c d+3 c^2 C\right)-b \left(c d^2 (A+2 C)-2 B c^2 d-B d^3+3 c^3 C\right)\right)}{d^3 f \left(c^2+d^2\right)}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{b \left(d^2 (2 A+C)-2 B c d+3 c^2 C\right) (a+b \tan (e+f x))^2}{2 d^2 f \left(c^2+d^2\right)}+\frac{(b c-a d)^2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(c^2 d^2 (A+5 C)+3 A d^4-2 B c^3 d-4 B c d^3+3 c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^4 f \left(c^2+d^2\right)^2}",1,"-(((a^3*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a*b^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a^2*b*(2*c*(A - C)*d - B*(c^2 - d^2)) + b^3*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/(c^2 + d^2)^2) + ((3*a^2*b*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^3*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + a^3*(2*c*(A - C)*d - B*(c^2 - d^2)) - 3*a*b^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[Cos[e + f*x]])/((c^2 + d^2)^2*f) + ((b*c - a*d)^2*(b*(3*c^4*C - 2*B*c^3*d + c^2*(A + 5*C)*d^2 - 4*B*c*d^3 + 3*A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c + d*Tan[e + f*x]])/(d^4*(c^2 + d^2)^2*f) + (b^2*(a*d*(3*c^2*C - B*c*d + (A + 2*C)*d^2) - b*(3*c^3*C - 2*B*c^2*d + c*(A + 2*C)*d^2 - B*d^3))*Tan[e + f*x])/(d^3*(c^2 + d^2)*f) + (b*(3*c^2*C - 2*B*c*d + (2*A + C)*d^2)*(a + b*Tan[e + f*x])^2)/(2*d^2*(c^2 + d^2)*f) - ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^3)/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",7,7,45,0.1556,1,"{3645, 3647, 3637, 3626, 3617, 31, 3475}"
78,1,417,0,1.1129406,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^2} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^2,x]","\frac{\log (\cos (e+f x)) \left(a^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+2 a b \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-b^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-2 a b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{\left(c^2+d^2\right)^2}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{(b c-a d) \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(2 A d^4-B c^3 d-3 B c d^3+4 c^2 C d^2+2 c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^2}+\frac{b^2 \tan (e+f x) \left(d^2 (A+C)-B c d+2 c^2 C\right)}{d^2 f \left(c^2+d^2\right)}","\frac{\log (\cos (e+f x)) \left(a^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+2 a b \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-b^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-2 a b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{\left(c^2+d^2\right)^2}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{(b c-a d) \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(2 A d^4-B c^3 d-3 B c d^3+4 c^2 C d^2+2 c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^2}+\frac{b^2 \tan (e+f x) \left(d^2 (A+C)-B c d+2 c^2 C\right)}{d^2 f \left(c^2+d^2\right)}",1,"-(((a^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 2*a*b*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/(c^2 + d^2)^2) + ((2*a*b*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + a^2*(2*c*(A - C)*d - B*(c^2 - d^2)) - b^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[Cos[e + f*x]])/((c^2 + d^2)^2*f) - ((b*c - a*d)*(b*(2*c^4*C - B*c^3*d + 4*c^2*C*d^2 - 3*B*c*d^3 + 2*A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^2*f) + (b^2*(2*c^2*C - B*c*d + (A + C)*d^2)*Tan[e + f*x])/(d^2*(c^2 + d^2)*f) - ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^2)/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",6,6,45,0.1333,1,"{3645, 3637, 3626, 3617, 31, 3475}"
79,1,288,0,0.5538933,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^2} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^2,x]","\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right)}{d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)^2}+\frac{\log (\cos (e+f x)) \left(2 a A c d-a B \left(c^2-d^2\right)-2 a c C d-A b \left(c^2-d^2\right)+b \left(-2 B c d+c^2 C-C d^2\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(a \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(c^2+d^2\right)^2}","\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right)}{d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right) \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)^2}-\frac{\log (\cos (e+f x)) \left(-A \left(2 a c d-b \left(c^2-d^2\right)\right)+a \left(B c^2-B d^2+2 c C d\right)-b \left(-2 B c d+c^2 C-C d^2\right)\right)}{f \left(c^2+d^2\right)^2}-\frac{x \left(a \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)-b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(c^2+d^2\right)^2}",1,"-(((a*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/(c^2 + d^2)^2) + ((2*a*A*c*d - 2*a*c*C*d - A*b*(c^2 - d^2) - a*B*(c^2 - d^2) + b*(c^2*C - 2*B*c*d - C*d^2))*Log[Cos[e + f*x]])/((c^2 + d^2)^2*f) + ((b*(c^4*C - c^2*(A - 3*C)*d^2 - 2*B*c*d^3 + A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)^2*f) + ((b*c - a*d)*(c^2*C - B*c*d + A*d^2))/(d^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",5,5,43,0.1163,1,"{3635, 3626, 3617, 31, 3475}"
80,1,140,0,0.2090395,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(c + d*Tan[e + f*x])^2,x]","-\frac{A d^2-B c d+c^2 C}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 c d (A-C)-B \left(c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}-\frac{x \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)}{\left(c^2+d^2\right)^2}","-\frac{A d^2-B c d+c^2 C}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 c d (A-C)-B \left(c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}-\frac{x \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)}{\left(c^2+d^2\right)^2}",1,"-(((c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2))*x)/(c^2 + d^2)^2) + ((2*c*(A - C)*d - B*(c^2 - d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^2*f) - (c^2*C - B*c*d + A*d^2)/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",3,3,33,0.09091,1,"{3628, 3531, 3530}"
81,1,293,0,0.8116423,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2),x]","-\frac{x \left(a \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^2}+\frac{b \left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^2}+\frac{A d^2-B c d+c^2 C}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}-\frac{\left(b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^2}","-\frac{x \left(a \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^2}+\frac{b \left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^2}+\frac{A d^2-B c d+c^2 C}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}-\frac{\left(b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^2}",1,"-(((a*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + b*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/((a^2 + b^2)*(c^2 + d^2)^2)) + (b*(A*b^2 - a*(b*B - a*C))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^2*f) - ((b*(c^4*C - 2*B*c^3*d + c^2*(3*A - C)*d^2 + A*d^4) - a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^2*(c^2 + d^2)^2*f) + (c^2*C - B*c*d + A*d^2)/((b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",4,3,45,0.06667,1,"{3649, 3651, 3530}"
82,1,508,0,2.1511918,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2),x]","-\frac{d \left(a^2 A d^2+a^2 \left(-B c d+2 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+A b^2 \left(c^2+2 d^2\right)+b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+2 a b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))}+\frac{b \left(-a^2 b^2 (4 A d+B c)+3 a^3 b B d-2 a^4 C d+a b^3 (2 A c+B d-2 c C)+b^4 (B c-2 A d)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^3}+\frac{d \left(b \left(4 A c^2 d^2+2 A d^4-3 B c^3 d-B c d^3+2 c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^3}","-\frac{d \left(A \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right)+a^2 \left(-B c d+2 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))}-\frac{x \left(a^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)+2 a b \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b^2 \left(-A \left(c^2-d^2\right)-2 B c d+c^2 C-C d^2\right)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))}+\frac{b \left(-a^2 b^2 (4 A d+B c)+3 a^3 b B d-2 a^4 C d+a b^3 (2 A c+B d-2 c C)+b^4 (B c-2 A d)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^3}+\frac{d \left(b \left(4 A c^2 d^2+2 A d^4-3 B c^3 d-B c d^3+2 c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^3}",1,"-(((a^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - b^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + 2*a*b*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/((a^2 + b^2)^2*(c^2 + d^2)^2)) + (b*(3*a^3*b*B*d - 2*a^4*C*d + b^4*(B*c - 2*A*d) - a^2*b^2*(B*c + 4*A*d) + a*b^3*(2*A*c - 2*c*C + B*d))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^3*f) + (d*(b*(2*c^4*C - 3*B*c^3*d + 4*A*c^2*d^2 - B*c*d^3 + 2*A*d^4) - a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)^2*f) - (d*(a^2*A*d^2 + b^2*c*(c*C - B*d) - a*b*B*(c^2 + d^2) + A*b^2*(c^2 + 2*d^2) + a^2*(2*c^2*C - B*c*d + C*d^2)))/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",5,3,45,0.06667,1,"{3649, 3651, 3530}"
83,1,841,0,4.0757422,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2),x]","-\frac{\left(b \left(3 C c^4-4 B d c^3+(5 A+C) d^2 c^2-2 B d^3 c+3 A d^4\right)-a d^2 \left(2 c (A-C) d-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x)) d^2}{(b c-a d)^4 \left(c^2+d^2\right)^2 f}-\frac{\left(-d \left(3 C c^2-B d c+(A+2 C) d^2\right) a^4+3 b B d \left(c^2+d^2\right) a^3-b^2 \left(B c^3+4 A d c^2+2 C d c^2-B d^2 c+6 A d^3\right) a^2+b^3 (2 A c-2 C c+B d) \left(c^2+d^2\right) a-b^4 \left(d \left(2 A c^2+C c^2+3 A d^2\right)-B \left(c^3+2 d^2 c\right)\right)\right) d}{\left(a^2+b^2\right)^2 (b c-a d)^3 \left(c^2+d^2\right) f (c+d \tan (e+f x))}-\frac{\left(\left(C c^2-2 B d c-C d^2-A \left(c^2-d^2\right)\right) a^3+3 b \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) a^2-3 b^2 \left(C c^2-2 B d c-C d^2-A \left(c^2-d^2\right)\right) a-b^3 \left(2 c (A-C) d-B \left(c^2-d^2\right)\right)\right) x}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)^2}-\frac{b \left(-3 C d^2 a^6+6 b B d^2 a^5-b^2 d (4 B c+(10 A-C) d) a^4+b^3 \left(10 c (A-C) d+B \left(c^2+3 d^2\right)\right) a^3+3 b^4 \left(c (c C+2 B d)-A \left(c^2+3 d^2\right)\right) a^2+b^5 \left(2 c (A-C) d-B \left(3 c^2-d^2\right)\right) a-b^6 \left(c (c C-2 B d)-A \left(c^2-3 d^2\right)\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{\left(a^2+b^2\right)^3 (b c-a d)^4 f}-\frac{-3 C d a^4+5 b B d a^3-b^2 (2 B c+(7 A-C) d) a^2+b^3 (4 A c-4 C c+B d) a+b^4 (2 B c-3 A d)}{2 \left(a^2+b^2\right)^2 (b c-a d)^2 f (a+b \tan (e+f x)) (c+d \tan (e+f x))}-\frac{A b^2-a (b B-a C)}{2 \left(a^2+b^2\right) (b c-a d) f (a+b \tan (e+f x))^2 (c+d \tan (e+f x))}","-\frac{\left(b \left(3 C c^4-4 B d c^3+(5 A+C) d^2 c^2-2 B d^3 c+3 A d^4\right)-a d^2 \left(2 c (A-C) d-B \left(c^2-d^2\right)\right)\right) \log (c \cos (e+f x)+d \sin (e+f x)) d^2}{(b c-a d)^4 \left(c^2+d^2\right)^2 f}-\frac{\left(-d \left(3 C c^2-B d c+(A+2 C) d^2\right) a^4+3 b B d \left(c^2+d^2\right) a^3-b^2 \left(B c^3+4 A d c^2+2 C d c^2-B d^2 c+6 A d^3\right) a^2+b^3 (2 A c-2 C c+B d) \left(c^2+d^2\right) a-b^4 \left(d \left(2 A c^2+C c^2+3 A d^2\right)-B \left(c^3+2 d^2 c\right)\right)\right) d}{\left(a^2+b^2\right)^2 (b c-a d)^3 \left(c^2+d^2\right) f (c+d \tan (e+f x))}-\frac{\left(\left(C c^2-2 B d c-C d^2-A \left(c^2-d^2\right)\right) a^3+3 b \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) a^2-3 b^2 \left(C c^2-2 B d c-C d^2-A \left(c^2-d^2\right)\right) a-b^3 \left(2 c (A-C) d-B \left(c^2-d^2\right)\right)\right) x}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)^2}-\frac{b \left(-3 C d^2 a^6+6 b B d^2 a^5-b^2 d (4 B c+(10 A-C) d) a^4+b^3 \left(10 c (A-C) d+B \left(c^2+3 d^2\right)\right) a^3+3 b^4 \left(c (c C+2 B d)-A \left(c^2+3 d^2\right)\right) a^2+b^5 \left(2 c (A-C) d-B \left(3 c^2-d^2\right)\right) a-b^6 \left(c (c C-2 B d)-A \left(c^2-3 d^2\right)\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{\left(a^2+b^2\right)^3 (b c-a d)^4 f}-\frac{-3 C d a^4+5 b B d a^3-b^2 (2 B c+(7 A-C) d) a^2+b^3 (4 A c-4 C c+B d) a+b^4 (2 B c-3 A d)}{2 \left(a^2+b^2\right)^2 (b c-a d)^2 f (a+b \tan (e+f x)) (c+d \tan (e+f x))}-\frac{A b^2-a (b B-a C)}{2 \left(a^2+b^2\right) (b c-a d) f (a+b \tan (e+f x))^2 (c+d \tan (e+f x))}",1,"-(((a^3*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - 3*a*b^2*(c^2*C - 2*B*c*d - C*d^2 - A*(c^2 - d^2)) + 3*a^2*b*(2*c*(A - C)*d - B*(c^2 - d^2)) - b^3*(2*c*(A - C)*d - B*(c^2 - d^2)))*x)/((a^2 + b^2)^3*(c^2 + d^2)^2)) - (b*(6*a^5*b*B*d^2 - 3*a^6*C*d^2 - a^4*b^2*d*(4*B*c + (10*A - C)*d) - b^6*(c*(c*C - 2*B*d) - A*(c^2 - 3*d^2)) + a*b^5*(2*c*(A - C)*d - B*(3*c^2 - d^2)) + 3*a^2*b^4*(c*(c*C + 2*B*d) - A*(c^2 + 3*d^2)) + a^3*b^3*(10*c*(A - C)*d + B*(c^2 + 3*d^2)))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*(b*c - a*d)^4*f) - (d^2*(b*(3*c^4*C - 4*B*c^3*d + c^2*(5*A + C)*d^2 - 2*B*c*d^3 + 3*A*d^4) - a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^4*(c^2 + d^2)^2*f) - (d*(3*a^3*b*B*d*(c^2 + d^2) + a*b^3*(2*A*c - 2*c*C + B*d)*(c^2 + d^2) - a^4*d*(3*c^2*C - B*c*d + (A + 2*C)*d^2) - a^2*b^2*(B*c^3 + 4*A*c^2*d + 2*c^2*C*d - B*c*d^2 + 6*A*d^3) - b^4*(d*(2*A*c^2 + c^2*C + 3*A*d^2) - B*(c^3 + 2*c*d^2))))/((a^2 + b^2)^2*(b*c - a*d)^3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])) - (A*b^2 - a*(b*B - a*C))/(2*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])) - (5*a^3*b*B*d - 3*a^4*C*d + b^4*(2*B*c - 3*A*d) + a*b^3*(4*A*c - 4*c*C + B*d) - a^2*b^2*(2*B*c + (7*A - C)*d))/(2*(a^2 + b^2)^2*(b*c - a*d)^2*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",6,3,45,0.06667,1,"{3649, 3651, 3530}"
84,1,804,0,2.7473245,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^3} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^3,x]","-\frac{\left(C c^2-B d c+A d^2\right) (a+b \tan (e+f x))^3}{2 d \left(c^2+d^2\right) f (c+d \tan (e+f x))^2}-\frac{\left(2 a \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) d^2+b \left(3 C c^4-B d c^3-(A-7 C) d^2 c^2-5 B d^3 c+3 A d^4\right)\right) (a+b \tan (e+f x))^2}{2 d^2 \left(c^2+d^2\right)^2 f (c+d \tan (e+f x))}-\frac{\left(\left(C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left(c^3-3 c d^2\right)\right) a^3-3 b \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a^2+3 b^2 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right) a+b^3 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right) x}{\left(c^2+d^2\right)^3}-\frac{\left(-\left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a^3+3 b \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right) a^2+3 b^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a-b^3 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right)\right) \log (\cos (e+f x))}{\left(c^2+d^2\right)^3 f}-\frac{(b c-a d) \left(a^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) d^3+a b \left(8 c (A-C) d^3-B \left(c^4+6 d^2 c^2-3 d^4\right)\right) d^2+b^2 \left(3 C c^6-B d c^5+9 C d^2 c^4-3 B d^3 c^3-(A-10 C) d^4 c^2-6 B d^5 c+3 A d^6\right)\right) \log (c+d \tan (e+f x))}{d^4 \left(c^2+d^2\right)^3 f}+\frac{b^2 \left(a \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) d^2+b \left(3 C c^4-B d c^3+6 C d^2 c^2-3 B d^3 c+(2 A+C) d^4\right)\right) \tan (e+f x)}{d^3 \left(c^2+d^2\right)^2 f}","-\frac{\left(C c^2-B d c+A d^2\right) (a+b \tan (e+f x))^3}{2 d \left(c^2+d^2\right) f (c+d \tan (e+f x))^2}-\frac{\left(2 a \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) d^2+b \left(3 C c^4-B d c^3-(A-7 C) d^2 c^2-5 B d^3 c+3 A d^4\right)\right) (a+b \tan (e+f x))^2}{2 d^2 \left(c^2+d^2\right)^2 f (c+d \tan (e+f x))}-\frac{\left(\left(C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left(c^3-3 c d^2\right)\right) a^3-3 b \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a^2+3 b^2 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right) a+b^3 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right) x}{\left(c^2+d^2\right)^3}-\frac{\left(-\left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a^3+3 b \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right) a^2+3 b^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a-b^3 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right)\right) \log (\cos (e+f x))}{\left(c^2+d^2\right)^3 f}-\frac{(b c-a d) \left(a^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) d^3+a b \left(8 c (A-C) d^3-B \left(c^4+6 d^2 c^2-3 d^4\right)\right) d^2+b^2 \left(3 C c^6-B d c^5+9 C d^2 c^4-3 B d^3 c^3-(A-10 C) d^4 c^2-6 B d^5 c+3 A d^6\right)\right) \log (c+d \tan (e+f x))}{d^4 \left(c^2+d^2\right)^3 f}+\frac{b^2 \left(a \left(2 c (A-C) d-B \left(c^2-d^2\right)\right) d^2+b \left(3 C c^4-B d c^3+6 C d^2 c^2-3 B d^3 c+(2 A+C) d^4\right)\right) \tan (e+f x)}{d^3 \left(c^2+d^2\right)^2 f}",1,"-(((3*a*b^2*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) + a^3*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2)) - 3*a^2*b*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) + b^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*x)/(c^2 + d^2)^3) - ((3*a^2*b*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) - b^3*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) - a^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) + 3*a*b^2*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/((c^2 + d^2)^3*f) - ((b*c - a*d)*(b^2*(3*c^6*C - B*c^5*d + 9*c^4*C*d^2 - 3*B*c^3*d^3 - c^2*(A - 10*C)*d^4 - 6*B*c*d^5 + 3*A*d^6) + a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) + a*b*d^2*(8*c*(A - C)*d^3 - B*(c^4 + 6*c^2*d^2 - 3*d^4)))*Log[c + d*Tan[e + f*x]])/(d^4*(c^2 + d^2)^3*f) + (b^2*(b*(3*c^4*C - B*c^3*d + 6*c^2*C*d^2 - 3*B*c*d^3 + (2*A + C)*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Tan[e + f*x])/(d^3*(c^2 + d^2)^2*f) - ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^3)/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - ((b*(3*c^4*C - B*c^3*d - c^2*(A - 7*C)*d^2 - 5*B*c*d^3 + 3*A*d^4) + 2*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*(a + b*Tan[e + f*x])^2)/(2*d^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",7,6,45,0.1333,1,"{3645, 3637, 3626, 3617, 31, 3475}"
85,1,597,0,1.3850815,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^3} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^3,x]","-\frac{\left(-a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)+2 a b d^3 \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)-b^2 \left(-3 c^2 d^4 (A-2 C)+A d^6+B c^3 d^3-3 B c d^5+3 c^4 C d^2+c^6 C\right)\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^3}-\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)}{f \left(c^2+d^2\right)^3}-\frac{x \left(a^2 \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)+b^2 \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}+\frac{(b c-a d) \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^3 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}","-\frac{\left(-a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)+2 a b d^3 \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)-b^2 \left(-3 c^2 d^4 (A-2 C)+A d^6+B c^3 d^3-3 B c d^5+3 c^4 C d^2+c^6 C\right)\right) \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^3}-\frac{\log (\cos (e+f x)) \left(a^2 \left(-\left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)+2 a b \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)+b^2 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)}{f \left(c^2+d^2\right)^3}-\frac{x \left(a^2 \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)-2 a b \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)+b^2 \left(A c^3-3 A c d^2+3 B c^2 d-B d^3-c^3 C+3 c C d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}+\frac{(b c-a d) \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^3 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}",1,"-(((b^2*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) + a^2*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2)) - 2*a*b*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*x)/(c^2 + d^2)^3) - ((2*a*b*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) - a^2*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) + b^2*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*Log[Cos[e + f*x]])/((c^2 + d^2)^3*f) - ((2*a*b*d^3*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) - b^2*(c^6*C + 3*c^4*C*d^2 + B*c^3*d^3 - 3*c^2*(A - 2*C)*d^4 - 3*B*c*d^5 + A*d^6) - a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^3*f) - ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^2)/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) + ((b*c - a*d)*(b*(c^4*C - c^2*(A - 3*C)*d^2 - 2*B*c*d^3 + A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2))))/(d^3*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",6,6,45,0.1333,1,"{3645, 3635, 3626, 3617, 31, 3475}"
