1,1,91,0,0.110829,"\int \tan ^2(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{a (B+i A) \tan ^2(c+d x)}{2 d}+\frac{a (A-i B) \tan (c+d x)}{d}+\frac{a (B+i A) \log (\cos (c+d x))}{d}-a x (A-i B)+\frac{i a B \tan ^3(c+d x)}{3 d}","\frac{a (B+i A) \tan ^2(c+d x)}{2 d}+\frac{a (A-i B) \tan (c+d x)}{d}+\frac{a (B+i A) \log (\cos (c+d x))}{d}-a x (A-i B)+\frac{i a B \tan ^3(c+d x)}{3 d}",1,"-(a*(A - I*B)*x) + (a*(I*A + B)*Log[Cos[c + d*x]])/d + (a*(A - I*B)*Tan[c + d*x])/d + (a*(I*A + B)*Tan[c + d*x]^2)/(2*d) + ((I/3)*a*B*Tan[c + d*x]^3)/d","A",4,4,32,0.1250,1,"{3592, 3528, 3525, 3475}"
2,1,69,0,0.0555895,"\int \tan (c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{a (B+i A) \tan (c+d x)}{d}-\frac{a (A-i B) \log (\cos (c+d x))}{d}-a x (B+i A)+\frac{i a B \tan ^2(c+d x)}{2 d}","\frac{a (B+i A) \tan (c+d x)}{d}-\frac{a (A-i B) \log (\cos (c+d x))}{d}-a x (B+i A)+\frac{i a B \tan ^2(c+d x)}{2 d}",1,"-(a*(I*A + B)*x) - (a*(A - I*B)*Log[Cos[c + d*x]])/d + (a*(I*A + B)*Tan[c + d*x])/d + ((I/2)*a*B*Tan[c + d*x]^2)/d","A",3,3,30,0.1000,1,"{3592, 3525, 3475}"
3,1,46,0,0.0278612,"\int (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{a (B+i A) \log (\cos (c+d x))}{d}+a x (A-i B)+\frac{i a B \tan (c+d x)}{d}","-\frac{a (B+i A) \log (\cos (c+d x))}{d}+a x (A-i B)+\frac{i a B \tan (c+d x)}{d}",1,"a*(A - I*B)*x - (a*(I*A + B)*Log[Cos[c + d*x]])/d + (I*a*B*Tan[c + d*x])/d","A",2,2,24,0.08333,1,"{3525, 3475}"
4,1,40,0,0.0711095,"\int \cot (c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","a x (B+i A)+\frac{a A \log (\sin (c+d x))}{d}-\frac{i a B \log (\cos (c+d x))}{d}","a x (B+i A)+\frac{a A \log (\sin (c+d x))}{d}-\frac{i a B \log (\cos (c+d x))}{d}",1,"a*(I*A + B)*x - (I*a*B*Log[Cos[c + d*x]])/d + (a*A*Log[Sin[c + d*x]])/d","A",4,3,30,0.1000,1,"{3589, 3475, 3531}"
5,1,44,0,0.0840953,"\int \cot ^2(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{a (B+i A) \log (\sin (c+d x))}{d}-a x (A-i B)-\frac{a A \cot (c+d x)}{d}","\frac{a (B+i A) \log (\sin (c+d x))}{d}-a x (A-i B)-\frac{a A \cot (c+d x)}{d}",1,"-(a*(A - I*B)*x) - (a*A*Cot[c + d*x])/d + (a*(I*A + B)*Log[Sin[c + d*x]])/d","A",3,3,32,0.09375,1,"{3591, 3531, 3475}"
6,1,68,0,0.1212354,"\int \cot ^3(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{a (B+i A) \cot (c+d x)}{d}-\frac{a (A-i B) \log (\sin (c+d x))}{d}-a x (B+i A)-\frac{a A \cot ^2(c+d x)}{2 d}","-\frac{a (B+i A) \cot (c+d x)}{d}-\frac{a (A-i B) \log (\sin (c+d x))}{d}-a x (B+i A)-\frac{a A \cot ^2(c+d x)}{2 d}",1,"-(a*(I*A + B)*x) - (a*(I*A + B)*Cot[c + d*x])/d - (a*A*Cot[c + d*x]^2)/(2*d) - (a*(A - I*B)*Log[Sin[c + d*x]])/d","A",4,4,32,0.1250,1,"{3591, 3529, 3531, 3475}"
7,1,89,0,0.1523814,"\int \cot ^4(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{a (B+i A) \cot ^2(c+d x)}{2 d}+\frac{a (A-i B) \cot (c+d x)}{d}-\frac{a (B+i A) \log (\sin (c+d x))}{d}+a x (A-i B)-\frac{a A \cot ^3(c+d x)}{3 d}","-\frac{a (B+i A) \cot ^2(c+d x)}{2 d}+\frac{a (A-i B) \cot (c+d x)}{d}-\frac{a (B+i A) \log (\sin (c+d x))}{d}+a x (A-i B)-\frac{a A \cot ^3(c+d x)}{3 d}",1,"a*(A - I*B)*x + (a*(A - I*B)*Cot[c + d*x])/d - (a*(I*A + B)*Cot[c + d*x]^2)/(2*d) - (a*A*Cot[c + d*x]^3)/(3*d) - (a*(I*A + B)*Log[Sin[c + d*x]])/d","A",5,4,32,0.1250,1,"{3591, 3529, 3531, 3475}"
8,1,111,0,0.1859321,"\int \cot ^5(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{a (B+i A) \cot ^3(c+d x)}{3 d}+\frac{a (A-i B) \cot ^2(c+d x)}{2 d}+\frac{a (B+i A) \cot (c+d x)}{d}+\frac{a (A-i B) \log (\sin (c+d x))}{d}+a x (B+i A)-\frac{a A \cot ^4(c+d x)}{4 d}","-\frac{a (B+i A) \cot ^3(c+d x)}{3 d}+\frac{a (A-i B) \cot ^2(c+d x)}{2 d}+\frac{a (B+i A) \cot (c+d x)}{d}+\frac{a (A-i B) \log (\sin (c+d x))}{d}+a x (B+i A)-\frac{a A \cot ^4(c+d x)}{4 d}",1,"a*(I*A + B)*x + (a*(I*A + B)*Cot[c + d*x])/d + (a*(A - I*B)*Cot[c + d*x]^2)/(2*d) - (a*(I*A + B)*Cot[c + d*x]^3)/(3*d) - (a*A*Cot[c + d*x]^4)/(4*d) + (a*(A - I*B)*Log[Sin[c + d*x]])/d","A",6,4,32,0.1250,1,"{3591, 3529, 3531, 3475}"
9,1,141,0,0.2521526,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{a^2 (4 A-5 i B) \tan ^3(c+d x)}{12 d}+\frac{a^2 (B+i A) \tan ^2(c+d x)}{d}+\frac{2 a^2 (A-i B) \tan (c+d x)}{d}+\frac{2 a^2 (B+i A) \log (\cos (c+d x))}{d}-2 a^2 x (A-i B)+\frac{i B \tan ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}","-\frac{a^2 (4 A-5 i B) \tan ^3(c+d x)}{12 d}+\frac{a^2 (B+i A) \tan ^2(c+d x)}{d}+\frac{2 a^2 (A-i B) \tan (c+d x)}{d}+\frac{2 a^2 (B+i A) \log (\cos (c+d x))}{d}-2 a^2 x (A-i B)+\frac{i B \tan ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}",1,"-2*a^2*(A - I*B)*x + (2*a^2*(I*A + B)*Log[Cos[c + d*x]])/d + (2*a^2*(A - I*B)*Tan[c + d*x])/d + (a^2*(I*A + B)*Tan[c + d*x]^2)/d - (a^2*(4*A - (5*I)*B)*Tan[c + d*x]^3)/(12*d) + ((I/4)*B*Tan[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,5,34,0.1471,1,"{3594, 3592, 3528, 3525, 3475}"
10,1,107,0,0.1154648,"\int \tan (c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{a^2 (B+i A) \tan (c+d x)}{d}-\frac{2 a^2 (A-i B) \log (\cos (c+d x))}{d}-2 a^2 x (B+i A)+\frac{A (a+i a \tan (c+d x))^2}{2 d}-\frac{i B (a+i a \tan (c+d x))^3}{3 a d}","\frac{a^2 (B+i A) \tan (c+d x)}{d}-\frac{2 a^2 (A-i B) \log (\cos (c+d x))}{d}-2 a^2 x (B+i A)+\frac{A (a+i a \tan (c+d x))^2}{2 d}-\frac{i B (a+i a \tan (c+d x))^3}{3 a d}",1,"-2*a^2*(I*A + B)*x - (2*a^2*(A - I*B)*Log[Cos[c + d*x]])/d + (a^2*(I*A + B)*Tan[c + d*x])/d + (A*(a + I*a*Tan[c + d*x])^2)/(2*d) - ((I/3)*B*(a + I*a*Tan[c + d*x])^3)/(a*d)","A",4,4,32,0.1250,1,"{3592, 3527, 3477, 3475}"
11,1,80,0,0.0691261,"\int (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{a^2 (A-i B) \tan (c+d x)}{d}-\frac{2 a^2 (B+i A) \log (\cos (c+d x))}{d}+2 a^2 x (A-i B)+\frac{B (a+i a \tan (c+d x))^2}{2 d}","-\frac{a^2 (A-i B) \tan (c+d x)}{d}-\frac{2 a^2 (B+i A) \log (\cos (c+d x))}{d}+2 a^2 x (A-i B)+\frac{B (a+i a \tan (c+d x))^2}{2 d}",1,"2*a^2*(A - I*B)*x - (2*a^2*(I*A + B)*Log[Cos[c + d*x]])/d - (a^2*(A - I*B)*Tan[c + d*x])/d + (B*(a + I*a*Tan[c + d*x])^2)/(2*d)","A",3,3,26,0.1154,1,"{3527, 3477, 3475}"
12,1,75,0,0.1586762,"\int \cot (c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{a^2 (A-2 i B) \log (\cos (c+d x))}{d}+2 a^2 x (B+i A)+\frac{a^2 A \log (\sin (c+d x))}{d}+\frac{i B \left(a^2+i a^2 \tan (c+d x)\right)}{d}","\frac{a^2 (A-2 i B) \log (\cos (c+d x))}{d}+2 a^2 x (B+i A)+\frac{a^2 A \log (\sin (c+d x))}{d}+\frac{i B \left(a^2+i a^2 \tan (c+d x)\right)}{d}",1,"2*a^2*(I*A + B)*x + (a^2*(A - (2*I)*B)*Log[Cos[c + d*x]])/d + (a^2*A*Log[Sin[c + d*x]])/d + (I*B*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,4,32,0.1250,1,"{3594, 3589, 3475, 3531}"
13,1,79,0,0.1778567,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{a^2 (B+2 i A) \log (\sin (c+d x))}{d}-2 a^2 x (A-i B)-\frac{A \cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{d}+\frac{a^2 B \log (\cos (c+d x))}{d}","\frac{a^2 (B+2 i A) \log (\sin (c+d x))}{d}-2 a^2 x (A-i B)-\frac{A \cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{d}+\frac{a^2 B \log (\cos (c+d x))}{d}",1,"-2*a^2*(A - I*B)*x + (a^2*B*Log[Cos[c + d*x]])/d + (a^2*((2*I)*A + B)*Log[Sin[c + d*x]])/d - (A*Cot[c + d*x]*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,4,34,0.1176,1,"{3593, 3589, 3475, 3531}"
14,1,94,0,0.2078932,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{a^2 (2 B+3 i A) \cot (c+d x)}{2 d}-\frac{2 a^2 (A-i B) \log (\sin (c+d x))}{d}-2 a^2 x (B+i A)-\frac{A \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{2 d}","-\frac{a^2 (2 B+3 i A) \cot (c+d x)}{2 d}-\frac{2 a^2 (A-i B) \log (\sin (c+d x))}{d}-2 a^2 x (B+i A)-\frac{A \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{2 d}",1,"-2*a^2*(I*A + B)*x - (a^2*((3*I)*A + 2*B)*Cot[c + d*x])/(2*d) - (2*a^2*(A - I*B)*Log[Sin[c + d*x]])/d - (A*Cot[c + d*x]^2*(a^2 + I*a^2*Tan[c + d*x]))/(2*d)","A",4,4,34,0.1176,1,"{3593, 3591, 3531, 3475}"
15,1,117,0,0.255599,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{a^2 (3 B+4 i A) \cot ^2(c+d x)}{6 d}+\frac{2 a^2 (A-i B) \cot (c+d x)}{d}-\frac{2 a^2 (B+i A) \log (\sin (c+d x))}{d}+2 a^2 x (A-i B)-\frac{A \cot ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}","-\frac{a^2 (3 B+4 i A) \cot ^2(c+d x)}{6 d}+\frac{2 a^2 (A-i B) \cot (c+d x)}{d}-\frac{2 a^2 (B+i A) \log (\sin (c+d x))}{d}+2 a^2 x (A-i B)-\frac{A \cot ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}",1,"2*a^2*(A - I*B)*x + (2*a^2*(A - I*B)*Cot[c + d*x])/d - (a^2*((4*I)*A + 3*B)*Cot[c + d*x]^2)/(6*d) - (2*a^2*(I*A + B)*Log[Sin[c + d*x]])/d - (A*Cot[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x]))/(3*d)","A",5,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
16,1,139,0,0.2932712,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{a^2 (4 B+5 i A) \cot ^3(c+d x)}{12 d}+\frac{a^2 (A-i B) \cot ^2(c+d x)}{d}+\frac{2 a^2 (B+i A) \cot (c+d x)}{d}+\frac{2 a^2 (A-i B) \log (\sin (c+d x))}{d}+2 a^2 x (B+i A)-\frac{A \cot ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}","-\frac{a^2 (4 B+5 i A) \cot ^3(c+d x)}{12 d}+\frac{a^2 (A-i B) \cot ^2(c+d x)}{d}+\frac{2 a^2 (B+i A) \cot (c+d x)}{d}+\frac{2 a^2 (A-i B) \log (\sin (c+d x))}{d}+2 a^2 x (B+i A)-\frac{A \cot ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{4 d}",1,"2*a^2*(I*A + B)*x + (2*a^2*(I*A + B)*Cot[c + d*x])/d + (a^2*(A - I*B)*Cot[c + d*x]^2)/d - (a^2*((5*I)*A + 4*B)*Cot[c + d*x]^3)/(12*d) + (2*a^2*(A - I*B)*Log[Sin[c + d*x]])/d - (A*Cot[c + d*x]^4*(a^2 + I*a^2*Tan[c + d*x]))/(4*d)","A",6,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
17,1,182,0,0.4239908,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{a^3 (45 A-47 i B) \tan ^3(c+d x)}{60 d}+\frac{2 a^3 (B+i A) \tan ^2(c+d x)}{d}-\frac{(5 A-7 i B) \tan ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}+\frac{4 a^3 (A-i B) \tan (c+d x)}{d}+\frac{4 a^3 (B+i A) \log (\cos (c+d x))}{d}-4 a^3 x (A-i B)+\frac{i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^2}{5 d}","-\frac{a^3 (45 A-47 i B) \tan ^3(c+d x)}{60 d}+\frac{2 a^3 (B+i A) \tan ^2(c+d x)}{d}-\frac{(5 A-7 i B) \tan ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}+\frac{4 a^3 (A-i B) \tan (c+d x)}{d}+\frac{4 a^3 (B+i A) \log (\cos (c+d x))}{d}-4 a^3 x (A-i B)+\frac{i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^2}{5 d}",1,"-4*a^3*(A - I*B)*x + (4*a^3*(I*A + B)*Log[Cos[c + d*x]])/d + (4*a^3*(A - I*B)*Tan[c + d*x])/d + (2*a^3*(I*A + B)*Tan[c + d*x]^2)/d - (a^3*(45*A - (47*I)*B)*Tan[c + d*x]^3)/(60*d) + ((I/5)*a*B*Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^2)/d - ((5*A - (7*I)*B)*Tan[c + d*x]^3*(a^3 + I*a^3*Tan[c + d*x]))/(20*d)","A",6,5,34,0.1471,1,"{3594, 3592, 3528, 3525, 3475}"
18,1,138,0,0.1346452,"\int \tan (c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 a^3 (B+i A) \tan (c+d x)}{d}-\frac{4 a^3 (A-i B) \log (\cos (c+d x))}{d}-4 a^3 x (B+i A)+\frac{a (A-i B) (a+i a \tan (c+d x))^2}{2 d}+\frac{A (a+i a \tan (c+d x))^3}{3 d}-\frac{i B (a+i a \tan (c+d x))^4}{4 a d}","\frac{2 a^3 (B+i A) \tan (c+d x)}{d}-\frac{4 a^3 (A-i B) \log (\cos (c+d x))}{d}-4 a^3 x (B+i A)+\frac{a (A-i B) (a+i a \tan (c+d x))^2}{2 d}+\frac{A (a+i a \tan (c+d x))^3}{3 d}-\frac{i B (a+i a \tan (c+d x))^4}{4 a d}",1,"-4*a^3*(I*A + B)*x - (4*a^3*(A - I*B)*Log[Cos[c + d*x]])/d + (2*a^3*(I*A + B)*Tan[c + d*x])/d + (a*(A - I*B)*(a + I*a*Tan[c + d*x])^2)/(2*d) + (A*(a + I*a*Tan[c + d*x])^3)/(3*d) - ((I/4)*B*(a + I*a*Tan[c + d*x])^4)/(a*d)","A",5,5,32,0.1562,1,"{3592, 3527, 3478, 3477, 3475}"
19,1,110,0,0.0890933,"\int (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{2 a^3 (A-i B) \tan (c+d x)}{d}-\frac{4 a^3 (B+i A) \log (\cos (c+d x))}{d}+4 a^3 x (A-i B)+\frac{a (B+i A) (a+i a \tan (c+d x))^2}{2 d}+\frac{B (a+i a \tan (c+d x))^3}{3 d}","-\frac{2 a^3 (A-i B) \tan (c+d x)}{d}-\frac{4 a^3 (B+i A) \log (\cos (c+d x))}{d}+4 a^3 x (A-i B)+\frac{a (B+i A) (a+i a \tan (c+d x))^2}{2 d}+\frac{B (a+i a \tan (c+d x))^3}{3 d}",1,"4*a^3*(A - I*B)*x - (4*a^3*(I*A + B)*Log[Cos[c + d*x]])/d - (2*a^3*(A - I*B)*Tan[c + d*x])/d + (a*(I*A + B)*(a + I*a*Tan[c + d*x])^2)/(2*d) + (B*(a + I*a*Tan[c + d*x])^3)/(3*d)","A",4,4,26,0.1538,1,"{3527, 3478, 3477, 3475}"
20,1,107,0,0.2809631,"\int \cot (c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{(A-2 i B) \left(a^3+i a^3 \tan (c+d x)\right)}{d}+\frac{a^3 (3 A-4 i B) \log (\cos (c+d x))}{d}+4 a^3 x (B+i A)+\frac{a^3 A \log (\sin (c+d x))}{d}+\frac{i a B (a+i a \tan (c+d x))^2}{2 d}","-\frac{(A-2 i B) \left(a^3+i a^3 \tan (c+d x)\right)}{d}+\frac{a^3 (3 A-4 i B) \log (\cos (c+d x))}{d}+4 a^3 x (B+i A)+\frac{a^3 A \log (\sin (c+d x))}{d}+\frac{i a B (a+i a \tan (c+d x))^2}{2 d}",1,"4*a^3*(I*A + B)*x + (a^3*(3*A - (4*I)*B)*Log[Cos[c + d*x]])/d + (a^3*A*Log[Sin[c + d*x]])/d + ((I/2)*a*B*(a + I*a*Tan[c + d*x])^2)/d - ((A - (2*I)*B)*(a^3 + I*a^3*Tan[c + d*x]))/d","A",6,4,32,0.1250,1,"{3594, 3589, 3475, 3531}"
21,1,116,0,0.2958904,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{(-B+i A) \left(a^3+i a^3 \tan (c+d x)\right)}{d}+\frac{a^3 (B+3 i A) \log (\sin (c+d x))}{d}+\frac{a^3 (3 B+i A) \log (\cos (c+d x))}{d}-4 a^3 x (A-i B)-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^2}{d}","\frac{(-B+i A) \left(a^3+i a^3 \tan (c+d x)\right)}{d}+\frac{a^3 (B+3 i A) \log (\sin (c+d x))}{d}+\frac{a^3 (3 B+i A) \log (\cos (c+d x))}{d}-4 a^3 x (A-i B)-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^2}{d}",1,"-4*a^3*(A - I*B)*x + (a^3*(I*A + 3*B)*Log[Cos[c + d*x]])/d + (a^3*((3*I)*A + B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^2)/d + ((I*A - B)*(a^3 + I*a^3*Tan[c + d*x]))/d","A",6,5,34,0.1471,1,"{3593, 3594, 3589, 3475, 3531}"
22,1,123,0,0.3152145,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{a^3 (4 A-3 i B) \log (\sin (c+d x))}{d}-\frac{(B+2 i A) \cot (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{d}-4 a^3 x (B+i A)+\frac{i a^3 B \log (\cos (c+d x))}{d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}","-\frac{a^3 (4 A-3 i B) \log (\sin (c+d x))}{d}-\frac{(B+2 i A) \cot (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{d}-4 a^3 x (B+i A)+\frac{i a^3 B \log (\cos (c+d x))}{d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}",1,"-4*a^3*(I*A + B)*x + (I*a^3*B*Log[Cos[c + d*x]])/d - (a^3*(4*A - (3*I)*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^2)/(2*d) - (((2*I)*A + B)*Cot[c + d*x]*(a^3 + I*a^3*Tan[c + d*x]))/d","A",6,4,34,0.1176,1,"{3593, 3589, 3475, 3531}"
23,1,134,0,0.3649666,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a^3 (17 A-15 i B) \cot (c+d x)}{6 d}-\frac{4 a^3 (B+i A) \log (\sin (c+d x))}{d}-\frac{(3 B+5 i A) \cot ^2(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+4 a^3 x (A-i B)-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^2}{3 d}","\frac{a^3 (17 A-15 i B) \cot (c+d x)}{6 d}-\frac{4 a^3 (B+i A) \log (\sin (c+d x))}{d}-\frac{(3 B+5 i A) \cot ^2(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+4 a^3 x (A-i B)-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^2}{3 d}",1,"4*a^3*(A - I*B)*x + (a^3*(17*A - (15*I)*B)*Cot[c + d*x])/(6*d) - (4*a^3*(I*A + B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^2)/(3*d) - (((5*I)*A + 3*B)*Cot[c + d*x]^2*(a^3 + I*a^3*Tan[c + d*x]))/(6*d)","A",5,4,34,0.1176,1,"{3593, 3591, 3531, 3475}"
24,1,157,0,0.4180882,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a^3 (15 A-14 i B) \cot ^2(c+d x)}{12 d}+\frac{4 a^3 (B+i A) \cot (c+d x)}{d}+\frac{4 a^3 (A-i B) \log (\sin (c+d x))}{d}-\frac{(2 B+3 i A) \cot ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+4 a^3 x (B+i A)-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^2}{4 d}","\frac{a^3 (15 A-14 i B) \cot ^2(c+d x)}{12 d}+\frac{4 a^3 (B+i A) \cot (c+d x)}{d}+\frac{4 a^3 (A-i B) \log (\sin (c+d x))}{d}-\frac{(2 B+3 i A) \cot ^3(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{6 d}+4 a^3 x (B+i A)-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^2}{4 d}",1,"4*a^3*(I*A + B)*x + (4*a^3*(I*A + B)*Cot[c + d*x])/d + (a^3*(15*A - (14*I)*B)*Cot[c + d*x]^2)/(12*d) + (4*a^3*(A - I*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^2)/(4*d) - (((3*I)*A + 2*B)*Cot[c + d*x]^3*(a^3 + I*a^3*Tan[c + d*x]))/(6*d)","A",6,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
25,1,180,0,0.4602849,"\int \cot ^6(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a^3 (47 A-45 i B) \cot ^3(c+d x)}{60 d}+\frac{2 a^3 (B+i A) \cot ^2(c+d x)}{d}-\frac{4 a^3 (A-i B) \cot (c+d x)}{d}+\frac{4 a^3 (B+i A) \log (\sin (c+d x))}{d}-\frac{(5 B+7 i A) \cot ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}-4 a^3 x (A-i B)-\frac{a A \cot ^5(c+d x) (a+i a \tan (c+d x))^2}{5 d}","\frac{a^3 (47 A-45 i B) \cot ^3(c+d x)}{60 d}+\frac{2 a^3 (B+i A) \cot ^2(c+d x)}{d}-\frac{4 a^3 (A-i B) \cot (c+d x)}{d}+\frac{4 a^3 (B+i A) \log (\sin (c+d x))}{d}-\frac{(5 B+7 i A) \cot ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{20 d}-4 a^3 x (A-i B)-\frac{a A \cot ^5(c+d x) (a+i a \tan (c+d x))^2}{5 d}",1,"-4*a^3*(A - I*B)*x - (4*a^3*(A - I*B)*Cot[c + d*x])/d + (2*a^3*(I*A + B)*Cot[c + d*x]^2)/d + (a^3*(47*A - (45*I)*B)*Cot[c + d*x]^3)/(60*d) + (4*a^3*(I*A + B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^2)/(5*d) - (((7*I)*A + 5*B)*Cot[c + d*x]^4*(a^3 + I*a^3*Tan[c + d*x]))/(20*d)","A",7,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
26,1,225,0,0.6423051,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{a^4 (92 A-93 i B) \tan ^3(c+d x)}{60 d}+\frac{4 a^4 (B+i A) \tan ^2(c+d x)}{d}-\frac{(2 A-3 i B) \tan ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}-\frac{(12 A-13 i B) \tan ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{20 d}+\frac{8 a^4 (A-i B) \tan (c+d x)}{d}+\frac{8 a^4 (B+i A) \log (\cos (c+d x))}{d}-8 a^4 x (A-i B)+\frac{i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^3}{6 d}","-\frac{a^4 (92 A-93 i B) \tan ^3(c+d x)}{60 d}+\frac{4 a^4 (B+i A) \tan ^2(c+d x)}{d}-\frac{(2 A-3 i B) \tan ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}-\frac{(12 A-13 i B) \tan ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{20 d}+\frac{8 a^4 (A-i B) \tan (c+d x)}{d}+\frac{8 a^4 (B+i A) \log (\cos (c+d x))}{d}-8 a^4 x (A-i B)+\frac{i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^3}{6 d}",1,"-8*a^4*(A - I*B)*x + (8*a^4*(I*A + B)*Log[Cos[c + d*x]])/d + (8*a^4*(A - I*B)*Tan[c + d*x])/d + (4*a^4*(I*A + B)*Tan[c + d*x]^2)/d - (a^4*(92*A - (93*I)*B)*Tan[c + d*x]^3)/(60*d) + ((I/6)*a*B*Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d - ((2*A - (3*I)*B)*Tan[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x])^2)/(10*d) - ((12*A - (13*I)*B)*Tan[c + d*x]^3*(a^4 + I*a^4*Tan[c + d*x]))/(20*d)","A",7,5,34,0.1471,1,"{3594, 3592, 3528, 3525, 3475}"
27,1,168,0,0.1577472,"\int \tan (c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+\frac{4 a^4 (B+i A) \tan (c+d x)}{d}-\frac{8 a^4 (A-i B) \log (\cos (c+d x))}{d}-8 a^4 x (B+i A)+\frac{a (A-i B) (a+i a \tan (c+d x))^3}{3 d}+\frac{A (a+i a \tan (c+d x))^4}{4 d}-\frac{i B (a+i a \tan (c+d x))^5}{5 a d}","\frac{(A-i B) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+\frac{4 a^4 (B+i A) \tan (c+d x)}{d}-\frac{8 a^4 (A-i B) \log (\cos (c+d x))}{d}-8 a^4 x (B+i A)+\frac{a (A-i B) (a+i a \tan (c+d x))^3}{3 d}+\frac{A (a+i a \tan (c+d x))^4}{4 d}-\frac{i B (a+i a \tan (c+d x))^5}{5 a d}",1,"-8*a^4*(I*A + B)*x - (8*a^4*(A - I*B)*Log[Cos[c + d*x]])/d + (4*a^4*(I*A + B)*Tan[c + d*x])/d + (a*(A - I*B)*(a + I*a*Tan[c + d*x])^3)/(3*d) + (A*(a + I*a*Tan[c + d*x])^4)/(4*d) - ((I/5)*B*(a + I*a*Tan[c + d*x])^5)/(a*d) + ((A - I*B)*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",6,5,32,0.1562,1,"{3592, 3527, 3478, 3477, 3475}"
28,1,140,0,0.1147676,"\int (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{4 a^4 (A-i B) \tan (c+d x)}{d}+\frac{(B+i A) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 a^4 (B+i A) \log (\cos (c+d x))}{d}+8 a^4 x (A-i B)+\frac{a (B+i A) (a+i a \tan (c+d x))^3}{3 d}+\frac{B (a+i a \tan (c+d x))^4}{4 d}","-\frac{4 a^4 (A-i B) \tan (c+d x)}{d}+\frac{(B+i A) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 a^4 (B+i A) \log (\cos (c+d x))}{d}+8 a^4 x (A-i B)+\frac{a (B+i A) (a+i a \tan (c+d x))^3}{3 d}+\frac{B (a+i a \tan (c+d x))^4}{4 d}",1,"8*a^4*(A - I*B)*x - (8*a^4*(I*A + B)*Log[Cos[c + d*x]])/d - (4*a^4*(A - I*B)*Tan[c + d*x])/d + (a*(I*A + B)*(a + I*a*Tan[c + d*x])^3)/(3*d) + (B*(a + I*a*Tan[c + d*x])^4)/(4*d) + ((I*A + B)*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",5,4,26,0.1538,1,"{3527, 3478, 3477, 3475}"
29,1,142,0,0.4207669,"\int \cot (c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{(A-2 i B) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{(3 A-4 i B) \left(a^4+i a^4 \tan (c+d x)\right)}{d}+\frac{a^4 (7 A-8 i B) \log (\cos (c+d x))}{d}+8 a^4 x (B+i A)+\frac{a^4 A \log (\sin (c+d x))}{d}+\frac{i a B (a+i a \tan (c+d x))^3}{3 d}","-\frac{(A-2 i B) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{(3 A-4 i B) \left(a^4+i a^4 \tan (c+d x)\right)}{d}+\frac{a^4 (7 A-8 i B) \log (\cos (c+d x))}{d}+8 a^4 x (B+i A)+\frac{a^4 A \log (\sin (c+d x))}{d}+\frac{i a B (a+i a \tan (c+d x))^3}{3 d}",1,"8*a^4*(I*A + B)*x + (a^4*(7*A - (8*I)*B)*Log[Cos[c + d*x]])/d + (a^4*A*Log[Sin[c + d*x]])/d + ((I/3)*a*B*(a + I*a*Tan[c + d*x])^3)/d - ((A - (2*I)*B)*(a^2 + I*a^2*Tan[c + d*x])^2)/(2*d) - ((3*A - (4*I)*B)*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,4,32,0.1250,1,"{3594, 3589, 3475, 3531}"
30,1,144,0,0.432015,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{(-B+2 i A) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}+\frac{a^4 (B+4 i A) \log (\sin (c+d x))}{d}+\frac{a^4 (7 B+4 i A) \log (\cos (c+d x))}{d}-8 a^4 x (A-i B)-\frac{3 B \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^3}{d}","\frac{(-B+2 i A) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}+\frac{a^4 (B+4 i A) \log (\sin (c+d x))}{d}+\frac{a^4 (7 B+4 i A) \log (\cos (c+d x))}{d}-8 a^4 x (A-i B)-\frac{3 B \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^3}{d}",1,"-8*a^4*(A - I*B)*x + (a^4*((4*I)*A + 7*B)*Log[Cos[c + d*x]])/d + (a^4*((4*I)*A + B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^3)/d + (((2*I)*A - B)*(a^2 + I*a^2*Tan[c + d*x])^2)/(2*d) - (3*B*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,5,34,0.1471,1,"{3593, 3594, 3589, 3475, 3531}"
31,1,156,0,0.4423787,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{a^4 (7 A-4 i B) \log (\sin (c+d x))}{d}-\frac{a^4 (A-4 i B) \log (\cos (c+d x))}{d}-\frac{(2 B+5 i A) \cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-8 a^4 x (B+i A)-\frac{3 A \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^3}{2 d}","-\frac{a^4 (7 A-4 i B) \log (\sin (c+d x))}{d}-\frac{a^4 (A-4 i B) \log (\cos (c+d x))}{d}-\frac{(2 B+5 i A) \cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-8 a^4 x (B+i A)-\frac{3 A \left(a^4+i a^4 \tan (c+d x)\right)}{d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^3}{2 d}",1,"-8*a^4*(I*A + B)*x - (a^4*(A - (4*I)*B)*Log[Cos[c + d*x]])/d - (a^4*(7*A - (4*I)*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^3)/(2*d) - (((5*I)*A + 2*B)*Cot[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^2)/(2*d) - (3*A*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,5,34,0.1471,1,"{3593, 3594, 3589, 3475, 3531}"
32,1,163,0,0.4527091,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{a^4 (7 B+8 i A) \log (\sin (c+d x))}{d}-\frac{(B+2 i A) \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}+\frac{(4 A-3 i B) \cot (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}+8 a^4 x (A-i B)-\frac{a^4 B \log (\cos (c+d x))}{d}-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}","-\frac{a^4 (7 B+8 i A) \log (\sin (c+d x))}{d}-\frac{(B+2 i A) \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}+\frac{(4 A-3 i B) \cot (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}+8 a^4 x (A-i B)-\frac{a^4 B \log (\cos (c+d x))}{d}-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}",1,"8*a^4*(A - I*B)*x - (a^4*B*Log[Cos[c + d*x]])/d - (a^4*((8*I)*A + 7*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/(3*d) - (((2*I)*A + B)*Cot[c + d*x]^2*(a^2 + I*a^2*Tan[c + d*x])^2)/(2*d) + ((4*A - (3*I)*B)*Cot[c + d*x]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,4,34,0.1176,1,"{3593, 3589, 3475, 3531}"
33,1,177,0,0.5315035,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^4 (64 B+67 i A) \cot (c+d x)}{12 d}+\frac{8 a^4 (A-i B) \log (\sin (c+d x))}{d}-\frac{(4 B+7 i A) \cot ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{12 d}+\frac{(19 A-16 i B) \cot ^2(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{12 d}+8 a^4 x (B+i A)-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^3}{4 d}","\frac{a^4 (64 B+67 i A) \cot (c+d x)}{12 d}+\frac{8 a^4 (A-i B) \log (\sin (c+d x))}{d}-\frac{(4 B+7 i A) \cot ^3(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{12 d}+\frac{(19 A-16 i B) \cot ^2(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{12 d}+8 a^4 x (B+i A)-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^3}{4 d}",1,"8*a^4*(I*A + B)*x + (a^4*((67*I)*A + 64*B)*Cot[c + d*x])/(12*d) + (8*a^4*(A - I*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^3)/(4*d) - (((7*I)*A + 4*B)*Cot[c + d*x]^3*(a^2 + I*a^2*Tan[c + d*x])^2)/(12*d) + ((19*A - (16*I)*B)*Cot[c + d*x]^2*(a^4 + I*a^4*Tan[c + d*x]))/(12*d)","A",6,4,34,0.1176,1,"{3593, 3591, 3531, 3475}"
34,1,200,0,0.5919383,"\int \cot ^6(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^4 (145 B+148 i A) \cot ^2(c+d x)}{60 d}-\frac{8 a^4 (A-i B) \cot (c+d x)}{d}+\frac{8 a^4 (B+i A) \log (\sin (c+d x))}{d}-\frac{(5 B+8 i A) \cot ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{20 d}+\frac{(28 A-25 i B) \cot ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{30 d}-8 a^4 x (A-i B)-\frac{a A \cot ^5(c+d x) (a+i a \tan (c+d x))^3}{5 d}","\frac{a^4 (145 B+148 i A) \cot ^2(c+d x)}{60 d}-\frac{8 a^4 (A-i B) \cot (c+d x)}{d}+\frac{8 a^4 (B+i A) \log (\sin (c+d x))}{d}-\frac{(5 B+8 i A) \cot ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{20 d}+\frac{(28 A-25 i B) \cot ^3(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{30 d}-8 a^4 x (A-i B)-\frac{a A \cot ^5(c+d x) (a+i a \tan (c+d x))^3}{5 d}",1,"-8*a^4*(A - I*B)*x - (8*a^4*(A - I*B)*Cot[c + d*x])/d + (a^4*((148*I)*A + 145*B)*Cot[c + d*x]^2)/(60*d) + (8*a^4*(I*A + B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^3)/(5*d) - (((8*I)*A + 5*B)*Cot[c + d*x]^4*(a^2 + I*a^2*Tan[c + d*x])^2)/(20*d) + ((28*A - (25*I)*B)*Cot[c + d*x]^3*(a^4 + I*a^4*Tan[c + d*x]))/(30*d)","A",7,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