86,1,349,0,0.7112627,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^3} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^3,x]","\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right)}{2 d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)}{d^2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(a A d \left(3 c^2-d^2\right)-a \left(B c^3-3 B c d^2+3 c^2 C d-C d^3\right)-A b \left(c^3-3 c d^2\right)+b \left(-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}+\frac{x \left(-a \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)+b d (A-C) \left(3 c^2-d^2\right)-b B \left(c^3-3 c d^2\right)\right)}{\left(c^2+d^2\right)^3}","\frac{(b c-a d) \left(A d^2-B c d+c^2 C\right)}{2 d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)}{d^2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(A \left(a d \left(3 c^2-d^2\right)-b \left(c^3-3 c d^2\right)\right)-a \left(B c^3-3 B c d^2+3 c^2 C d-C d^3\right)+b \left(-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(a \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)-b \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)}{\left(c^2+d^2\right)^3}",1,"((b*(A - C)*d*(3*c^2 - d^2) - b*B*(c^3 - 3*c*d^2) - a*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2)))*x)/(c^2 + d^2)^3 + ((a*A*d*(3*c^2 - d^2) - A*b*(c^3 - 3*c*d^2) + b*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3) - a*(B*c^3 + 3*c^2*C*d - 3*B*c*d^2 - C*d^3))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^3*f) + ((b*c - a*d)*(c^2*C - B*c*d + A*d^2))/(2*d^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (b*(c^4*C - c^2*(A - 3*C)*d^2 - 2*B*c*d^3 + A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))/(d^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",4,4,43,0.09302,1,"{3635, 3628, 3531, 3530}"
87,1,209,0,0.3758884,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(c + d*Tan[e + f*x])^3,x]","-\frac{A d^2-B c d+c^2 C}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{2 c d (A-C)-B \left(c^2-d^2\right)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)}{\left(c^2+d^2\right)^3}","-\frac{A d^2-B c d+c^2 C}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{2 c d (A-C)-B \left(c^2-d^2\right)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)}{\left(c^2+d^2\right)^3}",1,"-(((c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2))*x)/(c^2 + d^2)^3) + (((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^3*f) - (c^2*C - B*c*d + A*d^2)/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (2*c*(A - C)*d - B*(c^2 - d^2))/((c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",4,4,33,0.1212,1,"{3628, 3529, 3531, 3530}"
88,1,487,0,1.8296094,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^3),x]","-\frac{\left(a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)-a b d^2 \left(8 c^3 d (A-C)-B \left(-6 c^2 d^2+3 c^4-d^4\right)\right)+b^2 \left(3 c^4 d^2 (2 A-C)+3 A c^2 d^4+A d^6+B c^3 d^3-3 B c^5 d+c^6 C\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{x \left(a \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)+b \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^3}+\frac{b^2 \left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^3}+\frac{b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{A d^2-B c d+c^2 C}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}","-\frac{\left(a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)-a b d^2 \left(8 c^3 d (A-C)-B \left(-6 c^2 d^2+3 c^4-d^4\right)\right)+b^2 \left(3 c^4 d^2 (2 A-C)+3 A c^2 d^4+A d^6+B c^3 d^3-3 B c^5 d+c^6 C\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{x \left(a \left(-A \left(c^3-3 c d^2\right)-3 B c^2 d+B d^3+c^3 C-3 c C d^2\right)+b \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^3}+\frac{b^2 \left(A b^2-a (b B-a C)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^3}+\frac{b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{A d^2-B c d+c^2 C}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}",1,"-(((a*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2)) + b*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*x)/((a^2 + b^2)*(c^2 + d^2)^3)) + (b^2*(A*b^2 - a*(b*B - a*C))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^3*f) - ((b^2*(c^6*C - 3*B*c^5*d + 3*c^4*(2*A - C)*d^2 + B*c^3*d^3 + 3*A*c^2*d^4 + A*d^6) + a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) - a*b*d^2*(8*c^3*(A - C)*d - B*(3*c^4 - 6*c^2*d^2 - d^4)))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)^3*f) + (c^2*C - B*c*d + A*d^2)/(2*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) + (b*(c^4*C - 2*B*c^3*d + c^2*(3*A - C)*d^2 + A*d^4) - a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))/((b*c - a*d)^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",5,3,45,0.06667,1,"{3649, 3651, 3530}"
89,1,860,0,4.2760075,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3),x]","\frac{\left(-3 C d a^4+4 b B d a^3-b^2 (B c+(5 A+C) d) a^2+2 b^3 (A c-C c+B d) a+b^4 (B c-3 A d)\right) \log (a \cos (e+f x)+b \sin (e+f x)) b^2}{\left(a^2+b^2\right)^2 (b c-a d)^4 f}-\frac{\left(\left(C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left(c^3-3 c d^2\right)\right) a^2+2 b \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a+b^2 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right)\right) x}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^3}+\frac{d \left(a^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) d^3-2 a b \left(c (A-C) d \left(5 c^2+d^2\right)-B \left(2 c^4-3 d^2 c^2-d^4\right)\right) d^2+b^2 \left(3 C c^6-6 B d c^5+(10 A-C) d^2 c^4-3 B d^3 c^3+9 A d^4 c^2-B d^5 c+3 A d^6\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^4 \left(c^2+d^2\right)^3 f}-\frac{d \left(d^2 \left(2 c C d+B \left(c^2-d^2\right)\right) a^3+b \left(3 C c^4-3 B d c^3+2 C d^2 c^2-B d^3 c+C d^4\right) a^2+b^2 \left(2 c C d^3-B \left(c^4+d^2 c^2+2 d^4\right)\right) a+b^3 c \left(2 C c^3-3 B d c^2-B d^3\right)-A \left(-\left(c^4+6 d^2 c^2+3 d^4\right) b^3+2 a c d^3 b^2-2 a^2 d^2 \left(2 c^2+d^2\right) b+2 a^3 c d^3\right)\right)}{\left(a^2+b^2\right) (b c-a d)^3 \left(c^2+d^2\right)^2 f (c+d \tan (e+f x))}-\frac{d \left(A d^2 a^2+\left(3 C c^2-B d c+2 C d^2\right) a^2-2 b B \left(c^2+d^2\right) a+b^2 c (c C-B d)+A b^2 \left(2 c^2+3 d^2\right)\right)}{2 \left(a^2+b^2\right) (b c-a d)^2 \left(c^2+d^2\right) f (c+d \tan (e+f x))^2}-\frac{A b^2-a (b B-a C)}{\left(a^2+b^2\right) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}","\frac{\left(-3 C d a^4+4 b B d a^3-b^2 (B c+(5 A+C) d) a^2+2 b^3 (A c-C c+B d) a+b^4 (B c-3 A d)\right) \log (a \cos (e+f x)+b \sin (e+f x)) b^2}{\left(a^2+b^2\right)^2 (b c-a d)^4 f}-\frac{\left(\left(C c^3-3 B d c^2-3 C d^2 c+B d^3-A \left(c^3-3 c d^2\right)\right) a^2+2 b \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) a+b^2 \left(A c^3-C c^3+3 B d c^2-3 A d^2 c+3 C d^2 c-B d^3\right)\right) x}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^3}+\frac{d \left(a^2 \left((A-C) d \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right) d^3-2 a b \left(c (A-C) d \left(5 c^2+d^2\right)-B \left(2 c^4-3 d^2 c^2-d^4\right)\right) d^2+b^2 \left(3 C c^6-6 B d c^5+(10 A-C) d^2 c^4-3 B d^3 c^3+9 A d^4 c^2-B d^5 c+3 A d^6\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{(b c-a d)^4 \left(c^2+d^2\right)^3 f}-\frac{d \left(d^2 \left(2 c C d+B \left(c^2-d^2\right)\right) a^3+b \left(3 C c^4-3 B d c^3+2 C d^2 c^2-B d^3 c+C d^4\right) a^2+b^2 \left(2 c C d^3-B \left(c^4+d^2 c^2+2 d^4\right)\right) a+b^3 c \left(2 C c^3-3 B d c^2-B d^3\right)-A \left(-\left(c^4+6 d^2 c^2+3 d^4\right) b^3+2 a c d^3 b^2-2 a^2 d^2 \left(2 c^2+d^2\right) b+2 a^3 c d^3\right)\right)}{\left(a^2+b^2\right) (b c-a d)^3 \left(c^2+d^2\right)^2 f (c+d \tan (e+f x))}-\frac{d \left(\left(3 C c^2-B d c+2 C d^2\right) a^2-2 b B \left(c^2+d^2\right) a+b^2 c (c C-B d)+A \left(\left(2 c^2+3 d^2\right) b^2+a^2 d^2\right)\right)}{2 \left(a^2+b^2\right) (b c-a d)^2 \left(c^2+d^2\right) f (c+d \tan (e+f x))^2}-\frac{A b^2-a (b B-a C)}{\left(a^2+b^2\right) (b c-a d) f (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}",1,"-(((b^2*(A*c^3 - c^3*C + 3*B*c^2*d - 3*A*c*d^2 + 3*c*C*d^2 - B*d^3) + a^2*(c^3*C - 3*B*c^2*d - 3*c*C*d^2 + B*d^3 - A*(c^3 - 3*c*d^2)) + 2*a*b*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)))*x)/((a^2 + b^2)^2*(c^2 + d^2)^3)) + (b^2*(4*a^3*b*B*d - 3*a^4*C*d + b^4*(B*c - 3*A*d) + 2*a*b^3*(A*c - c*C + B*d) - a^2*b^2*(B*c + (5*A + C)*d))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^4*f) + (d*(b^2*(3*c^6*C - 6*B*c^5*d + c^4*(10*A - C)*d^2 - 3*B*c^3*d^3 + 9*A*c^2*d^4 - B*c*d^5 + 3*A*d^6) + a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) - 2*a*b*d^2*(c*(A - C)*d*(5*c^2 + d^2) - B*(2*c^4 - 3*c^2*d^2 - d^4)))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^4*(c^2 + d^2)^3*f) - (d*(a^2*A*d^2 + b^2*c*(c*C - B*d) - 2*a*b*B*(c^2 + d^2) + A*b^2*(2*c^2 + 3*d^2) + a^2*(3*c^2*C - B*c*d + 2*C*d^2)))/(2*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) - (d*(b^3*c*(2*c^3*C - 3*B*c^2*d - B*d^3) + a^2*b*(3*c^4*C - 3*B*c^3*d + 2*c^2*C*d^2 - B*c*d^3 + C*d^4) + a^3*d^2*(2*c*C*d + B*(c^2 - d^2)) + a*b^2*(2*c*C*d^3 - B*(c^4 + c^2*d^2 + 2*d^4)) - A*(2*a^3*c*d^3 + 2*a*b^2*c*d^3 - 2*a^2*b*d^2*(2*c^2 + d^2) - b^3*(c^4 + 6*c^2*d^2 + 3*d^4))))/((a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",6,3,45,0.06667,1,"{3649, 3651, 3530}"
90,1,464,0,2.0889838,"\int (a+b \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (c+d \tan (e+f x))^{3/2} \left(-6 a^2 b d^2 (16 c C-45 B d)+40 a^3 C d^3+9 a b^2 d \left(35 d^2 (A-C)-14 B c d+8 c^2 C\right)+b^3 \left(-\left(42 c d^2 (A-C)-24 B c^2 d+105 B d^3+16 c^3 C\right)\right)\right)}{315 d^4 f}+\frac{2 \left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 b \tan (e+f x) (c+d \tan (e+f x))^{3/2} \left(21 b d^2 (a B+A b-b C)+4 (b c-a d) (-2 a C d-3 b B d+2 b c C)\right)}{105 d^3 f}-\frac{(a-i b)^3 \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^3 \sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-2 a C d-3 b B d+2 b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}{21 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2}}{9 d f}","\frac{2 (c+d \tan (e+f x))^{3/2} \left(-6 a^2 b d^2 (16 c C-45 B d)+40 a^3 C d^3+9 a b^2 d \left(35 d^2 (A-C)-14 B c d+8 c^2 C\right)+b^3 \left(-\left(42 c d^2 (A-C)-24 B c^2 d+105 B d^3+16 c^3 C\right)\right)\right)}{315 d^4 f}+\frac{2 \left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 b \tan (e+f x) (c+d \tan (e+f x))^{3/2} \left(21 b d^2 (a B+A b-b C)+4 (b c-a d) (-2 a C d-3 b B d+2 b c C)\right)}{105 d^3 f}-\frac{(a-i b)^3 \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^3 \sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-2 a C d-3 b B d+2 b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}{21 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2}}{9 d f}",1,"-(((a - I*b)^3*(I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((a + I*b)^3*(I*A - B - I*C)*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(a^3*B - 3*a*b^2*B + 3*a^2*b*(A - C) - b^3*(A - C))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(40*a^3*C*d^3 - 6*a^2*b*d^2*(16*c*C - 45*B*d) + 9*a*b^2*d*(8*c^2*C - 14*B*c*d + 35*(A - C)*d^2) - b^3*(16*c^3*C - 24*B*c^2*d + 42*c*(A - C)*d^2 + 105*B*d^3))*(c + d*Tan[e + f*x])^(3/2))/(315*d^4*f) + (2*b*(21*b*(A*b + a*B - b*C)*d^2 + 4*(b*c - a*d)*(2*b*c*C - 3*b*B*d - 2*a*C*d))*Tan[e + f*x]*(c + d*Tan[e + f*x])^(3/2))/(105*d^3*f) - (2*(2*b*c*C - 3*b*B*d - 2*a*C*d)*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2))/(21*d^2*f) + (2*C*(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2))/(9*d*f)","A",12,8,47,0.1702,1,"{3647, 3637, 3630, 3528, 3539, 3537, 63, 208}"
91,1,325,0,1.3063194,"\int (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (c+d \tan (e+f x))^{3/2} \left(20 a^2 C d^2-14 a b d (2 c C-5 B d)+b^2 \left(35 d^2 (A-C)-14 B c d+8 c^2 C\right)\right)}{105 d^3 f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(a-i b)^2 \sqrt{c-i d} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(a+i b)^2 \sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-7 b B d+4 b c C) (c+d \tan (e+f x))^{3/2}}{35 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}{7 d f}","\frac{2 (c+d \tan (e+f x))^{3/2} \left(20 a^2 C d^2-14 a b d (2 c C-5 B d)+b^2 \left(35 d^2 (A-C)-14 B c d+8 c^2 C\right)\right)}{105 d^3 f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(a-i b)^2 \sqrt{c-i d} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(a+i b)^2 \sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-7 b B d+4 b c C) (c+d \tan (e+f x))^{3/2}}{35 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}{7 d f}",1,"-(((a - I*b)^2*(B + I*(A - C))*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) - ((a + I*b)^2*(B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(a^2*B - b^2*B + 2*a*b*(A - C))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(20*a^2*C*d^2 - 14*a*b*d*(2*c*C - 5*B*d) + b^2*(8*c^2*C - 14*B*c*d + 35*(A - C)*d^2))*(c + d*Tan[e + f*x])^(3/2))/(105*d^3*f) - (2*b*(4*b*c*C - 7*b*B*d - 4*a*C*d)*Tan[e + f*x]*(c + d*Tan[e + f*x])^(3/2))/(35*d^2*f) + (2*C*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2))/(7*d*f)","A",11,8,47,0.1702,1,"{3647, 3637, 3630, 3528, 3539, 3537, 63, 208}"
92,1,224,0,0.6283109,"\int (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (a B+A b-b C) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(b+i a) \sqrt{c-i d} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) \sqrt{c+i d} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-5 a C d-5 b B d+2 b c C) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{3/2}}{5 d f}","\frac{2 (a B+A b-b C) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(b+i a) \sqrt{c-i d} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) \sqrt{c+i d} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-5 a C d-5 b B d+2 b c C) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{3/2}}{5 d f}",1,"-(((I*a + b)*(A - I*B - C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*(A + I*B - C)*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(A*b + a*B - b*C)*Sqrt[c + d*Tan[e + f*x]])/f - (2*(2*b*c*C - 5*b*B*d - 5*a*C*d)*(c + d*Tan[e + f*x])^(3/2))/(15*d^2*f) + (2*b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^(3/2))/(5*d*f)","A",10,7,45,0.1556,1,"{3637, 3630, 3528, 3539, 3537, 63, 208}"
93,1,155,0,0.3058371,"\int \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 C (c+d \tan (e+f x))^{3/2}}{3 d f}","-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 C (c+d \tan (e+f x))^{3/2}}{3 d f}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*B*Sqrt[c + d*Tan[e + f*x]])/f + (2*C*(c + d*Tan[e + f*x])^(3/2))/(3*d*f)","A",9,6,35,0.1714,1,"{3630, 3528, 3539, 3537, 63, 208}"
94,1,234,0,1.0873347,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","-\frac{2 \sqrt{b c-a d} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}+\frac{\sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)}+\frac{2 C \sqrt{c+d \tan (e+f x)}}{b f}","-\frac{2 \sqrt{b c-a d} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}+\frac{\sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)}+\frac{2 C \sqrt{c+d \tan (e+f x)}}{b f}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)*f)) + ((I*A - B - I*C)*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2)*f) + (2*C*Sqrt[c + d*Tan[e + f*x]])/(b*f)","A",12,7,47,0.1489,1,"{3647, 3653, 3539, 3537, 63, 208, 3634}"
95,1,317,0,1.4394213,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\left(-a^2 b^2 (3 A d+2 B c-5 C d)+a^3 b B d+a^4 C d+a b^3 (4 A c-3 B d-4 c C)+b^4 (A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)^2 \sqrt{b c-a d}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\left(-a^2 b^2 (3 A d+2 B c-5 C d)+a^3 b B d+a^4 C d+a b^3 (4 A c-3 B d-4 c C)+b^4 (A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)^2 \sqrt{b c-a d}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f)) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) - ((a^3*b*B*d + a^4*C*d + b^4*(2*B*c + A*d) + a*b^3*(4*A*c - 4*c*C - 3*B*d) - a^2*b^2*(2*B*c + 3*A*d - 5*C*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2)^2*Sqrt[b*c - a*d]*f) - ((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",12,7,47,0.1489,1,"{3645, 3653, 3539, 3537, 63, 208, 3634}"
96,1,543,0,4.0367063,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","\frac{\left(2 a^3 b^3 \left(20 c d (A-C)+B \left(4 c^2-13 d^2\right)\right)-3 a^2 b^4 \left(8 A c^2-6 A d^2-16 B c d-8 c^2 C+5 C d^2\right)-3 a^4 b^2 d (5 A d+4 B c-6 C d)+3 a^5 b B d^2+a^6 C d^2-3 a b^5 \left(8 c d (A-C)+B \left(8 c^2-d^2\right)\right)-b^6 \left(4 c (B d+2 c C)-A \left(8 c^2+d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} f \left(a^2+b^2\right)^3 (b c-a d)^{3/2}}-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (7 A d+4 B c-9 C d)+3 a^3 b B d+a^4 C d+a b^3 (8 A c-5 B d-8 c C)+b^4 (A d+4 B c)\right)}{4 b f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))}-\frac{\sqrt{c-i d} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{\sqrt{c+i d} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","\frac{\left(2 a^3 b^3 \left(20 c d (A-C)+B \left(4 c^2-13 d^2\right)\right)-3 a^2 b^4 \left(8 A c^2-6 A d^2-16 B c d-8 c^2 C+5 C d^2\right)-3 a^4 b^2 d (5 A d+4 B c-6 C d)+3 a^5 b B d^2+a^6 C d^2-3 a b^5 \left(8 c d (A-C)+B \left(8 c^2-d^2\right)\right)-b^6 \left(4 c (B d+2 c C)-A \left(8 c^2+d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} f \left(a^2+b^2\right)^3 (b c-a d)^{3/2}}-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (7 A d+4 B c-9 C d)+3 a^3 b B d+a^4 C d+a b^3 (8 A c-5 B d-8 c C)+b^4 (A d+4 B c)\right)}{4 b f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))}-\frac{\sqrt{c-i d} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{\sqrt{c+i d} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-(((A - I*B - C)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + ((A + I*B - C)*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) + ((3*a^5*b*B*d^2 + a^6*C*d^2 - 3*a^4*b^2*d*(4*B*c + 5*A*d - 6*C*d) - 3*a^2*b^4*(8*A*c^2 - 8*c^2*C - 16*B*c*d - 6*A*d^2 + 5*C*d^2) + 2*a^3*b^3*(20*c*(A - C)*d + B*(4*c^2 - 13*d^2)) - 3*a*b^5*(8*c*(A - C)*d + B*(8*c^2 - d^2)) - b^6*(4*c*(2*c*C + B*d) - A*(8*c^2 + d^2)))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*b^(3/2)*(a^2 + b^2)^3*(b*c - a*d)^(3/2)*f) - ((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - ((3*a^3*b*B*d + a^4*C*d + b^4*(4*B*c + A*d) + a*b^3*(8*A*c - 8*c*C - 5*B*d) - a^2*b^2*(4*B*c + 7*A*d - 9*C*d))*Sqrt[c + d*Tan[e + f*x]])/(4*b*(a^2 + b^2)^2*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",13,8,47,0.1702,1,"{3645, 3649, 3653, 3539, 3537, 63, 208, 3634}"