35,1,223,0,0.6456575,"\int \cot ^7(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^7*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^4 (92 B+93 i A) \cot ^3(c+d x)}{60 d}-\frac{4 a^4 (A-i B) \cot ^2(c+d x)}{d}-\frac{8 a^4 (B+i A) \cot (c+d x)}{d}-\frac{8 a^4 (A-i B) \log (\sin (c+d x))}{d}-\frac{(2 B+3 i A) \cot ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}+\frac{(13 A-12 i B) \cot ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{20 d}-8 a^4 x (B+i A)-\frac{a A \cot ^6(c+d x) (a+i a \tan (c+d x))^3}{6 d}","\frac{a^4 (92 B+93 i A) \cot ^3(c+d x)}{60 d}-\frac{4 a^4 (A-i B) \cot ^2(c+d x)}{d}-\frac{8 a^4 (B+i A) \cot (c+d x)}{d}-\frac{8 a^4 (A-i B) \log (\sin (c+d x))}{d}-\frac{(2 B+3 i A) \cot ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{10 d}+\frac{(13 A-12 i B) \cot ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{20 d}-8 a^4 x (B+i A)-\frac{a A \cot ^6(c+d x) (a+i a \tan (c+d x))^3}{6 d}",1,"-8*a^4*(I*A + B)*x - (8*a^4*(I*A + B)*Cot[c + d*x])/d - (4*a^4*(A - I*B)*Cot[c + d*x]^2)/d + (a^4*((93*I)*A + 92*B)*Cot[c + d*x]^3)/(60*d) - (8*a^4*(A - I*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^3)/(6*d) - (((3*I)*A + 2*B)*Cot[c + d*x]^5*(a^2 + I*a^2*Tan[c + d*x])^2)/(10*d) + ((13*A - (12*I)*B)*Cot[c + d*x]^4*(a^4 + I*a^4*Tan[c + d*x]))/(20*d)","A",8,5,34,0.1471,1,"{3593, 3591, 3529, 3531, 3475}"
36,1,129,0,0.1731583,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(-B+i A) \tan ^3(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(A+2 i B) \tan ^2(c+d x)}{2 a d}-\frac{3 (-B+i A) \tan (c+d x)}{2 a d}-\frac{(A+2 i B) \log (\cos (c+d x))}{a d}+\frac{3 x (-B+i A)}{2 a}","\frac{(-B+i A) \tan ^3(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(A+2 i B) \tan ^2(c+d x)}{2 a d}-\frac{3 (-B+i A) \tan (c+d x)}{2 a d}-\frac{(A+2 i B) \log (\cos (c+d x))}{a d}+\frac{3 x (-B+i A)}{2 a}",1,"(3*(I*A - B)*x)/(2*a) - ((A + (2*I)*B)*Log[Cos[c + d*x]])/(a*d) - (3*(I*A - B)*Tan[c + d*x])/(2*a*d) - ((A + (2*I)*B)*Tan[c + d*x]^2)/(2*a*d) + ((I*A - B)*Tan[c + d*x]^3)/(2*d*(a + I*a*Tan[c + d*x]))","A",4,4,34,0.1176,1,"{3595, 3528, 3525, 3475}"
37,1,101,0,0.1246435,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(-B+i A) \tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(A+3 i B) \tan (c+d x)}{2 a d}+\frac{(-B+i A) \log (\cos (c+d x))}{a d}+\frac{x (A+3 i B)}{2 a}","\frac{(-B+i A) \tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(A+3 i B) \tan (c+d x)}{2 a d}+\frac{(-B+i A) \log (\cos (c+d x))}{a d}+\frac{x (A+3 i B)}{2 a}",1,"((A + (3*I)*B)*x)/(2*a) + ((I*A - B)*Log[Cos[c + d*x]])/(a*d) - ((A + (3*I)*B)*Tan[c + d*x])/(2*a*d) + ((I*A - B)*Tan[c + d*x]^2)/(2*d*(a + I*a*Tan[c + d*x]))","A",3,3,34,0.08824,1,"{3595, 3525, 3475}"
38,1,67,0,0.093083,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","-\frac{A+i B}{2 a d (1+i \tan (c+d x))}-\frac{x (-B+i A)}{2 a}+\frac{i B \log (\cos (c+d x))}{a d}","-\frac{A+i B}{2 a d (1+i \tan (c+d x))}-\frac{x (-B+i A)}{2 a}+\frac{i B \log (\cos (c+d x))}{a d}",1,"-((I*A - B)*x)/(2*a) + (I*B*Log[Cos[c + d*x]])/(a*d) - (A + I*B)/(2*a*d*(1 + I*Tan[c + d*x]))","A",5,5,32,0.1562,1,"{3589, 3475, 12, 3526, 8}"
39,1,47,0,0.0427031,"\int \frac{A+B \tan (c+d x)}{a+i a \tan (c+d x)} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x]),x]","\frac{-B+i A}{2 d (a+i a \tan (c+d x))}+\frac{x (A-i B)}{2 a}","\frac{-B+i A}{2 d (a+i a \tan (c+d x))}+\frac{x (A-i B)}{2 a}",1,"((A - I*B)*x)/(2*a) + (I*A - B)/(2*d*(a + I*a*Tan[c + d*x]))","A",2,2,26,0.07692,1,"{3526, 8}"
40,1,62,0,0.109208,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{A+i B}{2 d (a+i a \tan (c+d x))}-\frac{x (-B+i A)}{2 a}+\frac{A \log (\sin (c+d x))}{a d}","\frac{A+i B}{2 d (a+i a \tan (c+d x))}-\frac{x (-B+i A)}{2 a}+\frac{A \log (\sin (c+d x))}{a d}",1,"-((I*A - B)*x)/(2*a) + (A*Log[Sin[c + d*x]])/(a*d) + (A + I*B)/(2*d*(a + I*a*Tan[c + d*x]))","A",3,3,32,0.09375,1,"{3596, 3531, 3475}"
41,1,102,0,0.1747076,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","-\frac{(3 A+i B) \cot (c+d x)}{2 a d}-\frac{(-B+i A) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot (c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{x (3 A+i B)}{2 a}","-\frac{(3 A+i B) \cot (c+d x)}{2 a d}-\frac{(-B+i A) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot (c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{x (3 A+i B)}{2 a}",1,"-((3*A + I*B)*x)/(2*a) - ((3*A + I*B)*Cot[c + d*x])/(2*a*d) - ((I*A - B)*Log[Sin[c + d*x]])/(a*d) + ((A + I*B)*Cot[c + d*x])/(2*d*(a + I*a*Tan[c + d*x]))","A",4,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
42,1,131,0,0.212175,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","-\frac{(2 A+i B) \cot ^2(c+d x)}{2 a d}+\frac{3 (-B+i A) \cot (c+d x)}{2 a d}-\frac{(2 A+i B) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot ^2(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{3 x (-B+i A)}{2 a}","-\frac{(2 A+i B) \cot ^2(c+d x)}{2 a d}+\frac{3 (-B+i A) \cot (c+d x)}{2 a d}-\frac{(2 A+i B) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot ^2(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{3 x (-B+i A)}{2 a}",1,"(3*(I*A - B)*x)/(2*a) + (3*(I*A - B)*Cot[c + d*x])/(2*a*d) - ((2*A + I*B)*Cot[c + d*x]^2)/(2*a*d) - ((2*A + I*B)*Log[Sin[c + d*x]])/(a*d) + ((A + I*B)*Cot[c + d*x]^2)/(2*d*(a + I*a*Tan[c + d*x]))","A",5,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
43,1,155,0,0.2462089,"\int \frac{\cot ^4(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","-\frac{(5 A+3 i B) \cot ^3(c+d x)}{6 a d}+\frac{(-B+i A) \cot ^2(c+d x)}{a d}+\frac{(5 A+3 i B) \cot (c+d x)}{2 a d}+\frac{2 (-B+i A) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot ^3(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{x (5 A+3 i B)}{2 a}","-\frac{(5 A+3 i B) \cot ^3(c+d x)}{6 a d}+\frac{(-B+i A) \cot ^2(c+d x)}{a d}+\frac{(5 A+3 i B) \cot (c+d x)}{2 a d}+\frac{2 (-B+i A) \log (\sin (c+d x))}{a d}+\frac{(A+i B) \cot ^3(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{x (5 A+3 i B)}{2 a}",1,"((5*A + (3*I)*B)*x)/(2*a) + ((5*A + (3*I)*B)*Cot[c + d*x])/(2*a*d) + ((I*A - B)*Cot[c + d*x]^2)/(a*d) - ((5*A + (3*I)*B)*Cot[c + d*x]^3)/(6*a*d) + (2*(I*A - B)*Log[Sin[c + d*x]])/(a*d) + ((A + I*B)*Cot[c + d*x]^3)/(2*d*(a + I*a*Tan[c + d*x]))","A",6,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
44,1,142,0,0.2800722,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{(A+2 i B) \tan ^2(c+d x)}{2 a^2 d (1+i \tan (c+d x))}+\frac{3 (-3 B+i A) \tan (c+d x)}{4 a^2 d}+\frac{(A+2 i B) \log (\cos (c+d x))}{a^2 d}-\frac{3 x (-3 B+i A)}{4 a^2}+\frac{(-B+i A) \tan ^3(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{(A+2 i B) \tan ^2(c+d x)}{2 a^2 d (1+i \tan (c+d x))}+\frac{3 (-3 B+i A) \tan (c+d x)}{4 a^2 d}+\frac{(A+2 i B) \log (\cos (c+d x))}{a^2 d}-\frac{3 x (-3 B+i A)}{4 a^2}+\frac{(-B+i A) \tan ^3(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-3*(I*A - 3*B)*x)/(4*a^2) + ((A + (2*I)*B)*Log[Cos[c + d*x]])/(a^2*d) + (3*(I*A - 3*B)*Tan[c + d*x])/(4*a^2*d) + ((A + (2*I)*B)*Tan[c + d*x]^2)/(2*a^2*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",4,3,34,0.08824,1,"{3595, 3525, 3475}"
45,1,103,0,0.2109475,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{-3 B+i A}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (A+3 i B)}{4 a^2}+\frac{B \log (\cos (c+d x))}{a^2 d}+\frac{(-B+i A) \tan ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{-3 B+i A}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (A+3 i B)}{4 a^2}+\frac{B \log (\cos (c+d x))}{a^2 d}+\frac{(-B+i A) \tan ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"-((A + (3*I)*B)*x)/(4*a^2) + (B*Log[Cos[c + d*x]])/(a^2*d) + (I*A - 3*B)/(4*a^2*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^2)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",6,6,34,0.1765,1,"{3595, 3589, 3475, 12, 3526, 8}"
46,1,76,0,0.1307032,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{A+3 i B}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (B+i A)}{4 a^2}-\frac{A+i B}{4 d (a+i a \tan (c+d x))^2}","\frac{A+3 i B}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (B+i A)}{4 a^2}-\frac{A+i B}{4 d (a+i a \tan (c+d x))^2}",1,"-((I*A + B)*x)/(4*a^2) + (A + (3*I)*B)/(4*a^2*d*(1 + I*Tan[c + d*x])) - (A + I*B)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",3,3,32,0.09375,1,"{3590, 3526, 8}"
47,1,80,0,0.0615542,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^2,x]","\frac{B+i A}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x (A-i B)}{4 a^2}+\frac{-B+i A}{4 d (a+i a \tan (c+d x))^2}","\frac{B+i A}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x (A-i B)}{4 a^2}+\frac{-B+i A}{4 d (a+i a \tan (c+d x))^2}",1,"((A - I*B)*x)/(4*a^2) + (I*A - B)/(4*d*(a + I*a*Tan[c + d*x])^2) + (I*A + B)/(4*d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,3,26,0.1154,1,"{3526, 3479, 8}"
48,1,95,0,0.2286867,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{3 A+i B}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (-B+3 i A)}{4 a^2}+\frac{A \log (\sin (c+d x))}{a^2 d}+\frac{A+i B}{4 d (a+i a \tan (c+d x))^2}","\frac{3 A+i B}{4 a^2 d (1+i \tan (c+d x))}-\frac{x (-B+3 i A)}{4 a^2}+\frac{A \log (\sin (c+d x))}{a^2 d}+\frac{A+i B}{4 d (a+i a \tan (c+d x))^2}",1,"-(((3*I)*A - B)*x)/(4*a^2) + (A*Log[Sin[c + d*x]])/(a^2*d) + (3*A + I*B)/(4*a^2*d*(1 + I*Tan[c + d*x])) + (A + I*B)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",4,3,32,0.09375,1,"{3596, 3531, 3475}"
49,1,141,0,0.345708,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","-\frac{3 (3 A+i B) \cot (c+d x)}{4 a^2 d}-\frac{(-B+2 i A) \log (\sin (c+d x))}{a^2 d}+\frac{(2 A+i B) \cot (c+d x)}{2 a^2 d (1+i \tan (c+d x))}-\frac{3 x (3 A+i B)}{4 a^2}+\frac{(A+i B) \cot (c+d x)}{4 d (a+i a \tan (c+d x))^2}","-\frac{3 (3 A+i B) \cot (c+d x)}{4 a^2 d}-\frac{(-B+2 i A) \log (\sin (c+d x))}{a^2 d}+\frac{(2 A+i B) \cot (c+d x)}{2 a^2 d (1+i \tan (c+d x))}-\frac{3 x (3 A+i B)}{4 a^2}+\frac{(A+i B) \cot (c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-3*(3*A + I*B)*x)/(4*a^2) - (3*(3*A + I*B)*Cot[c + d*x])/(4*a^2*d) - (((2*I)*A - B)*Log[Sin[c + d*x]])/(a^2*d) + ((2*A + I*B)*Cot[c + d*x])/(2*a^2*d*(1 + I*Tan[c + d*x])) + ((A + I*B)*Cot[c + d*x])/(4*d*(a + I*a*Tan[c + d*x])^2)","A",5,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
50,1,170,0,0.4048787,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","-\frac{(2 A+i B) \cot ^2(c+d x)}{a^2 d}+\frac{3 (-3 B+5 i A) \cot (c+d x)}{4 a^2 d}-\frac{2 (2 A+i B) \log (\sin (c+d x))}{a^2 d}+\frac{(5 A+3 i B) \cot ^2(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{3 x (-3 B+5 i A)}{4 a^2}+\frac{(A+i B) \cot ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}","-\frac{(2 A+i B) \cot ^2(c+d x)}{a^2 d}+\frac{3 (-3 B+5 i A) \cot (c+d x)}{4 a^2 d}-\frac{2 (2 A+i B) \log (\sin (c+d x))}{a^2 d}+\frac{(5 A+3 i B) \cot ^2(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{3 x (-3 B+5 i A)}{4 a^2}+\frac{(A+i B) \cot ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(3*((5*I)*A - 3*B)*x)/(4*a^2) + (3*((5*I)*A - 3*B)*Cot[c + d*x])/(4*a^2*d) - ((2*A + I*B)*Cot[c + d*x]^2)/(a^2*d) - (2*(2*A + I*B)*Log[Sin[c + d*x]])/(a^2*d) + ((5*A + (3*I)*B)*Cot[c + d*x]^2)/(4*a^2*d*(1 + I*Tan[c + d*x])) + ((A + I*B)*Cot[c + d*x]^2)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",6,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
51,1,191,0,0.4734843,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{(-3 B+i A) \tan ^2(c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(7 A+25 i B) \tan (c+d x)}{8 a^3 d}-\frac{(-3 B+i A) \log (\cos (c+d x))}{a^3 d}-\frac{x (7 A+25 i B)}{8 a^3}+\frac{(-B+i A) \tan ^4(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(5 A+11 i B) \tan ^3(c+d x)}{24 a d (a+i a \tan (c+d x))^2}","-\frac{(-3 B+i A) \tan ^2(c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(7 A+25 i B) \tan (c+d x)}{8 a^3 d}-\frac{(-3 B+i A) \log (\cos (c+d x))}{a^3 d}-\frac{x (7 A+25 i B)}{8 a^3}+\frac{(-B+i A) \tan ^4(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(5 A+11 i B) \tan ^3(c+d x)}{24 a d (a+i a \tan (c+d x))^2}",1,"-((7*A + (25*I)*B)*x)/(8*a^3) - ((I*A - 3*B)*Log[Cos[c + d*x]])/(a^3*d) + ((7*A + (25*I)*B)*Tan[c + d*x])/(8*a^3*d) + ((I*A - B)*Tan[c + d*x]^4)/(6*d*(a + I*a*Tan[c + d*x])^3) + ((5*A + (11*I)*B)*Tan[c + d*x]^3)/(24*a*d*(a + I*a*Tan[c + d*x])^2) - ((I*A - 3*B)*Tan[c + d*x]^2)/(2*d*(a^3 + I*a^3*Tan[c + d*x]))","A",5,3,34,0.08824,1,"{3595, 3525, 3475}"
52,1,148,0,0.3682362,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{A+7 i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x (-7 B+i A)}{8 a^3}-\frac{i B \log (\cos (c+d x))}{a^3 d}+\frac{(-B+i A) \tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+3 i B) \tan ^2(c+d x)}{8 a d (a+i a \tan (c+d x))^2}","\frac{A+7 i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x (-7 B+i A)}{8 a^3}-\frac{i B \log (\cos (c+d x))}{a^3 d}+\frac{(-B+i A) \tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+3 i B) \tan ^2(c+d x)}{8 a d (a+i a \tan (c+d x))^2}",1,"((I*A - 7*B)*x)/(8*a^3) - (I*B*Log[Cos[c + d*x]])/(a^3*d) + ((I*A - B)*Tan[c + d*x]^3)/(6*d*(a + I*a*Tan[c + d*x])^3) + ((A + (3*I)*B)*Tan[c + d*x]^2)/(8*a*d*(a + I*a*Tan[c + d*x])^2) + (A + (7*I)*B)/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",7,6,34,0.1765,1,"{3595, 3589, 3475, 12, 3526, 8}"
53,1,124,0,0.2887537,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{17 B+i A}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (A-i B)}{8 a^3}+\frac{(-B+i A) \tan ^2(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{-7 B+i A}{24 a d (a+i a \tan (c+d x))^2}","\frac{17 B+i A}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (A-i B)}{8 a^3}+\frac{(-B+i A) \tan ^2(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{-7 B+i A}{24 a d (a+i a \tan (c+d x))^2}",1,"-((A - I*B)*x)/(8*a^3) + ((I*A - B)*Tan[c + d*x]^2)/(6*d*(a + I*a*Tan[c + d*x])^3) + (I*A - 7*B)/(24*a*d*(a + I*a*Tan[c + d*x])^2) + (I*A + 17*B)/(24*d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,4,34,0.1176,1,"{3595, 3590, 3526, 8}"
54,1,110,0,0.1649543,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{A-i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (B+i A)}{8 a^3}+\frac{A+3 i B}{8 a d (a+i a \tan (c+d x))^2}-\frac{A+i B}{6 d (a+i a \tan (c+d x))^3}","\frac{A-i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (B+i A)}{8 a^3}+\frac{A+3 i B}{8 a d (a+i a \tan (c+d x))^2}-\frac{A+i B}{6 d (a+i a \tan (c+d x))^3}",1,"-((I*A + B)*x)/(8*a^3) - (A + I*B)/(6*d*(a + I*a*Tan[c + d*x])^3) + (A + (3*I)*B)/(8*a*d*(a + I*a*Tan[c + d*x])^2) + (A - I*B)/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,4,32,0.1250,1,"{3590, 3526, 3479, 8}"
55,1,112,0,0.0836763,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^3,x]","\frac{B+i A}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x (A-i B)}{8 a^3}+\frac{-B+i A}{6 d (a+i a \tan (c+d x))^3}+\frac{B+i A}{8 a d (a+i a \tan (c+d x))^2}","\frac{B+i A}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x (A-i B)}{8 a^3}+\frac{-B+i A}{6 d (a+i a \tan (c+d x))^3}+\frac{B+i A}{8 a d (a+i a \tan (c+d x))^2}",1,"((A - I*B)*x)/(8*a^3) + (I*A - B)/(6*d*(a + I*a*Tan[c + d*x])^3) + (I*A + B)/(8*a*d*(a + I*a*Tan[c + d*x])^2) + (I*A + B)/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,26,0.1154,1,"{3526, 3479, 8}"
56,1,131,0,0.3606025,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{7 A+i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (-B+7 i A)}{8 a^3}+\frac{A \log (\sin (c+d x))}{a^3 d}+\frac{A+i B}{6 d (a+i a \tan (c+d x))^3}+\frac{3 A+i B}{8 a d (a+i a \tan (c+d x))^2}","\frac{7 A+i B}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (-B+7 i A)}{8 a^3}+\frac{A \log (\sin (c+d x))}{a^3 d}+\frac{A+i B}{6 d (a+i a \tan (c+d x))^3}+\frac{3 A+i B}{8 a d (a+i a \tan (c+d x))^2}",1,"-(((7*I)*A - B)*x)/(8*a^3) + (A*Log[Sin[c + d*x]])/(a^3*d) + (A + I*B)/(6*d*(a + I*a*Tan[c + d*x])^3) + (3*A + I*B)/(8*a*d*(a + I*a*Tan[c + d*x])^2) + (7*A + I*B)/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",5,3,32,0.09375,1,"{3596, 3531, 3475}"
57,1,183,0,0.5296287,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{(25 A+7 i B) \cot (c+d x)}{8 a^3 d}-\frac{(-B+3 i A) \log (\sin (c+d x))}{a^3 d}+\frac{(3 A+i B) \cot (c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (25 A+7 i B)}{8 a^3}+\frac{(11 A+5 i B) \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \cot (c+d x)}{6 d (a+i a \tan (c+d x))^3}","-\frac{(25 A+7 i B) \cot (c+d x)}{8 a^3 d}-\frac{(-B+3 i A) \log (\sin (c+d x))}{a^3 d}+\frac{(3 A+i B) \cot (c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x (25 A+7 i B)}{8 a^3}+\frac{(11 A+5 i B) \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \cot (c+d x)}{6 d (a+i a \tan (c+d x))^3}",1,"-((25*A + (7*I)*B)*x)/(8*a^3) - ((25*A + (7*I)*B)*Cot[c + d*x])/(8*a^3*d) - (((3*I)*A - B)*Log[Sin[c + d*x]])/(a^3*d) + ((A + I*B)*Cot[c + d*x])/(6*d*(a + I*a*Tan[c + d*x])^3) + ((11*A + (5*I)*B)*Cot[c + d*x])/(24*a*d*(a + I*a*Tan[c + d*x])^2) + ((3*A + I*B)*Cot[c + d*x])/(2*d*(a^3 + I*a^3*Tan[c + d*x]))","A",6,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
58,1,216,0,0.5983471,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{(7 A+3 i B) \cot ^2(c+d x)}{2 a^3 d}+\frac{5 (-5 B+11 i A) \cot (c+d x)}{8 a^3 d}-\frac{(7 A+3 i B) \log (\sin (c+d x))}{a^3 d}+\frac{5 (11 A+5 i B) \cot ^2(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{5 x (-5 B+11 i A)}{8 a^3}+\frac{(13 A+7 i B) \cot ^2(c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \cot ^2(c+d x)}{6 d (a+i a \tan (c+d x))^3}","-\frac{(7 A+3 i B) \cot ^2(c+d x)}{2 a^3 d}+\frac{5 (-5 B+11 i A) \cot (c+d x)}{8 a^3 d}-\frac{(7 A+3 i B) \log (\sin (c+d x))}{a^3 d}+\frac{5 (11 A+5 i B) \cot ^2(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{5 x (-5 B+11 i A)}{8 a^3}+\frac{(13 A+7 i B) \cot ^2(c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \cot ^2(c+d x)}{6 d (a+i a \tan (c+d x))^3}",1,"(5*((11*I)*A - 5*B)*x)/(8*a^3) + (5*((11*I)*A - 5*B)*Cot[c + d*x])/(8*a^3*d) - ((7*A + (3*I)*B)*Cot[c + d*x]^2)/(2*a^3*d) - ((7*A + (3*I)*B)*Log[Sin[c + d*x]])/(a^3*d) + ((A + I*B)*Cot[c + d*x]^2)/(6*d*(a + I*a*Tan[c + d*x])^3) + ((13*A + (7*I)*B)*Cot[c + d*x]^2)/(24*a*d*(a + I*a*Tan[c + d*x])^2) + (5*(11*A + (5*I)*B)*Cot[c + d*x]^2)/(24*d*(a^3 + I*a^3*Tan[c + d*x]))","A",7,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
59,1,185,0,0.5087084,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","-\frac{(-7 B+i A) \tan ^2(c+d x)}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{-15 B+i A}{16 a^4 d (1+i \tan (c+d x))}+\frac{x (A+15 i B)}{16 a^4}-\frac{B \log (\cos (c+d x))}{a^4 d}+\frac{(-B+i A) \tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{(A+3 i B) \tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}","-\frac{(-7 B+i A) \tan ^2(c+d x)}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{-15 B+i A}{16 a^4 d (1+i \tan (c+d x))}+\frac{x (A+15 i B)}{16 a^4}-\frac{B \log (\cos (c+d x))}{a^4 d}+\frac{(-B+i A) \tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{(A+3 i B) \tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}",1,"((A + (15*I)*B)*x)/(16*a^4) - (B*Log[Cos[c + d*x]])/(a^4*d) - (I*A - 15*B)/(16*a^4*d*(1 + I*Tan[c + d*x])) - ((I*A - 7*B)*Tan[c + d*x]^2)/(16*a^4*d*(1 + I*Tan[c + d*x])^2) + ((I*A - B)*Tan[c + d*x]^4)/(8*d*(a + I*a*Tan[c + d*x])^4) + ((A + (3*I)*B)*Tan[c + d*x]^3)/(12*a*d*(a + I*a*Tan[c + d*x])^3)","A",8,6,34,0.1765,1,"{3595, 3589, 3475, 12, 3526, 8}"
60,1,159,0,0.4656665,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","\frac{5 A-29 i B}{48 a^4 d (1+i \tan (c+d x))}-\frac{A-13 i B}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{x (B+i A)}{16 a^4}+\frac{(-B+i A) \tan ^3(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{(A+5 i B) \tan ^2(c+d x)}{24 a d (a+i a \tan (c+d x))^3}","\frac{5 A-29 i B}{48 a^4 d (1+i \tan (c+d x))}-\frac{A-13 i B}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{x (B+i A)}{16 a^4}+\frac{(-B+i A) \tan ^3(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{(A+5 i B) \tan ^2(c+d x)}{24 a d (a+i a \tan (c+d x))^3}",1,"((I*A + B)*x)/(16*a^4) - (A - (13*I)*B)/(48*a^4*d*(1 + I*Tan[c + d*x])^2) + (5*A - (29*I)*B)/(48*a^4*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^3)/(8*d*(a + I*a*Tan[c + d*x])^4) + ((A + (5*I)*B)*Tan[c + d*x]^2)/(24*a*d*(a + I*a*Tan[c + d*x])^3)","A",5,4,34,0.1176,1,"{3595, 3590, 3526, 8}"
61,1,145,0,0.2906712,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","-\frac{B+i A}{16 a^4 d (1+i \tan (c+d x))}+\frac{5 B+i A}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{x (A-i B)}{16 a^4}+\frac{(-B+i A) \tan ^2(c+d x)}{8 d (a+i a \tan (c+d x))^4}-\frac{B}{6 a d (a+i a \tan (c+d x))^3}","-\frac{B+i A}{16 a^4 d (1+i \tan (c+d x))}+\frac{5 B+i A}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{x (A-i B)}{16 a^4}+\frac{(-B+i A) \tan ^2(c+d x)}{8 d (a+i a \tan (c+d x))^4}-\frac{B}{6 a d (a+i a \tan (c+d x))^3}",1,"-((A - I*B)*x)/(16*a^4) + (I*A + 5*B)/(16*a^4*d*(1 + I*Tan[c + d*x])^2) - (I*A + B)/(16*a^4*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^2)/(8*d*(a + I*a*Tan[c + d*x])^4) - B/(6*a*d*(a + I*a*Tan[c + d*x])^3)","A",5,5,34,0.1471,1,"{3595, 3590, 3526, 3479, 8}"
62,1,143,0,0.1922475,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","\frac{A-i B}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{A-i B}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{x (B+i A)}{16 a^4}+\frac{A+3 i B}{12 a d (a+i a \tan (c+d x))^3}-\frac{A+i B}{8 d (a+i a \tan (c+d x))^4}","\frac{A-i B}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{A-i B}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{x (B+i A)}{16 a^4}+\frac{A+3 i B}{12 a d (a+i a \tan (c+d x))^3}-\frac{A+i B}{8 d (a+i a \tan (c+d x))^4}",1,"-((I*A + B)*x)/(16*a^4) - (A + I*B)/(8*d*(a + I*a*Tan[c + d*x])^4) + (A + (3*I)*B)/(12*a*d*(a + I*a*Tan[c + d*x])^3) + (A - I*B)/(16*d*(a^2 + I*a^2*Tan[c + d*x])^2) + (A - I*B)/(16*d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,32,0.1250,1,"{3590, 3526, 3479, 8}"
63,1,145,0,0.1064138,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^4,x]","\frac{B+i A}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{B+i A}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x (A-i B)}{16 a^4}+\frac{-B+i A}{8 d (a+i a \tan (c+d x))^4}+\frac{B+i A}{12 a d (a+i a \tan (c+d x))^3}","\frac{B+i A}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{B+i A}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x (A-i B)}{16 a^4}+\frac{-B+i A}{8 d (a+i a \tan (c+d x))^4}+\frac{B+i A}{12 a d (a+i a \tan (c+d x))^3}",1,"((A - I*B)*x)/(16*a^4) + (I*A - B)/(8*d*(a + I*a*Tan[c + d*x])^4) + (I*A + B)/(12*a*d*(a + I*a*Tan[c + d*x])^3) + (I*A + B)/(16*d*(a^2 + I*a^2*Tan[c + d*x])^2) + (I*A + B)/(16*d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,26,0.1154,1,"{3526, 3479, 8}"
64,1,162,0,0.4942433,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","\frac{15 A+i B}{16 a^4 d (1+i \tan (c+d x))}+\frac{7 A+i B}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{x (-B+15 i A)}{16 a^4}+\frac{A \log (\sin (c+d x))}{a^4 d}+\frac{A+i B}{8 d (a+i a \tan (c+d x))^4}+\frac{3 A+i B}{12 a d (a+i a \tan (c+d x))^3}","\frac{15 A+i B}{16 a^4 d (1+i \tan (c+d x))}+\frac{7 A+i B}{16 a^4 d (1+i \tan (c+d x))^2}-\frac{x (-B+15 i A)}{16 a^4}+\frac{A \log (\sin (c+d x))}{a^4 d}+\frac{A+i B}{8 d (a+i a \tan (c+d x))^4}+\frac{3 A+i B}{12 a d (a+i a \tan (c+d x))^3}",1,"-(((15*I)*A - B)*x)/(16*a^4) + (A*Log[Sin[c + d*x]])/(a^4*d) + (7*A + I*B)/(16*a^4*d*(1 + I*Tan[c + d*x])^2) + (15*A + I*B)/(16*a^4*d*(1 + I*Tan[c + d*x])) + (A + I*B)/(8*d*(a + I*a*Tan[c + d*x])^4) + (3*A + I*B)/(12*a*d*(a + I*a*Tan[c + d*x])^3)","A",6,3,32,0.09375,1,"{3596, 3531, 3475}"
65,1,220,0,0.7206515,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","-\frac{5 (13 A+3 i B) \cot (c+d x)}{16 a^4 d}-\frac{(-B+4 i A) \log (\sin (c+d x))}{a^4 d}+\frac{(4 A+i B) \cot (c+d x)}{2 a^4 d (1+i \tan (c+d x))}+\frac{(31 A+9 i B) \cot (c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{5 x (13 A+3 i B)}{16 a^4}+\frac{(7 A+3 i B) \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \cot (c+d x)}{8 d (a+i a \tan (c+d x))^4}","-\frac{5 (13 A+3 i B) \cot (c+d x)}{16 a^4 d}-\frac{(-B+4 i A) \log (\sin (c+d x))}{a^4 d}+\frac{(4 A+i B) \cot (c+d x)}{2 a^4 d (1+i \tan (c+d x))}+\frac{(31 A+9 i B) \cot (c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{5 x (13 A+3 i B)}{16 a^4}+\frac{(7 A+3 i B) \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \cot (c+d x)}{8 d (a+i a \tan (c+d x))^4}",1,"(-5*(13*A + (3*I)*B)*x)/(16*a^4) - (5*(13*A + (3*I)*B)*Cot[c + d*x])/(16*a^4*d) - (((4*I)*A - B)*Log[Sin[c + d*x]])/(a^4*d) + ((31*A + (9*I)*B)*Cot[c + d*x])/(48*a^4*d*(1 + I*Tan[c + d*x])^2) + ((4*A + I*B)*Cot[c + d*x])/(2*a^4*d*(1 + I*Tan[c + d*x])) + ((A + I*B)*Cot[c + d*x])/(8*d*(a + I*a*Tan[c + d*x])^4) + ((7*A + (3*I)*B)*Cot[c + d*x])/(24*a*d*(a + I*a*Tan[c + d*x])^3)","A",7,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
66,1,255,0,0.789628,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","-\frac{(11 A+4 i B) \cot ^2(c+d x)}{2 a^4 d}+\frac{5 (-13 B+35 i A) \cot (c+d x)}{16 a^4 d}-\frac{(11 A+4 i B) \log (\sin (c+d x))}{a^4 d}+\frac{5 (35 A+13 i B) \cot ^2(c+d x)}{48 a^4 d (1+i \tan (c+d x))}+\frac{(43 A+17 i B) \cot ^2(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{5 x (-13 B+35 i A)}{16 a^4}+\frac{(2 A+i B) \cot ^2(c+d x)}{6 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \cot ^2(c+d x)}{8 d (a+i a \tan (c+d x))^4}","-\frac{(11 A+4 i B) \cot ^2(c+d x)}{2 a^4 d}+\frac{5 (-13 B+35 i A) \cot (c+d x)}{16 a^4 d}-\frac{(11 A+4 i B) \log (\sin (c+d x))}{a^4 d}+\frac{5 (35 A+13 i B) \cot ^2(c+d x)}{48 a^4 d (1+i \tan (c+d x))}+\frac{(43 A+17 i B) \cot ^2(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{5 x (-13 B+35 i A)}{16 a^4}+\frac{(2 A+i B) \cot ^2(c+d x)}{6 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \cot ^2(c+d x)}{8 d (a+i a \tan (c+d x))^4}",1,"(5*((35*I)*A - 13*B)*x)/(16*a^4) + (5*((35*I)*A - 13*B)*Cot[c + d*x])/(16*a^4*d) - ((11*A + (4*I)*B)*Cot[c + d*x]^2)/(2*a^4*d) - ((11*A + (4*I)*B)*Log[Sin[c + d*x]])/(a^4*d) + ((43*A + (17*I)*B)*Cot[c + d*x]^2)/(48*a^4*d*(1 + I*Tan[c + d*x])^2) + (5*(35*A + (13*I)*B)*Cot[c + d*x]^2)/(48*a^4*d*(1 + I*Tan[c + d*x])) + ((A + I*B)*Cot[c + d*x]^2)/(8*d*(a + I*a*Tan[c + d*x])^4) + ((2*A + I*B)*Cot[c + d*x]^2)/(6*a*d*(a + I*a*Tan[c + d*x])^3)","A",8,4,34,0.1176,1,"{3596, 3529, 3531, 3475}"
67,1,194,0,0.5182695,"\int \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{2 (7 A-i B) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{2 (7 A-31 i B) (a+i a \tan (c+d x))^{3/2}}{105 a d}-\frac{8 (7 A-i B) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 B \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}","\frac{2 (7 A-i B) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{2 (7 A-31 i B) (a+i a \tan (c+d x))^{3/2}}{105 a d}-\frac{8 (7 A-i B) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 B \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}",1,"(Sqrt[2]*Sqrt[a]*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (8*(7*A - I*B)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) + (2*(7*A - I*B)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) + (2*B*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(7*d) - (2*(7*A - (31*I)*B)*(a + I*a*Tan[c + d*x])^(3/2))/(105*a*d)","A",6,5,36,0.1389,1,"{3597, 3592, 3527, 3480, 206}"