97,1,550,0,2.7338474,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (c+d \tan (e+f x))^{5/2} \left(-2 a^2 b d^2 (192 c C-847 B d)+168 a^3 C d^3+33 a b^2 d \left(63 d^2 (A-C)-18 B c d+8 c^2 C\right)+b^3 \left(-\left(198 c d^2 (A-C)-88 B c^2 d+693 B d^3+48 c^3 C\right)\right)\right)}{3465 d^4 f}+\frac{2 \left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+\frac{2 b \tan (e+f x) (c+d \tan (e+f x))^{5/2} \left(99 b d^2 (a B+A b-b C)+4 (b c-a d) (-6 a C d-11 b B d+6 b c C)\right)}{693 d^3 f}+\frac{(a+i b)^3 (c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 (c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{2 (-6 a C d-11 b B d+6 b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}}{99 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{5/2}}{11 d f}","\frac{2 (c+d \tan (e+f x))^{5/2} \left(-2 a^2 b d^2 (192 c C-847 B d)+168 a^3 C d^3+33 a b^2 d \left(63 d^2 (A-C)-18 B c d+8 c^2 C\right)+b^3 \left(-\left(198 c d^2 (A-C)-88 B c^2 d+693 B d^3+48 c^3 C\right)\right)\right)}{3465 d^4 f}+\frac{2 \left(3 a^2 b (A-C)+a^3 B-3 a b^2 B-b^3 (A-C)\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} \left(3 a^2 b (A c-B d-c C)+a^3 (d (A-C)+B c)-3 a b^2 (d (A-C)+B c)-b^3 (A c-B d-c C)\right)}{f}+\frac{2 b \tan (e+f x) (c+d \tan (e+f x))^{5/2} \left(99 b d^2 (a B+A b-b C)+4 (b c-a d) (-6 a C d-11 b B d+6 b c C)\right)}{693 d^3 f}+\frac{(a+i b)^3 (c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 (c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{2 (-6 a C d-11 b B d+6 b c C) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}}{99 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{5/2}}{11 d f}",1,"((I*a + b)^3*(A - I*B - C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((a + I*b)^3*(I*A - B - I*C)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(3*a^2*b*(A*c - c*C - B*d) - b^3*(A*c - c*C - B*d) + a^3*(B*c + (A - C)*d) - 3*a*b^2*(B*c + (A - C)*d))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(a^3*B - 3*a*b^2*B + 3*a^2*b*(A - C) - b^3*(A - C))*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*(168*a^3*C*d^3 - 2*a^2*b*d^2*(192*c*C - 847*B*d) + 33*a*b^2*d*(8*c^2*C - 18*B*c*d + 63*(A - C)*d^2) - b^3*(48*c^3*C - 88*B*c^2*d + 198*c*(A - C)*d^2 + 693*B*d^3))*(c + d*Tan[e + f*x])^(5/2))/(3465*d^4*f) + (2*b*(99*b*(A*b + a*B - b*C)*d^2 + 4*(b*c - a*d)*(6*b*c*C - 11*b*B*d - 6*a*C*d))*Tan[e + f*x]*(c + d*Tan[e + f*x])^(5/2))/(693*d^3*f) - (2*(6*b*c*C - 11*b*B*d - 6*a*C*d)*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2))/(99*d^2*f) + (2*C*(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(5/2))/(11*d*f)","A",13,8,47,0.1702,1,"{3647, 3637, 3630, 3528, 3539, 3537, 63, 208}"
98,1,396,0,1.7265141,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (c+d \tan (e+f x))^{5/2} \left(28 a^2 C d^2-18 a b d (2 c C-7 B d)+b^2 \left(63 d^2 (A-C)-18 B c d+8 c^2 C\right)\right)}{315 d^3 f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{(a-i b)^2 (c-i d)^{3/2} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^2 (c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-9 b B d+4 b c C) (c+d \tan (e+f x))^{5/2}}{63 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}}{9 d f}","\frac{2 (c+d \tan (e+f x))^{5/2} \left(28 a^2 C d^2-18 a b d (2 c C-7 B d)+b^2 \left(63 d^2 (A-C)-18 B c d+8 c^2 C\right)\right)}{315 d^3 f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{f}-\frac{(a-i b)^2 (c-i d)^{3/2} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^2 (c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-9 b B d+4 b c C) (c+d \tan (e+f x))^{5/2}}{63 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}}{9 d f}",1,"-(((a - I*b)^2*(B + I*(A - C))*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((a + I*b)^2*(I*A - B - I*C)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(a^2*B - b^2*B + 2*a*b*(A - C))*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*(28*a^2*C*d^2 - 18*a*b*d*(2*c*C - 7*B*d) + b^2*(8*c^2*C - 18*B*c*d + 63*(A - C)*d^2))*(c + d*Tan[e + f*x])^(5/2))/(315*d^3*f) - (2*b*(4*b*c*C - 9*b*B*d - 4*a*C*d)*Tan[e + f*x]*(c + d*Tan[e + f*x])^(5/2))/(63*d^2*f) + (2*C*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2))/(9*d*f)","A",12,8,47,0.1702,1,"{3647, 3637, 3630, 3528, 3539, 3537, 63, 208}"
99,1,273,0,0.8793813,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (a B+A b-b C) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(b+i a) (c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-7 a C d-7 b B d+2 b c C) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{5/2}}{7 d f}","\frac{2 (a B+A b-b C) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \sqrt{c+d \tan (e+f x)} (a A d+a B c-a C d+A b c-b B d-b c C)}{f}-\frac{(b+i a) (c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-7 a C d-7 b B d+2 b c C) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{5/2}}{7 d f}",1,"-(((I*a + b)*(A - I*B - C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*(A + I*B - C)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*Sqrt[c + d*Tan[e + f*x]])/f + (2*(A*b + a*B - b*C)*(c + d*Tan[e + f*x])^(3/2))/(3*f) - (2*(2*b*c*C - 7*b*B*d - 7*a*C*d)*(c + d*Tan[e + f*x])^(5/2))/(35*d^2*f) + (2*b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^(5/2))/(7*d*f)","A",11,7,45,0.1556,1,"{3637, 3630, 3528, 3539, 3537, 63, 208}"
100,1,187,0,0.4596589,"\int (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (d (A-C)+B c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 C (c+d \tan (e+f x))^{5/2}}{5 d f}","\frac{2 (d (A-C)+B c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 C (c+d \tan (e+f x))^{5/2}}{5 d f}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) - ((B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(B*c + (A - C)*d)*Sqrt[c + d*Tan[e + f*x]])/f + (2*B*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*C*(c + d*Tan[e + f*x])^(5/2))/(5*d*f)","A",10,6,35,0.1714,1,"{3630, 3528, 3539, 3537, 63, 208}"
101,1,271,0,1.8140887,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","-\frac{2 (b c-a d)^{3/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{5/2} f \left(a^2+b^2\right)}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}-\frac{(c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}+\frac{2 (-a C d+b B d+b c C) \sqrt{c+d \tan (e+f x)}}{b^2 f}+\frac{2 C (c+d \tan (e+f x))^{3/2}}{3 b f}","-\frac{2 (b c-a d)^{3/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{5/2} f \left(a^2+b^2\right)}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}-\frac{(c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}+\frac{2 (-a C d+b B d+b c C) \sqrt{c+d \tan (e+f x)}}{b^2 f}+\frac{2 C (c+d \tan (e+f x))^{3/2}}{3 b f}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)*f)) - ((A + I*B - C)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)*f) - (2*(A*b^2 - a*(b*B - a*C))*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(5/2)*(a^2 + b^2)*f) + (2*(b*c*C + b*B*d - a*C*d)*Sqrt[c + d*Tan[e + f*x]])/(b^2*f) + (2*C*(c + d*Tan[e + f*x])^(3/2))/(3*b*f)","A",13,7,47,0.1489,1,"{3647, 3653, 3539, 3537, 63, 208, 3634}"
102,1,372,0,2.5473079,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(3 a^2 C-a b B+A b^2+2 b^2 C\right) \sqrt{c+d \tan (e+f x)}}{b^2 f \left(a^2+b^2\right)}+\frac{\sqrt{b c-a d} \left(a^2 b^2 (d (A-7 C)+2 B c)+a^3 b B d-3 a^4 C d-a b^3 (4 A c-5 B d-4 c C)-b^4 (3 A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{5/2} f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(3 a^2 C-a b B+A b^2+2 b^2 C\right) \sqrt{c+d \tan (e+f x)}}{b^2 f \left(a^2+b^2\right)}+\frac{\sqrt{b c-a d} \left(a^2 b^2 (d (A-7 C)+2 B c)+a^3 b B d-3 a^4 C d-a b^3 (4 A c-5 B d-4 c C)-b^4 (3 A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{5/2} f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f)) - ((B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) + (Sqrt[b*c - a*d]*(a^3*b*B*d - 3*a^4*C*d - b^4*(2*B*c + 3*A*d) - a*b^3*(4*A*c - 4*c*C - 5*B*d) + a^2*b^2*(2*B*c + (A - 7*C)*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(5/2)*(a^2 + b^2)^2*f) + ((A*b^2 - a*b*B + 3*a^2*C + 2*b^2*C)*d*Sqrt[c + d*Tan[e + f*x]])/(b^2*(a^2 + b^2)*f) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(3/2))/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",13,8,47,0.1702,1,"{3645, 3647, 3653, 3539, 3537, 63, 208, 3634}"
103,1,532,0,4.0869603,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","-\frac{\left(-2 a^3 b^3 \left(12 c d (A-C)+B \left(4 c^2-9 d^2\right)\right)+a^2 b^4 \left(24 A c^2-26 A d^2-48 B c d-24 c^2 C+35 C d^2\right)+a^4 b^2 d (3 d (A+2 C)+4 B c)+a^5 b B d^2+3 a^6 C d^2+a b^5 \left(40 c d (A-C)+3 B \left(8 c^2-5 d^2\right)\right)-b^6 \left(8 A c^2-3 A d^2-12 B c d-8 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} f \left(a^2+b^2\right)^3 \sqrt{b c-a d}}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (5 A d+4 B c-11 C d)+a^3 b B d+3 a^4 C d+a b^3 (8 A c-7 B d-8 c C)+b^4 (3 A d+4 B c)\right)}{4 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","-\frac{\left(-2 a^3 b^3 \left(12 c d (A-C)+B \left(4 c^2-9 d^2\right)\right)+a^2 b^4 \left(24 A c^2-26 A d^2-48 B c d-24 c^2 C+35 C d^2\right)+a^4 b^2 d (3 d (A+2 C)+4 B c)+a^5 b B d^2+3 a^6 C d^2+a b^5 \left(40 c d (A-C)+3 B \left(8 c^2-5 d^2\right)\right)-b^6 \left(8 A c^2-3 A d^2-12 B c d-8 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} f \left(a^2+b^2\right)^3 \sqrt{b c-a d}}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (5 A d+4 B c-11 C d)+a^3 b B d+3 a^4 C d+a b^3 (8 A c-7 B d-8 c C)+b^4 (3 A d+4 B c)\right)}{4 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(c-i d)^{3/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{3/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-(((A - I*B - C)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + ((A + I*B - C)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) - ((a^5*b*B*d^2 + 3*a^6*C*d^2 + a^4*b^2*d*(4*B*c + 3*(A + 2*C)*d) - b^6*(8*A*c^2 - 8*c^2*C - 12*B*c*d - 3*A*d^2) + a^2*b^4*(24*A*c^2 - 24*c^2*C - 48*B*c*d - 26*A*d^2 + 35*C*d^2) - 2*a^3*b^3*(12*c*(A - C)*d + B*(4*c^2 - 9*d^2)) + a*b^5*(40*c*(A - C)*d + 3*B*(8*c^2 - 5*d^2)))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*b^(5/2)*(a^2 + b^2)^3*Sqrt[b*c - a*d]*f) - ((a^3*b*B*d + 3*a^4*C*d + b^4*(4*B*c + 3*A*d) + a*b^3*(8*A*c - 8*c*C - 7*B*d) - a^2*b^2*(4*B*c + 5*A*d - 11*C*d))*Sqrt[c + d*Tan[e + f*x]])/(4*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(3/2))/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2)","A",13,7,47,0.1489,1,"{3645, 3653, 3539, 3537, 63, 208, 3634}"
104,1,503,0,2.3122933,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 (c+d \tan (e+f x))^{7/2} \left(36 a^2 C d^2-22 a b d (2 c C-9 B d)+b^2 \left(99 d^2 (A-C)-22 B c d+8 c^2 C\right)\right)}{693 d^3 f}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 (c+d \tan (e+f x))^{3/2} \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{3 f}-\frac{(a-i b)^2 (c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^2 (c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-11 b B d+4 b c C) (c+d \tan (e+f x))^{7/2}}{99 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{7/2}}{11 d f}","\frac{2 (c+d \tan (e+f x))^{7/2} \left(36 a^2 C d^2-22 a b d (2 c C-9 B d)+b^2 \left(99 d^2 (A-C)-22 B c d+8 c^2 C\right)\right)}{693 d^3 f}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^2 \left(-\left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)+2 a b \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-C d^2\right)+b^2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)\right)}{f}+\frac{2 \left(a^2 B+2 a b (A-C)-b^2 B\right) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 (c+d \tan (e+f x))^{3/2} \left(a^2 (d (A-C)+B c)+2 a b (A c-B d-c C)-b^2 (d (A-C)+B c)\right)}{3 f}-\frac{(a-i b)^2 (c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(a+i b)^2 (c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 b \tan (e+f x) (-4 a C d-11 b B d+4 b c C) (c+d \tan (e+f x))^{7/2}}{99 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{7/2}}{11 d f}",1,"-(((a - I*b)^2*(I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((a + I*b)^2*(I*A - B - I*C)*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f - (2*(2*a*b*(c^2*C + 2*B*c*d - C*d^2 - A*(c^2 - d^2)) - a^2*(2*c*(A - C)*d + B*(c^2 - d^2)) + b^2*(2*c*(A - C)*d + B*(c^2 - d^2)))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(2*a*b*(A*c - c*C - B*d) + a^2*(B*c + (A - C)*d) - b^2*(B*c + (A - C)*d))*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*(a^2*B - b^2*B + 2*a*b*(A - C))*(c + d*Tan[e + f*x])^(5/2))/(5*f) + (2*(36*a^2*C*d^2 - 22*a*b*d*(2*c*C - 9*B*d) + b^2*(8*c^2*C - 22*B*c*d + 99*(A - C)*d^2))*(c + d*Tan[e + f*x])^(7/2))/(693*d^3*f) - (2*b*(4*b*c*C - 11*b*B*d - 4*a*C*d)*Tan[e + f*x]*(c + d*Tan[e + f*x])^(7/2))/(99*d^2*f) + (2*C*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(7/2))/(11*d*f)","A",13,8,47,0.1702,1,"{3647, 3637, 3630, 3528, 3539, 3537, 63, 208}"
105,1,351,0,1.2123223,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 \sqrt{c+d \tan (e+f x)} \left(2 a A c d+a B \left(c^2-d^2\right)-2 a c C d+A b \left(c^2-d^2\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}+\frac{2 (a B+A b-b C) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 (c+d \tan (e+f x))^{3/2} (a A d+a B c-a C d+A b c-b B d-b c C)}{3 f}-\frac{(b+i a) (c-i d)^{5/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{5/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-9 a C d-9 b B d+2 b c C) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{7/2}}{9 d f}","\frac{2 \sqrt{c+d \tan (e+f x)} \left(A \left(2 a c d+b \left(c^2-d^2\right)\right)+a \left(B c^2-B d^2-2 c C d\right)-b \left(2 B c d+c^2 C-C d^2\right)\right)}{f}+\frac{2 (a B+A b-b C) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 (c+d \tan (e+f x))^{3/2} (a A d+a B c-a C d+A b c-b B d-b c C)}{3 f}-\frac{(b+i a) (c-i d)^{5/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{5/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}-\frac{2 (-9 a C d-9 b B d+2 b c C) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}+\frac{2 b C \tan (e+f x) (c+d \tan (e+f x))^{7/2}}{9 d f}",1,"-(((I*a + b)*(A - I*B - C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*(A + I*B - C)*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*a*A*c*d - 2*a*c*C*d + A*b*(c^2 - d^2) + a*B*(c^2 - d^2) - b*(c^2*C + 2*B*c*d - C*d^2))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*(A*b + a*B - b*C)*(c + d*Tan[e + f*x])^(5/2))/(5*f) - (2*(2*b*c*C - 9*b*B*d - 9*a*C*d)*(c + d*Tan[e + f*x])^(7/2))/(63*d^2*f) + (2*b*C*Tan[e + f*x]*(c + d*Tan[e + f*x])^(7/2))/(9*d*f)","A",12,7,45,0.1556,1,"{3637, 3630, 3528, 3539, 3537, 63, 208}"
106,1,229,0,0.6285632,"\int (c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 (d (A-C)+B c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 C (c+d \tan (e+f x))^{7/2}}{7 d f}","\frac{2 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 (d (A-C)+B c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 B (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 C (c+d \tan (e+f x))^{7/2}}{7 d f}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*c*(A - C)*d + B*(c^2 - d^2))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(B*c + (A - C)*d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*B*(c + d*Tan[e + f*x])^(5/2))/(5*f) + (2*C*(c + d*Tan[e + f*x])^(7/2))/(7*d*f)","A",11,6,35,0.1714,1,"{3630, 3528, 3539, 3537, 63, 208}"
107,1,336,0,2.8117258,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{a+b \tan (e+f x)} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x]),x]","-\frac{2 (b c-a d)^{5/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{7/2} f \left(a^2+b^2\right)}+\frac{2 \sqrt{c+d \tan (e+f x)} \left((b c-a d) (-a C d+b B d+b c C)+b^2 d (d (A-C)+B c)\right)}{b^3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}+\frac{(c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)}+\frac{2 (-a C d+b B d+b c C) (c+d \tan (e+f x))^{3/2}}{3 b^2 f}+\frac{2 C (c+d \tan (e+f x))^{5/2}}{5 b f}","-\frac{2 (b c-a d)^{5/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{7/2} f \left(a^2+b^2\right)}+\frac{2 \sqrt{c+d \tan (e+f x)} \left((b c-a d) (-a C d+b B d+b c C)+b^2 d (d (A-C)+B c)\right)}{b^3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)}+\frac{(c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)}+\frac{2 (-a C d+b B d+b c C) (c+d \tan (e+f x))^{3/2}}{3 b^2 f}+\frac{2 C (c+d \tan (e+f x))^{5/2}}{5 b f}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)*f)) + ((I*A - B - I*C)*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)*f) - (2*(A*b^2 - a*(b*B - a*C))*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(7/2)*(a^2 + b^2)*f) + (2*(b^2*d*(B*c + (A - C)*d) + (b*c - a*d)*(b*c*C + b*B*d - a*C*d))*Sqrt[c + d*Tan[e + f*x]])/(b^3*f) + (2*(b*c*C + b*B*d - a*C*d)*(c + d*Tan[e + f*x])^(3/2))/(3*b^2*f) + (2*C*(c + d*Tan[e + f*x])^(5/2))/(5*b*f)","A",14,7,47,0.1489,1,"{3647, 3653, 3539, 3537, 63, 208, 3634}"
108,1,473,0,3.8957699,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^2} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^2,x]","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(5 a^2 C-3 a b B+3 A b^2+2 b^2 C\right) (c+d \tan (e+f x))^{3/2}}{3 b^2 f \left(a^2+b^2\right)}-\frac{d \sqrt{c+d \tan (e+f x)} \left(-a^2 b (3 B d+5 c C)+5 a^3 C d-A b^2 (b c-a d)+a b^2 (B c+4 C d)-2 b^3 (B d+2 c C)\right)}{b^3 f \left(a^2+b^2\right)}+\frac{(b c-a d)^{3/2} \left(a^2 b^2 (2 B c-d (A+9 C))+3 a^3 b B d-5 a^4 C d-a b^3 (4 A c-7 B d-4 c C)-b^4 (5 A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{7/2} f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{d \left(5 a^2 C-3 a b B+3 A b^2+2 b^2 C\right) (c+d \tan (e+f x))^{3/2}}{3 b^2 f \left(a^2+b^2\right)}-\frac{d \sqrt{c+d \tan (e+f x)} \left(-a^2 b (3 B d+5 c C)+5 a^3 C d-A b^2 (b c-a d)+a b^2 (B c+4 C d)-2 b^3 (B d+2 c C)\right)}{b^3 f \left(a^2+b^2\right)}+\frac{(b c-a d)^{3/2} \left(a^2 b^2 (2 B c-d (A+9 C))+3 a^3 b B d-5 a^4 C d-a b^3 (4 A c-7 B d-4 c C)-b^4 (5 A d+2 B c)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{7/2} f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) + ((b*c - a*d)^(3/2)*(3*a^3*b*B*d - 5*a^4*C*d - b^4*(2*B*c + 5*A*d) - a*b^3*(4*A*c - 4*c*C - 7*B*d) + a^2*b^2*(2*B*c - (A + 9*C)*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(7/2)*(a^2 + b^2)^2*f) - (d*(5*a^3*C*d - A*b^2*(b*c - a*d) - 2*b^3*(2*c*C + B*d) - a^2*b*(5*c*C + 3*B*d) + a*b^2*(B*c + 4*C*d))*Sqrt[c + d*Tan[e + f*x]])/(b^3*(a^2 + b^2)*f) + ((3*A*b^2 - 3*a*b*B + 5*a^2*C + 2*b^2*C)*d*(c + d*Tan[e + f*x])^(3/2))/(3*b^2*(a^2 + b^2)*f) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",14,8,47,0.1702,1,"{3645, 3647, 3653, 3539, 3537, 63, 208, 3634}"
109,1,643,0,6.0651896,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^3} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^3,x]","\frac{\sqrt{b c-a d} \left(2 a^3 b^3 \left(4 c d (A-C)+B \left(4 c^2+3 d^2\right)\right)-3 a^2 b^4 \left(8 A c^2-6 A d^2-16 B c d-8 c^2 C+21 C d^2\right)+a^4 b^2 d (d (A-46 C)+4 B c)+3 a^5 b B d^2-15 a^6 C d^2-a b^5 \left(56 c d (A-C)+B \left(24 c^2-35 d^2\right)\right)-b^6 \left(4 c (5 B d+2 c C)-A \left(8 c^2-15 d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{7/2} f \left(a^2+b^2\right)^3}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}+\frac{(c+d \tan (e+f x))^{3/2} \left(a^2 b^2 (3 A d+4 B c-13 C d)+a^3 b B d-5 a^4 C d-a b^3 (8 A c-9 B d-8 c C)-b^4 (5 A d+4 B c)\right)}{4 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{d \sqrt{c+d \tan (e+f x)} \left(a^2 b^2 (d (A-31 C)+4 B c)+3 a^3 b B d-15 a^4 C d-a b^3 (8 A c-11 B d-8 c C)-b^4 (7 A d+4 B c+8 C d)\right)}{4 b^3 f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{5/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","\frac{\sqrt{b c-a d} \left(2 a^3 b^3 \left(4 c d (A-C)+B \left(4 c^2+3 d^2\right)\right)-3 a^2 b^4 \left(8 A c^2-6 A d^2-16 B c d-8 c^2 C+21 C d^2\right)+a^4 b^2 d (d (A-46 C)+4 B c)+3 a^5 b B d^2-15 a^6 C d^2-a b^5 \left(56 c d (A-C)+B \left(24 c^2-35 d^2\right)\right)-b^6 \left(4 c (5 B d+2 c C)-A \left(8 c^2-15 d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{7/2} f \left(a^2+b^2\right)^3}-\frac{\left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}+\frac{(c+d \tan (e+f x))^{3/2} \left(a^2 b^2 (3 A d+4 B c-13 C d)+a^3 b B d-5 a^4 C d-a b^3 (8 A c-9 B d-8 c C)-b^4 (5 A d+4 B c)\right)}{4 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{d \sqrt{c+d \tan (e+f x)} \left(a^2 b^2 (d (A-31 C)+4 B c)+3 a^3 b B d-15 a^4 C d-a b^3 (8 A c-11 B d-8 c C)-b^4 (7 A d+4 B c+8 C d)\right)}{4 b^3 f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{5/2} (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-(((A - I*B - C)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + ((A + I*B - C)*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) + (Sqrt[b*c - a*d]*(3*a^5*b*B*d^2 - 15*a^6*C*d^2 + a^4*b^2*d*(4*B*c + (A - 46*C)*d) - 3*a^2*b^4*(8*A*c^2 - 8*c^2*C - 16*B*c*d - 6*A*d^2 + 21*C*d^2) - a*b^5*(56*c*(A - C)*d + B*(24*c^2 - 35*d^2)) - b^6*(4*c*(2*c*C + 5*B*d) - A*(8*c^2 - 15*d^2)) + 2*a^3*b^3*(4*c*(A - C)*d + B*(4*c^2 + 3*d^2)))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*b^(7/2)*(a^2 + b^2)^3*f) - (d*(3*a^3*b*B*d - 15*a^4*C*d - a*b^3*(8*A*c - 8*c*C - 11*B*d) + a^2*b^2*(4*B*c + (A - 31*C)*d) - b^4*(4*B*c + 7*A*d + 8*C*d))*Sqrt[c + d*Tan[e + f*x]])/(4*b^3*(a^2 + b^2)^2*f) + ((a^3*b*B*d - 5*a^4*C*d - b^4*(4*B*c + 5*A*d) - a*b^3*(8*A*c - 8*c*C - 9*B*d) + a^2*b^2*(4*B*c + 3*A*d - 13*C*d))*(c + d*Tan[e + f*x])^(3/2))/(4*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])) - ((A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2)","A",14,8,47,0.1702,1,"{3645, 3647, 3653, 3539, 3537, 63, 208, 3634}"