68,1,143,0,0.3021001,"\int \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{2 (B+5 i A) (a+i a \tan (c+d x))^{3/2}}{15 a d}+\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 B \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{8 B \sqrt{a+i a \tan (c+d x)}}{5 d}","-\frac{2 (B+5 i A) (a+i a \tan (c+d x))^{3/2}}{15 a d}+\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 B \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{8 B \sqrt{a+i a \tan (c+d x)}}{5 d}",1,"(Sqrt[2]*Sqrt[a]*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (8*B*Sqrt[a + I*a*Tan[c + d*x]])/(5*d) + (2*B*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(5*d) - (2*((5*I)*A + B)*(a + I*a*Tan[c + d*x])^(3/2))/(15*a*d)","A",5,5,36,0.1389,1,"{3597, 3592, 3527, 3480, 206}"
69,1,105,0,0.1367878,"\int \tan (c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 A \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 i B (a+i a \tan (c+d x))^{3/2}}{3 a d}","-\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 A \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 i B (a+i a \tan (c+d x))^{3/2}}{3 a d}",1,"-((Sqrt[2]*Sqrt[a]*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d) + (2*A*Sqrt[a + I*a*Tan[c + d*x]])/d - (((2*I)/3)*B*(a + I*a*Tan[c + d*x])^(3/2))/(a*d)","A",4,4,34,0.1176,1,"{3592, 3527, 3480, 206}"
70,1,75,0,0.0721885,"\int \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{2 B \sqrt{a+i a \tan (c+d x)}}{d}-\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","\frac{2 B \sqrt{a+i a \tan (c+d x)}}{d}-\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"-((Sqrt[2]*Sqrt[a]*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d) + (2*B*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,3,28,0.1071,1,"{3527, 3480, 206}"
71,1,86,0,0.2273183,"\int \cot (c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}","\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}",1,"(-2*Sqrt[a]*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (Sqrt[2]*Sqrt[a]*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d","A",6,6,34,0.1765,1,"{3600, 3480, 206, 3599, 63, 208}"
72,1,123,0,0.3847092,"\int \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{a} (2 B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{A \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{\sqrt{a} (2 B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{A \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"-((Sqrt[a]*(I*A + 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d) + (Sqrt[2]*Sqrt[a]*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (A*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,7,36,0.1944,1,"{3598, 3600, 3480, 206, 3599, 63, 208}"
73,1,169,0,0.5650971,"\int \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{a} (7 A-4 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{(4 B+i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{A \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}","\frac{\sqrt{a} (7 A-4 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{\sqrt{2} \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{(4 B+i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{A \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}",1,"(Sqrt[a]*(7*A - (4*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (Sqrt[2]*Sqrt[a]*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((I*A + 4*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) - (A*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",8,7,36,0.1944,1,"{3598, 3600, 3480, 206, 3599, 63, 208}"
74,1,210,0,0.7519378,"\int \cot ^4(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{a} (14 B+9 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{(6 B+i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{(7 A-2 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{A \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","\frac{\sqrt{a} (14 B+9 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{\sqrt{2} \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{(6 B+i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{(7 A-2 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{A \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"(Sqrt[a]*((9*I)*A + 14*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(8*d) - (Sqrt[2]*Sqrt[a]*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + ((7*A - (2*I)*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) - ((I*A + 6*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(12*d) - (A*Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",9,7,36,0.1944,1,"{3598, 3600, 3480, 206, 3599, 63, 208}"
75,1,197,0,0.5324754,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (8 B+7 i A) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{4 (19 B+21 i A) (a+i a \tan (c+d x))^{3/2}}{105 d}-\frac{8 a (8 B+7 i A) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{2 i a B \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}","\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (8 B+7 i A) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{4 (19 B+21 i A) (a+i a \tan (c+d x))^{3/2}}{105 d}-\frac{8 a (8 B+7 i A) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{2 i a B \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}",1,"(2*Sqrt[2]*a^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (8*a*((7*I)*A + 8*B)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) + (2*a*((7*I)*A + 8*B)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) + (((2*I)/7)*a*B*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (4*((21*I)*A + 19*B)*(a + I*a*Tan[c + d*x])^(3/2))/(105*d)","A",6,6,36,0.1667,1,"{3594, 3597, 3592, 3527, 3480, 206}"
76,1,137,0,0.1763068,"\int \tan (c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (A-i B) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{2 A (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i B (a+i a \tan (c+d x))^{5/2}}{5 a d}","-\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (A-i B) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{2 A (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i B (a+i a \tan (c+d x))^{5/2}}{5 a d}",1,"(-2*Sqrt[2]*a^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (2*a*(A - I*B)*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*A*(a + I*a*Tan[c + d*x])^(3/2))/(3*d) - (((2*I)/5)*B*(a + I*a*Tan[c + d*x])^(5/2))/(a*d)","A",5,5,34,0.1471,1,"{3592, 3527, 3478, 3480, 206}"
77,1,107,0,0.0999415,"\int (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (B+i A) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{2 B (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (B+i A) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{2 B (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(-2*Sqrt[2]*a^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (2*a*(I*A + B)*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*B*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",4,4,28,0.1429,1,"{3527, 3478, 3480, 206}"
78,1,113,0,0.3749434,"\int \cot (c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i a B \sqrt{a+i a \tan (c+d x)}}{d}","\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i a B \sqrt{a+i a \tan (c+d x)}}{d}",1,"(-2*a^(3/2)*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (2*Sqrt[2]*a^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + ((2*I)*a*B*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,7,34,0.2059,1,"{3594, 3600, 3480, 206, 3599, 63, 208}"
79,1,125,0,0.3902212,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{a^{3/2} (2 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a A \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{a^{3/2} (2 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a A \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"-((a^(3/2)*((3*I)*A + 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d) + (2*Sqrt[2]*a^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (a*A*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,7,36,0.1944,1,"{3593, 3600, 3480, 206, 3599, 63, 208}"
80,1,171,0,0.5830503,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{a^{3/2} (11 A-12 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a (4 B+5 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}","\frac{a^{3/2} (11 A-12 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{2 \sqrt{2} a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a (4 B+5 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}",1,"(a^(3/2)*(11*A - (12*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (2*Sqrt[2]*a^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (a*((5*I)*A + 4*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",8,8,36,0.2222,1,"{3593, 3598, 3600, 3480, 206, 3599, 63, 208}"
81,1,213,0,0.7719339,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{a^{3/2} (22 B+23 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a (6 B+7 i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{a (9 A-10 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{a A \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","\frac{a^{3/2} (22 B+23 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{2 \sqrt{2} a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a (6 B+7 i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{a (9 A-10 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{a A \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"(a^(3/2)*((23*I)*A + 22*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(8*d) - (2*Sqrt[2]*a^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (a*(9*A - (10*I)*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) - (a*((7*I)*A + 6*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(12*d) - (a*A*Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",9,8,36,0.2222,1,"{3593, 3598, 3600, 3480, 206, 3599, 63, 208}"
82,1,246,0,0.7534769,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (3 A-4 i B) \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 a^2 (46 B+45 i A) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{8 a^2 (46 B+45 i A) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{8 a (59 B+60 i A) (a+i a \tan (c+d x))^{3/2}}{315 d}+\frac{2 i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}","-\frac{2 a^2 (3 A-4 i B) \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 a^2 (46 B+45 i A) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{8 a^2 (46 B+45 i A) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{8 a (59 B+60 i A) (a+i a \tan (c+d x))^{3/2}}{315 d}+\frac{2 i a B \tan ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}",1,"(4*Sqrt[2]*a^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (8*a^2*((45*I)*A + 46*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) + (2*a^2*((45*I)*A + 46*B)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) - (2*a^2*(3*A - (4*I)*B)*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(21*d) - (8*a*((60*I)*A + 59*B)*(a + I*a*Tan[c + d*x])^(3/2))/(315*d) + (((2*I)/9)*a*B*Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/d","A",7,6,36,0.1667,1,"{3594, 3597, 3592, 3527, 3480, 206}"
83,1,171,0,0.1997216,"\int \tan (c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{4 a^2 (A-i B) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (A-i B) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 A (a+i a \tan (c+d x))^{5/2}}{5 d}-\frac{2 i B (a+i a \tan (c+d x))^{7/2}}{7 a d}","\frac{4 a^2 (A-i B) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (A-i B) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 A (a+i a \tan (c+d x))^{5/2}}{5 d}-\frac{2 i B (a+i a \tan (c+d x))^{7/2}}{7 a d}",1,"(-4*Sqrt[2]*a^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (4*a^2*(A - I*B)*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*a*(A - I*B)*(a + I*a*Tan[c + d*x])^(3/2))/(3*d) + (2*A*(a + I*a*Tan[c + d*x])^(5/2))/(5*d) - (((2*I)/7)*B*(a + I*a*Tan[c + d*x])^(7/2))/(a*d)","A",6,5,34,0.1471,1,"{3592, 3527, 3478, 3480, 206}"
84,1,141,0,0.1256641,"\int (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{4 a^2 (B+i A) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (B+i A) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 B (a+i a \tan (c+d x))^{5/2}}{5 d}","\frac{4 a^2 (B+i A) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (B+i A) (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 B (a+i a \tan (c+d x))^{5/2}}{5 d}",1,"(-4*Sqrt[2]*a^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (4*a^2*(I*A + B)*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*a*(I*A + B)*(a + I*a*Tan[c + d*x])^(3/2))/(3*d) + (2*B*(a + I*a*Tan[c + d*x])^(5/2))/(5*d)","A",5,4,28,0.1429,1,"{3527, 3478, 3480, 206}"
85,1,147,0,0.5341409,"\int \cot (c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (A-2 i B) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i a B (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{2 a^2 (A-2 i B) \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i a B (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(-2*a^(5/2)*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (4*Sqrt[2]*a^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (2*a^2*(A - (2*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/d + (((2*I)/3)*a*B*(a + I*a*Tan[c + d*x])^(3/2))/d","A",8,7,34,0.2059,1,"{3594, 3600, 3480, 206, 3599, 63, 208}"
86,1,158,0,0.5520721,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{a^2 (-2 B+i A) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{a^{5/2} (2 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^{3/2}}{d}","\frac{a^2 (-2 B+i A) \sqrt{a+i a \tan (c+d x)}}{d}-\frac{a^{5/2} (2 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a A \cot (c+d x) (a+i a \tan (c+d x))^{3/2}}{d}",1,"-((a^(5/2)*((5*I)*A + 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d) + (4*Sqrt[2]*a^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (a^2*(I*A - 2*B)*Sqrt[a + I*a*Tan[c + d*x]])/d - (a*A*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",8,8,36,0.2222,1,"{3593, 3594, 3600, 3480, 206, 3599, 63, 208}"
87,1,173,0,0.6059624,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{a^{5/2} (23 A-20 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (4 B+7 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^{3/2}}{2 d}","\frac{a^{5/2} (23 A-20 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (4 B+7 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) (a+i a \tan (c+d x))^{3/2}}{2 d}",1,"(a^(5/2)*(23*A - (20*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (4*Sqrt[2]*a^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (a^2*((7*I)*A + 4*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2))/(2*d)","A",8,7,36,0.1944,1,"{3593, 3600, 3480, 206, 3599, 63, 208}"
88,1,217,0,0.7973163,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{a^{5/2} (46 B+45 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (2 B+3 i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{a^2 (19 A-18 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}","\frac{a^{5/2} (46 B+45 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{4 \sqrt{2} a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (2 B+3 i A) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{a^2 (19 A-18 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{a A \cot ^3(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(a^(5/2)*((45*I)*A + 46*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(8*d) - (4*Sqrt[2]*a^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (a^2*(19*A - (18*I)*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) - (a^2*((3*I)*A + 2*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",9,8,36,0.2222,1,"{3593, 3598, 3600, 3480, 206, 3599, 63, 208}"
89,1,261,0,1.0046015,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{3 a^{5/2} (121 A-120 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{64 d}+\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (8 B+11 i A) \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{a^2 (107 A-104 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{a^2 (152 B+149 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 d}-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^{3/2}}{4 d}","-\frac{3 a^{5/2} (121 A-120 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{64 d}+\frac{4 \sqrt{2} a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 (8 B+11 i A) \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{a^2 (107 A-104 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{a^2 (152 B+149 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{64 d}-\frac{a A \cot ^4(c+d x) (a+i a \tan (c+d x))^{3/2}}{4 d}",1,"(-3*a^(5/2)*(121*A - (120*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(64*d) + (4*Sqrt[2]*a^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (a^2*((149*I)*A + 152*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(64*d) + (a^2*(107*A - (104*I)*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(96*d) - (a^2*((11*I)*A + 8*B)*Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(24*d) - (a*A*Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^(3/2))/(4*d)","A",10,8,36,0.2222,1,"{3593, 3598, 3600, 3480, 206, 3599, 63, 208}"
90,1,205,0,0.524372,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{(25 A+23 i B) (a+i a \tan (c+d x))^{3/2}}{15 a^2 d}+\frac{(-B+i A) \tan ^3(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(5 A+7 i B) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{4 (5 A+7 i B) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","-\frac{(25 A+23 i B) (a+i a \tan (c+d x))^{3/2}}{15 a^2 d}+\frac{(-B+i A) \tan ^3(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(5 A+7 i B) \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{4 (5 A+7 i B) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + ((I*A - B)*Tan[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (4*(5*A + (7*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(5*a*d) - ((5*A + (7*I)*B)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(5*a*d) - ((25*A + (23*I)*B)*(a + I*a*Tan[c + d*x])^(3/2))/(15*a^2*d)","A",6,6,36,0.1667,1,"{3595, 3597, 3592, 3527, 3480, 206}"
91,1,159,0,0.3346693,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(-5 B+3 i A) (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}+\frac{(-B+i A) \tan ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{4 (-B+i A) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","\frac{(-5 B+3 i A) (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}+\frac{(-B+i A) \tan ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{4 (-B+i A) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + ((I*A - B)*Tan[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (4*(I*A - B)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) + (((3*I)*A - 5*B)*(a + I*a*Tan[c + d*x])^(3/2))/(3*a^2*d)","A",5,5,36,0.1389,1,"{3595, 3592, 3527, 3480, 206}"
92,1,109,0,0.1411399,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{A+i B}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 i B \sqrt{a+i a \tan (c+d x)}}{a d}","-\frac{A+i B}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 i B \sqrt{a+i a \tan (c+d x)}}{a d}",1,"-(((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d)) - (A + I*B)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((2*I)*B*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",4,4,34,0.1176,1,"{3592, 3526, 3480, 206}"
93,1,82,0,0.073144,"\int \frac{A+B \tan (c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{-B+i A}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","\frac{-B+i A}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"-(((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d)) + (I*A - B)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,3,28,0.1071,1,"{3526, 3480, 206}"
94,1,114,0,0.3477435,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{A+i B}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}","\frac{A+i B}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(-2*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + (A + I*B)/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",7,7,34,0.2059,1,"{3596, 3600, 3480, 206, 3599, 63, 208}"
95,1,167,0,0.5670877,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(-2 B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{(2 A+i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{(A+i B) \cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{(-2 B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{(2 A+i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{(A+i B) \cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}",1,"((I*A - 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + ((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + ((A + I*B)*Cot[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((2*A + I*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",8,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
96,1,219,0,0.7615274,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(11 A+4 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{(3 A+2 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{(A+i B) \cot ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-8 B+7 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}","\frac{(11 A+4 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{(3 A+2 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{(A+i B) \cot ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-8 B+7 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}",1,"((11*A + (4*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*Sqrt[a]*d) - ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + ((A + I*B)*Cot[c + d*x]^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((7*I)*A - 8*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a*d) - ((3*A + (2*I)*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*a*d)","A",9,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
97,1,209,0,0.535262,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(11 A+21 i B) (a+i a \tan (c+d x))^{3/2}}{6 a^3 d}-\frac{2 (3 A+5 i B) \sqrt{a+i a \tan (c+d x)}}{a^2 d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{(-B+i A) \tan ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(3 A+5 i B) \tan ^2(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}","\frac{(11 A+21 i B) (a+i a \tan (c+d x))^{3/2}}{6 a^3 d}-\frac{2 (3 A+5 i B) \sqrt{a+i a \tan (c+d x)}}{a^2 d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{(-B+i A) \tan ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(3 A+5 i B) \tan ^2(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + ((I*A - B)*Tan[c + d*x]^3)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((3*A + (5*I)*B)*Tan[c + d*x]^2)/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (2*(3*A + (5*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) + ((11*A + (21*I)*B)*(a + I*a*Tan[c + d*x])^(3/2))/(6*a^3*d)","A",6,5,36,0.1389,1,"{3595, 3592, 3527, 3480, 206}"
98,1,167,0,0.3534509,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(-7 B+i A) \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{(-B+i A) \tan ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{-11 B+5 i A}{6 a d \sqrt{a+i a \tan (c+d x)}}","\frac{(-7 B+i A) \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{(-B+i A) \tan ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{-11 B+5 i A}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + ((I*A - B)*Tan[c + d*x]^2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((5*I)*A - 11*B)/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((I*A - 7*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3*a^2*d)","A",5,5,36,0.1389,1,"{3595, 3592, 3526, 3480, 206}"
99,1,119,0,0.1855389,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{A+i B}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{A+3 i B}{2 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{A+i B}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{A+3 i B}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"-((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) - (A + I*B)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (A + (3*I)*B)/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,34,0.1176,1,"{3590, 3526, 3480, 206}"
100,1,121,0,0.1017534,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{-B+i A}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{B+i A}{2 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{-B+i A}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{B+i A}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"-((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + (I*A - B)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (I*A + B)/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3526, 3479, 3480, 206}"
101,1,156,0,0.5141276,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{3 A+i B}{2 a d \sqrt{a+i a \tan (c+d x)}}","\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{3 A+i B}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"(-2*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + (A + I*B)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (3*A + I*B)/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,7,34,0.2059,1,"{3596, 3600, 3480, 206, 3599, 63, 208}"
102,1,217,0,0.8040596,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(-2 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{(7 A+3 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{(13 A+7 i B) \cot (c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \cot (c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{(-2 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{(7 A+3 i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{(13 A+7 i B) \cot (c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \cot (c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"(((3*I)*A - 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + ((A + I*B)*Cot[c + d*x])/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((13*A + (7*I)*B)*Cot[c + d*x])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - ((7*A + (3*I)*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d)","A",9,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