110,1,407,0,1.6989264,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","\frac{2 \sqrt{c+d \tan (e+f x)} \left(-6 a^2 b d^2 (32 c C-49 B d)+72 a^3 C d^3+21 a b^2 d \left(15 d^2 (A-C)-10 B c d+8 c^2 C\right)+b^3 \left(-\left(70 c d^2 (A-C)-56 B c^2 d+105 B d^3+48 c^3 C\right)\right)\right)}{105 d^4 f}+\frac{2 b \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(35 b d^2 (a B+A b-b C)+4 (b c-a d) (-6 a C d-7 b B d+6 b c C)\right)}{105 d^3 f}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{(b+i a)^3 (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}-\frac{2 (-6 a C d-7 b B d+6 b c C) (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{35 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)}}{7 d f}","\frac{2 \sqrt{c+d \tan (e+f x)} \left(-6 a^2 b d^2 (32 c C-49 B d)+72 a^3 C d^3+21 a b^2 d \left(15 d^2 (A-C)-10 B c d+8 c^2 C\right)+b^3 \left(-\left(70 c d^2 (A-C)-56 B c^2 d+105 B d^3+48 c^3 C\right)\right)\right)}{105 d^4 f}+\frac{2 b \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(35 b d^2 (a B+A b-b C)+4 (b c-a d) (-6 a C d-7 b B d+6 b c C)\right)}{105 d^3 f}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{(b+i a)^3 (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}-\frac{2 (-6 a C d-7 b B d+6 b c C) (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{35 d^2 f}+\frac{2 C (a+b \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)}}{7 d f}",1,"((I*a + b)^3*(A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) - ((I*a - b)^3*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) + (2*(72*a^3*C*d^3 - 6*a^2*b*d^2*(32*c*C - 49*B*d) + 21*a*b^2*d*(8*c^2*C - 10*B*c*d + 15*(A - C)*d^2) - b^3*(48*c^3*C - 56*B*c^2*d + 70*c*(A - C)*d^2 + 105*B*d^3))*Sqrt[c + d*Tan[e + f*x]])/(105*d^4*f) + (2*b*(35*b*(A*b + a*B - b*C)*d^2 + 4*(b*c - a*d)*(6*b*c*C - 7*b*B*d - 6*a*C*d))*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(105*d^3*f) - (2*(6*b*c*C - 7*b*B*d - 6*a*C*d)*(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]])/(35*d^2*f) + (2*C*(a + b*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]])/(7*d*f)","A",11,7,47,0.1489,1,"{3647, 3637, 3630, 3539, 3537, 63, 208}"
111,1,287,0,1.001397,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","\frac{2 \sqrt{c+d \tan (e+f x)} \left(12 a^2 C d^2-10 a b d (2 c C-3 B d)+b^2 \left(15 d^2 (A-C)-10 B c d+8 c^2 C\right)\right)}{15 d^3 f}-\frac{(a-i b)^2 (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{(a+i b)^2 (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{2 b \tan (e+f x) (-4 a C d-5 b B d+4 b c C) \sqrt{c+d \tan (e+f x)}}{15 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d f}","\frac{2 \sqrt{c+d \tan (e+f x)} \left(12 a^2 C d^2-10 a b d (2 c C-3 B d)+b^2 \left(15 d^2 (A-C)-10 B c d+8 c^2 C\right)\right)}{15 d^3 f}-\frac{(a-i b)^2 (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{(a+i b)^2 (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{2 b \tan (e+f x) (-4 a C d-5 b B d+4 b c C) \sqrt{c+d \tan (e+f x)}}{15 d^2 f}+\frac{2 C (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d f}",1,"-(((a - I*b)^2*(B + I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f)) + ((a + I*b)^2*(I*A - B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) + (2*(12*a^2*C*d^2 - 10*a*b*d*(2*c*C - 3*B*d) + b^2*(8*c^2*C - 10*B*c*d + 15*(A - C)*d^2))*Sqrt[c + d*Tan[e + f*x]])/(15*d^3*f) - (2*b*(4*b*c*C - 5*b*B*d - 4*a*C*d)*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(15*d^2*f) + (2*C*(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]])/(5*d*f)","A",10,7,47,0.1489,1,"{3647, 3637, 3630, 3539, 3537, 63, 208}"
112,1,194,0,0.4983119,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{(b+i a) (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{2 (-3 a C d-3 b B d+2 b c C) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}+\frac{2 b C \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{3 d f}","-\frac{(b+i a) (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{2 (-3 a C d-3 b B d+2 b c C) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}+\frac{2 b C \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{3 d f}",1,"-(((I*a + b)*(A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f)) + ((I*a - b)*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) - (2*(2*b*c*C - 3*b*B*d - 3*a*C*d)*Sqrt[c + d*Tan[e + f*x]])/(3*d^2*f) + (2*b*C*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(3*d*f)","A",9,6,45,0.1333,1,"{3637, 3630, 3539, 3537, 63, 208}"
113,1,133,0,0.2157006,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{2 C \sqrt{c+d \tan (e+f x)}}{d f}","-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{2 C \sqrt{c+d \tan (e+f x)}}{d f}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) + (2*C*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",8,5,35,0.1429,1,"{3630, 3539, 3537, 63, 208}"
114,1,210,0,0.6148006,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right) \sqrt{b c-a d}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b) \sqrt{c-i d}}-\frac{(A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) \sqrt{c+i d}}","-\frac{2 \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right) \sqrt{b c-a d}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b) \sqrt{c-i d}}-\frac{(A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) \sqrt{c+i d}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)*Sqrt[c - I*d]*f)) - ((A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)*Sqrt[c + I*d]*f) - (2*(A*b^2 - a*(b*B - a*C))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(Sqrt[b]*(a^2 + b^2)*Sqrt[b*c - a*d]*f)","A",11,6,47,0.1277,1,"{3653, 3539, 3537, 63, 208, 3634}"
115,1,327,0,1.3793718,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}-\frac{\left(-a^2 b^2 (5 A d+2 B c-3 C d)+3 a^3 b B d+a^4 (-C) d+a b^3 (4 A c-B d-4 c C)+b^4 (2 B c-A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)^2 (b c-a d)^{3/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 \sqrt{c+i d}}","-\frac{\left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}-\frac{\left(-a^2 b^2 (5 A d+2 B c-3 C d)+3 a^3 b B d+a^4 (-C) d+a b^3 (4 A c-B d-4 c C)+b^4 (2 B c-A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)^2 (b c-a d)^{3/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 \sqrt{c+i d}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*Sqrt[c - I*d]*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*Sqrt[c + I*d]*f) - ((3*a^3*b*B*d - a^4*C*d + b^4*(2*B*c - A*d) + a*b^3*(4*A*c - 4*c*C - B*d) - a^2*b^2*(2*B*c + 5*A*d - 3*C*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(Sqrt[b]*(a^2 + b^2)^2*(b*c - a*d)^(3/2)*f) - ((A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",12,7,47,0.1489,1,"{3649, 3653, 3539, 3537, 63, 208, 3634}"
116,1,511,0,2.4649435,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a^2 d^2 \left(d^2 (5 A+7 C)-5 B c d+12 c^2 C\right)-15 a b d \left(c d^2 (3 A+5 C)-6 B c^2 d-3 B d^3+8 c^3 C\right)+b^2 \left(6 c^2 d^2 (5 A+3 C)+15 d^4 (A-C)-40 B c^3 d-25 B c d^3+48 c^4 C\right)\right)}{15 d^4 f \left(c^2+d^2\right)}-\frac{2 b^2 \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(4 (b c-a d) \left(d^2 (5 A+C)-5 B c d+6 c^2 C\right)-5 d^2 ((A-C) (b c-a d)+B (a c+b d))\right)}{15 d^3 f \left(c^2+d^2\right)}+\frac{2 b \left(d^2 (5 A+C)-5 B c d+6 c^2 C\right) (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d^2 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}-\frac{(a-i b)^3 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a^2 d^2 \left(d^2 (5 A+7 C)-5 B c d+12 c^2 C\right)-15 a b d \left(c d^2 (3 A+5 C)-6 B c^2 d-3 B d^3+8 c^3 C\right)+b^2 \left(6 c^2 d^2 (5 A+3 C)+15 d^4 (A-C)-40 B c^3 d-25 B c d^3+48 c^4 C\right)\right)}{15 d^4 f \left(c^2+d^2\right)}-\frac{2 b^2 \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(4 (b c-a d) \left(d^2 (5 A+C)-5 B c d+6 c^2 C\right)-5 d^2 ((A-C) (b c-a d)+B (a c+b d))\right)}{15 d^3 f \left(c^2+d^2\right)}+\frac{2 b \left(d^2 (5 A+C)-5 B c d+6 c^2 C\right) (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d^2 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}-\frac{(a-i b)^3 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}",1,"-(((a - I*b)^3*(I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) - ((I*a - b)^3*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^3)/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b*(6*a^2*d^2*(12*c^2*C - 5*B*c*d + (5*A + 7*C)*d^2) - 15*a*b*d*(8*c^3*C - 6*B*c^2*d + c*(3*A + 5*C)*d^2 - 3*B*d^3) + b^2*(48*c^4*C - 40*B*c^3*d + 6*c^2*(5*A + 3*C)*d^2 - 25*B*c*d^3 + 15*(A - C)*d^4))*Sqrt[c + d*Tan[e + f*x]])/(15*d^4*(c^2 + d^2)*f) - (2*b^2*(4*(b*c - a*d)*(6*c^2*C - 5*B*c*d + (5*A + C)*d^2) - 5*d^2*((A - C)*(b*c - a*d) + B*(a*c + b*d)))*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(15*d^3*(c^2 + d^2)*f) + (2*b*(6*c^2*C - 5*B*c*d + (5*A + C)*d^2)*(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]])/(5*d^2*(c^2 + d^2)*f)","A",11,8,47,0.1702,1,"{3645, 3647, 3637, 3630, 3539, 3537, 63, 208}"
117,1,343,0,1.3536603,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a d \left(d^2 (A+C)-B c d+2 c^2 C\right)-b \left(c d^2 (3 A+5 C)-6 B c^2 d-3 B d^3+8 c^3 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^2 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^2 (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{2 b^2 \tan (e+f x) \left(d^2 (3 A+C)-3 B c d+4 c^2 C\right) \sqrt{c+d \tan (e+f x)}}{3 d^2 f \left(c^2+d^2\right)}","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a d \left(d^2 (A+C)-B c d+2 c^2 C\right)-b \left(c d^2 (3 A+5 C)-6 B c^2 d-3 B d^3+8 c^3 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^2 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^2 (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{2 b^2 \tan (e+f x) \left(d^2 (3 A+C)-3 B c d+4 c^2 C\right) \sqrt{c+d \tan (e+f x)}}{3 d^2 f \left(c^2+d^2\right)}",1,"-(((a - I*b)^2*(I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) - ((a + I*b)^2*(B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^2)/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b*(6*a*d*(2*c^2*C - B*c*d + (A + C)*d^2) - b*(8*c^3*C - 6*B*c^2*d + c*(3*A + 5*C)*d^2 - 3*B*d^3))*Sqrt[c + d*Tan[e + f*x]])/(3*d^3*(c^2 + d^2)*f) + (2*b^2*(4*c^2*C - 3*B*c*d + (3*A + C)*d^2)*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(3*d^2*(c^2 + d^2)*f)","A",10,7,47,0.1489,1,"{3645, 3637, 3630, 3539, 3537, 63, 208}"
118,1,201,0,0.554369,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 (b c-a d) \left(A d^2-B c d+c^2 C\right)}{d^2 f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{2 b C \sqrt{c+d \tan (e+f x)}}{d^2 f}","\frac{2 (b c-a d) \left(A d^2-B c d+c^2 C\right)}{d^2 f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{2 b C \sqrt{c+d \tan (e+f x)}}{d^2 f}",1,"-(((I*a + b)*(A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) + ((I*a - b)*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) + (2*(b*c - a*d)*(c^2*C - B*c*d + A*d^2))/(d^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b*C*Sqrt[c + d*Tan[e + f*x]])/(d^2*f)","A",9,6,45,0.1333,1,"{3635, 3630, 3539, 3537, 63, 208}"
119,1,157,0,0.2939924,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 \left(A d^2-B c d+c^2 C\right)}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}","-\frac{2 \left(A d^2-B c d+c^2 C\right)}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(c^2*C - B*c*d + A*d^2))/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,35,0.1429,1,"{3628, 3539, 3537, 63, 208}"
120,1,262,0,1.277483,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{2 \sqrt{b} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{3/2}}+\frac{2 \left(A d^2-B c d+c^2 C\right)}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}+\frac{(A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{3/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b) (c+i d)^{3/2}}","-\frac{2 \sqrt{b} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{3/2}}+\frac{2 \left(A d^2-B c d+c^2 C\right)}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}+\frac{(A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{3/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b) (c+i d)^{3/2}}",1,"((A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)*(c - I*d)^(3/2)*f) + ((I*A - B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)*(c + I*d)^(3/2)*f) - (2*Sqrt[b]*(A*b^2 - a*(b*B - a*C))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*(b*c - a*d)^(3/2)*f) + (2*(c^2*C - B*c*d + A*d^2))/((b*c - a*d)*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",12,7,47,0.1489,1,"{3649, 3653, 3539, 3537, 63, 208, 3634}"
121,1,446,0,2.8814761,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{d \left(2 a^2 A d^2+a^2 \left(-2 B c d+3 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+A b^2 \left(c^2+3 d^2\right)+2 b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{b} \left(-a^2 b^2 (d (7 A-C)+2 B c)+5 a^3 b B d-3 a^4 C d+a b^3 (4 A c+B d-4 c C)+b^4 (2 B c-3 A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{5/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{3/2}}","-\frac{d \left(A \left(2 a^2 d^2+b^2 \left(c^2+3 d^2\right)\right)+a^2 \left(-2 B c d+3 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+2 b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{b} \left(-a^2 b^2 (d (7 A-C)+2 B c)+5 a^3 b B d-3 a^4 C d+a b^3 (4 A c+B d-4 c C)+b^4 (2 B c-3 A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{5/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{3/2}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*(c - I*d)^(3/2)*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*(c + I*d)^(3/2)*f) - (Sqrt[b]*(5*a^3*b*B*d - 3*a^4*C*d + b^4*(2*B*c - 3*A*d) + a*b^3*(4*A*c - 4*c*C + B*d) - a^2*b^2*(2*B*c + (7*A - C)*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*(b*c - a*d)^(5/2)*f) - (d*(2*a^2*A*d^2 + 2*b^2*c*(c*C - B*d) - a*b*B*(c^2 + d^2) + A*b^2*(c^2 + 3*d^2) + a^2*(3*c^2*C - 2*B*c*d + C*d^2)))/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])","A",13,7,47,0.1489,1,"{3649, 3653, 3539, 3537, 63, 208, 3634}"
122,1,585,0,2.9675232,"\int \frac{(a+b \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[((a + b*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a^2 d^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+3 a b d \left(-c^2 d^2 (A-17 C)+d^4 (5 A+3 C)-2 B c^3 d-8 B c d^3+8 c^4 C\right)-b^2 \left(2 c^3 d^2 (A+15 C)+8 c d^4 (A+C)-17 B c^2 d^3-8 B c^4 d-3 B d^5+16 c^5 C\right)\right)}{3 d^4 f \left(c^2+d^2\right)^2}+\frac{2 b^2 \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(c^2 d^2 (A+15 C)+d^4 (7 A+C)-4 B c^3 d-10 B c d^3+8 c^4 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)^2}-\frac{2 (a+b \tan (e+f x))^2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(2 A d^4-B c^3 d-3 B c d^3+4 c^2 C d^2+2 c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}-\frac{(a-i b)^3 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}","\frac{2 b \sqrt{c+d \tan (e+f x)} \left(6 a^2 d^3 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+3 a b d \left(-c^2 d^2 (A-17 C)+d^4 (5 A+3 C)-2 B c^3 d-8 B c d^3+8 c^4 C\right)-b^2 \left(2 c^3 d^2 (A+15 C)+8 c d^4 (A+C)-17 B c^2 d^3-8 B c^4 d-3 B d^5+16 c^5 C\right)\right)}{3 d^4 f \left(c^2+d^2\right)^2}+\frac{2 b^2 \tan (e+f x) \sqrt{c+d \tan (e+f x)} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(c^2 d^2 (A+15 C)+d^4 (7 A+C)-4 B c^3 d-10 B c d^3+8 c^4 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)^2}-\frac{2 (a+b \tan (e+f x))^2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(2 A d^4-B c^3 d-3 B c d^3+4 c^2 C d^2+2 c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^3}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(-b+i a)^3 (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}-\frac{(a-i b)^3 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}",1,"-(((a - I*b)^3*(I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f)) - ((I*a - b)^3*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^3)/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*(2*c^4*C - B*c^3*d + 4*c^2*C*d^2 - 3*B*c*d^3 + 2*A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*(a + b*Tan[e + f*x])^2)/(d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b*(3*a*b*d*(8*c^4*C - 2*B*c^3*d - c^2*(A - 17*C)*d^2 - 8*B*c*d^3 + (5*A + 3*C)*d^4) - b^2*(16*c^5*C - 8*B*c^4*d + 2*c^3*(A + 15*C)*d^2 - 17*B*c^2*d^3 + 8*c*(A + C)*d^4 - 3*B*d^5) + 6*a^2*d^3*(2*c*(A - C)*d - B*(c^2 - d^2)))*Sqrt[c + d*Tan[e + f*x]])/(3*d^4*(c^2 + d^2)^2*f) + (2*b^2*(b*(8*c^4*C - 4*B*c^3*d + c^2*(A + 15*C)*d^2 - 10*B*c*d^3 + (7*A + C)*d^4) + 3*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(3*d^3*(c^2 + d^2)^2*f)","A",11,7,47,0.1489,1,"{3645, 3637, 3630, 3539, 3537, 63, 208}"
123,1,358,0,1.5510686,"\int \frac{(a+b \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[((a + b*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 (b c-a d) \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-2 c^2 d^2 (A-5 C)+4 A d^4-B c^3 d-7 B c d^3+4 c^4 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^2 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^2 (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}+\frac{2 b^2 \left(d^2 (A+3 C)-B c d+4 c^2 C\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}","\frac{2 (b c-a d) \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-2 c^2 d^2 (A-5 C)+4 A d^4-B c^3 d-7 B c d^3+4 c^4 C\right)\right)}{3 d^3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^2 (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^2 (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}+\frac{2 b^2 \left(d^2 (A+3 C)-B c d+4 c^2 C\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}",1,"-(((a - I*b)^2*(I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f)) - ((a + I*b)^2*(B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^2)/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(b*c - a*d)*(b*(4*c^4*C - B*c^3*d - 2*c^2*(A - 5*C)*d^2 - 7*B*c*d^3 + 4*A*d^4) + 3*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2))))/(3*d^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]]) + (2*b^2*(4*c^2*C - B*c*d + (A + 3*C)*d^2)*Sqrt[c + d*Tan[e + f*x]])/(3*d^3*(c^2 + d^2)*f)","A",10,7,47,0.1489,1,"{3645, 3635, 3630, 3539, 3537, 63, 208}"