103,1,268,0,0.9826285,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(23 A+12 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{(22 A+13 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d}+\frac{7 (-2 B+3 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^2 d}+\frac{(17 A+11 i B) \cot ^2(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \cot ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{(23 A+12 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{(22 A+13 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d}+\frac{7 (-2 B+3 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^2 d}+\frac{(17 A+11 i B) \cot ^2(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \cot ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((23*A + (12*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*a^(3/2)*d) - ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*d) + ((A + I*B)*Cot[c + d*x]^2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((17*A + (11*I)*B)*Cot[c + d*x]^2)/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) + (7*((3*I)*A - 2*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a^2*d) - ((22*A + (13*I)*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d)","A",10,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
104,1,255,0,0.7792805,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{(-89 B+39 i A) \tan ^2(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(-361 B+151 i A) (a+i a \tan (c+d x))^{3/2}}{60 a^4 d}+\frac{(-89 B+39 i A) \sqrt{a+i a \tan (c+d x)}}{5 a^3 d}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^4(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(11 A+21 i B) \tan ^3(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{(-89 B+39 i A) \tan ^2(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(-361 B+151 i A) (a+i a \tan (c+d x))^{3/2}}{60 a^4 d}+\frac{(-89 B+39 i A) \sqrt{a+i a \tan (c+d x)}}{5 a^3 d}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^4(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(11 A+21 i B) \tan ^3(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"-((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + ((I*A - B)*Tan[c + d*x]^4)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((11*A + (21*I)*B)*Tan[c + d*x]^3)/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - (((39*I)*A - 89*B)*Tan[c + d*x]^2)/(20*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((39*I)*A - 89*B)*Sqrt[a + I*a*Tan[c + d*x]])/(5*a^3*d) - (((151*I)*A - 361*B)*(a + I*a*Tan[c + d*x])^(3/2))/(60*a^4*d)","A",7,5,36,0.1389,1,"{3595, 3592, 3527, 3480, 206}"
105,1,211,0,0.5686285,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{(13 A+83 i B) \sqrt{a+i a \tan (c+d x)}}{30 a^3 d}+\frac{41 A+151 i B}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(7 A+17 i B) \tan ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{(13 A+83 i B) \sqrt{a+i a \tan (c+d x)}}{30 a^3 d}+\frac{41 A+151 i B}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(7 A+17 i B) \tan ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + ((I*A - B)*Tan[c + d*x]^3)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((7*A + (17*I)*B)*Tan[c + d*x]^2)/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (41*A + (151*I)*B)/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((13*A + (83*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(30*a^3*d)","A",6,5,36,0.1389,1,"{3595, 3592, 3526, 3480, 206}"
106,1,167,0,0.3950803,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{-31 B+i A}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{-13 B+3 i A}{30 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{-31 B+i A}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{(-B+i A) \tan ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{-13 B+3 i A}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + ((I*A - B)*Tan[c + d*x]^2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((3*I)*A - 13*B)/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - (I*A - 31*B)/(20*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,36,0.1389,1,"{3595, 3590, 3526, 3480, 206}"
107,1,153,0,0.2282042,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{A-i B}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{A+3 i B}{6 a d (a+i a \tan (c+d x))^{3/2}}-\frac{A+i B}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{A-i B}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{A+3 i B}{6 a d (a+i a \tan (c+d x))^{3/2}}-\frac{A+i B}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"-((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) - (A + I*B)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (A + (3*I)*B)/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (A - I*B)/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,34,0.1471,1,"{3590, 3526, 3479, 3480, 206}"
108,1,155,0,0.1299718,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{B+i A}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{-B+i A}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{B+i A}{6 a d (a+i a \tan (c+d x))^{3/2}}","\frac{B+i A}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}+\frac{-B+i A}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{B+i A}{6 a d (a+i a \tan (c+d x))^{3/2}}",1,"-((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + (I*A - B)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (I*A + B)/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (I*A + B)/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,28,0.1429,1,"{3526, 3479, 3480, 206}"
109,1,192,0,0.6764412,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{7 A+i B}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{3 A+i B}{6 a d (a+i a \tan (c+d x))^{3/2}}","\frac{7 A+i B}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{3 A+i B}{6 a d (a+i a \tan (c+d x))^{3/2}}",1,"(-2*A*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + (A + I*B)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (3*A + I*B)/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (7*A + I*B)/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,7,34,0.2059,1,"{3596, 3600, 3480, 206, 3599, 63, 208}"
110,1,259,0,1.0484795,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{(-2 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{7 (3 A+i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{(41 A+15 i B) \cot (c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(19 A+9 i B) \cot (c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \cot (c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{(-2 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{7 (3 A+i B) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{(41 A+15 i B) \cot (c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(19 A+9 i B) \cot (c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \cot (c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"(((5*I)*A - 2*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + ((A + I*B)*Cot[c + d*x])/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((19*A + (9*I)*B)*Cot[c + d*x])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((41*A + (15*I)*B)*Cot[c + d*x])/(12*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (7*(3*A + I*B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a^3*d)","A",10,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
111,1,312,0,1.2367066,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{(43 A+20 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{(85 A+41 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 a^3 d}+\frac{(337 A+167 i B) \cot ^2(c+d x)}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{21 (-B+2 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{(23 A+13 i B) \cot ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \cot ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{(43 A+20 i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{4 \sqrt{2} a^{5/2} d}-\frac{(85 A+41 i B) \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 a^3 d}+\frac{(337 A+167 i B) \cot ^2(c+d x)}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{21 (-B+2 i A) \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{(23 A+13 i B) \cot ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \cot ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((43*A + (20*I)*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*a^(5/2)*d) - ((A - I*B)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(4*Sqrt[2]*a^(5/2)*d) + ((A + I*B)*Cot[c + d*x]^2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((23*A + (13*I)*B)*Cot[c + d*x]^2)/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((337*A + (167*I)*B)*Cot[c + d*x]^2)/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (21*((2*I)*A - B)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a^3*d) - ((85*A + (41*I)*B)*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(12*a^3*d)","A",11,8,36,0.2222,1,"{3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
112,1,130,0,0.1981782,"\int \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 a (B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a (A-i B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{7}{2}}(c+d x)}{7 d}","\frac{2 a (B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a (A-i B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{7}{2}}(c+d x)}{7 d}",1,"(-2*(-1)^(1/4)*a*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a*(I*A + B)*Sqrt[Tan[c + d*x]])/d + (2*a*(A - I*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*a*(I*A + B)*Tan[c + d*x]^(5/2))/(5*d) + (((2*I)/7)*a*B*Tan[c + d*x]^(7/2))/d","A",6,4,34,0.1176,1,"{3592, 3528, 3533, 205}"
113,1,105,0,0.1657149,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 a (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{5}{2}}(c+d x)}{5 d}","\frac{2 a (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{5}{2}}(c+d x)}{5 d}",1,"(2*(-1)^(1/4)*a*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (2*a*(A - I*B)*Sqrt[Tan[c + d*x]])/d + (2*a*(I*A + B)*Tan[c + d*x]^(3/2))/(3*d) + (((2*I)/5)*a*B*Tan[c + d*x]^(5/2))/d","A",5,4,34,0.1176,1,"{3592, 3528, 3533, 205}"
114,1,80,0,0.1209461,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{3}{2}}(c+d x)}{3 d}","\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{3}{2}}(c+d x)}{3 d}",1,"(2*(-1)^(1/4)*a*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (2*a*(I*A + B)*Sqrt[Tan[c + d*x]])/d + (((2*I)/3)*a*B*Tan[c + d*x]^(3/2))/d","A",4,4,34,0.1176,1,"{3592, 3528, 3533, 205}"
115,1,55,0,0.0903108,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","\frac{2 i a B \sqrt{\tan (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}","\frac{2 i a B \sqrt{\tan (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}",1,"(-2*(-1)^(1/4)*a*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + ((2*I)*a*B*Sqrt[Tan[c + d*x]])/d","A",3,3,34,0.08824,1,"{3592, 3533, 205}"
116,1,53,0,0.0929169,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{2 a A}{d \sqrt{\tan (c+d x)}}-\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}","-\frac{2 a A}{d \sqrt{\tan (c+d x)}}-\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}",1,"(-2*(-1)^(1/4)*a*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a*A)/(d*Sqrt[Tan[c + d*x]])","A",3,3,34,0.08824,1,"{3591, 3533, 205}"
117,1,78,0,0.1269428,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{2 \sqrt[4]{-1} a (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(2*(-1)^(1/4)*a*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a*A)/(3*d*Tan[c + d*x]^(3/2)) - (2*a*(I*A + B))/(d*Sqrt[Tan[c + d*x]])","A",4,4,34,0.1176,1,"{3591, 3529, 3533, 205}"
118,1,103,0,0.1545326,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A)}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a (A-i B)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 \sqrt[4]{-1} a (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a (B+i A)}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a (A-i B)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"(2*(-1)^(1/4)*a*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a*A)/(5*d*Tan[c + d*x]^(5/2)) - (2*a*(I*A + B))/(3*d*Tan[c + d*x]^(3/2)) + (2*a*(A - I*B))/(d*Sqrt[Tan[c + d*x]])","A",5,4,34,0.1176,1,"{3591, 3529, 3533, 205}"
119,1,183,0,0.3568002,"\int \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (9 A-11 i B) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{4 a^2 (B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{4 a^2 (A-i B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{4 a^2 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{7}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{9 d}","-\frac{2 a^2 (9 A-11 i B) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{4 a^2 (B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{4 a^2 (A-i B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{4 a^2 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{7}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{9 d}",1,"(-4*(-1)^(1/4)*a^2*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (4*a^2*(I*A + B)*Sqrt[Tan[c + d*x]])/d + (4*a^2*(A - I*B)*Tan[c + d*x]^(3/2))/(3*d) + (4*a^2*(I*A + B)*Tan[c + d*x]^(5/2))/(5*d) - (2*a^2*(9*A - (11*I)*B)*Tan[c + d*x]^(7/2))/(63*d) + (((2*I)/9)*B*Tan[c + d*x]^(7/2)*(a^2 + I*a^2*Tan[c + d*x]))/d","A",7,5,36,0.1389,1,"{3594, 3592, 3528, 3533, 205}"
120,1,156,0,0.3103718,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (7 A-9 i B) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{4 a^2 (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{5}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{7 d}","-\frac{2 a^2 (7 A-9 i B) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{4 a^2 (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{5}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{7 d}",1,"(4*(-1)^(1/4)*a^2*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (4*a^2*(A - I*B)*Sqrt[Tan[c + d*x]])/d + (4*a^2*(I*A + B)*Tan[c + d*x]^(3/2))/(3*d) - (2*a^2*(7*A - (9*I)*B)*Tan[c + d*x]^(5/2))/(35*d) + (((2*I)/7)*B*Tan[c + d*x]^(5/2)*(a^2 + I*a^2*Tan[c + d*x]))/d","A",6,5,36,0.1389,1,"{3594, 3592, 3528, 3533, 205}"
121,1,129,0,0.2593408,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (5 A-7 i B) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{3}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{5 d}","-\frac{2 a^2 (5 A-7 i B) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i B \tan ^{\frac{3}{2}}(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)}{5 d}",1,"(4*(-1)^(1/4)*a^2*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (4*a^2*(I*A + B)*Sqrt[Tan[c + d*x]])/d - (2*a^2*(5*A - (7*I)*B)*Tan[c + d*x]^(3/2))/(15*d) + (((2*I)/5)*B*Tan[c + d*x]^(3/2)*(a^2 + I*a^2*Tan[c + d*x]))/d","A",5,5,36,0.1389,1,"{3594, 3592, 3528, 3533, 205}"
122,1,104,0,0.2244367,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (3 A-5 i B) \sqrt{\tan (c+d x)}}{3 d}+\frac{2 i B \sqrt{\tan (c+d x)} \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}","-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (3 A-5 i B) \sqrt{\tan (c+d x)}}{3 d}+\frac{2 i B \sqrt{\tan (c+d x)} \left(a^2+i a^2 \tan (c+d x)\right)}{3 d}",1,"(-4*(-1)^(1/4)*a^2*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a^2*(3*A - (5*I)*B)*Sqrt[Tan[c + d*x]])/(3*d) + (((2*I)/3)*B*Sqrt[Tan[c + d*x]]*(a^2 + I*a^2*Tan[c + d*x]))/d","A",4,4,36,0.1111,1,"{3594, 3592, 3533, 205}"
123,1,98,0,0.2137562,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a^2 (-B+i A) \sqrt{\tan (c+d x)}}{d}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{d \sqrt{\tan (c+d x)}}","-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 a^2 (-B+i A) \sqrt{\tan (c+d x)}}{d}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{d \sqrt{\tan (c+d x)}}",1,"(-4*(-1)^(1/4)*a^2*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (2*a^2*(I*A - B)*Sqrt[Tan[c + d*x]])/d - (2*A*(a^2 + I*a^2*Tan[c + d*x]))/(d*Sqrt[Tan[c + d*x]])","A",4,4,36,0.1111,1,"{3593, 3592, 3533, 205}"
124,1,102,0,0.2176485,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (3 B+5 i A)}{3 d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (3 B+5 i A)}{3 d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(4*(-1)^(1/4)*a^2*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a^2*((5*I)*A + 3*B))/(3*d*Sqrt[Tan[c + d*x]]) - (2*A*(a^2 + I*a^2*Tan[c + d*x]))/(3*d*Tan[c + d*x]^(3/2))","A",4,4,36,0.1111,1,"{3593, 3591, 3533, 205}"
125,1,127,0,0.2574916,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (5 B+7 i A)}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (A-i B)}{d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 a^2 (5 B+7 i A)}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (A-i B)}{d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"(4*(-1)^(1/4)*a^2*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a^2*((7*I)*A + 5*B))/(15*d*Tan[c + d*x]^(3/2)) + (4*a^2*(A - I*B))/(d*Sqrt[Tan[c + d*x]]) - (2*A*(a^2 + I*a^2*Tan[c + d*x]))/(5*d*Tan[c + d*x]^(5/2))","A",5,5,36,0.1389,1,"{3593, 3591, 3529, 3533, 205}"
126,1,154,0,0.2986429,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (A-i B)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2 (7 B+9 i A)}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2 (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{7 d \tan ^{\frac{7}{2}}(c+d x)}","-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{4 a^2 (A-i B)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2 (7 B+9 i A)}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2 (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 A \left(a^2+i a^2 \tan (c+d x)\right)}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"(-4*(-1)^(1/4)*a^2*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (2*a^2*((9*I)*A + 7*B))/(35*d*Tan[c + d*x]^(5/2)) + (4*a^2*(A - I*B))/(3*d*Tan[c + d*x]^(3/2)) + (4*a^2*(I*A + B))/(d*Sqrt[Tan[c + d*x]]) - (2*A*(a^2 + I*a^2*Tan[c + d*x]))/(7*d*Tan[c + d*x]^(7/2))","A",6,5,36,0.1389,1,"{3593, 3591, 3529, 3533, 205}"
127,1,198,0,0.4674446,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{16 a^3 (18 A-19 i B) \tan ^{\frac{5}{2}}(c+d x)}{315 d}+\frac{8 a^3 (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (9 A-13 i B) \tan ^{\frac{5}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{63 d}+\frac{8 a^3 (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2}{9 d}","-\frac{16 a^3 (18 A-19 i B) \tan ^{\frac{5}{2}}(c+d x)}{315 d}+\frac{8 a^3 (B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (9 A-13 i B) \tan ^{\frac{5}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{63 d}+\frac{8 a^3 (A-i B) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2}{9 d}",1,"(8*(-1)^(1/4)*a^3*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (8*a^3*(A - I*B)*Sqrt[Tan[c + d*x]])/d + (8*a^3*(I*A + B)*Tan[c + d*x]^(3/2))/(3*d) - (16*a^3*(18*A - (19*I)*B)*Tan[c + d*x]^(5/2))/(315*d) + (((2*I)/9)*a*B*Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2)/d - (2*(9*A - (13*I)*B)*Tan[c + d*x]^(5/2)*(a^3 + I*a^3*Tan[c + d*x]))/(63*d)","A",7,5,36,0.1389,1,"{3594, 3592, 3528, 3533, 205}"
128,1,171,0,0.4214447,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{8 a^3 (21 A-23 i B) \tan ^{\frac{3}{2}}(c+d x)}{105 d}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (7 A-11 i B) \tan ^{\frac{3}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{35 d}+\frac{8 a^3 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}{7 d}","-\frac{8 a^3 (21 A-23 i B) \tan ^{\frac{3}{2}}(c+d x)}{105 d}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (7 A-11 i B) \tan ^{\frac{3}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{35 d}+\frac{8 a^3 (B+i A) \sqrt{\tan (c+d x)}}{d}+\frac{2 i a B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}{7 d}",1,"(8*(-1)^(1/4)*a^3*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (8*a^3*(I*A + B)*Sqrt[Tan[c + d*x]])/d - (8*a^3*(21*A - (23*I)*B)*Tan[c + d*x]^(3/2))/(105*d) + (((2*I)/7)*a*B*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2)/d - (2*(7*A - (11*I)*B)*Tan[c + d*x]^(3/2)*(a^3 + I*a^3*Tan[c + d*x]))/(35*d)","A",6,5,36,0.1389,1,"{3594, 3592, 3528, 3533, 205}"
129,1,146,0,0.3765538,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{16 a^3 (5 A-6 i B) \sqrt{\tan (c+d x)}}{15 d}-\frac{2 (5 A-9 i B) \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}{15 d}+\frac{2 i a B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}{5 d}","-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{16 a^3 (5 A-6 i B) \sqrt{\tan (c+d x)}}{15 d}-\frac{2 (5 A-9 i B) \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}{15 d}+\frac{2 i a B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}{5 d}",1,"(-8*(-1)^(1/4)*a^3*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (16*a^3*(5*A - (6*I)*B)*Sqrt[Tan[c + d*x]])/(15*d) + (((2*I)/5)*a*B*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^2)/d - (2*(5*A - (9*I)*B)*Sqrt[Tan[c + d*x]]*(a^3 + I*a^3*Tan[c + d*x]))/(15*d)","A",5,4,36,0.1111,1,"{3594, 3592, 3533, 205}"
130,1,134,0,0.3548617,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 (-B+3 i A) \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}{3 d}-\frac{16 a^3 B \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+i a \tan (c+d x))^2}{d \sqrt{\tan (c+d x)}}","-\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{2 (-B+3 i A) \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}{3 d}-\frac{16 a^3 B \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+i a \tan (c+d x))^2}{d \sqrt{\tan (c+d x)}}",1,"(-8*(-1)^(1/4)*a^3*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (16*a^3*B*Sqrt[Tan[c + d*x]])/(3*d) - (2*a*A*(a + I*a*Tan[c + d*x])^2)/(d*Sqrt[Tan[c + d*x]]) + (2*((3*I)*A - B)*Sqrt[Tan[c + d*x]]*(a^3 + I*a^3*Tan[c + d*x]))/(3*d)","A",5,5,36,0.1389,1,"{3593, 3594, 3592, 3533, 205}"
131,1,136,0,0.357701,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (3 B+7 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{3 d \sqrt{\tan (c+d x)}}-\frac{16 a^3 A \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+i a \tan (c+d x))^2}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (3 B+7 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{3 d \sqrt{\tan (c+d x)}}-\frac{16 a^3 A \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+i a \tan (c+d x))^2}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(8*(-1)^(1/4)*a^3*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d - (16*a^3*A*Sqrt[Tan[c + d*x]])/(3*d) - (2*a*A*(a + I*a*Tan[c + d*x])^2)/(3*d*Tan[c + d*x]^(3/2)) - (2*((7*I)*A + 3*B)*(a^3 + I*a^3*Tan[c + d*x]))/(3*d*Sqrt[Tan[c + d*x]])","A",5,4,36,0.1111,1,"{3593, 3592, 3533, 205}"
132,1,144,0,0.376675,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (5 B+9 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{16 a^3 (6 A-5 i B)}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a A (a+i a \tan (c+d x))^2}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}-\frac{2 (5 B+9 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{16 a^3 (6 A-5 i B)}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a A (a+i a \tan (c+d x))^2}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"(8*(-1)^(1/4)*a^3*(I*A + B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (16*a^3*(6*A - (5*I)*B))/(15*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^2)/(5*d*Tan[c + d*x]^(5/2)) - (2*((9*I)*A + 5*B)*(a^3 + I*a^3*Tan[c + d*x]))/(15*d*Tan[c + d*x]^(3/2))","A",5,4,36,0.1111,1,"{3593, 3591, 3533, 205}"
133,1,169,0,0.4247362,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{8 a^3 (23 A-21 i B)}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 B+11 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{8 a^3 (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A (a+i a \tan (c+d x))^2}{7 d \tan ^{\frac{7}{2}}(c+d x)}","-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tan ^{-1}\left((-1)^{3/4} \sqrt{\tan (c+d x)}\right)}{d}+\frac{8 a^3 (23 A-21 i B)}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 B+11 i A) \left(a^3+i a^3 \tan (c+d x)\right)}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{8 a^3 (B+i A)}{d \sqrt{\tan (c+d x)}}-\frac{2 a A (a+i a \tan (c+d x))^2}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"(-8*(-1)^(1/4)*a^3*(A - I*B)*ArcTan[(-1)^(3/4)*Sqrt[Tan[c + d*x]]])/d + (8*a^3*(23*A - (21*I)*B))/(105*d*Tan[c + d*x]^(3/2)) + (8*a^3*(I*A + B))/(d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^2)/(7*d*Tan[c + d*x]^(7/2)) - (2*((11*I)*A + 7*B)*(a^3 + I*a^3*Tan[c + d*x]))/(35*d*Tan[c + d*x]^(5/2))","A",6,5,36,0.1389,1,"{3593, 3591, 3529, 3533, 205}"
134,1,306,0,0.4080789,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(3 A+7 i B) \tan ^{\frac{3}{2}}(c+d x)}{6 a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{5 (-B+i A) \sqrt{\tan (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((1+4 i) A-(6+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{((3-5 i) A+(5+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}","\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{(3 A+7 i B) \tan ^{\frac{3}{2}}(c+d x)}{6 a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{5 (-B+i A) \sqrt{\tan (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((1+4 i) A-(6+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{((3-5 i) A+(5+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}",1,"((-1/4 - I/4)*((4 + I)*A + (1 + 6*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) + ((1/4 + I/4)*((4 + I)*A + (1 + 6*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) - ((1/8 + I/8)*((1 + 4*I)*A - (6 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) - (((3 - 5*I)*A + (5 + 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) - (5*(I*A - B)*Sqrt[Tan[c + d*x]])/(2*a*d) - ((3*A + (7*I)*B)*Tan[c + d*x]^(3/2))/(6*a*d) + ((I*A - B)*Tan[c + d*x]^(5/2))/(2*d*(a + I*a*Tan[c + d*x]))","A",13,9,36,0.2500,1,"{3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
135,1,275,0,0.3543257,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{((1-3 i) A+(3+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((1+2 i) A-(4+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{(A+5 i B) \sqrt{\tan (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{((1-3 i) A+(3+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((1+2 i) A-(4+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{(A+5 i B) \sqrt{\tan (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}",1,"-(((1 - 3*I)*A + (3 + 5*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(4*Sqrt[2]*a*d) - ((1/4 + I/4)*((1 + 2*I)*A - (4 + I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) - ((1/8 + I/8)*((2 + I)*A + (1 + 4*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) + ((1/8 + I/8)*((2 + I)*A + (1 + 4*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) - ((A + (5*I)*B)*Sqrt[Tan[c + d*x]])/(2*a*d) + ((I*A - B)*Tan[c + d*x]^(3/2))/(2*d*(a + I*a*Tan[c + d*x]))","A",12,9,36,0.2500,1,"{3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
136,1,236,0,0.2862594,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((-1/4 + I/4)*(A + (2 - I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) + ((1/4 - I/4)*(A + (2 - I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) + ((1/8 + I/8)*(A - (2 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) - ((1/8 + I/8)*(A - (2 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(2*d*(a + I*a*Tan[c + d*x]))","A",11,8,36,0.2222,1,"{3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
137,1,234,0,0.2913003,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])),x]","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}-\frac{((3+i) A-(1+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3+i) A-(1+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}-\frac{((3+i) A-(1+i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3+i) A-(1+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}",1,"((-1/4 + I/4)*((2 + I)*A + B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) + ((1/4 - I/4)*((2 + I)*A + B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) - (((3 + I)*A - (1 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) + (((3 + I)*A - (1 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(2*d*(a + I*a*Tan[c + d*x]))","A",11,8,36,0.2222,1,"{3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
138,1,267,0,0.3656882,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])),x]","\frac{((5+3 i) A-(3-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{((3-i) B-(5+3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{4 \sqrt{2} a d}+\frac{A+i B}{2 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))}-\frac{5 A+i B}{2 a d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) ((4+i) A+(1+2 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((5-3 i) A+(3+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}","\frac{((5+3 i) A-(3-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{((3-i) B-(5+3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{4 \sqrt{2} a d}+\frac{A+i B}{2 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))}-\frac{5 A+i B}{2 a d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) ((4+i) A+(1+2 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((5-3 i) A+(3+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}",1,"(((5 + 3*I)*A - (3 - I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(4*Sqrt[2]*a*d) + (((-5 - 3*I)*A + (3 - I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(4*Sqrt[2]*a*d) - ((1/8 - I/8)*((4 + I)*A + (1 + 2*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a*d) + (((5 - 3*I)*A + (3 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) - (5*A + I*B)/(2*a*d*Sqrt[Tan[c + d*x]]) + (A + I*B)/(2*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x]))","A",12,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
139,1,296,0,0.401374,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])),x]","\frac{((7-5 i) A+(5+3 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) ((6+i) A+(1+4 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{A+i B}{2 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))}-\frac{7 A+3 i B}{6 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{5 (-B+i A)}{2 a d \sqrt{\tan (c+d x)}}+\frac{((7+5 i) A-(5-3 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((5-3 i) B-(7+5 i) A) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}","\frac{((7-5 i) A+(5+3 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{4 \sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) ((6+i) A+(1+4 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{A+i B}{2 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))}-\frac{7 A+3 i B}{6 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{5 (-B+i A)}{2 a d \sqrt{\tan (c+d x)}}+\frac{((7+5 i) A-(5-3 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((5-3 i) B-(7+5 i) A) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{8 \sqrt{2} a d}",1,"(((7 - 5*I)*A + (5 + 3*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(4*Sqrt[2]*a*d) - ((1/4 - I/4)*((6 + I)*A + (1 + 4*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a*d) + (((7 + 5*I)*A - (5 - 3*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) + (((-7 - 5*I)*A + (5 - 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(8*Sqrt[2]*a*d) - (7*A + (3*I)*B)/(6*a*d*Tan[c + d*x]^(3/2)) + (5*(I*A - B))/(2*a*d*Sqrt[Tan[c + d*x]]) + (A + I*B)/(2*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x]))","A",13,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
140,1,316,0,0.5749818,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{(3 A+7 i B) \tan ^{\frac{3}{2}}(c+d x)}{8 a^2 d (1+i \tan (c+d x))}+\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{5 (-5 B+i A) \sqrt{\tan (c+d x)}}{8 a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{(3 A+7 i B) \tan ^{\frac{3}{2}}(c+d x)}{8 a^2 d (1+i \tan (c+d x))}+\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{5 (-5 B+i A) \sqrt{\tan (c+d x)}}{8 a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((9 + 5*I)*A - (25 - 21*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) - (((9 + 5*I)*A - (25 - 21*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) - ((1/32 - I/32)*((7 + 2*I)*A + (2 + 23*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) + ((1/32 - I/32)*((7 + 2*I)*A + (2 + 23*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) + (5*(I*A - 5*B)*Sqrt[Tan[c + d*x]])/(8*a^2*d) + ((3*A + (7*I)*B)*Tan[c + d*x]^(3/2))/(8*a^2*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^(5/2))/(4*d*(a + I*a*Tan[c + d*x])^2)","A",13,9,36,0.2500,1,"{3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
141,1,277,0,0.5005447,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+5 i B) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{((1-3 i) A-(9-5 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1-3 i) A-(9-5 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+5 i B) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{((1-3 i) A-(9-5 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1-3 i) A-(9-5 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((1 + 3*I)*A + (9 + 5*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) - (((1 + 3*I)*A + (9 + 5*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) + (((1 - 3*I)*A - (9 - 5*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) - (((1 - 3*I)*A - (9 - 5*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) + ((A + (5*I)*B)*Sqrt[Tan[c + d*x]])/(8*a^2*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Tan[c + d*x]^(3/2))/(4*d*(a + I*a*Tan[c + d*x])^2)","A",12,8,36,0.2222,1,"{3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
142,1,279,0,0.4688384,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(3 B+i A) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{((1+3 i) A+(1-3 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(1-3 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}","\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(3 B+i A) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{((1+3 i) A+(1-3 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(1-3 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}",1,"(((-1 + 3*I)*A + (1 + 3*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) - (((-1 + 3*I)*A + (1 + 3*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) + (((1 + 3*I)*A + (1 - 3*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) - (((1 + 3*I)*A + (1 - 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) + ((I*A + 3*B)*Sqrt[Tan[c + d*x]])/(8*a^2*d*(1 + I*Tan[c + d*x])) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(4*d*(a + I*a*Tan[c + d*x])^2)","A",12,9,36,0.2500,1,"{3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
143,1,285,0,0.4996082,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^2),x]","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+2 i) B-(2-7 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((9-5 i) A+(1-3 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(5 A+i B) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((2+i) B-(7-2 i) A) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(1+3 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+2 i) B-(2-7 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((9-5 i) A+(1-3 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(5 A+i B) \sqrt{\tan (c+d x)}}{8 a^2 d (1+i \tan (c+d x))}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((2+i) B-(7-2 i) A) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(1+3 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}",1,"((1/16 + I/16)*((-2 + 7*I)*A + (1 + 2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^2*d) + (((9 - 5*I)*A + (1 - 3*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) + ((1/32 + I/32)*((-7 + 2*I)*A + (2 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) + (((9 + 5*I)*A - (1 + 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) + ((5*A + I*B)*Sqrt[Tan[c + d*x]])/(8*a^2*d*(1 + I*Tan[c + d*x])) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(4*d*(a + I*a*Tan[c + d*x])^2)","A",12,8,36,0.2222,1,"{3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
144,1,318,0,0.5781408,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{((25+21 i) A-(9-5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+23 i) A-(7+2 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{5 (5 A+i B)}{8 a^2 d \sqrt{\tan (c+d x)}}+\frac{7 A+3 i B}{8 a^2 d (1+i \tan (c+d x)) \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{A+i B}{4 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}","\frac{((25+21 i) A-(9-5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+23 i) A-(7+2 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{5 (5 A+i B)}{8 a^2 d \sqrt{\tan (c+d x)}}+\frac{7 A+3 i B}{8 a^2 d (1+i \tan (c+d x)) \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{A+i B}{4 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}",1,"(((25 + 21*I)*A - (9 - 5*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^2*d) - ((1/16 - I/16)*((2 + 23*I)*A - (7 + 2*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^2*d) - ((1/32 - I/32)*((23 + 2*I)*A + (2 + 7*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) + ((1/32 - I/32)*((23 + 2*I)*A + (2 + 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) - (5*(5*A + I*B))/(8*a^2*d*Sqrt[Tan[c + d*x]]) + (7*A + (3*I)*B)/(8*a^2*d*(1 + I*Tan[c + d*x])*Sqrt[Tan[c + d*x]]) + (A + I*B)/(4*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^2)","A",13,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
145,1,347,0,0.6309575,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((47+2 i) A+(2+23 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((47+2 i) A+(2+23 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{7 (7 A+3 i B)}{24 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{9 A+5 i B}{8 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{3}{2}}(c+d x)}+\frac{5 (-5 B+9 i A)}{8 a^2 d \sqrt{\tan (c+d x)}}+\frac{((49+45 i) A-(25-21 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((2+47 i) A-(23+2 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{A+i B}{4 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}","\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((47+2 i) A+(2+23 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((47+2 i) A+(2+23 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{7 (7 A+3 i B)}{24 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{9 A+5 i B}{8 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{3}{2}}(c+d x)}+\frac{5 (-5 B+9 i A)}{8 a^2 d \sqrt{\tan (c+d x)}}+\frac{((49+45 i) A-(25-21 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((2+47 i) A-(23+2 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{A+i B}{4 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}",1,"((1/16 - I/16)*((47 + 2*I)*A + (2 + 23*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^2*d) - ((1/16 - I/16)*((47 + 2*I)*A + (2 + 23*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^2*d) + (((49 + 45*I)*A - (25 - 21*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^2*d) - ((1/32 - I/32)*((2 + 47*I)*A - (23 + 2*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^2*d) - (7*(7*A + (3*I)*B))/(24*a^2*d*Tan[c + d*x]^(3/2)) + (9*A + (5*I)*B)/(8*a^2*d*(1 + I*Tan[c + d*x])*Tan[c + d*x]^(3/2)) + (5*((9*I)*A - 5*B))/(8*a^2*d*Sqrt[Tan[c + d*x]]) + (A + I*B)/(4*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2)","A",14,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
146,1,393,0,0.8271699,"\int \frac{\tan ^{\frac{9}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(9/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{3 (-5 B+2 i A) \tan ^{\frac{5}{2}}(c+d x)}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{7 (4 A+11 i B) \tan ^{\frac{3}{2}}(c+d x)}{24 a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((29+i) A+(1+76 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((29+i) A+(1+76 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{15 (-5 B+2 i A) \sqrt{\tan (c+d x)}}{8 a^3 d}-\frac{((28-30 i) A+(75+77 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((1+29 i) A-(76+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{9}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+2 i B) \tan ^{\frac{7}{2}}(c+d x)}{4 a d (a+i a \tan (c+d x))^2}","-\frac{3 (-5 B+2 i A) \tan ^{\frac{5}{2}}(c+d x)}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{7 (4 A+11 i B) \tan ^{\frac{3}{2}}(c+d x)}{24 a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((29+i) A+(1+76 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((29+i) A+(1+76 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{15 (-5 B+2 i A) \sqrt{\tan (c+d x)}}{8 a^3 d}-\frac{((28-30 i) A+(75+77 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((1+29 i) A-(76+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{9}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+2 i B) \tan ^{\frac{7}{2}}(c+d x)}{4 a d (a+i a \tan (c+d x))^2}",1,"((1/16 + I/16)*((29 + I)*A + (1 + 76*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - ((1/16 + I/16)*((29 + I)*A + (1 + 76*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - (((28 - 30*I)*A + (75 + 77*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) - ((1/32 + I/32)*((1 + 29*I)*A - (76 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) + (15*((2*I)*A - 5*B)*Sqrt[Tan[c + d*x]])/(8*a^3*d) + (7*(4*A + (11*I)*B)*Tan[c + d*x]^(3/2))/(24*a^3*d) + ((I*A - B)*Tan[c + d*x]^(9/2))/(6*d*(a + I*a*Tan[c + d*x])^3) + ((A + (2*I)*B)*Tan[c + d*x]^(7/2))/(4*a*d*(a + I*a*Tan[c + d*x])^2) - (3*((2*I)*A - 5*B)*Tan[c + d*x]^(5/2))/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",15,9,36,0.2500,1,"{3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
147,1,364,0,0.7713265,"\int \frac{\tan ^{\frac{7}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(7/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{7 (-4 B+i A) \tan ^{\frac{3}{2}}(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+6 i) A-(29+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{((5-7 i) A+(28+30 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 (A+6 i B) \sqrt{\tan (c+d x)}}{8 a^3 d}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{7}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(2 A+5 i B) \tan ^{\frac{5}{2}}(c+d x)}{12 a d (a+i a \tan (c+d x))^2}","-\frac{7 (-4 B+i A) \tan ^{\frac{3}{2}}(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+6 i) A-(29+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{((5-7 i) A+(28+30 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 (A+6 i B) \sqrt{\tan (c+d x)}}{8 a^3 d}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{7}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(2 A+5 i B) \tan ^{\frac{5}{2}}(c+d x)}{12 a d (a+i a \tan (c+d x))^2}",1,"((-1/16 - I/16)*((1 + 6*I)*A - (29 + I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - (((5 - 7*I)*A + (28 + 30*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) + ((1/32 + I/32)*((6 + I)*A + (1 + 29*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) - ((1/32 + I/32)*((6 + I)*A + (1 + 29*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) + (5*(A + (6*I)*B)*Sqrt[Tan[c + d*x]])/(8*a^3*d) + ((I*A - B)*Tan[c + d*x]^(7/2))/(6*d*(a + I*a*Tan[c + d*x])^3) + ((2*A + (5*I)*B)*Tan[c + d*x]^(5/2))/(12*a*d*(a + I*a*Tan[c + d*x])^2) - (7*(I*A - 4*B)*Tan[c + d*x]^(3/2))/(24*d*(a^3 + I*a^3*Tan[c + d*x]))","A",14,9,36,0.2500,1,"{3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
148,1,307,0,0.6381018,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{(2 A-(5+7 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 A-(5+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{5 B \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+4 i B) \tan ^{\frac{3}{2}}(c+d x)}{12 a d (a+i a \tan (c+d x))^2}","\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{(2 A-(5+7 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 A-(5+7 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{5 B \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{(A+4 i B) \tan ^{\frac{3}{2}}(c+d x)}{12 a d (a+i a \tan (c+d x))^2}",1,"((2*A + (5 - 7*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - ((2*A + (5 - 7*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - ((2*A - (5 + 7*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((2*A - (5 + 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((I*A - B)*Tan[c + d*x]^(5/2))/(6*d*(a + I*a*Tan[c + d*x])^3) + ((A + (4*I)*B)*Tan[c + d*x]^(3/2))/(12*a*d*(a + I*a*Tan[c + d*x])^2) + (5*B*Sqrt[Tan[c + d*x]])/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",13,8,36,0.2222,1,"{3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
149,1,309,0,0.6272016,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{(2 B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{(2 B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{(A-2 i B) \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{(2 B-(1-i) A) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 B-(1-i) A) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{i B \sqrt{\tan (c+d x)}}{4 a d (a+i a \tan (c+d x))^2}","\frac{(2 B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{(2 B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{(A-2 i B) \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{(2 B-(1-i) A) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 B-(1-i) A) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{i B \sqrt{\tan (c+d x)}}{4 a d (a+i a \tan (c+d x))^2}",1,"(((1 + I)*A + 2*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - (((1 + I)*A + 2*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - (((-1 + I)*A + 2*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + (((-1 + I)*A + 2*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((I*A - B)*Tan[c + d*x]^(3/2))/(6*d*(a + I*a*Tan[c + d*x])^3) + ((I/4)*B*Sqrt[Tan[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^2) + ((A - (2*I)*B)*Sqrt[Tan[c + d*x]])/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",13,9,36,0.2500,1,"{3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
150,1,317,0,0.6242981,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(2 i A+(1-i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i A+(1-i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{B \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{6 d (a+i a \tan (c+d x))^3}+\frac{(2 B+i A) \sqrt{\tan (c+d x)}}{12 a d (a+i a \tan (c+d x))^2}","\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(2 i A+(1-i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i A+(1-i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{B \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{6 d (a+i a \tan (c+d x))^3}+\frac{(2 B+i A) \sqrt{\tan (c+d x)}}{12 a d (a+i a \tan (c+d x))^2}",1,"((1/16 + I/16)*((1 + I)*A + B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - ((1/16 + I/16)*((1 + I)*A + B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) + (((2*I)*A + (1 - I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) - (((2*I)*A + (1 - I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(6*d*(a + I*a*Tan[c + d*x])^3) + ((I*A + 2*B)*Sqrt[Tan[c + d*x]])/(12*a*d*(a + I*a*Tan[c + d*x])^2) + (B*Sqrt[Tan[c + d*x]])/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",13,9,36,0.2500,1,"{3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
151,1,315,0,0.6400666,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^3),x]","-\frac{((7-5 i) A-2 i B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{((7-5 i) A-2 i B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{((7+5 i) A-2 i B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{((7+5 i) A-2 i B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{5 A \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(4 A+i B) \sqrt{\tan (c+d x)}}{12 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{6 d (a+i a \tan (c+d x))^3}","-\frac{((7-5 i) A-2 i B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{((7-5 i) A-2 i B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{((7+5 i) A-2 i B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{((7+5 i) A-2 i B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{5 A \sqrt{\tan (c+d x)}}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(4 A+i B) \sqrt{\tan (c+d x)}}{12 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{6 d (a+i a \tan (c+d x))^3}",1,"-(((7 - 5*I)*A - (2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) + (((7 - 5*I)*A - (2*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - (((7 + 5*I)*A - (2*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + (((7 + 5*I)*A - (2*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(6*d*(a + I*a*Tan[c + d*x])^3) + ((4*A + I*B)*Sqrt[Tan[c + d*x]])/(12*a*d*(a + I*a*Tan[c + d*x])^2) + (5*A*Sqrt[Tan[c + d*x]])/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",13,8,36,0.2222,1,"{3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
152,1,364,0,0.8043277,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3),x]","\frac{((30+28 i) A-(7-5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((1+29 i) A-(6+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{5 (6 A+i B)}{8 a^3 d \sqrt{\tan (c+d x)}}+\frac{7 (4 A+i B)}{24 d \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{A+i B}{6 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^3}+\frac{5 A+2 i B}{12 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}","\frac{((30+28 i) A-(7-5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{16 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((1+29 i) A-(6+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{5 (6 A+i B)}{8 a^3 d \sqrt{\tan (c+d x)}}+\frac{7 (4 A+i B)}{24 d \sqrt{\tan (c+d x)} \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{A+i B}{6 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^3}+\frac{5 A+2 i B}{12 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^2}",1,"(((30 + 28*I)*A - (7 - 5*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(16*Sqrt[2]*a^3*d) - ((1/16 - I/16)*((1 + 29*I)*A - (6 + I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - ((1/32 - I/32)*((29 + I)*A + (1 + 6*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) + ((1/32 - I/32)*((29 + I)*A + (1 + 6*I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) - (5*(6*A + I*B))/(8*a^3*d*Sqrt[Tan[c + d*x]]) + (A + I*B)/(6*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^3) + (5*A + (2*I)*B)/(12*a*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^2) + (7*(4*A + I*B))/(24*d*Sqrt[Tan[c + d*x]]*(a^3 + I*a^3*Tan[c + d*x]))","A",14,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
153,1,393,0,0.8605967,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^3),x]","\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((76+i) A+(1+29 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((76+i) A+(1+29 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{3 (5 A+2 i B)}{8 d \tan ^{\frac{3}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{7 (11 A+4 i B)}{24 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{15 (-2 B+5 i A)}{8 a^3 d \sqrt{\tan (c+d x)}}+\frac{((77+75 i) A-(30-28 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((1+76 i) A-(29+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{2 A+i B}{4 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}+\frac{A+i B}{6 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3}","\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((76+i) A+(1+29 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((76+i) A+(1+29 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{3 (5 A+2 i B)}{8 d \tan ^{\frac{3}{2}}(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{7 (11 A+4 i B)}{24 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{15 (-2 B+5 i A)}{8 a^3 d \sqrt{\tan (c+d x)}}+\frac{((77+75 i) A-(30-28 i) B) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((1+76 i) A-(29+i) B) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{2 A+i B}{4 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2}+\frac{A+i B}{6 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3}",1,"((1/16 - I/16)*((76 + I)*A + (1 + 29*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) - ((1/16 - I/16)*((76 + I)*A + (1 + 29*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*a^3*d) + (((77 + 75*I)*A - (30 - 28*I)*B)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(32*Sqrt[2]*a^3*d) - ((1/32 - I/32)*((1 + 76*I)*A - (29 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(Sqrt[2]*a^3*d) - (7*(11*A + (4*I)*B))/(24*a^3*d*Tan[c + d*x]^(3/2)) + (15*((5*I)*A - 2*B))/(8*a^3*d*Sqrt[Tan[c + d*x]]) + (A + I*B)/(6*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3) + (2*A + I*B)/(4*a*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2) + (3*(5*A + (2*I)*B))/(8*d*Tan[c + d*x]^(3/2)*(a^3 + I*a^3*Tan[c + d*x]))","A",15,9,36,0.2500,1,"{3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
154,1,200,0,0.6800829,"\int \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{(-1)^{3/4} \sqrt{a} (7 B+4 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}+\frac{(4 A-i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}","\frac{(-1)^{3/4} \sqrt{a} (7 B+4 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}+\frac{(4 A-i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}",1,"((-1)^(3/4)*Sqrt[a]*((4*I)*A + 7*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(4*d) + ((1 + I)*Sqrt[a]*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((4*A - I*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) + (B*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",9,8,38,0.2105,1,"{3597, 3601, 3544, 205, 3599, 63, 217, 203}"