124,1,271,0,0.797563,"\int \frac{(a+b \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[((a + b*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 (b c-a d) \left(A d^2-B c d+c^2 C\right)}{3 d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) (A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}","\frac{2 (b c-a d) \left(A d^2-B c d+c^2 C\right)}{3 d^2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b) (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{(-b+i a) (A+i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}",1,"-(((I*a + b)*(A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f)) + ((I*a - b)*(A + I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) + (2*(b*c - a*d)*(c^2*C - B*c*d + A*d^2))/(3*d^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*(c^4*C - c^2*(A - 3*C)*d^2 - 2*B*c*d^3 + A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2))))/(d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,45,0.1333,1,"{3635, 3628, 3539, 3537, 63, 208}"
125,1,209,0,0.4860265,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 \left(A d^2-B c d+c^2 C\right)}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}","-\frac{2 \left(A d^2-B c d+c^2 C\right)}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(2*c*(A - C)*d - B*(c^2 - d^2)))/((c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,35,0.1714,1,"{3628, 3529, 3539, 3537, 63, 208}"
126,1,365,0,2.4657212,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{2 b^{3/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{5/2}}+\frac{2 \left(b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 \left(A d^2-B c d+c^2 C\right)}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{(A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{5/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b) (c+i d)^{5/2}}","-\frac{2 b^{3/2} \left(A b^2-a (b B-a C)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{5/2}}+\frac{2 \left(b \left(c^2 d^2 (3 A-C)+A d^4-2 B c^3 d+c^4 C\right)-a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 \left(A d^2-B c d+c^2 C\right)}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{(A-i B-C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{5/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b) (c+i d)^{5/2}}",1,"((A - I*B - C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)*(c - I*d)^(5/2)*f) + ((I*A - B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)*(c + I*d)^(5/2)*f) - (2*b^(3/2)*(A*b^2 - a*(b*B - a*C))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*(b*c - a*d)^(5/2)*f) + (2*(c^2*C - B*c*d + A*d^2))/(3*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(b*(c^4*C - 2*B*c^3*d + c^2*(3*A - C)*d^2 + A*d^4) - a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2))))/((b*c - a*d)^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",13,7,47,0.1489,1,"{3649, 3653, 3539, 3537, 63, 208, 3634}"
127,1,678,0,5.0616981,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{d \left(-A \left(-4 a^2 b d^2 \left(2 c^2+d^2\right)+4 a^3 c d^3+4 a b^2 c d^3+b^3 \left(-\left(10 c^2 d^2+c^4+5 d^4\right)\right)\right)+a^2 b \left(-6 B c^3 d-2 B c d^3+2 c^2 C d^2+5 c^4 C+C d^4\right)+2 a^3 d^2 \left(B c^2-B d^2+2 c C d\right)-a b^2 \left(B c^4+3 B d^4-4 c C d^3\right)+2 b^3 c \left(-3 B c^2 d-B d^3+2 c^3 C\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{d \left(2 a^2 A d^2+a^2 \left(-2 B c d+5 c^2 C+3 C d^2\right)-3 a b B \left(c^2+d^2\right)+A b^2 \left(3 c^2+5 d^2\right)+2 b^2 c (c C-B d)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{b^{3/2} \left(-a^2 b^2 (d (9 A+C)+2 B c)+7 a^3 b B d-5 a^4 C d+a b^3 (4 A c+3 B d-4 c C)+b^4 (2 B c-5 A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{7/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{5/2}}","-\frac{d \left(-A \left(-4 a^2 b d^2 \left(2 c^2+d^2\right)+4 a^3 c d^3+4 a b^2 c d^3+b^3 \left(-\left(10 c^2 d^2+c^4+5 d^4\right)\right)\right)+a^2 b \left(-6 B c^3 d-2 B c d^3+2 c^2 C d^2+5 c^4 C+C d^4\right)+2 a^3 d^2 \left(B c^2-B d^2+2 c C d\right)-a b^2 \left(B c^4+3 B d^4-4 c C d^3\right)+2 b^3 c \left(-3 B c^2 d-B d^3+2 c^3 C\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{d \left(A \left(2 a^2 d^2+b^2 \left(3 c^2+5 d^2\right)\right)+a^2 \left(-2 B c d+5 c^2 C+3 C d^2\right)-3 a b B \left(c^2+d^2\right)+2 b^2 c (c C-B d)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{A b^2-a (b B-a C)}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{b^{3/2} \left(-a^2 b^2 (d (9 A+C)+2 B c)+7 a^3 b B d-5 a^4 C d+a b^3 (4 A c+3 B d-4 c C)+b^4 (2 B c-5 A d)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{7/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{5/2}}",1,"-(((I*A + B - I*C)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*(c - I*d)^(5/2)*f)) - ((B - I*(A - C))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*(c + I*d)^(5/2)*f) - (b^(3/2)*(7*a^3*b*B*d - 5*a^4*C*d + b^4*(2*B*c - 5*A*d) + a*b^3*(4*A*c - 4*c*C + 3*B*d) - a^2*b^2*(2*B*c + (9*A + C)*d))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*(b*c - a*d)^(7/2)*f) - (d*(2*a^2*A*d^2 + 2*b^2*c*(c*C - B*d) - 3*a*b*B*(c^2 + d^2) + A*b^2*(3*c^2 + 5*d^2) + a^2*(5*c^2*C - 2*B*c*d + 3*C*d^2)))/(3*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (A*b^2 - a*(b*B - a*C))/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)) - (d*(2*a^3*d^2*(B*c^2 + 2*c*C*d - B*d^2) + 2*b^3*c*(2*c^3*C - 3*B*c^2*d - B*d^3) - a*b^2*(B*c^4 - 4*c*C*d^3 + 3*B*d^4) + a^2*b*(5*c^4*C - 6*B*c^3*d + 2*c^2*C*d^2 - 2*B*c*d^3 + C*d^4) - A*(4*a^3*c*d^3 + 4*a*b^2*c*d^3 - 4*a^2*b*d^2*(2*c^2 + d^2) - b^3*(c^4 + 10*c^2*d^2 + 5*d^4))))/((a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",14,7,47,0.1489,1,"{3649, 3653, 3539, 3537, 63, 208, 3634}"
128,1,679,0,9.9262706,"\int (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\left(30 a^2 b^2 d^2 \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)-20 a^3 b d^3 (2 B d+c C)+5 a^4 C d^4-20 a b^3 d \left(8 c d^2 (A-C)-2 B c^2 d-16 B d^3+c^3 C\right)+b^4 \left(16 c^2 d^2 (A-C)+128 d^4 (A-C)-8 B c^3 d+64 B c d^3+5 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{3/2} d^{7/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b d^3 \left(a^2 B+2 a b (A-C)-b^2 B\right)-(b c-a d) \left(16 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-8 b B d+5 b c C)\right)\right)}{64 b d^3 f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(16 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-8 b B d+5 b c C)\right)}{32 d^3 f}-\frac{(a-i b)^{5/2} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(a+i b)^{5/2} \sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-5 a C d-8 b B d+5 b c C) (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}{24 d^2 f}+\frac{C (a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}}{4 d f}","-\frac{\left(30 a^2 b^2 d^2 \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)-20 a^3 b d^3 (2 B d+c C)+5 a^4 C d^4-20 a b^3 d \left(8 c d^2 (A-C)-2 B c^2 d-16 B d^3+c^3 C\right)+b^4 \left(16 c^2 d^2 (A-C)+128 d^4 (A-C)-8 B c^3 d+64 B c d^3+5 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{3/2} d^{7/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b d^3 \left(a^2 B+2 a b (A-C)-b^2 B\right)-(b c-a d) \left(16 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-8 b B d+5 b c C)\right)\right)}{64 b d^3 f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(16 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-8 b B d+5 b c C)\right)}{32 d^3 f}-\frac{(a-i b)^{5/2} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(a+i b)^{5/2} \sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-5 a C d-8 b B d+5 b c C) (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}{24 d^2 f}+\frac{C (a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}}{4 d f}",1,"-(((a - I*b)^(5/2)*(I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) - ((a + I*b)^(5/2)*(B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f - ((5*a^4*C*d^4 - 20*a^3*b*d^3*(c*C + 2*B*d) + 30*a^2*b^2*d^2*(c^2*C - 4*B*c*d - 8*(A - C)*d^2) - 20*a*b^3*d*(c^3*C - 2*B*c^2*d + 8*c*(A - C)*d^2 - 16*B*d^3) + b^4*(5*c^4*C - 8*B*c^3*d + 16*c^2*(A - C)*d^2 + 64*B*c*d^3 + 128*(A - C)*d^4))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(64*b^(3/2)*d^(7/2)*f) + ((64*b*(a^2*B - b^2*B + 2*a*b*(A - C))*d^3 - (b*c - a*d)*(16*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(5*b*c*C - 8*b*B*d - 5*a*C*d)))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(64*b*d^3*f) + ((16*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(5*b*c*C - 8*b*B*d - 5*a*C*d))*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(32*d^3*f) - ((5*b*c*C - 8*b*B*d - 5*a*C*d)*(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2))/(24*d^2*f) + (C*(a + b*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2))/(4*d*f)","A",16,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
129,1,505,0,7.3378705,"\int (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\left(-3 a^2 b d^2 (2 B d+c C)+a^3 C d^3+3 a b^2 d \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)+b^3 \left(-\left(8 c d^2 (A-C)-2 B c^2 d-16 B d^3+c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{3/2} d^{5/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)+(b c-a d) (-a C d-2 b B d+b c C)\right)}{8 b d^2 f}-\frac{(a-i b)^{3/2} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{(a+i b)^{3/2} \sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-2 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{4 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}{3 d f}","-\frac{\left(-3 a^2 b d^2 (2 B d+c C)+a^3 C d^3+3 a b^2 d \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)+b^3 \left(-\left(8 c d^2 (A-C)-2 B c^2 d-16 B d^3+c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{3/2} d^{5/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)+(b c-a d) (-a C d-2 b B d+b c C)\right)}{8 b d^2 f}-\frac{(a-i b)^{3/2} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{(a+i b)^{3/2} \sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-2 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{4 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}{3 d f}",1,"-(((a - I*b)^(3/2)*(I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) + ((a + I*b)^(3/2)*(I*A - B - I*C)*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f - ((a^3*C*d^3 - 3*a^2*b*d^2*(c*C + 2*B*d) + 3*a*b^2*d*(c^2*C - 4*B*c*d - 8*(A - C)*d^2) - b^3*(c^3*C - 2*B*c^2*d + 8*c*(A - C)*d^2 - 16*B*d^3))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(8*b^(3/2)*d^(5/2)*f) + ((8*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(b*c*C - 2*b*B*d - a*C*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*b*d^2*f) - ((b*c*C - 2*b*B*d - a*C*d)*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(4*d^2*f) + (C*(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2))/(3*d*f)","A",15,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
130,1,383,0,4.9730477,"\int \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\left(a^2 C d^2-2 a b d (2 B d+c C)+b^2 \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{3/2} d^{3/2} f}-\frac{\sqrt{a-i b} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{a+i b} \sqrt{c+i d} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-4 b B d+b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}","-\frac{\left(a^2 C d^2-2 a b d (2 B d+c C)+b^2 \left(-8 d^2 (A-C)-4 B c d+c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{3/2} d^{3/2} f}-\frac{\sqrt{a-i b} \sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{\sqrt{a+i b} \sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-4 b B d+b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) + (Sqrt[a + I*b]*(I*A - B - I*C)*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f - ((a^2*C*d^2 - 2*a*b*d*(c*C + 2*B*d) + b^2*(c^2*C - 4*B*c*d - 8*(A - C)*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*b^(3/2)*d^(3/2)*f) - ((b*c*C - 4*b*B*d - a*C*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*b*d*f) + (C*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*d*f)","A",14,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
131,1,287,0,2.6333368,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[a + b*Tan[e + f*x]],x]","-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-a C d+2 b B d+b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} \sqrt{d} f}+\frac{C \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b f}","-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-a C d+2 b B d+b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} \sqrt{d} f}+\frac{C \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b f}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f)) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f) + ((b*c*C + 2*b*B*d - a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(3/2)*Sqrt[d]*f) + (C*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(b*f)","A",13,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
132,1,300,0,3.7959199,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(3/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}+\frac{2 C \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}+\frac{2 C \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f)) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) + (2*C*Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(3/2)*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(b*(a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",13,8,49,0.1633,1,"{3645, 3655, 6725, 63, 217, 206, 93, 208}"
133,1,370,0,2.0518554,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (5 A d+3 B c-7 C d)+2 a^3 b B d+a^4 C d+2 a b^3 (3 A c-2 B d-3 c C)+b^4 (A d+3 B c)\right)}{3 b f \left(a^2+b^2\right)^2 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (5 A d+3 B c-7 C d)+2 a^3 b B d+a^4 C d+2 a b^3 (3 A c-2 B d-3 c C)+b^4 (A d+3 B c)\right)}{3 b f \left(a^2+b^2\right)^2 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f)) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(3*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(2*a^3*b*B*d + a^4*C*d + b^4*(3*B*c + A*d) + 2*a*b^3*(3*A*c - 3*c*C - 2*B*d) - a^2*b^2*(3*B*c + 5*A*d - 7*C*d))*Sqrt[c + d*Tan[e + f*x]])/(3*b*(a^2 + b^2)^2*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]])","A",9,6,49,0.1224,1,"{3645, 3649, 3616, 3615, 93, 208}"
134,1,597,0,3.5885268,"\int \frac{\sqrt{c+d \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{7/2}} \, dx","Int[(Sqrt[c + d*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(7/2),x]","\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^3 b^3 \left(80 c d (A-C)+B \left(15 c^2-49 d^2\right)\right)-a^2 b^4 \left(45 A c^2-29 A d^2-90 B c d-45 c^2 C+23 C d^2\right)-a^4 b^2 d (33 A d+25 B c-39 C d)+8 a^5 b B d^2+2 a^6 C d^2-a b^5 \left(40 c d (A-C)+B \left(45 c^2-3 d^2\right)\right)-b^6 \left(5 c (B d+3 c C)-A \left(15 c^2+2 d^2\right)\right)\right)}{15 b f \left(a^2+b^2\right)^3 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (9 A d+5 B c-11 C d)+4 a^3 b B d+a^4 C d+2 a b^3 (5 A c-3 B d-5 c C)+b^4 (A d+5 B c)\right)}{15 b f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}","\frac{2 \sqrt{c+d \tan (e+f x)} \left(a^3 b^3 \left(80 c d (A-C)+B \left(15 c^2-49 d^2\right)\right)-a^2 b^4 \left(45 A c^2-29 A d^2-90 B c d-45 c^2 C+23 C d^2\right)-a^4 b^2 d (33 A d+25 B c-39 C d)+8 a^5 b B d^2+2 a^6 C d^2-a b^5 \left(40 c d (A-C)+B \left(45 c^2-3 d^2\right)\right)-b^6 \left(5 c (B d+3 c C)-A \left(15 c^2+2 d^2\right)\right)\right)}{15 b f \left(a^2+b^2\right)^3 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (9 A d+5 B c-11 C d)+4 a^3 b B d+a^4 C d+2 a b^3 (5 A c-3 B d-5 c C)+b^4 (A d+5 B c)\right)}{15 b f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{\sqrt{c-i d} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{\sqrt{c+i d} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}",1,"-(((I*A + B - I*C)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(7/2)*f)) - ((B - I*(A - C))*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(7/2)*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(5*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(5/2)) - (2*(4*a^3*b*B*d + a^4*C*d + b^4*(5*B*c + A*d) + 2*a*b^3*(5*A*c - 5*c*C - 3*B*d) - a^2*b^2*(5*B*c + 9*A*d - 11*C*d))*Sqrt[c + d*Tan[e + f*x]])/(15*b*(a^2 + b^2)^2*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)) + (2*(8*a^5*b*B*d^2 + 2*a^6*C*d^2 - a^4*b^2*d*(25*B*c + 33*A*d - 39*C*d) - a^2*b^4*(45*A*c^2 - 45*c^2*C - 90*B*c*d - 29*A*d^2 + 23*C*d^2) + a^3*b^3*(80*c*(A - C)*d + B*(15*c^2 - 49*d^2)) - a*b^5*(40*c*(A - C)*d + B*(45*c^2 - 3*d^2)) - b^6*(5*c*(3*c*C + B*d) - A*(15*c^2 + 2*d^2)))*Sqrt[c + d*Tan[e + f*x]])/(15*b*(a^2 + b^2)^3*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]])","A",10,6,49,0.1224,1,"{3645, 3649, 3616, 3615, 93, 208}"
135,1,682,0,11.8964721,"\int (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{\left(6 a^2 b^2 d^2 \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)-4 a^3 b d^3 (2 B d+3 c C)+3 a^4 C d^4-12 a b^3 d \left(-24 c d^2 (A-C)-6 B c^2 d+16 B d^3+c^3 C\right)+b^4 \left(48 c^2 d^2 (A-C)-128 d^4 (A-C)-8 B c^3 d-192 B c d^3+3 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{5/2} d^{5/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b d^3 \left(a^2 B+2 a b (A-C)-b^2 B\right)+(b c-a d) \left(48 b d^2 (a B+A b-b C)+(b c-a d) (-3 a C d-8 b B d+3 b c C)\right)\right)}{64 b^2 d^2 f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(48 b d^2 (a B+A b-b C)+(b c-a d) (-3 a C d-8 b B d+3 b c C)\right)}{96 b d^2 f}-\frac{(a-i b)^{3/2} (c-i d)^{3/2} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(a+i b)^{3/2} (c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-3 a C d-8 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}}{4 d f}","\frac{\left(6 a^2 b^2 d^2 \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)-4 a^3 b d^3 (2 B d+3 c C)+3 a^4 C d^4-12 a b^3 d \left(-24 c d^2 (A-C)-6 B c^2 d+16 B d^3+c^3 C\right)+b^4 \left(48 c^2 d^2 (A-C)-128 d^4 (A-C)-8 B c^3 d-192 B c d^3+3 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{5/2} d^{5/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b d^3 \left(a^2 B+2 a b (A-C)-b^2 B\right)+(b c-a d) \left(48 b d^2 (a B+A b-b C)+(b c-a d) (-3 a C d-8 b B d+3 b c C)\right)\right)}{64 b^2 d^2 f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(48 b d^2 (a B+A b-b C)+(b c-a d) (-3 a C d-8 b B d+3 b c C)\right)}{96 b d^2 f}-\frac{(a-i b)^{3/2} (c-i d)^{3/2} (B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(a+i b)^{3/2} (c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-3 a C d-8 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}}{4 d f}",1,"-(((a - I*b)^(3/2)*(B + I*(A - C))*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) - ((a + I*b)^(3/2)*(B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + ((3*a^4*C*d^4 - 4*a^3*b*d^3*(3*c*C + 2*B*d) + 6*a^2*b^2*d^2*(3*c^2*C + 12*B*c*d + 8*(A - C)*d^2) - 12*a*b^3*d*(c^3*C - 6*B*c^2*d - 24*c*(A - C)*d^2 + 16*B*d^3) + b^4*(3*c^4*C - 8*B*c^3*d + 48*c^2*(A - C)*d^2 - 192*B*c*d^3 - 128*(A - C)*d^4))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(64*b^(5/2)*d^(5/2)*f) + ((64*b*(a^2*B - b^2*B + 2*a*b*(A - C))*d^3 + (b*c - a*d)*(48*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(3*b*c*C - 8*b*B*d - 3*a*C*d)))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(64*b^2*d^2*f) + ((48*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(3*b*c*C - 8*b*B*d - 3*a*C*d))*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(96*b*d^2*f) - ((3*b*c*C - 8*b*B*d - 3*a*C*d)*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(24*d^2*f) + (C*(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2))/(4*d*f)","A",16,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