155,1,152,0,0.4886681,"\int \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{(-1)^{3/4} \sqrt{a} (2 A-i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{(-1)^{3/4} \sqrt{a} (2 A-i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"-(((-1)^(3/4)*Sqrt[a]*(2*A - I*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d) - ((1 + I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (B*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",8,8,38,0.2105,1,"{3597, 3601, 3544, 205, 3599, 63, 217, 203}"
156,1,112,0,0.3230594,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 (-1)^{3/4} \sqrt{a} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","-\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 (-1)^{3/4} \sqrt{a} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-2*(-1)^(3/4)*Sqrt[a]*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - ((1 + I)*Sqrt[a]*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d","A",7,7,38,0.1842,1,"{3601, 3544, 205, 3599, 63, 217, 203}"
157,1,90,0,0.1860928,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"((1 + I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*A*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",4,4,38,0.1053,1,"{3598, 12, 3544, 205}"
158,1,135,0,0.3424611,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","-\frac{2 (3 B+i A) \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{2 (3 B+i A) \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(1+i) \sqrt{a} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((1 + I)*Sqrt[a]*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*A*Sqrt[a + I*a*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (2*(I*A + 3*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d*Sqrt[Tan[c + d*x]])","A",5,4,38,0.1053,1,"{3598, 12, 3544, 205}"
159,1,178,0,0.5350272,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{2 (5 B+i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 (13 A-5 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{2 (5 B+i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 (13 A-5 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(1+i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"((-1 - I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*A*Sqrt[a + I*a*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (2*(I*A + 5*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (2*(13*A - (5*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]])","A",6,4,38,0.1053,1,"{3598, 12, 3544, 205}"
160,1,221,0,0.7133574,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{2 (31 A-7 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 B+i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 (91 B+43 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}+\frac{(1-i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 (31 A-7 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 B+i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 (91 B+43 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}+\frac{(1-i) \sqrt{a} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"((1 - I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*A*Sqrt[a + I*a*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (2*(I*A + 7*B)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (2*(31*A - (7*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(3/2)) + (2*((43*I)*A + 91*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Sqrt[Tan[c + d*x]])","A",7,4,38,0.1053,1,"{3598, 12, 3544, 205}"
161,1,248,0,0.9020848,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(-1)^{3/4} a^{3/2} (23 B+22 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}+\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (7 B+6 i A) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{a (10 A-9 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{i a B \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","\frac{(-1)^{3/4} a^{3/2} (23 B+22 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}+\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (7 B+6 i A) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{a (10 A-9 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}+\frac{i a B \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"((-1)^(3/4)*a^(3/2)*((22*I)*A + 23*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(8*d) + ((2 + 2*I)*a^(3/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (a*(10*A - (9*I)*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) + (a*((6*I)*A + 7*B)*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(12*d) + ((I/3)*a*B*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",10,9,38,0.2368,1,"{3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
162,1,204,0,0.699549,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-1)^{3/4} a^{3/2} (12 A-11 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (5 B+4 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{i a B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}","-\frac{(-1)^{3/4} a^{3/2} (12 A-11 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (5 B+4 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{i a B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}",1,"-((-1)^(3/4)*a^(3/2)*(12*A - (11*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(4*d) - ((2 + 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (a*((4*I)*A + 5*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) + ((I/2)*a*B*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",9,9,38,0.2368,1,"{3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
163,1,156,0,0.4934812,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{(-1)^{3/4} a^{3/2} (3 B+2 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{(-1)^{3/4} a^{3/2} (3 B+2 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"-(((-1)^(3/4)*a^(3/2)*((2*I)*A + 3*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d) - ((2 + 2*I)*a^(3/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (I*a*B*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",8,8,38,0.2105,1,"{3594, 3601, 3544, 205, 3599, 63, 217, 203}"
164,1,146,0,0.4830964,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt[4]{-1} a^{3/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt[4]{-1} a^{3/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"(2*(-1)^(1/4)*a^(3/2)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((2 + 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",8,8,38,0.2105,1,"{3593, 3601, 3544, 205, 3599, 63, 217, 203}"
165,1,137,0,0.3655254,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (3 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{(2+2 i) a^{3/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (3 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((2 + 2*I)*a^(3/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + I*a*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (2*a*((4*I)*A + 3*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d*Sqrt[Tan[c + d*x]])","A",5,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
166,1,181,0,0.5502669,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (5 B+6 i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a (9 A-10 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (5 B+6 i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a (9 A-10 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"((-2 - 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + I*a*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (2*a*((6*I)*A + 5*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (4*a*(9*A - (10*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]])","A",6,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
167,1,225,0,0.7352211,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{(2-2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{4 a (19 A-21 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a (7 B+8 i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a (63 B+67 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{(2-2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{4 a (19 A-21 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a (7 B+8 i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a (63 B+67 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"((2 - 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + I*a*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (2*a*((8*I)*A + 7*B)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (4*a*(19*A - (21*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(3/2)) + (4*a*((67*I)*A + 63*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Sqrt[Tan[c + d*x]])","A",7,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
168,1,269,0,0.9363023,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(11/2),x]","\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{4 a (57 B+61 i A) \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a (11 A-12 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a (9 B+10 i A) \sqrt{a+i a \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{4 a (193 A-201 i B) \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}","\frac{(2+2 i) a^{3/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{4 a (57 B+61 i A) \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a (11 A-12 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a (9 B+10 i A) \sqrt{a+i a \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{4 a (193 A-201 i B) \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}-\frac{2 a A \sqrt{a+i a \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}",1,"((2 + 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + I*a*Tan[c + d*x]])/(9*d*Tan[c + d*x]^(9/2)) - (2*a*((10*I)*A + 9*B)*Sqrt[a + I*a*Tan[c + d*x]])/(63*d*Tan[c + d*x]^(7/2)) + (4*a*(11*A - (12*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(5/2)) + (4*a*((61*I)*A + 57*B)*Sqrt[a + I*a*Tan[c + d*x]])/(315*d*Tan[c + d*x]^(3/2)) - (4*a*(193*A - (201*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(315*d*Sqrt[Tan[c + d*x]])","A",8,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
169,1,298,0,1.1321934,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{3 (-1)^{3/4} a^{5/2} (121 B+120 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{64 d}-\frac{a^2 (8 A-11 i B) \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{a^2 (107 B+104 i A) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{a^2 (152 A-149 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{4 d}","\frac{3 (-1)^{3/4} a^{5/2} (121 B+120 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{64 d}-\frac{a^2 (8 A-11 i B) \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{a^2 (107 B+104 i A) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{a^2 (152 A-149 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{4 d}",1,"(3*(-1)^(3/4)*a^(5/2)*((120*I)*A + 121*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(64*d) + ((4 + 4*I)*a^(5/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (a^2*(152*A - (149*I)*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(64*d) + (a^2*((104*I)*A + 107*B)*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(96*d) - (a^2*(8*A - (11*I)*B)*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(24*d) + ((I/4)*a*B*Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2))/d","A",11,9,38,0.2368,1,"{3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
170,1,252,0,0.9222512,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-1)^{3/4} a^{5/2} (46 A-45 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}-\frac{a^2 (2 A-3 i B) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{a^2 (19 B+18 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{(-1)^{3/4} a^{5/2} (46 A-45 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}-\frac{a^2 (2 A-3 i B) \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{a^2 (19 B+18 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"-((-1)^(3/4)*a^(5/2)*(46*A - (45*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(8*d) - ((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (a^2*((18*I)*A + 19*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) - (a^2*(2*A - (3*I)*B)*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) + ((I/3)*a*B*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/d","A",10,9,38,0.2368,1,"{3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
171,1,206,0,0.7118224,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{(-1)^{3/4} a^{5/2} (23 B+20 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{a^2 (4 A-7 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(4-4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}{2 d}","-\frac{(-1)^{3/4} a^{5/2} (23 B+20 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{a^2 (4 A-7 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(4-4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}{2 d}",1,"-((-1)^(3/4)*a^(5/2)*((20*I)*A + 23*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(4*d) + ((4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (a^2*(4*A - (7*I)*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d) + ((I/2)*a*B*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",9,8,38,0.2105,1,"{3594, 3601, 3544, 205, 3599, 63, 217, 203}"
172,1,196,0,0.6995687,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{(-1)^{3/4} a^{5/2} (2 A-5 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a^2 (-B+2 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{d \sqrt{\tan (c+d x)}}","\frac{(-1)^{3/4} a^{5/2} (2 A-5 i B) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a^2 (-B+2 i A) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{d \sqrt{\tan (c+d x)}}",1,"((-1)^(3/4)*a^(5/2)*(2*A - (5*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (a^2*((2*I)*A - B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(d*Sqrt[Tan[c + d*x]])","A",9,9,38,0.2368,1,"{3593, 3594, 3601, 3544, 205, 3599, 63, 217, 203}"
173,1,190,0,0.6649946,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","-\frac{2 a^2 (B+2 i A) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{2 a^2 (B+2 i A) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(2*(-1)^(3/4)*a^(5/2)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((4 + 4*I)*a^(5/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*((2*I)*A + B)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(3*d*Tan[c + d*x]^(3/2))","A",9,8,38,0.2105,1,"{3593, 3601, 3544, 205, 3599, 63, 217, 203}"
174,1,185,0,0.5749955,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{2 a^2 (5 B+8 i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a^2 (38 A-35 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{2 a^2 (5 B+8 i A) \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a^2 (38 A-35 i B) \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"((-4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*((8*I)*A + 5*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (2*a^2*(38*A - (35*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(5*d*Tan[c + d*x]^(5/2))","A",6,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
175,1,231,0,0.7567603,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{2 a^2 (80 A-77 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2 (7 B+10 i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2 (133 B+130 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}+\frac{(4-4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 a^2 (80 A-77 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2 (7 B+10 i A) \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2 (133 B+130 i A) \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}+\frac{(4-4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"((4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*((10*I)*A + 7*B)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (2*a^2*(80*A - (77*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(3/2)) + (4*a^2*((130*I)*A + 133*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(7*d*Tan[c + d*x]^(7/2))","A",7,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
176,1,277,0,0.9505014,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(11/2),x]","\frac{8 a^2 (60 B+59 i A) \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a^2 (46 A-45 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a^2 (3 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{21 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{8 a^2 (197 A-195 i B) \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{9 d \tan ^{\frac{9}{2}}(c+d x)}","\frac{8 a^2 (60 B+59 i A) \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 a^2 (46 A-45 i B) \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a^2 (3 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{21 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{8 a^2 (197 A-195 i B) \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{9 d \tan ^{\frac{9}{2}}(c+d x)}",1,"((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*((4*I)*A + 3*B)*Sqrt[a + I*a*Tan[c + d*x]])/(21*d*Tan[c + d*x]^(7/2)) + (2*a^2*(46*A - (45*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(5/2)) + (8*a^2*((59*I)*A + 60*B)*Sqrt[a + I*a*Tan[c + d*x]])/(315*d*Tan[c + d*x]^(3/2)) - (8*a^2*(197*A - (195*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(315*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(9*d*Tan[c + d*x]^(9/2))","A",8,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
177,1,323,0,1.1608401,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{13}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(13/2),x]","-\frac{8 a^2 (655 A-649 i B) \sqrt{a+i a \tan (c+d x)}}{3465 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (253 B+250 i A) \sqrt{a+i a \tan (c+d x)}}{1155 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 a^2 (212 A-209 i B) \sqrt{a+i a \tan (c+d x)}}{693 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 a^2 (11 B+14 i A) \sqrt{a+i a \tan (c+d x)}}{99 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{8 a^2 (2167 B+2155 i A) \sqrt{a+i a \tan (c+d x)}}{3465 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{11 d \tan ^{\frac{11}{2}}(c+d x)}","-\frac{8 a^2 (655 A-649 i B) \sqrt{a+i a \tan (c+d x)}}{3465 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (253 B+250 i A) \sqrt{a+i a \tan (c+d x)}}{1155 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 a^2 (212 A-209 i B) \sqrt{a+i a \tan (c+d x)}}{693 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 a^2 (11 B+14 i A) \sqrt{a+i a \tan (c+d x)}}{99 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{8 a^2 (2167 B+2155 i A) \sqrt{a+i a \tan (c+d x)}}{3465 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+i a \tan (c+d x))^{3/2}}{11 d \tan ^{\frac{11}{2}}(c+d x)}",1,"((4 + 4*I)*a^(5/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*((14*I)*A + 11*B)*Sqrt[a + I*a*Tan[c + d*x]])/(99*d*Tan[c + d*x]^(9/2)) + (2*a^2*(212*A - (209*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(693*d*Tan[c + d*x]^(7/2)) + (4*a^2*((250*I)*A + 253*B)*Sqrt[a + I*a*Tan[c + d*x]])/(1155*d*Tan[c + d*x]^(5/2)) - (8*a^2*(655*A - (649*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3465*d*Tan[c + d*x]^(3/2)) - (8*a^2*((2155*I)*A + 2167*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3465*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + I*a*Tan[c + d*x])^(3/2))/(11*d*Tan[c + d*x]^(11/2))","A",9,5,38,0.1316,1,"{3593, 3598, 12, 3544, 205}"
178,1,190,0,0.7289401,"\int \frac{(a+i a \tan (c+d x))^{5/2} \left(\frac{3 b B}{2 a}+B \tan (c+d x)\right)}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*((3*b*B)/(2*a) + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{(2+2 i) a^{3/2} B (2 a+3 i b) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{b B (a+i a \tan (c+d x))^{3/2}}{d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a B (a+3 i b) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","\frac{(2+2 i) a^{3/2} B (2 a+3 i b) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{b B (a+i a \tan (c+d x))^{3/2}}{d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a B (a+3 i b) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"(2*(-1)^(3/4)*a^(5/2)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((2 + 2*I)*a^(3/2)*(2*a + (3*I)*b)*B*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a*(a + (3*I)*b)*B*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (b*B*(a + I*a*Tan[c + d*x])^(3/2))/(d*Tan[c + d*x]^(3/2))","A",9,8,46,0.1739,1,"{3593, 3601, 3544, 205, 3599, 63, 217, 203}"
179,1,205,0,0.6905171,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-1)^{3/4} (-B+2 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{(A+2 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-1)^{3/4} (-B+2 i A) \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{(A+2 i B) \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((-1)^(3/4)*((2*I)*A - B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) - ((1/2 - I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + ((I*A - B)*Tan[c + d*x]^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((A + (2*I)*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",9,9,38,0.2368,1,"{3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
180,1,156,0,0.480029,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(-B+i A) \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{2 \sqrt[4]{-1} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{(-B+i A) \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{2 \sqrt[4]{-1} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"(-2*(-1)^(1/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) - ((1/2 + I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,8,38,0.2105,1,"{3595, 3601, 3544, 205, 3599, 63, 217, 203}"
181,1,99,0,0.1933842,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{(A+i B) \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{(A+i B) \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 - I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,38,0.1053,1,"{3596, 12, 3544, 205}"
182,1,143,0,0.3653825,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{A+i B}{d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{(3 A+i B) \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{A+i B}{d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{(3 A+i B) \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 + I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + (A + I*B)/(d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((3*A + I*B)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",5,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
183,1,191,0,0.5458588,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{(5 A+3 i B) \sqrt{a+i a \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{A+i B}{d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(-9 B+7 i A) \sqrt{a+i a \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","-\frac{(5 A+3 i B) \sqrt{a+i a \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{A+i B}{d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(-9 B+7 i A) \sqrt{a+i a \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 + I/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + (A + I*B)/(d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - ((5*A + (3*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d*Tan[c + d*x]^(3/2)) + (((7*I)*A - 9*B)*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d*Sqrt[Tan[c + d*x]])","A",6,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
184,1,237,0,0.7394021,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{(-25 B+23 i A) \sqrt{a+i a \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{(7 A+5 i B) \sqrt{a+i a \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{A+i B}{d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(61 A+35 i B) \sqrt{a+i a \tan (c+d x)}}{15 a d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{(-25 B+23 i A) \sqrt{a+i a \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{(7 A+5 i B) \sqrt{a+i a \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{A+i B}{d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(61 A+35 i B) \sqrt{a+i a \tan (c+d x)}}{15 a d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((-1/2 - I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + (A + I*B)/(d*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) - ((7*A + (5*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(5*a*d*Tan[c + d*x]^(5/2)) + (((23*I)*A - 25*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*a*d*Tan[c + d*x]^(3/2)) + ((61*A + (35*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(15*a*d*Sqrt[Tan[c + d*x]])","A",7,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
185,1,203,0,0.6685431,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{2 (-1)^{3/4} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+3 i B) \sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{2 (-1)^{3/4} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+3 i B) \sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"(2*(-1)^(3/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) - ((1/4 - I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + ((I*A - B)*Tan[c + d*x]^(3/2))/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((A + (3*I)*B)*Sqrt[Tan[c + d*x]])/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,8,38,0.2105,1,"{3595, 3601, 3544, 205, 3599, 63, 217, 203}"
186,1,150,0,0.3793001,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(5 B+i A) \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(5 B+i A) \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 - I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((I*A + 5*B)*Sqrt[Tan[c + d*x]])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,38,0.1316,1,"{3595, 3596, 12, 3544, 205}"
187,1,148,0,0.3799649,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(7 A+i B) \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(7 A+i B) \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"((1/4 - I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((7*A + I*B)*Sqrt[Tan[c + d*x]])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,38,0.1053,1,"{3596, 12, 3544, 205}"
188,1,194,0,0.5772327,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{(25 A+7 i B) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{11 A+5 i B}{6 a d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{(25 A+7 i B) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{11 A+5 i B}{6 a d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((1/4 + I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + (A + I*B)/(3*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (11*A + (5*I)*B)/(6*a*d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((25*A + (7*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d*Sqrt[Tan[c + d*x]])","A",6,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