136,1,508,0,7.488246,"\int \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{\left(-a^2 b d^2 (2 B d+3 c C)+a^3 C d^3+a b^2 d \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)+b^3 \left(-\left(-24 c d^2 (A-C)-6 B c^2 d+16 B d^3+c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{5/2} d^{3/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)-(b c-a d) (-a C d-6 b B d+b c C)\right)}{8 b^2 d f}-\frac{\sqrt{a-i b} (c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{\sqrt{a+i b} (c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-6 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 d f}","\frac{\left(-a^2 b d^2 (2 B d+3 c C)+a^3 C d^3+a b^2 d \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)+b^3 \left(-\left(-24 c d^2 (A-C)-6 B c^2 d+16 B d^3+c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{5/2} d^{3/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)-(b c-a d) (-a C d-6 b B d+b c C)\right)}{8 b^2 d f}-\frac{\sqrt{a-i b} (c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{\sqrt{a+i b} (c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-6 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 d f}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) - (Sqrt[a + I*b]*(B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + ((a^3*C*d^3 - a^2*b*d^2*(3*c*C + 2*B*d) + a*b^2*d*(3*c^2*C + 12*B*c*d + 8*(A - C)*d^2) - b^3*(c^3*C - 6*B*c^2*d - 24*c*(A - C)*d^2 + 16*B*d^3))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(8*b^(5/2)*d^(3/2)*f) + ((8*b*(A*b + a*B - b*C)*d^2 - (b*c - a*d)*(b*c*C - 6*b*B*d - a*C*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*b^2*d*f) - ((b*c*C - 6*b*B*d - a*C*d)*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(12*b*d*f) + (C*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(3*d*f)","A",15,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
137,1,384,0,4.3106476,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[a + b*Tan[e + f*x]],x]","\frac{\left(3 a^2 C d^2-2 a b d (2 B d+3 c C)+b^2 \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{5/2} \sqrt{d} f}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{(c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-3 a C d+4 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b^2 f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 b f}","\frac{\left(3 a^2 C d^2-2 a b d (2 B d+3 c C)+b^2 \left(8 d^2 (A-C)+12 B c d+3 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{5/2} \sqrt{d} f}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{(c+i d)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-3 a C d+4 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b^2 f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 b f}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f)) + ((I*A - B - I*C)*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f) + ((3*a^2*C*d^2 - 2*a*b*d*(3*c*C + 2*B*d) + b^2*(3*c^2*C + 12*B*c*d + 8*(A - C)*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*b^(5/2)*Sqrt[d]*f) + ((3*b*c*C + 4*b*B*d - 3*a*C*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*b^2*f) + (C*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*b*f)","A",14,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
138,1,382,0,5.7386578,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(3/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{d \left(3 a^2 C-2 a b B+2 A b^2+b^2 C\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b^2 f \left(a^2+b^2\right)}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}+\frac{\sqrt{d} (-3 a C d+2 b B d+3 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{5/2} f}","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{d \left(3 a^2 C-2 a b B+2 A b^2+b^2 C\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b^2 f \left(a^2+b^2\right)}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}+\frac{\sqrt{d} (-3 a C d+2 b B d+3 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{5/2} f}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f)) - ((B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) + (Sqrt[d]*(3*b*c*C + 2*b*B*d - 3*a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(5/2)*f) + ((2*A*b^2 - 2*a*b*B + 3*a^2*C + b^2*C)*d*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(b^2*(a^2 + b^2)*f) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(3/2))/(b*(a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",14,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
139,1,402,0,7.1273194,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{b^2 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}+\frac{2 C d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{5/2} f}","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{b^2 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}+\frac{2 C d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{5/2} f}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f)) - ((B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) + (2*C*d^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(5/2)*f) - (2*(a^4*C*d + b^4*(B*c + A*d) + 2*a*b^3*(A*c - c*C - B*d) - a^2*b^2*(B*c + (A - 3*C)*d))*Sqrt[c + d*Tan[e + f*x]])/(b^2*(a^2 + b^2)^2*f*Sqrt[a + b*Tan[e + f*x]]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(3/2))/(3*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2))","A",14,8,49,0.1633,1,"{3645, 3655, 6725, 63, 217, 206, 93, 208}"
140,1,586,0,3.6680566,"\int \frac{(c+d \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{7/2}} \, dx","Int[((c + d*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(7/2),x]","-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^3 b^3 \left(50 c d (A-C)+B \left(15 c^2-39 d^2\right)\right)+a^2 b^4 \left(45 A c^2-49 A d^2-90 B c d-45 c^2 C+58 C d^2\right)+a^4 b^2 d (d (8 A+C)+10 B c)+2 a^5 b B d^2+3 a^6 C d^2+a b^5 \left(70 c d (A-C)+B \left(45 c^2-23 d^2\right)\right)+b^6 \left(5 c (4 B d+3 c C)-3 A \left(5 c^2-d^2\right)\right)\right)}{15 b^2 f \left(a^2+b^2\right)^3 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (7 A d+5 B c-13 C d)+2 a^3 b B d+3 a^4 C d+2 a b^3 (5 A c-4 B d-5 c C)+b^4 (3 A d+5 B c)\right)}{15 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}","-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^3 b^3 \left(50 c d (A-C)+B \left(15 c^2-39 d^2\right)\right)+a^2 b^4 \left(45 A c^2-49 A d^2-90 B c d-45 c^2 C+58 C d^2\right)+a^4 b^2 d (d (8 A+C)+10 B c)+2 a^5 b B d^2+3 a^6 C d^2+a b^5 \left(70 c d (A-C)+B \left(45 c^2-23 d^2\right)\right)+b^6 \left(5 c (4 B d+3 c C)-3 A \left(5 c^2-d^2\right)\right)\right)}{15 b^2 f \left(a^2+b^2\right)^3 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{3/2}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (7 A d+5 B c-13 C d)+2 a^3 b B d+3 a^4 C d+2 a b^3 (5 A c-4 B d-5 c C)+b^4 (3 A d+5 B c)\right)}{15 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{(c-i d)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{(c+i d)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}",1,"-(((I*A + B - I*C)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(7/2)*f)) - ((B - I*(A - C))*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(7/2)*f) - (2*(2*a^3*b*B*d + 3*a^4*C*d + b^4*(5*B*c + 3*A*d) + 2*a*b^3*(5*A*c - 5*c*C - 4*B*d) - a^2*b^2*(5*B*c + 7*A*d - 13*C*d))*Sqrt[c + d*Tan[e + f*x]])/(15*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(2*a^5*b*B*d^2 + 3*a^6*C*d^2 + a^4*b^2*d*(10*B*c + (8*A + C)*d) + a^2*b^4*(45*A*c^2 - 45*c^2*C - 90*B*c*d - 49*A*d^2 + 58*C*d^2) - a^3*b^3*(50*c*(A - C)*d + B*(15*c^2 - 39*d^2)) + a*b^5*(70*c*(A - C)*d + B*(45*c^2 - 23*d^2)) + b^6*(5*c*(3*c*C + 4*B*d) - 3*A*(5*c^2 - d^2)))*Sqrt[c + d*Tan[e + f*x]])/(15*b^2*(a^2 + b^2)^3*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(3/2))/(5*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(5/2))","A",10,6,49,0.1224,1,"{3645, 3649, 3616, 3615, 93, 208}"
141,1,697,0,10.4159224,"\int \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{\left(2 a^2 b^2 d^2 \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)-4 a^3 b d^3 (2 B d+5 c C)+5 a^4 C d^4-4 a b^3 d \left(40 c d^2 (A-C)+30 B c^2 d-16 B d^3+5 c^3 C\right)+b^4 \left(-240 c^2 d^2 (A-C)+128 d^4 (A-C)-40 B c^3 d+320 B c d^3+5 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{7/2} d^{3/2} f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(48 b d^2 (a B+A b-b C)-5 (b c-a d) (-a C d-8 b B d+b c C)\right)}{96 b^2 d f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b^2 d^2 (a A d+a B c-a C d+A b c-b B d-b c C)+(b c-a d) \left(48 b d^2 (a B+A b-b C)-5 (b c-a d) (-a C d-8 b B d+b c C)\right)\right)}{64 b^3 d f}-\frac{\sqrt{a-i b} (c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{a+i b} (c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-8 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{7/2}}{4 d f}","-\frac{\left(2 a^2 b^2 d^2 \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)-4 a^3 b d^3 (2 B d+5 c C)+5 a^4 C d^4-4 a b^3 d \left(40 c d^2 (A-C)+30 B c^2 d-16 B d^3+5 c^3 C\right)+b^4 \left(-240 c^2 d^2 (A-C)+128 d^4 (A-C)-40 B c^3 d+320 B c d^3+5 c^4 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{64 b^{7/2} d^{3/2} f}+\frac{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \left(48 b d^2 (a B+A b-b C)-5 (b c-a d) (-a C d-8 b B d+b c C)\right)}{96 b^2 d f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(64 b^2 d^2 (a A d+a B c-a C d+A b c-b B d-b c C)+(b c-a d) \left(48 b d^2 (a B+A b-b C)-5 (b c-a d) (-a C d-8 b B d+b c C)\right)\right)}{64 b^3 d f}-\frac{\sqrt{a-i b} (c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{a+i b} (c+i d)^{5/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{(-a C d-8 b B d+b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 b d f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{7/2}}{4 d f}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f) + (Sqrt[a + I*b]*(I*A - B - I*C)*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f - ((5*a^4*C*d^4 - 4*a^3*b*d^3*(5*c*C + 2*B*d) + 2*a^2*b^2*d^2*(15*c^2*C + 20*B*c*d + 8*(A - C)*d^2) - 4*a*b^3*d*(5*c^3*C + 30*B*c^2*d + 40*c*(A - C)*d^2 - 16*B*d^3) + b^4*(5*c^4*C - 40*B*c^3*d - 240*c^2*(A - C)*d^2 + 320*B*c*d^3 + 128*(A - C)*d^4))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(64*b^(7/2)*d^(3/2)*f) + ((64*b^2*d^2*(A*b*c + a*B*c - b*c*C + a*A*d - b*B*d - a*C*d) + (b*c - a*d)*(48*b*(A*b + a*B - b*C)*d^2 - 5*(b*c - a*d)*(b*c*C - 8*b*B*d - a*C*d)))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(64*b^3*d*f) + ((48*b*(A*b + a*B - b*C)*d^2 - 5*(b*c - a*d)*(b*c*C - 8*b*B*d - a*C*d))*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(96*b^2*d*f) - ((b*c*C - 8*b*B*d - a*C*d)*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(24*b*d*f) + (C*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(7/2))/(4*d*f)","A",16,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
142,1,505,0,6.2303166,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[a + b*Tan[e + f*x]],x]","-\frac{\left(-3 a^2 b d^2 (2 B d+5 c C)+5 a^3 C d^3+a b^2 d \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)+b^3 \left(-\left(40 c d^2 (A-C)+30 B c^2 d-16 B d^3+5 c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{7/2} \sqrt{d} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left((b c-a d) (-5 a C d+6 b B d+5 b c C)+8 b^2 d (d (A-C)+B c)\right)}{8 b^3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-5 a C d+6 b B d+5 b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 b^2 f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 b f}","-\frac{\left(-3 a^2 b d^2 (2 B d+5 c C)+5 a^3 C d^3+a b^2 d \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)+b^3 \left(-\left(40 c d^2 (A-C)+30 B c^2 d-16 B d^3+5 c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{7/2} \sqrt{d} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left((b c-a d) (-5 a C d+6 b B d+5 b c C)+8 b^2 d (d (A-C)+B c)\right)}{8 b^3 f}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}+\frac{(-5 a C d+6 b B d+5 b c C) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 b^2 f}+\frac{C \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 b f}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f) - ((5*a^3*C*d^3 - 3*a^2*b*d^2*(5*c*C + 2*B*d) + a*b^2*d*(15*c^2*C + 20*B*c*d + 8*(A - C)*d^2) - b^3*(5*c^3*C + 30*B*c^2*d + 40*c*(A - C)*d^2 - 16*B*d^3))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(8*b^(7/2)*Sqrt[d]*f) + ((8*b^2*d*(B*c + (A - C)*d) + (b*c - a*d)*(5*b*c*C + 6*b*B*d - 5*a*C*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*b^3*f) + ((5*b*c*C + 6*b*B*d - 5*a*C*d)*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(12*b^2*f) + (C*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(3*b*f)","A",15,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
143,1,535,0,8.3138421,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(3/2),x]","\frac{\sqrt{d} \left(15 a^2 C d^2-6 a b d (2 B d+5 c C)+b^2 \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{7/2} f}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{d \left(5 a^2 C-4 a b B+4 A b^2+b^2 C\right) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 b^2 f \left(a^2+b^2\right)}-\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(-3 a^2 b (4 B d+5 c C)+15 a^3 C d-8 A b^2 (b c-a d)+a b^2 (8 B c+7 C d)-b^3 (4 B d+7 c C)\right)}{4 b^3 f \left(a^2+b^2\right)}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}","\frac{\sqrt{d} \left(15 a^2 C d^2-6 a b d (2 B d+5 c C)+b^2 \left(8 d^2 (A-C)+20 B c d+15 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{7/2} f}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{d \left(5 a^2 C-4 a b B+4 A b^2+b^2 C\right) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 b^2 f \left(a^2+b^2\right)}-\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(-3 a^2 b (4 B d+5 c C)+15 a^3 C d-8 A b^2 (b c-a d)+a b^2 (8 B c+7 C d)-b^3 (4 B d+7 c C)\right)}{4 b^3 f \left(a^2+b^2\right)}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) + (Sqrt[d]*(15*a^2*C*d^2 - 6*a*b*d*(5*c*C + 2*B*d) + b^2*(15*c^2*C + 20*B*c*d + 8*(A - C)*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*b^(7/2)*f) - (d*(15*a^3*C*d - 8*A*b^2*(b*c - a*d) - 3*a^2*b*(5*c*C + 4*B*d) - b^3*(7*c*C + 4*B*d) + a*b^2*(8*B*c + 7*C*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*b^3*(a^2 + b^2)*f) + ((4*A*b^2 - 4*a*b*B + 5*a^2*C + b^2*C)*d*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*b^2*(a^2 + b^2)*f) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(b*(a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",15,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
144,1,545,0,11.0661627,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}+\frac{2 (c+d \tan (e+f x))^{3/2} \left(a^2 b^2 (d (A-11 C)+3 B c)+2 a^3 b B d-5 a^4 C d-2 a b^3 (3 A c-4 B d-3 c C)-b^4 (5 A d+3 B c)\right)}{3 b^2 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(2 a^2 b^2 (B c-5 C d)+2 a^3 b B d-5 a^4 C d-2 a b^3 (2 A c-3 B d-2 c C)-b^4 (d (4 A+C)+2 B c)\right)}{b^3 f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}+\frac{d^{3/2} (-5 a C d+2 b B d+5 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{7/2} f}","-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}+\frac{2 (c+d \tan (e+f x))^{3/2} \left(a^2 b^2 (d (A-11 C)+3 B c)+2 a^3 b B d-5 a^4 C d-2 a b^3 (3 A c-4 B d-3 c C)-b^4 (5 A d+3 B c)\right)}{3 b^2 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(2 a^2 b^2 (B c-5 C d)+2 a^3 b B d-5 a^4 C d-2 a b^3 (2 A c-3 B d-2 c C)-b^4 (d (4 A+C)+2 B c)\right)}{b^3 f \left(a^2+b^2\right)^2}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}+\frac{d^{3/2} (-5 a C d+2 b B d+5 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{7/2} f}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) + (d^(3/2)*(5*b*c*C + 2*b*B*d - 5*a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(7/2)*f) - (d*(2*a^3*b*B*d - 5*a^4*C*d - 2*a*b^3*(2*A*c - 2*c*C - 3*B*d) + 2*a^2*b^2*(B*c - 5*C*d) - b^4*(2*B*c + (4*A + C)*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(b^3*(a^2 + b^2)^2*f) + (2*(2*a^3*b*B*d - 5*a^4*C*d - b^4*(3*B*c + 5*A*d) - 2*a*b^3*(3*A*c - 3*c*C - 4*B*d) + a^2*b^2*(3*B*c + (A - 11*C)*d))*(c + d*Tan[e + f*x])^(3/2))/(3*b^2*(a^2 + b^2)^2*f*Sqrt[a + b*Tan[e + f*x]]) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(3*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2))","A",15,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
145,1,590,0,14.0201485,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{7/2}} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(7/2),x]","-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^3 b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-2 C d^2\right)+3 a^4 b^2 C d^2+a^6 C d^2+3 a b^5 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+b^6 \left(c (2 B d+c C)-A \left(c^2-d^2\right)\right)\right)}{b^3 f \left(a^2+b^2\right)^3 \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 (c+d \tan (e+f x))^{3/2} \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{3 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}+\frac{2 C d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{7/2} f}","-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^3 b^3 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-3 a^2 b^4 \left(-A \left(c^2-d^2\right)+2 B c d+c^2 C-2 C d^2\right)+3 a^4 b^2 C d^2+a^6 C d^2+3 a b^5 \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)+b^6 \left(c (2 B d+c C)-A \left(c^2-d^2\right)\right)\right)}{b^3 f \left(a^2+b^2\right)^3 \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{2 (c+d \tan (e+f x))^{3/2} \left(-a^2 b^2 (d (A-3 C)+B c)+a^4 C d+2 a b^3 (A c-B d-c C)+b^4 (A d+B c)\right)}{3 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{(c-i d)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}-\frac{(c+i d)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}+\frac{2 C d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{7/2} f}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(7/2)*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(7/2)*f) + (2*C*d^(5/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(7/2)*f) - (2*(a^6*C*d^2 + 3*a^4*b^2*C*d^2 - 3*a^2*b^4*(c^2*C + 2*B*c*d - 2*C*d^2 - A*(c^2 - d^2)) + b^6*(c*(c*C + 2*B*d) - A*(c^2 - d^2)) - a^3*b^3*(2*c*(A - C)*d + B*(c^2 - d^2)) + 3*a*b^5*(2*c*(A - C)*d + B*(c^2 - d^2)))*Sqrt[c + d*Tan[e + f*x]])/(b^3*(a^2 + b^2)^3*f*Sqrt[a + b*Tan[e + f*x]]) - (2*(a^4*C*d + b^4*(B*c + A*d) + 2*a*b^3*(A*c - c*C - B*d) - a^2*b^2*(B*c + (A - 3*C)*d))*(c + d*Tan[e + f*x])^(3/2))/(3*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(5*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(5/2))","A",15,8,49,0.1633,1,"{3645, 3655, 6725, 63, 217, 206, 93, 208}"
146,1,946,0,6.464192,"\int \frac{(c+d \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(a+b \tan (e+f x))^{9/2}} \, dx","Int[((c + d*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(a + b*Tan[e + f*x])^(9/2),x]","-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right) (c-i d)^{5/2}}{(a-i b)^{9/2} f}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{7 b \left(a^2+b^2\right) f (a+b \tan (e+f x))^{7/2}}-\frac{2 \left(5 C d a^4+2 b B d a^3-b^2 (7 B c+9 A d-19 C d) a^2+2 b^3 (7 A c-7 C c-6 B d) a+b^4 (7 B c+5 A d)\right) (c+d \tan (e+f x))^{3/2}}{35 b^2 \left(a^2+b^2\right)^2 f (a+b \tan (e+f x))^{5/2}}-\frac{(B-i (A-C)) (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{(a+i b)^{9/2} f}-\frac{2 \left(15 C d^3 a^8+6 b B d^3 a^7+2 b^2 d^2 (7 B c+4 A d+26 C d) a^6+2 b^3 d \left(56 c (A-C) d+B \left(35 c^2-12 d^2\right)\right) a^5-b^4 \left(105 B c^3+525 A d c^2-525 C d c^2-749 B d^2 c-311 A d^3+221 C d^3\right) a^4-2 b^5 \left(210 C c^3+700 B d c^2-798 C d^2 c-317 B d^3-42 A \left(5 c^3-19 c d^2\right)\right) a^3+2 b^6 \left(315 B c^3+875 A d c^2-875 C d c^2-812 B d^2 c-261 A d^3+291 C d^3\right) a^2-2 b^7 \left(210 A c^3-210 C c^3-525 B d c^2-406 A d^2 c+406 C d^2 c+88 B d^3\right) a-b^8 \left(5 d \left(49 A c^2-49 C c^2-3 A d^2\right)+7 B \left(15 c^3-23 c d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{105 b^3 \left(a^2+b^2\right)^4 (b c-a d) f \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(15 C d^2 a^6+6 b B d^2 a^5+b^2 d (14 B c+8 A d+37 C d) a^4-b^3 \left(98 c (A-C) d+B \left(35 c^2-75 d^2\right)\right) a^3+3 b^4 \left(35 A c^2-35 C c^2-70 B d c-39 A d^2+54 C d^2\right) a^2+b^5 \left(182 c (A-C) d+B \left(105 c^2-71 d^2\right)\right) a+b^6 \left(7 c (5 c C+8 B d)-5 A \left(7 c^2-3 d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{105 b^3 \left(a^2+b^2\right)^3 f (a+b \tan (e+f x))^{3/2}}","-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right) (c-i d)^{5/2}}{(a-i b)^{9/2} f}-\frac{2 \left(A b^2-a (b B-a C)\right) (c+d \tan (e+f x))^{5/2}}{7 b \left(a^2+b^2\right) f (a+b \tan (e+f x))^{7/2}}-\frac{2 \left(5 C d a^4+2 b B d a^3-b^2 (7 B c+9 A d-19 C d) a^2+2 b^3 (7 A c-7 C c-6 B d) a+b^4 (7 B c+5 A d)\right) (c+d \tan (e+f x))^{3/2}}{35 b^2 \left(a^2+b^2\right)^2 f (a+b \tan (e+f x))^{5/2}}-\frac{(B-i (A-C)) (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{(a+i b)^{9/2} f}-\frac{2 \left(15 C d^3 a^8+6 b B d^3 a^7+2 b^2 d^2 (7 B c+4 A d+26 C d) a^6+2 b^3 d \left(56 c (A-C) d+B \left(35 c^2-12 d^2\right)\right) a^5-b^4 \left(105 B c^3+525 A d c^2-525 C d c^2-749 B d^2 c-311 A d^3+221 C d^3\right) a^4-2 b^5 \left(210 C c^3+700 B d c^2-798 C d^2 c-317 B d^3-42 A \left(5 c^3-19 c d^2\right)\right) a^3+2 b^6 \left(315 B c^3+875 A d c^2-875 C d c^2-812 B d^2 c-261 A d^3+291 C d^3\right) a^2-2 b^7 \left(210 A c^3-210 C c^3-525 B d c^2-406 A d^2 c+406 C d^2 c+88 B d^3\right) a-b^8 \left(5 d \left(49 A c^2-49 C c^2-3 A d^2\right)+7 B \left(15 c^3-23 c d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{105 b^3 \left(a^2+b^2\right)^4 (b c-a d) f \sqrt{a+b \tan (e+f x)}}-\frac{2 \left(15 C d^2 a^6+6 b B d^2 a^5+b^2 d (14 B c+8 A d+37 C d) a^4-b^3 \left(98 c (A-C) d+B \left(35 c^2-75 d^2\right)\right) a^3+3 b^4 \left(35 A c^2-35 C c^2-70 B d c-39 A d^2+54 C d^2\right) a^2+b^5 \left(182 c (A-C) d+B \left(105 c^2-71 d^2\right)\right) a+b^6 \left(7 c (5 c C+8 B d)-5 A \left(7 c^2-3 d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{105 b^3 \left(a^2+b^2\right)^3 f (a+b \tan (e+f x))^{3/2}}",1,"-(((I*A + B - I*C)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(9/2)*f)) - ((B - I*(A - C))*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(9/2)*f) - (2*(6*a^5*b*B*d^2 + 15*a^6*C*d^2 + a^4*b^2*d*(14*B*c + 8*A*d + 37*C*d) + 3*a^2*b^4*(35*A*c^2 - 35*c^2*C - 70*B*c*d - 39*A*d^2 + 54*C*d^2) - a^3*b^3*(98*c*(A - C)*d + B*(35*c^2 - 75*d^2)) + a*b^5*(182*c*(A - C)*d + B*(105*c^2 - 71*d^2)) + b^6*(7*c*(5*c*C + 8*B*d) - 5*A*(7*c^2 - 3*d^2)))*Sqrt[c + d*Tan[e + f*x]])/(105*b^3*(a^2 + b^2)^3*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(6*a^7*b*B*d^3 + 15*a^8*C*d^3 + 2*a^6*b^2*d^2*(7*B*c + 4*A*d + 26*C*d) - 2*a*b^7*(210*A*c^3 - 210*c^3*C - 525*B*c^2*d - 406*A*c*d^2 + 406*c*C*d^2 + 88*B*d^3) - a^4*b^4*(105*B*c^3 + 525*A*c^2*d - 525*c^2*C*d - 749*B*c*d^2 - 311*A*d^3 + 221*C*d^3) + 2*a^2*b^6*(315*B*c^3 + 875*A*c^2*d - 875*c^2*C*d - 812*B*c*d^2 - 261*A*d^3 + 291*C*d^3) + 2*a^5*b^3*d*(56*c*(A - C)*d + B*(35*c^2 - 12*d^2)) - b^8*(5*d*(49*A*c^2 - 49*c^2*C - 3*A*d^2) + 7*B*(15*c^3 - 23*c*d^2)) - 2*a^3*b^5*(210*c^3*C + 700*B*c^2*d - 798*c*C*d^2 - 317*B*d^3 - 42*A*(5*c^3 - 19*c*d^2)))*Sqrt[c + d*Tan[e + f*x]])/(105*b^3*(a^2 + b^2)^4*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]) - (2*(2*a^3*b*B*d + 5*a^4*C*d + b^4*(7*B*c + 5*A*d) + 2*a*b^3*(7*A*c - 7*c*C - 6*B*d) - a^2*b^2*(7*B*c + 9*A*d - 19*C*d))*(c + d*Tan[e + f*x])^(3/2))/(35*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])^(5/2)) - (2*(A*b^2 - a*(b*B - a*C))*(c + d*Tan[e + f*x])^(5/2))/(7*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(7/2))","A",11,6,49,0.1224,1,"{3645, 3649, 3616, 3615, 93, 208}"
147,1,505,0,5.9530081,"\int \frac{(a+b \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[((a + b*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","\frac{\left(-15 a^2 b d^2 (c C-2 B d)+5 a^3 C d^3+5 a b^2 d \left(8 d^2 (A-C)-4 B c d+3 c^2 C\right)+b^3 \left(-\left(8 c d^2 (A-C)-6 B c^2 d+16 B d^3+5 c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 \sqrt{b} d^{7/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-6 b B d+5 b c C)\right)}{8 d^3 f}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-5 a C d-6 b B d+5 b c C) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{12 d^2 f}+\frac{C (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}{3 d f}","\frac{\left(-15 a^2 b d^2 (c C-2 B d)+5 a^3 C d^3+5 a b^2 d \left(8 d^2 (A-C)-4 B c d+3 c^2 C\right)+b^3 \left(-\left(8 c d^2 (A-C)-6 B c^2 d+16 B d^3+5 c^3 C\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 \sqrt{b} d^{7/2} f}+\frac{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(8 b d^2 (a B+A b-b C)+(b c-a d) (-5 a C d-6 b B d+5 b c C)\right)}{8 d^3 f}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-5 a C d-6 b B d+5 b c C) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{12 d^2 f}+\frac{C (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}{3 d f}",1,"-(((a - I*b)^(5/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f)) - ((a + I*b)^(5/2)*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f) + ((5*a^3*C*d^3 - 15*a^2*b*d^2*(c*C - 2*B*d) + 5*a*b^2*d*(3*c^2*C - 4*B*c*d + 8*(A - C)*d^2) - b^3*(5*c^3*C - 6*B*c^2*d + 8*c*(A - C)*d^2 + 16*B*d^3))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(8*Sqrt[b]*d^(7/2)*f) + ((8*b*(A*b + a*B - b*C)*d^2 + (b*c - a*d)*(5*b*c*C - 6*b*B*d - 5*a*C*d))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*d^3*f) - ((5*b*c*C - 6*b*B*d - 5*a*C*d)*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]])/(12*d^2*f) + (C*(a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]])/(3*d*f)","A",15,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
148,1,383,0,4.0766663,"\int \frac{(a+b \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[((a + b*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","\frac{\left(3 a^2 C d^2-6 a b d (c C-2 B d)+b^2 \left(8 d^2 (A-C)-4 B c d+3 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{b} d^{5/2} f}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{(a+i b)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-3 a C d-4 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 d f}","\frac{\left(3 a^2 C d^2-6 a b d (c C-2 B d)+b^2 \left(8 d^2 (A-C)-4 B c d+3 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{b} d^{5/2} f}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{(a+i b)^{3/2} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-3 a C d-4 b B d+3 b c C) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d^2 f}+\frac{C (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 d f}",1,"-(((a - I*b)^(3/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f)) + ((a + I*b)^(3/2)*(I*A - B - I*C)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f) + ((3*a^2*C*d^2 - 6*a*b*d*(c*C - 2*B*d) + b^2*(3*c^2*C - 4*B*c*d + 8*(A - C)*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*Sqrt[b]*d^(5/2)*f) - ((3*b*c*C - 4*b*B*d - 3*a*C*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*d^2*f) + (C*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]])/(2*d*f)","A",14,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
149,1,290,0,2.5549088,"\int \frac{\sqrt{a+b \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(Sqrt[a + b*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{\sqrt{a+i b} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-a C d-2 b B d+b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} d^{3/2} f}+\frac{C \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}","-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{\sqrt{a+i b} (i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{(-a C d-2 b B d+b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} d^{3/2} f}+\frac{C \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f)) + (Sqrt[a + I*b]*(I*A - B - I*C)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f) - ((b*c*C - 2*b*B*d - a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[b]*d^(3/2)*f) + (C*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",13,8,49,0.1633,1,"{3647, 3655, 6725, 63, 217, 206, 93, 208}"
150,1,239,0,1.4568805,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} \sqrt{c-i d}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} \sqrt{c+i d}}+\frac{2 C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} \sqrt{d} f}","-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} \sqrt{c-i d}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} \sqrt{c+i d}}+\frac{2 C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} \sqrt{d} f}",1,"-(((B + I*(A - C))*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*Sqrt[c - I*d]*f)) + ((I*A - B - I*C)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*Sqrt[c + I*d]*f) + (2*C*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[b]*Sqrt[d]*f)","A",12,7,49,0.1429,1,"{3655, 6725, 63, 217, 206, 93, 208}"
151,1,251,0,0.96859,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} \sqrt{c+i d}}","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} \sqrt{c+i d}}",1,"-(((I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*Sqrt[c - I*d]*f)) - ((B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*Sqrt[c + I*d]*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]])","A",8,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
152,1,375,0,1.7653019,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (8 A d+3 B c-4 C d)+5 a^3 b B d-2 a^4 C d+a b^3 (6 A c-B d-6 c C)+b^4 (3 B c-2 A d)\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} \sqrt{c+i d}}","-\frac{2 \left(A b^2-a (b B-a C)\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{2 \sqrt{c+d \tan (e+f x)} \left(-a^2 b^2 (8 A d+3 B c-4 C d)+5 a^3 b B d-2 a^4 C d+a b^3 (6 A c-B d-6 c C)+b^4 (3 B c-2 A d)\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} \sqrt{c-i d}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} \sqrt{c+i d}}",1,"-(((I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*Sqrt[c - I*d]*f)) - ((B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*Sqrt[c + I*d]*f) - (2*(A*b^2 - a*(b*B - a*C))*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(5*a^3*b*B*d - 2*a^4*C*d + b^4*(3*B*c - 2*A*d) + a*b^3*(6*A*c - 6*c*C - B*d) - a^2*b^2*(3*B*c + 8*A*d - 4*C*d))*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]])","A",9,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
153,1,528,0,8.1883198,"\int \frac{(a+b \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[((a + b*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","\frac{\sqrt{b} \left(15 a^2 C d^2-10 a b d (3 c C-2 B d)+b^2 \left(8 d^2 (A-C)-12 B c d+15 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{7/2} f}+\frac{b \left(d^2 (4 A+C)-4 B c d+5 c^2 C\right) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 d^2 f \left(c^2+d^2\right)}-\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(3 (b c-a d) \left(d^2 (4 A+C)-4 B c d+5 c^2 C\right)-4 d^2 ((A-C) (b c-a d)+B (a c+b d))\right)}{4 d^3 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{5/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}","\frac{\sqrt{b} \left(15 a^2 C d^2-10 a b d (3 c C-2 B d)+b^2 \left(8 d^2 (A-C)-12 B c d+15 c^2 C\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{7/2} f}+\frac{b \left(d^2 (4 A+C)-4 B c d+5 c^2 C\right) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 d^2 f \left(c^2+d^2\right)}-\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(3 (b c-a d) \left(d^2 (4 A+C)-4 B c d+5 c^2 C\right)-4 d^2 ((A-C) (b c-a d)+B (a c+b d))\right)}{4 d^3 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{5/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}",1,"-(((a - I*b)^(5/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f)) - ((a + I*b)^(5/2)*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) + (Sqrt[b]*(15*a^2*C*d^2 - 10*a*b*d*(3*c*C - 2*B*d) + b^2*(15*c^2*C - 12*B*c*d + 8*(A - C)*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*d^(7/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(5/2))/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - (b*(3*(b*c - a*d)*(5*c^2*C - 4*B*c*d + (4*A + C)*d^2) - 4*d^2*((A - C)*(b*c - a*d) + B*(a*c + b*d)))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*d^3*(c^2 + d^2)*f) + (b*(5*c^2*C - 4*B*c*d + (4*A + C)*d^2)*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]])/(2*d^2*(c^2 + d^2)*f)","A",15,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
154,1,380,0,5.6273278,"\int \frac{(a+b \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[((a + b*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","\frac{b \left(d^2 (2 A+C)-2 B c d+3 c^2 C\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{3/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}-\frac{\sqrt{b} (-3 a C d-2 b B d+3 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}","\frac{b \left(d^2 (2 A+C)-2 B c d+3 c^2 C\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{3/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{(a+i b)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}-\frac{\sqrt{b} (-3 a C d-2 b B d+3 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}",1,"-(((a - I*b)^(3/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f)) - ((a + I*b)^(3/2)*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) - (Sqrt[b]*(3*b*c*C - 2*b*B*d - 3*a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(3/2))/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) + (b*(3*c^2*C - 2*B*c*d + (2*A + C)*d^2)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)*f)","A",14,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
155,1,299,0,3.3331108,"\int \frac{\sqrt{a+b \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(Sqrt[a + b*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{\sqrt{a+i b} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}+\frac{2 \sqrt{b} C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}","-\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{\sqrt{a+i b} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}+\frac{2 \sqrt{b} C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f)) - (Sqrt[a + I*b]*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) + (2*Sqrt[b]*C*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(3/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*Sqrt[a + b*Tan[e + f*x]])/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",13,8,49,0.1633,1,"{3645, 3655, 6725, 63, 217, 206, 93, 208}"
156,1,251,0,1.0007943,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{3/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{3/2}}","\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{3/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{3/2}}",1,"-(((B + I*(A - C))*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*(c - I*d)^(3/2)*f)) + ((I*A - B - I*C)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*(c + I*d)^(3/2)*f) + (2*(c^2*C - B*c*d + A*d^2)*Sqrt[a + b*Tan[e + f*x]])/((b*c - a*d)*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
157,1,382,0,1.8775749,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(a^2 A d^2+a^2 \left(-B c d+2 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+A b^2 \left(c^2+2 d^2\right)+b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{3/2}}","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(A \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right)+a^2 \left(-B c d+2 c^2 C+C d^2\right)-a b B \left(c^2+d^2\right)+b^2 c (c C-B d)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{3/2}}",1,"-(((I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*(c - I*d)^(3/2)*f)) - ((B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*(c + I*d)^(3/2)*f) - (2*(A*b^2 - a*(b*B - a*C)))/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) - (2*d*(a^2*A*d^2 + b^2*c*(c*C - B*d) - a*b*B*(c^2 + d^2) + A*b^2*(c^2 + 2*d^2) + a^2*(2*c^2*C - B*c*d + C*d^2))*Sqrt[a + b*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",9,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
158,1,598,0,3.4346499,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(-a^2 b^2 \left(11 A c^2 d+17 A d^3+3 B c^3-3 B c d^2+5 c^2 C d-C d^3\right)+a^4 (-d) \left(d^2 (3 A+5 C)-3 B c d+8 c^2 C\right)+8 a^3 b B d \left(c^2+d^2\right)+2 a b^3 \left(c^2+d^2\right) (3 A c+B d-3 c C)-b^4 \left(d \left(5 A c^2+8 A d^2+3 c^2 C\right)-3 B \left(c^3+2 c d^2\right)\right)\right)}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(-a^2 b^2 (2 d (5 A-C)+3 B c)+7 a^3 b B d-4 a^4 C d+a b^3 (6 A c+B d-6 c C)+b^4 (3 B c-4 A d)\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{3/2}}","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(-a^2 b^2 \left(11 A c^2 d+17 A d^3+3 B c^3-3 B c d^2+5 c^2 C d-C d^3\right)+a^4 (-d) \left(d^2 (3 A+5 C)-3 B c d+8 c^2 C\right)+8 a^3 b B d \left(c^2+d^2\right)+2 a b^3 \left(c^2+d^2\right) (3 A c+B d-3 c C)-b^4 \left(d \left(5 A c^2+8 A d^2+3 c^2 C\right)-3 B \left(c^3+2 c d^2\right)\right)\right)}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(-a^2 b^2 (2 d (5 A-C)+3 B c)+7 a^3 b B d-4 a^4 C d+a b^3 (6 A c+B d-6 c C)+b^4 (3 B c-4 A d)\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{3/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{3/2}}",1,"-(((I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*(c - I*d)^(3/2)*f)) - ((B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*(c + I*d)^(3/2)*f) - (2*(A*b^2 - a*(b*B - a*C)))/(3*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]) - (2*(7*a^3*b*B*d - 4*a^4*C*d + b^4*(3*B*c - 4*A*d) + a*b^3*(6*A*c - 6*c*C + B*d) - a^2*b^2*(3*B*c + 2*(5*A - C)*d)))/(3*(a^2 + b^2)^2*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) - (2*d*(8*a^3*b*B*d*(c^2 + d^2) + 2*a*b^3*(3*A*c - 3*c*C + B*d)*(c^2 + d^2) - a^4*d*(8*c^2*C - 3*B*c*d + (3*A + 5*C)*d^2) - a^2*b^2*(3*B*c^3 + 11*A*c^2*d + 5*c^2*C*d - 3*B*c*d^2 + 17*A*d^3 - C*d^3) - b^4*(d*(5*A*c^2 + 3*c^2*C + 8*A*d^2) - 3*B*(c^3 + 2*c*d^2)))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^3*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",10,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
159,1,549,0,10.4996866,"\int \frac{(a+b \tan (e+f x))^{5/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[((a + b*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(2 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(d^4 (4 A+C)-2 B c^3 d-6 B c d^3+10 c^2 C d^2+5 c^4 C\right)\right)}{d^3 f \left(c^2+d^2\right)^2}-\frac{2 (a+b \tan (e+f x))^{3/2} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-11 C)+5 A d^4-2 B c^3 d-8 B c d^3+5 c^4 C\right)\right)}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{5/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}-\frac{b^{3/2} (-5 a C d-2 b B d+5 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{7/2} f}","\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \left(2 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(d^4 (4 A+C)-2 B c^3 d-6 B c d^3+10 c^2 C d^2+5 c^4 C\right)\right)}{d^3 f \left(c^2+d^2\right)^2}-\frac{2 (a+b \tan (e+f x))^{3/2} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-11 C)+5 A d^4-2 B c^3 d-8 B c d^3+5 c^4 C\right)\right)}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{5/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^{5/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^{5/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}-\frac{b^{3/2} (-5 a C d-2 b B d+5 b c C) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{7/2} f}",1,"-(((a - I*b)^(5/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f)) - ((a + I*b)^(5/2)*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) - (b^(3/2)*(5*b*c*C - 2*b*B*d - 5*a*C*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(7/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(5/2))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*(5*c^4*C - 2*B*c^3*d - c^2*(A - 11*C)*d^2 - 8*B*c*d^3 + 5*A*d^4) + 3*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*(a + b*Tan[e + f*x])^(3/2))/(3*d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]]) + (b*(b*(5*c^4*C - 2*B*c^3*d + 10*c^2*C*d^2 - 6*B*c*d^3 + (4*A + C)*d^4) + 2*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^2*f)","A",15,9,49,0.1837,1,"{3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