189,1,240,0,0.7694853,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{(21 A+11 i B) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(-25 B+39 i A) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{5 A+3 i B}{2 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{A+i B}{3 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}","-\frac{(21 A+11 i B) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(-25 B+39 i A) \sqrt{a+i a \tan (c+d x)}}{6 a^2 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{5 A+3 i B}{2 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{A+i B}{3 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}",1,"((1/4 + I/4)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + (A + I*B)/(3*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + (5*A + (3*I)*B)/(2*a*d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - ((21*A + (11*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d*Tan[c + d*x]^(3/2)) + (((39*I)*A - 25*B)*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d*Sqrt[Tan[c + d*x]])","A",7,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
190,1,249,0,0.8550086,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{(-7 B+i A) \sqrt{\tan (c+d x)}}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{2 \sqrt[4]{-1} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(A+3 i B) \tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{(-7 B+i A) \sqrt{\tan (c+d x)}}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{2 \sqrt[4]{-1} B \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(-B+i A) \tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(A+3 i B) \tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}",1,"(2*(-1)^(1/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((1/8 + I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((I*A - B)*Tan[c + d*x]^(5/2))/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((A + (3*I)*B)*Tan[c + d*x]^(3/2))/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I*A - 7*B)*Sqrt[Tan[c + d*x]])/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",10,8,38,0.2105,1,"{3595, 3601, 3544, 205, 3599, 63, 217, 203}"
191,1,194,0,0.5997916,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{(13 A-37 i B) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(A+11 i B) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{(13 A-37 i B) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(-B+i A) \tan ^{\frac{3}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(A+11 i B) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((-1/8 + I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((I*A - B)*Tan[c + d*x]^(3/2))/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((A + (11*I)*B)*Sqrt[Tan[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((13*A - (37*I)*B)*Sqrt[Tan[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,38,0.1316,1,"{3595, 3596, 12, 3544, 205}"
192,1,196,0,0.592109,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{(-13 B+3 i A) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(7 B+3 i A) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}","-\frac{(-13 B+3 i A) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(7 B+3 i A) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(-B+i A) \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 - I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((I*A - B)*Sqrt[Tan[c + d*x]])/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((3*I)*A + 7*B)*Sqrt[Tan[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - (((3*I)*A - 13*B)*Sqrt[Tan[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,38,0.1316,1,"{3595, 3596, 12, 3544, 205}"
193,1,194,0,0.5966922,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{(67 A-3 i B) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(13 A+3 i B) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{(67 A-3 i B) \sqrt{\tan (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(A+i B) \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(13 A+3 i B) \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 - I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((A + I*B)*Sqrt[Tan[c + d*x]])/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((13*A + (3*I)*B)*Sqrt[Tan[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((67*A - (3*I)*B)*Sqrt[Tan[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,4,38,0.1053,1,"{3596, 12, 3544, 205}"
194,1,240,0,0.8029758,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{(317 A+67 i B) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{151 A+41 i B}{60 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}}+\frac{17 A+7 i B}{30 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}","-\frac{(317 A+67 i B) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{151 A+41 i B}{60 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}}+\frac{17 A+7 i B}{30 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 + I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + (A + I*B)/(5*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + (17*A + (7*I)*B)/(30*a*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (151*A + (41*I)*B)/(60*a^2*d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - ((317*A + (67*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*Sqrt[Tan[c + d*x]])","A",7,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
195,1,286,0,1.0066307,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{(361 A+151 i B) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{89 A+39 i B}{20 a^2 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(-317 B+707 i A) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{21 A+11 i B}{30 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{A+i B}{5 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","-\frac{(361 A+151 i B) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{89 A+39 i B}{20 a^2 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(-317 B+707 i A) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (B+i A) \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{21 A+11 i B}{30 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{A+i B}{5 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 + I/8)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + (A + I*B)/(5*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)) + (21*A + (11*I)*B)/(30*a*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + (89*A + (39*I)*B)/(20*a^2*d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - ((361*A + (151*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*Tan[c + d*x]^(3/2)) + (((707*I)*A - 317*B)*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*Sqrt[Tan[c + d*x]])","A",8,5,38,0.1316,1,"{3596, 3598, 12, 3544, 205}"
196,1,201,0,0.1659433,"\int \sqrt[3]{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^(1/3)*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{3} \sqrt[3]{a} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2^{2/3} d}+\frac{3 \sqrt[3]{a} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2\ 2^{2/3} d}+\frac{\sqrt[3]{a} (B+i A) \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\sqrt[3]{a} x (A-i B)}{2\ 2^{2/3}}+\frac{3 B \sqrt[3]{a+i a \tan (c+d x)}}{d}","-\frac{\sqrt{3} \sqrt[3]{a} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2^{2/3} d}+\frac{3 \sqrt[3]{a} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2\ 2^{2/3} d}+\frac{\sqrt[3]{a} (B+i A) \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\sqrt[3]{a} x (A-i B)}{2\ 2^{2/3}}+\frac{3 B \sqrt[3]{a+i a \tan (c+d x)}}{d}",1,"-(a^(1/3)*(A - I*B)*x)/(2*2^(2/3)) - (Sqrt[3]*a^(1/3)*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(2/3)*d) + (a^(1/3)*(I*A + B)*Log[Cos[c + d*x]])/(2*2^(2/3)*d) + (3*a^(1/3)*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(2/3)*d) + (3*B*(a + I*a*Tan[c + d*x])^(1/3))/d","A",6,6,28,0.2143,1,"{3527, 3481, 57, 617, 204, 31}"
197,1,270,0,0.4443947,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}-\frac{3 (B+4 i A) (a+i a \tan (c+d x))^{5/3}}{20 a d}+\frac{3 B \tan ^2(c+d x) (a+i a \tan (c+d x))^{2/3}}{8 d}-\frac{9 B (a+i a \tan (c+d x))^{2/3}}{8 d}","-\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}-\frac{3 (B+4 i A) (a+i a \tan (c+d x))^{5/3}}{20 a d}+\frac{3 B \tan ^2(c+d x) (a+i a \tan (c+d x))^{2/3}}{8 d}-\frac{9 B (a+i a \tan (c+d x))^{2/3}}{8 d}",1,"(a^(2/3)*(A - I*B)*x)/(2*2^(1/3)) - (Sqrt[3]*a^(2/3)*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*d) - (a^(2/3)*(I*A + B)*Log[Cos[c + d*x]])/(2*2^(1/3)*d) - (3*a^(2/3)*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(1/3)*d) - (9*B*(a + I*a*Tan[c + d*x])^(2/3))/(8*d) + (3*B*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(2/3))/(8*d) - (3*((4*I)*A + B)*(a + I*a*Tan[c + d*x])^(5/3))/(20*a*d)","A",8,8,36,0.2222,1,"{3597, 3592, 3527, 3481, 55, 617, 204, 31}"
198,1,232,0,0.221381,"\int \tan (c+d x) (a+i a \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{3} a^{2/3} (A-i B) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}+\frac{3 a^{2/3} (A-i B) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{a^{2/3} (A-i B) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (B+i A)}{2 \sqrt[3]{2}}+\frac{3 A (a+i a \tan (c+d x))^{2/3}}{2 d}-\frac{3 i B (a+i a \tan (c+d x))^{5/3}}{5 a d}","\frac{\sqrt{3} a^{2/3} (A-i B) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}+\frac{3 a^{2/3} (A-i B) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{a^{2/3} (A-i B) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (B+i A)}{2 \sqrt[3]{2}}+\frac{3 A (a+i a \tan (c+d x))^{2/3}}{2 d}-\frac{3 i B (a+i a \tan (c+d x))^{5/3}}{5 a d}",1,"(a^(2/3)*(I*A + B)*x)/(2*2^(1/3)) + (Sqrt[3]*a^(2/3)*(A - I*B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*d) + (a^(2/3)*(A - I*B)*Log[Cos[c + d*x]])/(2*2^(1/3)*d) + (3*a^(2/3)*(A - I*B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(1/3)*d) + (3*A*(a + I*a*Tan[c + d*x])^(2/3))/(2*d) - (((3*I)/5)*B*(a + I*a*Tan[c + d*x])^(5/3))/(a*d)","A",7,7,34,0.2059,1,"{3592, 3527, 3481, 55, 617, 204, 31}"
199,1,202,0,0.1492277,"\int (a+i a \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}+\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}+\frac{3 B (a+i a \tan (c+d x))^{2/3}}{2 d}","\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}+\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}+\frac{3 B (a+i a \tan (c+d x))^{2/3}}{2 d}",1,"-(a^(2/3)*(A - I*B)*x)/(2*2^(1/3)) + (Sqrt[3]*a^(2/3)*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*d) + (a^(2/3)*(I*A + B)*Log[Cos[c + d*x]])/(2*2^(1/3)*d) + (3*a^(2/3)*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(1/3)*d) + (3*B*(a + I*a*Tan[c + d*x])^(2/3))/(2*d)","A",6,6,28,0.2143,1,"{3527, 3481, 55, 617, 204, 31}"
200,1,289,0,0.3730654,"\int \cot (c+d x) (a+i a \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{3} a^{2/3} (A-i B) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{3 a^{2/3} (A-i B) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (A-i B) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x (B+i A)}{2 \sqrt[3]{2}}+\frac{\sqrt{3} a^{2/3} A \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{d}-\frac{a^{2/3} A \log (\tan (c+d x))}{2 d}+\frac{3 a^{2/3} A \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}","-\frac{\sqrt{3} a^{2/3} (A-i B) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{3 a^{2/3} (A-i B) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (A-i B) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x (B+i A)}{2 \sqrt[3]{2}}+\frac{\sqrt{3} a^{2/3} A \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{d}-\frac{a^{2/3} A \log (\tan (c+d x))}{2 d}+\frac{3 a^{2/3} A \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}",1,"-(a^(2/3)*(I*A + B)*x)/(2*2^(1/3)) + (Sqrt[3]*a^(2/3)*A*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d - (Sqrt[3]*a^(2/3)*(A - I*B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*d) - (a^(2/3)*(A - I*B)*Log[Cos[c + d*x]])/(2*2^(1/3)*d) - (a^(2/3)*A*Log[Tan[c + d*x]])/(2*d) + (3*a^(2/3)*A*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*d) - (3*a^(2/3)*(A - I*B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(1/3)*d)","A",11,7,34,0.2059,1,"{3600, 3481, 55, 617, 204, 31, 3599}"
201,1,342,0,0.5900073,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","\frac{a^{2/3} (3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d}-\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{a^{2/3} (3 B+2 i A) \log (\tan (c+d x))}{6 d}+\frac{a^{2/3} (3 B+2 i A) \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}-\frac{A \cot (c+d x) (a+i a \tan (c+d x))^{2/3}}{d}","\frac{a^{2/3} (3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d}-\frac{\sqrt{3} a^{2/3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{2} d}-\frac{a^{2/3} (3 B+2 i A) \log (\tan (c+d x))}{6 d}+\frac{a^{2/3} (3 B+2 i A) \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 a^{2/3} (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}-\frac{a^{2/3} (B+i A) \log (\cos (c+d x))}{2 \sqrt[3]{2} d}+\frac{a^{2/3} x (A-i B)}{2 \sqrt[3]{2}}-\frac{A \cot (c+d x) (a+i a \tan (c+d x))^{2/3}}{d}",1,"(a^(2/3)*(A - I*B)*x)/(2*2^(1/3)) + (a^(2/3)*((2*I)*A + 3*B)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*d) - (Sqrt[3]*a^(2/3)*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*d) - (a^(2/3)*(I*A + B)*Log[Cos[c + d*x]])/(2*2^(1/3)*d) - (a^(2/3)*((2*I)*A + 3*B)*Log[Tan[c + d*x]])/(6*d) + (a^(2/3)*((2*I)*A + 3*B)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*d) - (3*a^(2/3)*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(1/3)*d) - (A*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(2/3))/d","A",12,8,36,0.2222,1,"{3598, 3600, 3481, 55, 617, 204, 31, 3599}"
202,1,213,0,0.1582279,"\int \frac{A+B \tan (c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{3 (-B+i A)}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{(B+i A) \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x (A-i B)}{4 \sqrt[3]{2} \sqrt[3]{a}}","\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{3 (-B+i A)}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{(B+i A) \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x (A-i B)}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"-((A - I*B)*x)/(4*2^(1/3)*a^(1/3)) + (Sqrt[3]*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2*2^(1/3)*a^(1/3)*d) + ((I*A + B)*Log[Cos[c + d*x]])/(4*2^(1/3)*a^(1/3)*d) + (3*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(4*2^(1/3)*a^(1/3)*d) + (3*(I*A - B))/(2*d*(a + I*a*Tan[c + d*x])^(1/3))","A",6,6,28,0.2143,1,"{3526, 3481, 55, 617, 204, 31}"
203,1,213,0,0.1597954,"\int \frac{A+B \tan (c+d x)}{(a+i a \tan (c+d x))^{2/3}} \, dx","Int[(A + B*Tan[c + d*x])/(a + I*a*Tan[c + d*x])^(2/3),x]","-\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2\ 2^{2/3} a^{2/3} d}+\frac{3 (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{4\ 2^{2/3} a^{2/3} d}+\frac{(B+i A) \log (\cos (c+d x))}{4\ 2^{2/3} a^{2/3} d}-\frac{x (A-i B)}{4\ 2^{2/3} a^{2/3}}+\frac{3 (-B+i A)}{4 d (a+i a \tan (c+d x))^{2/3}}","-\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{\sqrt[3]{a}+2^{2/3} \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{2\ 2^{2/3} a^{2/3} d}+\frac{3 (B+i A) \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{4\ 2^{2/3} a^{2/3} d}+\frac{(B+i A) \log (\cos (c+d x))}{4\ 2^{2/3} a^{2/3} d}-\frac{x (A-i B)}{4\ 2^{2/3} a^{2/3}}+\frac{3 (-B+i A)}{4 d (a+i a \tan (c+d x))^{2/3}}",1,"-((A - I*B)*x)/(4*2^(2/3)*a^(2/3)) - (Sqrt[3]*(I*A + B)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2*2^(2/3)*a^(2/3)*d) + ((I*A + B)*Log[Cos[c + d*x]])/(4*2^(2/3)*a^(2/3)*d) + (3*(I*A + B)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(4*2^(2/3)*a^(2/3)*d) + (3*(I*A - B))/(4*d*(a + I*a*Tan[c + d*x])^(2/3))","A",6,6,28,0.2143,1,"{3526, 3481, 57, 617, 204, 31}"
204,1,290,0,1.0680387,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{8 a^4 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}-\frac{2 a^4 \left(A \left(2 m^3+19 m^2+60 m+64\right)-i B \left(2 m^3+19 m^2+60 m+67\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+2) (m+3) (m+4)}-\frac{2 \left(A (m+4)^2-i B \left(m^2+8 m+19\right)\right) \left(a^4+i a^4 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2) (m+3) (m+4)}-\frac{(A (m+4)-i B (m+7)) \left(a^2+i a^2 \tan (c+d x)\right)^2 \tan ^{m+1}(c+d x)}{d (m+3) (m+4)}+\frac{i a B (a+i a \tan (c+d x))^3 \tan ^{m+1}(c+d x)}{d (m+4)}","\frac{8 a^4 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}-\frac{2 a^4 \left(A \left(2 m^3+19 m^2+60 m+64\right)-i B \left(2 m^3+19 m^2+60 m+67\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+2) (m+3) (m+4)}-\frac{2 \left(A (m+4)^2-i B \left(m^2+8 m+19\right)\right) \left(a^4+i a^4 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2) (m+3) (m+4)}-\frac{(A (m+4)-i B (m+7)) \left(a^2+i a^2 \tan (c+d x)\right)^2 \tan ^{m+1}(c+d x)}{d (m+3) (m+4)}+\frac{i a B (a+i a \tan (c+d x))^3 \tan ^{m+1}(c+d x)}{d (m+4)}",1,"(-2*a^4*(A*(64 + 60*m + 19*m^2 + 2*m^3) - I*B*(67 + 60*m + 19*m^2 + 2*m^3))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(2 + m)*(3 + m)*(4 + m)) + (8*a^4*(A - I*B)*Hypergeometric2F1[1, 1 + m, 2 + m, I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (I*a*B*Tan[c + d*x]^(1 + m)*(a + I*a*Tan[c + d*x])^3)/(d*(4 + m)) - ((A*(4 + m) - I*B*(7 + m))*Tan[c + d*x]^(1 + m)*(a^2 + I*a^2*Tan[c + d*x])^2)/(d*(3 + m)*(4 + m)) - (2*(A*(4 + m)^2 - I*B*(19 + 8*m + m^2))*Tan[c + d*x]^(1 + m)*(a^4 + I*a^4*Tan[c + d*x]))/(d*(2 + m)*(3 + m)*(4 + m))","A",7,5,34,0.1471,1,"{3594, 3592, 3537, 12, 64}"
205,1,205,0,0.6420776,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{4 a^3 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}-\frac{a^3 \left(A \left(2 m^2+11 m+15\right)-i B \left(2 m^2+11 m+17\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+2) (m+3)}-\frac{(A (m+3)-i B (m+5)) \left(a^3+i a^3 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2) (m+3)}+\frac{i a B (a+i a \tan (c+d x))^2 \tan ^{m+1}(c+d x)}{d (m+3)}","\frac{4 a^3 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}-\frac{a^3 \left(A \left(2 m^2+11 m+15\right)-i B \left(2 m^2+11 m+17\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+2) (m+3)}-\frac{(A (m+3)-i B (m+5)) \left(a^3+i a^3 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2) (m+3)}+\frac{i a B (a+i a \tan (c+d x))^2 \tan ^{m+1}(c+d x)}{d (m+3)}",1,"-((a^3*(A*(15 + 11*m + 2*m^2) - I*B*(17 + 11*m + 2*m^2))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(2 + m)*(3 + m))) + (4*a^3*(A - I*B)*Hypergeometric2F1[1, 1 + m, 2 + m, I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (I*a*B*Tan[c + d*x]^(1 + m)*(a + I*a*Tan[c + d*x])^2)/(d*(3 + m)) - ((A*(3 + m) - I*B*(5 + m))*Tan[c + d*x]^(1 + m)*(a^3 + I*a^3*Tan[c + d*x]))/(d*(2 + m)*(3 + m))","A",6,5,34,0.1471,1,"{3594, 3592, 3537, 12, 64}"
206,1,132,0,0.3596067,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{2 a^2 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}+\frac{i a^2 (B+(m+2) (B+i A)) \tan ^{m+1}(c+d x)}{d (m+1) (m+2)}+\frac{i B \left(a^2+i a^2 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2)}","\frac{2 a^2 (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}+\frac{i a^2 (B+(m+2) (B+i A)) \tan ^{m+1}(c+d x)}{d (m+1) (m+2)}+\frac{i B \left(a^2+i a^2 \tan (c+d x)\right) \tan ^{m+1}(c+d x)}{d (m+2)}",1,"(I*a^2*(B + (I*A + B)*(2 + m))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(2 + m)) + (2*a^2*(A - I*B)*Hypergeometric2F1[1, 1 + m, 2 + m, I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (I*B*Tan[c + d*x]^(1 + m)*(a^2 + I*a^2*Tan[c + d*x]))/(d*(2 + m))","A",5,5,34,0.1471,1,"{3594, 3592, 3537, 12, 64}"
207,1,70,0,0.116656,"\int \tan ^m(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{a (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}+\frac{i a B \tan ^{m+1}(c+d x)}{d (m+1)}","\frac{a (A-i B) \tan ^{m+1}(c+d x) \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d (m+1)}+\frac{i a B \tan ^{m+1}(c+d x)}{d (m+1)}",1,"(I*a*B*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (a*(A - I*B)*Hypergeometric2F1[1, 1 + m, 2 + m, I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m))","A",3,3,32,0.09375,1,"{3592, 3537, 64}"
208,1,168,0,0.220419,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(A (1-m)-i B (m+1)) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{2 a d (m+1)}+\frac{m (-B+i A) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{2 a d (m+2)}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{2 d (a+i a \tan (c+d x))}","\frac{(A (1-m)-i B (m+1)) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{2 a d (m+1)}+\frac{m (-B+i A) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{2 a d (m+2)}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{2 d (a+i a \tan (c+d x))}",1,"((A*(1 - m) - I*B*(1 + m))*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(2*a*d*(1 + m)) + ((I*A - B)*m*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(2*a*d*(2 + m)) + ((A + I*B)*Tan[c + d*x]^(1 + m))/(2*d*(a + I*a*Tan[c + d*x]))","A",6,4,34,0.1176,1,"{3596, 3538, 3476, 364}"
209,1,226,0,0.483971,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{(1-m) (A (1-m)-i B (m+1)) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{4 a^2 d (m+1)}+\frac{m (B m+i A (2-m)) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{4 a^2 d (m+2)}+\frac{(A (2-m)-i B m) \tan ^{m+1}(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{(1-m) (A (1-m)-i B (m+1)) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{4 a^2 d (m+1)}+\frac{m (B m+i A (2-m)) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{4 a^2 d (m+2)}+\frac{(A (2-m)-i B m) \tan ^{m+1}(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"((1 - m)*(A*(1 - m) - I*B*(1 + m))*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(4*a^2*d*(1 + m)) + ((A*(2 - m) - I*B*m)*Tan[c + d*x]^(1 + m))/(4*a^2*d*(1 + I*Tan[c + d*x])) + (m*(I*A*(2 - m) + B*m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(4*a^2*d*(2 + m)) + ((A + I*B)*Tan[c + d*x]^(1 + m))/(4*d*(a + I*a*Tan[c + d*x])^2)","A",7,4,34,0.1176,1,"{3596, 3538, 3476, 364}"
210,1,308,0,0.8329922,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{(1-m) \left(-A \left(2 m^2-7 m+3\right)+i B \left(-2 m^2+m+3\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{24 a^3 d (m+1)}+\frac{(2-m) m (i A (5-2 m)+2 B m+B) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{24 a^3 d (m+2)}+\frac{(2-m) (A (5-2 m)-i (2 B m+B)) \tan ^{m+1}(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(A (7-2 m)+i B (1-2 m)) \tan ^{m+1}(c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{6 d (a+i a \tan (c+d x))^3}","-\frac{(1-m) \left(-A \left(2 m^2-7 m+3\right)+i B \left(-2 m^2+m+3\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{24 a^3 d (m+1)}+\frac{(2-m) m (i A (5-2 m)+2 B m+B) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{24 a^3 d (m+2)}+\frac{(2-m) (A (5-2 m)-i (2 B m+B)) \tan ^{m+1}(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{(A (7-2 m)+i B (1-2 m)) \tan ^{m+1}(c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{6 d (a+i a \tan (c+d x))^3}",1,"-((1 - m)*(I*B*(3 + m - 2*m^2) - A*(3 - 7*m + 2*m^2))*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(24*a^3*d*(1 + m)) + ((2 - m)*m*(B + I*A*(5 - 2*m) + 2*B*m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(24*a^3*d*(2 + m)) + ((A + I*B)*Tan[c + d*x]^(1 + m))/(6*d*(a + I*a*Tan[c + d*x])^3) + ((I*B*(1 - 2*m) + A*(7 - 2*m))*Tan[c + d*x]^(1 + m))/(24*a*d*(a + I*a*Tan[c + d*x])^2) + ((2 - m)*(A*(5 - 2*m) - I*(B + 2*B*m))*Tan[c + d*x]^(1 + m))/(24*d*(a^3 + I*a^3*Tan[c + d*x]))","A",8,4,34,0.1176,1,"{3596, 3538, 3476, 364}"
211,1,386,0,1.2071857,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^4,x]","-\frac{\left(m^2-4 m+3\right) \left(-A \left(m^2-4 m+1\right)+i B \left(1-m^2\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{48 a^4 d (m+1)}+\frac{(2-m) m \left(B \left(-m^2+2 m+2\right)+i A \left(m^2-6 m+8\right)\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{48 a^4 d (m+2)}-\frac{(2-m) \left(-A \left(m^2-6 m+8\right)+i B \left(-m^2+2 m+2\right)\right) \tan ^{m+1}(c+d x)}{48 a^4 d (1+i \tan (c+d x))}-\frac{\left(-A \left(m^2-7 m+13\right)+i B \left(-m^2+3 m+1\right)\right) \tan ^{m+1}(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{(A (5-m)+i B (1-m)) \tan ^{m+1}(c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{8 d (a+i a \tan (c+d x))^4}","-\frac{\left(m^2-4 m+3\right) \left(-A \left(m^2-4 m+1\right)+i B \left(1-m^2\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{48 a^4 d (m+1)}+\frac{(2-m) m \left(B \left(-m^2+2 m+2\right)+i A \left(m^2-6 m+8\right)\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{48 a^4 d (m+2)}-\frac{(2-m) \left(-A \left(m^2-6 m+8\right)+i B \left(-m^2+2 m+2\right)\right) \tan ^{m+1}(c+d x)}{48 a^4 d (1+i \tan (c+d x))}-\frac{\left(-A \left(m^2-7 m+13\right)+i B \left(-m^2+3 m+1\right)\right) \tan ^{m+1}(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}+\frac{(A (5-m)+i B (1-m)) \tan ^{m+1}(c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{8 d (a+i a \tan (c+d x))^4}",1,"-((3 - 4*m + m^2)*(I*B*(1 - m^2) - A*(1 - 4*m + m^2))*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(48*a^4*d*(1 + m)) - ((I*B*(1 + 3*m - m^2) - A*(13 - 7*m + m^2))*Tan[c + d*x]^(1 + m))/(48*a^4*d*(1 + I*Tan[c + d*x])^2) - ((2 - m)*(I*B*(2 + 2*m - m^2) - A*(8 - 6*m + m^2))*Tan[c + d*x]^(1 + m))/(48*a^4*d*(1 + I*Tan[c + d*x])) + ((2 - m)*m*(B*(2 + 2*m - m^2) + I*A*(8 - 6*m + m^2))*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(48*a^4*d*(2 + m)) + ((A + I*B)*Tan[c + d*x]^(1 + m))/(8*d*(a + I*a*Tan[c + d*x])^4) + ((I*B*(1 - m) + A*(5 - m))*Tan[c + d*x]^(1 + m))/(24*a*d*(a + I*a*Tan[c + d*x])^3)","A",9,4,34,0.1176,1,"{3596, 3538, 3476, 364}"
212,1,316,0,0.9861552,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{4 a^3 (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 a^2 \left(2 B \left(4 m^2+17 m+19\right)+i A \left(8 m^2+34 m+35\right)\right) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d (2 m+3) (2 m+5)}+\frac{2 a^2 (-A (2 m+5)+2 i B (m+4)) \sqrt{a+i a \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3) (2 m+5)}+\frac{2 i a B (a+i a \tan (c+d x))^{3/2} \tan ^{m+1}(c+d x)}{d (2 m+5)}","\frac{4 a^3 (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 a^2 \left(2 B \left(4 m^2+17 m+19\right)+i A \left(8 m^2+34 m+35\right)\right) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d (2 m+3) (2 m+5)}+\frac{2 a^2 (-A (2 m+5)+2 i B (m+4)) \sqrt{a+i a \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3) (2 m+5)}+\frac{2 i a B (a+i a \tan (c+d x))^{3/2} \tan ^{m+1}(c+d x)}{d (2 m+5)}",1,"(4*a^3*(A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + (2*a^2*(2*B*(19 + 17*m + 4*m^2) + I*A*(35 + 34*m + 8*m^2))*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(d*(3 + 2*m)*(5 + 2*m)*((-I)*Tan[c + d*x])^m) + (2*a^2*((2*I)*B*(4 + m) - A*(5 + 2*m))*Tan[c + d*x]^(1 + m)*Sqrt[a + I*a*Tan[c + d*x]])/(d*(3 + 2*m)*(5 + 2*m)) + ((2*I)*a*B*Tan[c + d*x]^(1 + m)*(a + I*a*Tan[c + d*x])^(3/2))/(d*(5 + 2*m))","A",9,8,36,0.2222,1,"{3594, 3601, 3564, 135, 133, 3599, 67, 65}"