160,1,407,0,7.1625762,"\int \frac{(a+b \tan (e+f x))^{3/2} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[((a + b*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 \sqrt{a+b \tan (e+f x)} \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{3/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}+\frac{2 b^{3/2} C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}","-\frac{2 \sqrt{a+b \tan (e+f x)} \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (A-3 C)+A d^4-2 B c d^3+c^4 C\right)\right)}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 \left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{3/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(a-i b)^{3/2} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{(a+i b)^{3/2} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}+\frac{2 b^{3/2} C \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}",1,"-(((a - I*b)^(3/2)*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f)) - ((a + I*b)^(3/2)*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) + (2*b^(3/2)*C*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(3/2))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*(c^4*C - c^2*(A - 3*C)*d^2 - 2*B*c*d^3 + A*d^4) + a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Sqrt[a + b*Tan[e + f*x]])/(d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",14,8,49,0.1633,1,"{3645, 3655, 6725, 63, 217, 206, 93, 208}"
161,1,373,0,1.9218197,"\int \frac{\sqrt{a+b \tan (e+f x)} \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(Sqrt[a + b*Tan[e + f*x]]*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{2 \sqrt{a+b \tan (e+f x)} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (5 A-7 C)+A d^4+2 B c^3 d-4 B c d^3+c^4 C\right)\right)}{3 d f \left(c^2+d^2\right)^2 (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{\sqrt{a+i b} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","-\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{2 \sqrt{a+b \tan (e+f x)} \left(3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)+b \left(-c^2 d^2 (5 A-7 C)+A d^4+2 B c^3 d-4 B c d^3+c^4 C\right)\right)}{3 d f \left(c^2+d^2\right)^2 (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{\sqrt{a-i b} (i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{\sqrt{a+i b} (B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"-((Sqrt[a - I*b]*(I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f)) - (Sqrt[a + I*b]*(B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) - (2*(c^2*C - B*c*d + A*d^2)*Sqrt[a + b*Tan[e + f*x]])/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(b*(c^4*C + 2*B*c^3*d - c^2*(5*A - 7*C)*d^2 - 4*B*c*d^3 + A*d^4) + 3*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Sqrt[a + b*Tan[e + f*x]])/(3*d*(b*c - a*d)*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,49,0.1224,1,"{3645, 3649, 3616, 3615, 93, 208}"
162,1,379,0,1.8141316,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/(Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{2 \sqrt{a+b \tan (e+f x)} \left(b \left(4 c^2 d^2 (2 A-C)+2 A d^4-5 B c^3 d+B c d^3+2 c^4 C\right)-3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{3 f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{5/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{5/2}}","\frac{2 \left(A d^2-B c d+c^2 C\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{2 \sqrt{a+b \tan (e+f x)} \left(b \left(4 c^2 d^2 (2 A-C)+2 A d^4-5 B c^3 d+B c d^3+2 c^4 C\right)-3 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)\right)}{3 f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(B+i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{5/2}}+\frac{(i A-B-i C) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{5/2}}",1,"-(((B + I*(A - C))*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*(c - I*d)^(5/2)*f)) + ((I*A - B - I*C)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*(c + I*d)^(5/2)*f) + (2*(c^2*C - B*c*d + A*d^2)*Sqrt[a + b*Tan[e + f*x]])/(3*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(b*(2*c^4*C - 5*B*c^3*d + 4*c^2*(2*A - C)*d^2 + B*c*d^3 + 2*A*d^4) - 3*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)))*Sqrt[a + b*Tan[e + f*x]])/(3*(b*c - a*d)^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
163,1,650,0,3.4310886,"\int \frac{A+B \tan (e+f x)+C \tan ^2(e+f x)}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2)/((a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(-A \left(-a^2 b d^2 \left(11 c^2+5 d^2\right)+6 a^3 c d^3+6 a b^2 c d^3+b^3 \left(-\left(17 c^2 d^2+3 c^4+8 d^4\right)\right)\right)+a^2 b \left(-8 B c^3 d-2 B c d^3+5 c^2 C d^2+8 c^4 C+3 C d^4\right)+3 a^3 d^2 \left(B \left(c^2-d^2\right)+2 c C d\right)+3 a b^2 \left(2 c C d^3-B \left(c^2 d^2+c^4+2 d^4\right)\right)+b^3 c \left(-8 B c^2 d-2 B d^3+5 c^3 C-c C d^2\right)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(a^2 A d^2+a^2 \left(-B c d+4 c^2 C+3 C d^2\right)-3 a b B \left(c^2+d^2\right)+A b^2 \left(3 c^2+4 d^2\right)+b^2 c (c C-B d)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{5/2}}","-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(-A \left(-a^2 b d^2 \left(11 c^2+5 d^2\right)+6 a^3 c d^3+6 a b^2 c d^3+b^3 \left(-\left(17 c^2 d^2+3 c^4+8 d^4\right)\right)\right)+a^2 b \left(-8 B c^3 d-2 B c d^3+5 c^2 C d^2+8 c^4 C+3 C d^4\right)+3 a^3 d^2 \left(B \left(c^2-d^2\right)+2 c C d\right)+3 a b^2 \left(2 c C d^3-B \left(c^2 d^2+c^4+2 d^4\right)\right)+b^3 c \left(-8 B c^2 d-2 B d^3+5 c^3 C-c C d^2\right)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+b \tan (e+f x)} \left(A \left(a^2 d^2+b^2 \left(3 c^2+4 d^2\right)\right)+a^2 \left(-B c d+4 c^2 C+3 C d^2\right)-3 a b B \left(c^2+d^2\right)+b^2 c (c C-B d)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(A b^2-a (b B-a C)\right)}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{(i A+B-i C) \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{5/2}}-\frac{(B-i (A-C)) \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{5/2}}",1,"-(((I*A + B - I*C)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*(c - I*d)^(5/2)*f)) - ((B - I*(A - C))*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*(c + I*d)^(5/2)*f) - (2*(A*b^2 - a*(b*B - a*C)))/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) - (2*d*(a^2*A*d^2 + b^2*c*(c*C - B*d) - 3*a*b*B*(c^2 + d^2) + A*b^2*(3*c^2 + 4*d^2) + a^2*(4*c^2*C - B*c*d + 3*C*d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*d*(b^3*c*(5*c^3*C - 8*B*c^2*d - c*C*d^2 - 2*B*d^3) + a^2*b*(8*c^4*C - 8*B*c^3*d + 5*c^2*C*d^2 - 2*B*c*d^3 + 3*C*d^4) + 3*a^3*d^2*(2*c*C*d + B*(c^2 - d^2)) + 3*a*b^2*(2*c*C*d^3 - B*(c^4 + c^2*d^2 + 2*d^4)) - A*(6*a^3*c*d^3 + 6*a*b^2*c*d^3 - a^2*b*d^2*(11*c^2 + 5*d^2) - b^3*(3*c^4 + 17*c^2*d^2 + 8*d^4)))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",10,5,49,0.1020,1,"{3649, 3616, 3615, 93, 208}"
164,1,376,0,0.8998585,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^n \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","-\frac{(B+i (A-C)) (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (a-i b)}-\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}+\frac{C (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{b f (m+1)}","-\frac{(B+i (A-C)) (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (a-i b)}-\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}+\frac{C (a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{b f (m+1)}",1,"-((B + I*(A - C))*AppellF1[1 + m, -n, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^n)/(2*(a - I*b)*f*(1 + m)*((b*(c + d*Tan[e + f*x]))/(b*c - a*d))^n) - ((A + I*B - C)*AppellF1[1 + m, -n, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^n)/(2*(I*a - b)*f*(1 + m)*((b*(c + d*Tan[e + f*x]))/(b*c - a*d))^n) + (C*Hypergeometric2F1[1 + m, -n, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^n)/(b*f*(1 + m)*((b*(c + d*Tan[e + f*x]))/(b*c - a*d))^n)","A",9,6,45,0.1333,1,"{3655, 6725, 70, 69, 137, 136}"
165,1,551,0,2.3766363,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^3 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^3*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(a+b \tan (e+f x))^{m+1} \left(d \left(b^3 (m+2) (m+3) (m+4) \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-a \left(2 (b c-a d) (-3 a C d+b B d (m+4)+3 b c C)+b^2 d (m+3) (m+4) (d (A-C)+B c)\right)\right)+b c (m+2) \left(2 (b c-a d) (-3 a C d+b B d (m+4)+3 b c C)+b^2 d (m+3) (m+4) (d (A-C)+B c)\right)\right)}{b^4 f (m+1) (m+2) (m+3) (m+4)}+\frac{d \tan (e+f x) (a+b \tan (e+f x))^{m+1} \left(2 (b c-a d) (-3 a C d+b B d (m+4)+3 b c C)+b^2 d (m+3) (m+4) (d (A-C)+B c)\right)}{b^3 f (m+2) (m+3) (m+4)}+\frac{(c-i d)^3 (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d)^3 (A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}+\frac{(c+d \tan (e+f x))^2 (-3 a C d+b B d (m+4)+3 b c C) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+3) (m+4)}+\frac{C (c+d \tan (e+f x))^3 (a+b \tan (e+f x))^{m+1}}{b f (m+4)}","\frac{(a+b \tan (e+f x))^{m+1} \left(d \left(b^3 (m+2) (m+3) (m+4) \left(2 c d (A-C)+B \left(c^2-d^2\right)\right)-a \left(b^2 d (m+3) (m+4) (d (A-C)+B c)-2 (b c-a d) (3 a C d-b (B d (m+4)+3 c C))\right)\right)+b c (m+2) \left(b^2 d (m+3) (m+4) (d (A-C)+B c)-2 (b c-a d) (3 a C d-b (B d (m+4)+3 c C))\right)\right)}{b^4 f (m+1) (m+2) (m+3) (m+4)}+\frac{d \tan (e+f x) (a+b \tan (e+f x))^{m+1} \left(b^2 d (m+3) (m+4) (d (A-C)+B c)-2 (b c-a d) (3 a C d-b (B d (m+4)+3 c C))\right)}{b^3 f (m+2) (m+3) (m+4)}+\frac{(c-i d)^3 (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d)^3 (A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}-\frac{(c+d \tan (e+f x))^2 (3 a C d-b (B d (m+4)+3 c C)) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+3) (m+4)}+\frac{C (c+d \tan (e+f x))^3 (a+b \tan (e+f x))^{m+1}}{b f (m+4)}",1,"((b*c*(2 + m)*(b^2*d*(B*c + (A - C)*d)*(3 + m)*(4 + m) + 2*(b*c - a*d)*(3*b*c*C - 3*a*C*d + b*B*d*(4 + m))) + d*(b^3*(2*c*(A - C)*d + B*(c^2 - d^2))*(2 + m)*(3 + m)*(4 + m) - a*(b^2*d*(B*c + (A - C)*d)*(3 + m)*(4 + m) + 2*(b*c - a*d)*(3*b*c*C - 3*a*C*d + b*B*d*(4 + m)))))*(a + b*Tan[e + f*x])^(1 + m))/(b^4*f*(1 + m)*(2 + m)*(3 + m)*(4 + m)) + ((A - I*B - C)*(c - I*d)^3*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) - ((A + I*B - C)*(c + I*d)^3*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a - b)*f*(1 + m)) + (d*(b^2*d*(B*c + (A - C)*d)*(3 + m)*(4 + m) + 2*(b*c - a*d)*(3*b*c*C - 3*a*C*d + b*B*d*(4 + m)))*Tan[e + f*x]*(a + b*Tan[e + f*x])^(1 + m))/(b^3*f*(2 + m)*(3 + m)*(4 + m)) + ((3*b*c*C - 3*a*C*d + b*B*d*(4 + m))*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^2)/(b^2*f*(3 + m)*(4 + m)) + (C*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^3)/(b*f*(4 + m))","A",9,6,45,0.1333,1,"{3647, 3637, 3630, 3539, 3537, 68}"
166,1,360,0,1.1515335,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^2 \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^2*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(a+b \tan (e+f x))^{m+1} \left(2 a^2 C d^2-a b d (m+3) (B d+2 c C)+b^2 (m+2) \left(d^2 (m+3) (A-C)+2 B c d (m+3)+2 c^2 C\right)\right)}{b^3 f (m+1) (m+2) (m+3)}+\frac{(c-i d)^2 (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(c+i d)^2 (i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}+\frac{d \tan (e+f x) (-2 a C d+b B d (m+3)+2 b c C) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+2) (m+3)}+\frac{C (c+d \tan (e+f x))^2 (a+b \tan (e+f x))^{m+1}}{b f (m+3)}","\frac{(a+b \tan (e+f x))^{m+1} \left(2 a^2 C d^2-a b d (m+3) (B d+2 c C)+b^2 (m+2) \left(d^2 (m+3) (A-C)+2 B c d (m+3)+2 c^2 C\right)\right)}{b^3 f (m+1) (m+2) (m+3)}+\frac{(c-i d)^2 (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(c+i d)^2 (i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}-\frac{d \tan (e+f x) (2 a C d-b (B d (m+3)+2 c C)) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+2) (m+3)}+\frac{C (c+d \tan (e+f x))^2 (a+b \tan (e+f x))^{m+1}}{b f (m+3)}",1,"((2*a^2*C*d^2 - a*b*d*(2*c*C + B*d)*(3 + m) + b^2*(2 + m)*(2*c^2*C + 2*B*c*d*(3 + m) + (A - C)*d^2*(3 + m)))*(a + b*Tan[e + f*x])^(1 + m))/(b^3*f*(1 + m)*(2 + m)*(3 + m)) + ((A - I*B - C)*(c - I*d)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) + ((I*A - B - I*C)*(c + I*d)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*f*(1 + m)) + (d*(2*b*c*C - 2*a*C*d + b*B*d*(3 + m))*Tan[e + f*x]*(a + b*Tan[e + f*x])^(1 + m))/(b^2*f*(2 + m)*(3 + m)) + (C*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^2)/(b*f*(3 + m))","A",8,6,45,0.1333,1,"{3647, 3637, 3630, 3539, 3537, 68}"
167,1,247,0,0.5283257,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x)) \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(c-i d) (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d) (A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}-\frac{(a C d-b (m+2) (B d+c C)) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+1) (m+2)}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^{m+1}}{b f (m+2)}","\frac{(c-i d) (A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d) (A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}-\frac{(a C d-b (m+2) (B d+c C)) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+1) (m+2)}+\frac{C d \tan (e+f x) (a+b \tan (e+f x))^{m+1}}{b f (m+2)}",1,"-(((a*C*d - b*(c*C + B*d)*(2 + m))*(a + b*Tan[e + f*x])^(1 + m))/(b^2*f*(1 + m)*(2 + m))) + ((A - I*B - C)*(c - I*d)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) - ((A + I*B - C)*(c + I*d)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a - b)*f*(1 + m)) + (C*d*Tan[e + f*x]*(a + b*Tan[e + f*x])^(1 + m))/(b*f*(2 + m))","A",7,5,43,0.1163,1,"{3637, 3630, 3539, 3537, 68}"
168,1,178,0,0.1844509,"\int (a+b \tan (e+f x))^m \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right) \, dx","Int[(a + b*Tan[e + f*x])^m*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2),x]","\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}+\frac{C (a+b \tan (e+f x))^{m+1}}{b f (m+1)}","\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}+\frac{C (a+b \tan (e+f x))^{m+1}}{b f (m+1)}",1,"(C*(a + b*Tan[e + f*x])^(1 + m))/(b*f*(1 + m)) + ((A - I*B - C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) + ((I*A - B - I*C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*f*(1 + m))","A",6,4,33,0.1212,1,"{3630, 3539, 3537, 68}"
169,1,258,0,0.4822208,"\int \frac{(a+b \tan (e+f x))^m \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{c+d \tan (e+f x)} \, dx","Int[((a + b*Tan[e + f*x])^m*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x]),x]","\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right) (b c-a d)}-\frac{(i A+B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (a-i b) (c-i d)}-\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (c+i d)}","\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right) (b c-a d)}-\frac{(i A+B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (a-i b) (c-i d)}-\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (c+i d)}",1,"-((I*A + B - I*C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a - I*b)*(c - I*d)*f*(1 + m)) - ((A + I*B - C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a - b)*(c + I*d)*f*(1 + m)) + ((c^2*C - B*c*d + A*d^2)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)*(c^2 + d^2)*f*(1 + m))","A",8,5,45,0.1111,1,"{3653, 3539, 3537, 68, 3634}"
170,1,402,0,1.2150207,"\int \frac{(a+b \tan (e+f x))^m \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^2} \, dx","Int[((a + b*Tan[e + f*x])^m*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^2,x]","-\frac{(a+b \tan (e+f x))^{m+1} \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b \left(A c^2 d^2 (2-m)-A d^4 m-B \left(c^3 d (1-m)-c d^3 (m+1)\right)-c^2 C d^2 (m+2)+c^4 (-C) m\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right)^2 (b c-a d)^2}+\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1}}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^2}+\frac{(i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (c+i d)^2}","-\frac{(a+b \tan (e+f x))^{m+1} \left(a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b \left(A d^2 \left(c^2 (2-m)-d^2 m\right)-B c d \left(c^2 (1-m)-d^2 (m+1)\right)+c^2 (-C) \left(c^2 m+d^2 (m+2)\right)\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right)^2 (b c-a d)^2}+\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1}}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^2}+\frac{(i A-B-i C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (c+i d)^2}",1,"((A - I*B - C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*(c - I*d)^2*f*(1 + m)) + ((I*A - B - I*C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*(c + I*d)^2*f*(1 + m)) - ((a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)) - b*(A*c^2*d^2*(2 - m) - c^4*C*m - A*d^4*m - c^2*C*d^2*(2 + m) - B*(c^3*d*(1 - m) - c*d^3*(1 + m))))*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)^2*(c^2 + d^2)^2*f*(1 + m)) + ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",9,6,45,0.1333,1,"{3649, 3653, 3539, 3537, 68, 3634}"
171,1,702,0,2.937641,"\int \frac{(a+b \tan (e+f x))^m \left(A+B \tan (e+f x)+C \tan ^2(e+f x)\right)}{(c+d \tan (e+f x))^3} \, dx","Int[((a + b*Tan[e + f*x])^m*(A + B*Tan[e + f*x] + C*Tan[e + f*x]^2))/(c + d*Tan[e + f*x])^3,x]","\frac{(a+b \tan (e+f x))^{m+1} \left(2 a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)-2 a b d^2 \left(2 c d (A-C) \left(c^2 (3-m)-d^2 (m+1)\right)+B \left(6 c^2 d^2+c^4 (-(2-m))-d^4 m\right)\right)-b^2 \left(A d^2 \left(2 c^2 d^2 \left(-m^2+3 m+1\right)+c^4 \left(-\left(m^2-5 m+6\right)\right)+d^4 (1-m) m\right)+B \left(-2 c^3 d^3 \left(-m^2+m+3\right)+c^5 d \left(m^2-3 m+2\right)+c d^5 m (m+1)\right)+c^2 C \left(2 c^2 d^2 \left(-m^2-m+3\right)+c^4 (1-m) m-d^4 \left(m^2+3 m+2\right)\right)\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{2 f (m+1) \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{(a+b \tan (e+f x))^{m+1} \left(2 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b \left(c^2 d^2 (A (5-m)-C (m+3))+A d^4 (1-m)-B c^3 d (3-m)+B c d^3 (m+1)+c^4 C (1-m)\right)\right)}{2 f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}+\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^3}+\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)^3}","\frac{(a+b \tan (e+f x))^{m+1} \left(2 a^2 d^3 \left(d (A-C) \left(3 c^2-d^2\right)-B \left(c^3-3 c d^2\right)\right)-2 a b d^2 \left(2 c d (A-C) \left(c^2 (3-m)-d^2 (m+1)\right)+B \left(6 c^2 d^2+c^4 (-(2-m))-d^4 m\right)\right)-b^2 \left(A d^2 \left(2 c^2 d^2 \left(-m^2+3 m+1\right)+c^4 \left(-\left(m^2-5 m+6\right)\right)+d^4 (1-m) m\right)+B c d \left(-2 c^2 d^2 \left(-m^2+m+3\right)+c^4 \left(m^2-3 m+2\right)+d^4 m (m+1)\right)+c^2 C \left(2 c^2 d^2 \left(-m^2-m+3\right)+c^4 (1-m) m-d^4 \left(m^2+3 m+2\right)\right)\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{2 f (m+1) \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{(a+b \tan (e+f x))^{m+1} \left(2 a d^2 \left(2 c d (A-C)-B \left(c^2-d^2\right)\right)-b \left(c^2 d^2 (A (5-m)-C (m+3))+A d^4 (1-m)-B c^3 d (3-m)+B c d^3 (m+1)+c^4 C (1-m)\right)\right)}{2 f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{\left(A d^2-B c d+c^2 C\right) (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}+\frac{(A-i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^3}+\frac{(A+i B-C) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)^3}",1,"((A - I*B - C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*(c - I*d)^3*f*(1 + m)) + ((A + I*B - C)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*(I*c - d)^3*f*(1 + m)) + ((2*a^2*d^3*((A - C)*d*(3*c^2 - d^2) - B*(c^3 - 3*c*d^2)) - 2*a*b*d^2*(B*(6*c^2*d^2 - c^4*(2 - m) - d^4*m) + 2*c*(A - C)*d*(c^2*(3 - m) - d^2*(1 + m))) - b^2*(A*d^2*(d^4*(1 - m)*m + 2*c^2*d^2*(1 + 3*m - m^2) - c^4*(6 - 5*m + m^2)) + B*(c*d^5*m*(1 + m) - 2*c^3*d^3*(3 + m - m^2) + c^5*d*(2 - 3*m + m^2)) + c^2*C*(c^4*(1 - m)*m + 2*c^2*d^2*(3 - m - m^2) - d^4*(2 + 3*m + m^2))))*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)^3*(c^2 + d^2)^3*f*(1 + m)) + ((c^2*C - B*c*d + A*d^2)*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - ((2*a*d^2*(2*c*(A - C)*d - B*(c^2 - d^2)) - b*(c^4*C*(1 - m) + A*d^4*(1 - m) - B*c^3*d*(3 - m) + B*c*d^3*(1 + m) + c^2*d^2*(A*(5 - m) - C*(3 + m))))*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",10,6,45,0.1333,1,"{3649, 3653, 3539, 3537, 68, 3634}"