213,1,227,0,0.7034971,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 a^2 (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 a (B+(2 m+3) (B+i A)) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d (2 m+3)}+\frac{2 i a B \sqrt{a+i a \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3)}","\frac{2 a^2 (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 a (B+(2 m+3) (B+i A)) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d (2 m+3)}+\frac{2 i a B \sqrt{a+i a \tan (c+d x)} \tan ^{m+1}(c+d x)}{d (2 m+3)}",1,"(2*a^2*(A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + (2*a*(B + (I*A + B)*(3 + 2*m))*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(d*(3 + 2*m)*((-I)*Tan[c + d*x])^m) + ((2*I)*a*B*Tan[c + d*x]^(1 + m)*Sqrt[a + I*a*Tan[c + d*x]])/(d*(3 + 2*m))","A",8,8,36,0.2222,1,"{3594, 3601, 3564, 135, 133, 3599, 67, 65}"
214,1,159,0,0.3651631,"\int \tan ^m(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{a (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 B \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d}","\frac{a (A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{2 B \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{d}",1,"(a*(A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + (2*B*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(d*((-I)*Tan[c + d*x])^m)","A",7,7,36,0.1944,1,"{3601, 3564, 135, 133, 3599, 67, 65}"
215,1,214,0,0.6251673,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(2 m+1) (-B+i A) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{a d}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(2 m+1) (-B+i A) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{a d}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}",1,"((A + I*B)*Tan[c + d*x]^(1 + m))/(d*Sqrt[a + I*a*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(2*d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + ((I*A - B)*(1 + 2*m)*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*((-I)*Tan[c + d*x])^m)","A",8,8,36,0.2222,1,"{3596, 3601, 3564, 135, 133, 3599, 67, 65}"
216,1,285,0,0.9760203,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(2 m+1) (i A (5-4 m)+4 B m+B) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{6 a^2 d}+\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{4 a d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(A (5-4 m)-i (4 B m+B)) \tan ^{m+1}(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{(2 m+1) (i A (5-4 m)+4 B m+B) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{6 a^2 d}+\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{4 a d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(A (5-4 m)-i (4 B m+B)) \tan ^{m+1}(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((A + I*B)*Tan[c + d*x]^(1 + m))/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((A*(5 - 4*m) - I*(B + 4*B*m))*Tan[c + d*x]^(1 + m))/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(4*a*d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + ((1 + 2*m)*(B + I*A*(5 - 4*m) + 4*B*m)*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d*((-I)*Tan[c + d*x])^m)","A",9,8,36,0.2222,1,"{3596, 3601, 3564, 135, 133, 3599, 67, 65}"
217,1,363,0,1.3686783,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{8 a^2 d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(2 m+1) \left(B \left(-16 m^2+12 m+13\right)+i A \left(16 m^2-52 m+37\right)\right) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{60 a^3 d}-\frac{\left(-A \left(16 m^2-52 m+37\right)+i B \left(-16 m^2+12 m+13\right)\right) \tan ^{m+1}(c+d x)}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A (11-4 m)+i B (1-4 m)) \tan ^{m+1}(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{(A-i B) \sqrt{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{1}{2},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{8 a^2 d (m+1) \sqrt{a+i a \tan (c+d x)}}+\frac{(2 m+1) \left(B \left(-16 m^2+12 m+13\right)+i A \left(16 m^2-52 m+37\right)\right) \sqrt{a+i a \tan (c+d x)} \tan ^m(c+d x) (-i \tan (c+d x))^{-m} \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};i \tan (c+d x)+1\right)}{60 a^3 d}-\frac{\left(-A \left(16 m^2-52 m+37\right)+i B \left(-16 m^2+12 m+13\right)\right) \tan ^{m+1}(c+d x)}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{(A (11-4 m)+i B (1-4 m)) \tan ^{m+1}(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{(A+i B) \tan ^{m+1}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((A + I*B)*Tan[c + d*x]^(1 + m))/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((I*B*(1 - 4*m) + A*(11 - 4*m))*Tan[c + d*x]^(1 + m))/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I*B*(13 + 12*m - 16*m^2) - A*(37 - 52*m + 16*m^2))*Tan[c + d*x]^(1 + m))/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m))/(8*a^2*d*(1 + m)*Sqrt[a + I*a*Tan[c + d*x]]) + ((1 + 2*m)*(B*(13 + 12*m - 16*m^2) + I*A*(37 - 52*m + 16*m^2))*Hypergeometric2F1[1/2, -m, 3/2, 1 + I*Tan[c + d*x]]*Tan[c + d*x]^m*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*((-I)*Tan[c + d*x])^m)","A",10,8,36,0.2222,1,"{3596, 3601, 3564, 135, 133, 3599, 67, 65}"
218,1,167,0,0.30397,"\int \tan ^m(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) \tan ^{m+1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1(m+1;1-n,1;m+2;-i \tan (c+d x),i \tan (c+d x))}{d (m+1)}+\frac{i B \tan ^{m+1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1(m+1,1-n;m+2;-i \tan (c+d x))}{d (m+1)}","\frac{(A-i B) \tan ^{m+1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1(m+1;1-n,1;m+2;-i \tan (c+d x),i \tan (c+d x))}{d (m+1)}+\frac{i B \tan ^{m+1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1(m+1,1-n;m+2;-i \tan (c+d x))}{d (m+1)}",1,"((A - I*B)*AppellF1[1 + m, 1 - n, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*(a + I*a*Tan[c + d*x])^n)/(d*(1 + m)*(1 + I*Tan[c + d*x])^n) + (I*B*Hypergeometric2F1[1 + m, 1 - n, 2 + m, (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*(a + I*a*Tan[c + d*x])^n)/(d*(1 + m)*(1 + I*Tan[c + d*x])^n)","A",7,7,34,0.2059,1,"{3601, 3564, 135, 133, 3599, 66, 64}"
219,1,245,0,0.6493613,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{\left(A n (n+3)-i B \left(n^2+3 n+6\right)\right) (a+i a \tan (c+d x))^{n+1}}{a d (n+1) (n+2) (n+3)}-\frac{(-A (n+3)+i B n) \tan ^2(c+d x) (a+i a \tan (c+d x))^n}{d (n+2) (n+3)}+\frac{2 (-A (n+3)+i B n) (a+i a \tan (c+d x))^n}{d n (n+2) (n+3)}+\frac{B \tan ^3(c+d x) (a+i a \tan (c+d x))^n}{d (n+3)}","\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{\left(A n (n+3)-i B \left(n^2+3 n+6\right)\right) (a+i a \tan (c+d x))^{n+1}}{a d (n+1) (n+2) (n+3)}-\frac{(-A (n+3)+i B n) \tan ^2(c+d x) (a+i a \tan (c+d x))^n}{d (n+2) (n+3)}+\frac{2 (-A (n+3)+i B n) (a+i a \tan (c+d x))^n}{d n (n+2) (n+3)}+\frac{B \tan ^3(c+d x) (a+i a \tan (c+d x))^n}{d (n+3)}",1,"(2*(I*B*n - A*(3 + n))*(a + I*a*Tan[c + d*x])^n)/(d*n*(2 + n)*(3 + n)) + ((A - I*B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) - ((I*B*n - A*(3 + n))*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^n)/(d*(2 + n)*(3 + n)) + (B*Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^n)/(d*(3 + n)) - ((A*n*(3 + n) - I*B*(6 + 3*n + n^2))*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 + n)*(2 + n)*(3 + n))","A",6,5,34,0.1471,1,"{3597, 3592, 3527, 3481, 68}"
220,1,164,0,0.312751,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(B n+i A (n+2)) (a+i a \tan (c+d x))^{n+1}}{a d (n+1) (n+2)}+\frac{B \tan ^2(c+d x) (a+i a \tan (c+d x))^n}{d (n+2)}-\frac{2 B (a+i a \tan (c+d x))^n}{d n (n+2)}","\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(B n+i A (n+2)) (a+i a \tan (c+d x))^{n+1}}{a d (n+1) (n+2)}+\frac{B \tan ^2(c+d x) (a+i a \tan (c+d x))^n}{d (n+2)}-\frac{2 B (a+i a \tan (c+d x))^n}{d n (n+2)}",1,"(-2*B*(a + I*a*Tan[c + d*x])^n)/(d*n*(2 + n)) + ((I*A + B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) + (B*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^n)/(d*(2 + n)) - ((B*n + I*A*(2 + n))*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 + n)*(2 + n))","A",5,5,34,0.1471,1,"{3597, 3592, 3527, 3481, 68}"
221,1,111,0,0.1201645,"\int \tan (c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}+\frac{A (a+i a \tan (c+d x))^n}{d n}-\frac{i B (a+i a \tan (c+d x))^{n+1}}{a d (n+1)}","-\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}+\frac{A (a+i a \tan (c+d x))^n}{d n}-\frac{i B (a+i a \tan (c+d x))^{n+1}}{a d (n+1)}",1,"(A*(a + I*a*Tan[c + d*x])^n)/(d*n) - ((A - I*B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) - (I*B*(a + I*a*Tan[c + d*x])^(1 + n))/(a*d*(1 + n))","A",4,4,32,0.1250,1,"{3592, 3527, 3481, 68}"
222,1,78,0,0.0656323,"\int (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{B (a+i a \tan (c+d x))^n}{d n}-\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}","\frac{B (a+i a \tan (c+d x))^n}{d n}-\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}",1,"(B*(a + I*a*Tan[c + d*x])^n)/(d*n) - ((I*A + B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n)","A",3,3,26,0.1154,1,"{3527, 3481, 68}"
223,1,97,0,0.1784118,"\int \cot (c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{A (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{d n}","\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{A (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{d n}",1,"((A - I*B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) - (A*Hypergeometric2F1[1, n, 1 + n, 1 + I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*n)","A",5,5,32,0.1562,1,"{3600, 3481, 68, 3599, 65}"
224,1,131,0,0.3267243,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(B+i A n) (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{d n}-\frac{A \cot (c+d x) (a+i a \tan (c+d x))^n}{d}","\frac{(B+i A) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(B+i A n) (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{d n}-\frac{A \cot (c+d x) (a+i a \tan (c+d x))^n}{d}",1,"-((A*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^n)/d) + ((I*A + B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) - ((B + I*A*n)*Hypergeometric2F1[1, n, 1 + n, 1 + I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*n)","A",6,6,34,0.1765,1,"{3598, 3600, 3481, 68, 3599, 65}"
225,1,185,0,0.582882,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{\left(-A \left(n^2-n+2\right)+2 i B n\right) (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{2 d n}-\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(2 B+i A n) \cot (c+d x) (a+i a \tan (c+d x))^n}{2 d}-\frac{A \cot ^2(c+d x) (a+i a \tan (c+d x))^n}{2 d}","-\frac{\left(-A \left(n^2-n+2\right)+2 i B n\right) (a+i a \tan (c+d x))^n \, _2F_1(1,n;n+1;i \tan (c+d x)+1)}{2 d n}-\frac{(A-i B) (a+i a \tan (c+d x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d n}-\frac{(2 B+i A n) \cot (c+d x) (a+i a \tan (c+d x))^n}{2 d}-\frac{A \cot ^2(c+d x) (a+i a \tan (c+d x))^n}{2 d}",1,"-((2*B + I*A*n)*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^n)/(2*d) - (A*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^n)/(2*d) - ((A - I*B)*Hypergeometric2F1[1, n, 1 + n, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^n)/(2*d*n) - (((2*I)*B*n - A*(2 - n + n^2))*Hypergeometric2F1[1, n, 1 + n, 1 + I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(2*d*n)","A",7,6,34,0.1765,1,"{3598, 3600, 3481, 68, 3599, 65}"
226,1,383,0,1.1378929,"\int \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 \left(4 B n \left(2 n^2+8 n+9\right)+i A \left(8 n^3+32 n^2+36 n+15\right)\right) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) (2 n+5)}-\frac{2 \left(B \left(4 n^2+10 n+15\right)+2 i A n (2 n+5)\right) \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) (2 n+5)}-\frac{2 (-A (2 n+5)+2 i B n) \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+3) (2 n+5)}+\frac{2 B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+5)}","\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 \left(4 B n \left(2 n^2+8 n+9\right)+i A \left(8 n^3+32 n^2+36 n+15\right)\right) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) (2 n+5)}-\frac{2 \left(B \left(4 n^2+10 n+15\right)+2 i A n (2 n+5)\right) \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) (2 n+5)}-\frac{2 (-A (2 n+5)+2 i B n) \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+3) (2 n+5)}+\frac{2 B \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+5)}",1,"(-2*((2*I)*A*n*(5 + 2*n) + B*(15 + 10*n + 4*n^2))*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)) + (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) - (2*(4*B*n*(9 + 8*n + 2*n^2) + I*A*(15 + 36*n + 32*n^2 + 8*n^3))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(1 + I*Tan[c + d*x])^n) - (2*((2*I)*B*n - A*(5 + 2*n))*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n)/(d*(3 + 2*n)*(5 + 2*n)) + (2*B*Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^n)/(d*(5 + 2*n))","A",11,9,36,0.2500,1,"{3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
227,1,291,0,0.7792762,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 \left(2 A n (2 n+3)-i B \left(4 n^2+6 n+3\right)\right) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3)}-\frac{2 (-A (2 n+3)+2 i B n) \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3)}+\frac{2 B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+3)}","-\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 \left(2 A n (2 n+3)-i B \left(4 n^2+6 n+3\right)\right) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3)}-\frac{2 (-A (2 n+3)+2 i B n) \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3)}+\frac{2 B \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{d (2 n+3)}",1,"(-2*((2*I)*B*n - A*(3 + 2*n))*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)) - (2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) + (2*(2*A*n*(3 + 2*n) - I*B*(3 + 6*n + 4*n^2))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*(1 + I*Tan[c + d*x])^n) + (2*B*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n)/(d*(3 + 2*n))","A",10,9,36,0.2500,1,"{3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
228,1,215,0,0.4949584,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 (2 B n+i A (2 n+1)) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1)}+\frac{2 B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1)}","-\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 (2 B n+i A (2 n+1)) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1)}+\frac{2 B \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^n}{d (2 n+1)}",1,"(2*B*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)) - (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) + (2*(2*B*n + I*A*(1 + 2*n))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(1 + I*Tan[c + d*x])^n)","A",9,9,36,0.2500,1,"{3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
229,1,158,0,0.3084568,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 i B \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d}","\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}+\frac{2 i B \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d}",1,"(2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) + ((2*I)*B*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n)","A",8,8,36,0.2222,1,"{3601, 3564, 130, 430, 429, 3599, 66, 64}"
230,1,194,0,0.4897358,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 i A (1-2 n) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d}-\frac{2 A (a+i a \tan (c+d x))^n}{d \sqrt{\tan (c+d x)}}","\frac{2 (B+i A) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 i A (1-2 n) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d}-\frac{2 A (a+i a \tan (c+d x))^n}{d \sqrt{\tan (c+d x)}}",1,"(-2*A*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Tan[c + d*x]]) + (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) - ((2*I)*A*(1 - 2*n)*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n)","A",9,9,36,0.2500,1,"{3598, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
231,1,247,0,0.7229172,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","-\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 (1-2 n) (-2 A n+3 i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{3 d}-\frac{2 (3 B+2 i A n) (a+i a \tan (c+d x))^n}{3 d \sqrt{\tan (c+d x)}}-\frac{2 A (a+i a \tan (c+d x))^n}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{2 (A-i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}-\frac{2 (1-2 n) (-2 A n+3 i B) \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{3 d}-\frac{2 (3 B+2 i A n) (a+i a \tan (c+d x))^n}{3 d \sqrt{\tan (c+d x)}}-\frac{2 A (a+i a \tan (c+d x))^n}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(-2*A*(a + I*a*Tan[c + d*x])^n)/(3*d*Tan[c + d*x]^(3/2)) - (2*(3*B + (2*I)*A*n)*(a + I*a*Tan[c + d*x])^n)/(3*d*Sqrt[Tan[c + d*x]]) - (2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n) - (2*(1 - 2*n)*((3*I)*B - 2*A*n)*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(3*d*(1 + I*Tan[c + d*x])^n)","A",10,9,36,0.2500,1,"{3598, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
232,1,87,0,0.1174723,"\int \tan ^2(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{(a B+A b) \tan ^2(c+d x)}{2 d}+\frac{(a A-b B) \tan (c+d x)}{d}+\frac{(a B+A b) \log (\cos (c+d x))}{d}-x (a A-b B)+\frac{b B \tan ^3(c+d x)}{3 d}","\frac{(a B+A b) \tan ^2(c+d x)}{2 d}+\frac{(a A-b B) \tan (c+d x)}{d}+\frac{(a B+A b) \log (\cos (c+d x))}{d}-x (a A-b B)+\frac{b B \tan ^3(c+d x)}{3 d}",1,"-((a*A - b*B)*x) + ((A*b + a*B)*Log[Cos[c + d*x]])/d + ((a*A - b*B)*Tan[c + d*x])/d + ((A*b + a*B)*Tan[c + d*x]^2)/(2*d) + (b*B*Tan[c + d*x]^3)/(3*d)","A",4,4,29,0.1379,1,"{3592, 3528, 3525, 3475}"
233,1,65,0,0.0585006,"\int \tan (c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{(a B+A b) \tan (c+d x)}{d}-\frac{(a A-b B) \log (\cos (c+d x))}{d}-x (a B+A b)+\frac{b B \tan ^2(c+d x)}{2 d}","\frac{(a B+A b) \tan (c+d x)}{d}-\frac{(a A-b B) \log (\cos (c+d x))}{d}-x (a B+A b)+\frac{b B \tan ^2(c+d x)}{2 d}",1,"-((A*b + a*B)*x) - ((a*A - b*B)*Log[Cos[c + d*x]])/d + ((A*b + a*B)*Tan[c + d*x])/d + (b*B*Tan[c + d*x]^2)/(2*d)","A",3,3,27,0.1111,1,"{3592, 3525, 3475}"
234,1,42,0,0.0251823,"\int (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a B+A b) \log (\cos (c+d x))}{d}+x (a A-b B)+\frac{b B \tan (c+d x)}{d}","-\frac{(a B+A b) \log (\cos (c+d x))}{d}+x (a A-b B)+\frac{b B \tan (c+d x)}{d}",1,"(a*A - b*B)*x - ((A*b + a*B)*Log[Cos[c + d*x]])/d + (b*B*Tan[c + d*x])/d","A",2,2,21,0.09524,1,"{3525, 3475}"
235,1,37,0,0.0687638,"\int \cot (c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","x (a B+A b)+\frac{a A \log (\sin (c+d x))}{d}-\frac{b B \log (\cos (c+d x))}{d}","x (a B+A b)+\frac{a A \log (\sin (c+d x))}{d}-\frac{b B \log (\cos (c+d x))}{d}",1,"(A*b + a*B)*x - (b*B*Log[Cos[c + d*x]])/d + (a*A*Log[Sin[c + d*x]])/d","A",4,3,27,0.1111,1,"{3589, 3475, 3531}"
236,1,43,0,0.082227,"\int \cot ^2(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{(a B+A b) \log (\sin (c+d x))}{d}+x (-(a A-b B))-\frac{a A \cot (c+d x)}{d}","\frac{(a B+A b) \log (\sin (c+d x))}{d}+x (-(a A-b B))-\frac{a A \cot (c+d x)}{d}",1,"-((a*A - b*B)*x) - (a*A*Cot[c + d*x])/d + ((A*b + a*B)*Log[Sin[c + d*x]])/d","A",3,3,29,0.1034,1,"{3591, 3531, 3475}"
237,1,66,0,0.1198388,"\int \cot ^3(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a B+A b) \cot (c+d x)}{d}-\frac{(a A-b B) \log (\sin (c+d x))}{d}-x (a B+A b)-\frac{a A \cot ^2(c+d x)}{2 d}","-\frac{(a B+A b) \cot (c+d x)}{d}-\frac{(a A-b B) \log (\sin (c+d x))}{d}-x (a B+A b)-\frac{a A \cot ^2(c+d x)}{2 d}",1,"-((A*b + a*B)*x) - ((A*b + a*B)*Cot[c + d*x])/d - (a*A*Cot[c + d*x]^2)/(2*d) - ((a*A - b*B)*Log[Sin[c + d*x]])/d","A",4,4,29,0.1379,1,"{3591, 3529, 3531, 3475}"
238,1,87,0,0.1533539,"\int \cot ^4(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a B+A b) \cot ^2(c+d x)}{2 d}+\frac{(a A-b B) \cot (c+d x)}{d}-\frac{(a B+A b) \log (\sin (c+d x))}{d}+x (a A-b B)-\frac{a A \cot ^3(c+d x)}{3 d}","-\frac{(a B+A b) \cot ^2(c+d x)}{2 d}+\frac{(a A-b B) \cot (c+d x)}{d}-\frac{(a B+A b) \log (\sin (c+d x))}{d}+x (a A-b B)-\frac{a A \cot ^3(c+d x)}{3 d}",1,"(a*A - b*B)*x + ((a*A - b*B)*Cot[c + d*x])/d - ((A*b + a*B)*Cot[c + d*x]^2)/(2*d) - (a*A*Cot[c + d*x]^3)/(3*d) - ((A*b + a*B)*Log[Sin[c + d*x]])/d","A",5,4,29,0.1379,1,"{3591, 3529, 3531, 3475}"
239,1,108,0,0.1872601,"\int \cot ^5(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a B+A b) \cot ^3(c+d x)}{3 d}+\frac{(a A-b B) \cot ^2(c+d x)}{2 d}+\frac{(a B+A b) \cot (c+d x)}{d}+\frac{(a A-b B) \log (\sin (c+d x))}{d}+x (a B+A b)-\frac{a A \cot ^4(c+d x)}{4 d}","-\frac{(a B+A b) \cot ^3(c+d x)}{3 d}+\frac{(a A-b B) \cot ^2(c+d x)}{2 d}+\frac{(a B+A b) \cot (c+d x)}{d}+\frac{(a A-b B) \log (\sin (c+d x))}{d}+x (a B+A b)-\frac{a A \cot ^4(c+d x)}{4 d}",1,"(A*b + a*B)*x + ((A*b + a*B)*Cot[c + d*x])/d + ((a*A - b*B)*Cot[c + d*x]^2)/(2*d) - ((A*b + a*B)*Cot[c + d*x]^3)/(3*d) - (a*A*Cot[c + d*x]^4)/(4*d) + ((a*A - b*B)*Log[Sin[c + d*x]])/d","A",6,4,29,0.1379,1,"{3591, 3529, 3531, 3475}"
240,1,148,0,0.268616,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 B+2 a A b-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(a^2 A-2 a b B-A b^2\right)+\frac{(4 A b-a B) (a+b \tan (c+d x))^3}{12 b^2 d}-\frac{b (a B+A b) \tan (c+d x)}{d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^3}{4 b d}-\frac{B (a+b \tan (c+d x))^2}{2 d}","\frac{\left(a^2 B+2 a A b-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(a^2 A-2 a b B-A b^2\right)+\frac{(4 A b-a B) (a+b \tan (c+d x))^3}{12 b^2 d}-\frac{b (a B+A b) \tan (c+d x)}{d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^3}{4 b d}-\frac{B (a+b \tan (c+d x))^2}{2 d}",1,"-((a^2*A - A*b^2 - 2*a*b*B)*x) + ((2*a*A*b + a^2*B - b^2*B)*Log[Cos[c + d*x]])/d - (b*(A*b + a*B)*Tan[c + d*x])/d - (B*(a + b*Tan[c + d*x])^2)/(2*d) + ((4*A*b - a*B)*(a + b*Tan[c + d*x])^3)/(12*b^2*d) + (B*Tan[c + d*x]*(a + b*Tan[c + d*x])^3)/(4*b*d)","A",5,5,31,0.1613,1,"{3607, 3630, 3528, 3525, 3475}"
241,1,112,0,0.1240089,"\int \tan (c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\cos (c+d x))}{d}-x \left(a^2 B+2 a A b-b^2 B\right)+\frac{b (a A-b B) \tan (c+d x)}{d}+\frac{A (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 b d}","-\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\cos (c+d x))}{d}-x \left(a^2 B+2 a A b-b^2 B\right)+\frac{b (a A-b B) \tan (c+d x)}{d}+\frac{A (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 b d}",1,"-((2*a*A*b + a^2*B - b^2*B)*x) - ((a^2*A - A*b^2 - 2*a*b*B)*Log[Cos[c + d*x]])/d + (b*(a*A - b*B)*Tan[c + d*x])/d + (A*(a + b*Tan[c + d*x])^2)/(2*d) + (B*(a + b*Tan[c + d*x])^3)/(3*b*d)","A",4,4,29,0.1379,1,"{3592, 3528, 3525, 3475}"
242,1,87,0,0.0757501,"\int (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 B+2 a A b-b^2 B\right) \log (\cos (c+d x))}{d}+x \left(a^2 A-2 a b B-A b^2\right)+\frac{b (a B+A b) \tan (c+d x)}{d}+\frac{B (a+b \tan (c+d x))^2}{2 d}","-\frac{\left(a^2 B+2 a A b-b^2 B\right) \log (\cos (c+d x))}{d}+x \left(a^2 A-2 a b B-A b^2\right)+\frac{b (a B+A b) \tan (c+d x)}{d}+\frac{B (a+b \tan (c+d x))^2}{2 d}",1,"(a^2*A - A*b^2 - 2*a*b*B)*x - ((2*a*A*b + a^2*B - b^2*B)*Log[Cos[c + d*x]])/d + (b*(A*b + a*B)*Tan[c + d*x])/d + (B*(a + b*Tan[c + d*x])^2)/(2*d)","A",3,3,23,0.1304,1,"{3528, 3525, 3475}"
243,1,70,0,0.1139196,"\int \cot (c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","x \left(a^2 B+2 a A b-b^2 B\right)+\frac{a^2 A \log (\sin (c+d x))}{d}-\frac{b (2 a B+A b) \log (\cos (c+d x))}{d}+\frac{b^2 B \tan (c+d x)}{d}","x \left(a^2 B+2 a A b-b^2 B\right)+\frac{a^2 A \log (\sin (c+d x))}{d}-\frac{b (2 a B+A b) \log (\cos (c+d x))}{d}+\frac{b^2 B \tan (c+d x)}{d}",1,"(2*a*A*b + a^2*B - b^2*B)*x - (b*(A*b + 2*a*B)*Log[Cos[c + d*x]])/d + (a^2*A*Log[Sin[c + d*x]])/d + (b^2*B*Tan[c + d*x])/d","A",4,3,29,0.1034,1,"{3606, 3624, 3475}"
244,1,72,0,0.1330962,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-x \left(a^2 A-2 a b B-A b^2\right)-\frac{a^2 A \cot (c+d x)}{d}+\frac{a (a B+2 A b) \log (\sin (c+d x))}{d}-\frac{b^2 B \log (\cos (c+d x))}{d}","-x \left(a^2 A-2 a b B-A b^2\right)-\frac{a^2 A \cot (c+d x)}{d}+\frac{a (a B+2 A b) \log (\sin (c+d x))}{d}-\frac{b^2 B \log (\cos (c+d x))}{d}",1,"-((a^2*A - A*b^2 - 2*a*b*B)*x) - (a^2*A*Cot[c + d*x])/d - (b^2*B*Log[Cos[c + d*x]])/d + (a*(2*A*b + a*B)*Log[Sin[c + d*x]])/d","A",4,3,31,0.09677,1,"{3604, 3624, 3475}"
245,1,88,0,0.1913681,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 A \cot ^2(c+d x)}{2 d}+x \left(b^2 B-a (a B+2 A b)\right)-\frac{a (a B+2 A b) \cot (c+d x)}{d}","-\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 A \cot ^2(c+d x)}{2 d}+x \left(b^2 B-a (a B+2 A b)\right)-\frac{a (a B+2 A b) \cot (c+d x)}{d}",1,"(b^2*B - a*(2*A*b + a*B))*x - (a*(2*A*b + a*B)*Cot[c + d*x])/d - (a^2*A*Cot[c + d*x]^2)/(2*d) - ((a^2*A - A*b^2 - 2*a*b*B)*Log[Sin[c + d*x]])/d","A",4,4,31,0.1290,1,"{3604, 3628, 3531, 3475}"
246,1,118,0,0.2428966,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 A-2 a b B-A b^2\right) \cot (c+d x)}{d}+x \left(a^2 A-2 a b B-A b^2\right)-\frac{a^2 A \cot ^3(c+d x)}{3 d}+\frac{\left(b^2 B-a (a B+2 A b)\right) \log (\sin (c+d x))}{d}-\frac{a (a B+2 A b) \cot ^2(c+d x)}{2 d}","\frac{\left(a^2 A-2 a b B-A b^2\right) \cot (c+d x)}{d}+x \left(a^2 A-2 a b B-A b^2\right)-\frac{a^2 A \cot ^3(c+d x)}{3 d}+\frac{\left(b^2 B-a (a B+2 A b)\right) \log (\sin (c+d x))}{d}-\frac{a (a B+2 A b) \cot ^2(c+d x)}{2 d}",1,"(a^2*A - A*b^2 - 2*a*b*B)*x + ((a^2*A - A*b^2 - 2*a*b*B)*Cot[c + d*x])/d - (a*(2*A*b + a*B)*Cot[c + d*x]^2)/(2*d) - (a^2*A*Cot[c + d*x]^3)/(3*d) + ((b^2*B - a*(2*A*b + a*B))*Log[Sin[c + d*x]])/d","A",5,5,31,0.1613,1,"{3604, 3628, 3529, 3531, 3475}"
247,1,151,0,0.3006289,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 A-2 a b B-A b^2\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\sin (c+d x))}{d}+x \left(a^2 B+2 a A b-b^2 B\right)-\frac{a^2 A \cot ^4(c+d x)}{4 d}-\frac{\left(b^2 B-a (a B+2 A b)\right) \cot (c+d x)}{d}-\frac{a (a B+2 A b) \cot ^3(c+d x)}{3 d}","\frac{\left(a^2 A-2 a b B-A b^2\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2 A-2 a b B-A b^2\right) \log (\sin (c+d x))}{d}+x \left(a^2 B+2 a A b-b^2 B\right)-\frac{a^2 A \cot ^4(c+d x)}{4 d}-\frac{\left(b^2 B-a (a B+2 A b)\right) \cot (c+d x)}{d}-\frac{a (a B+2 A b) \cot ^3(c+d x)}{3 d}",1,"(2*a*A*b + a^2*B - b^2*B)*x - ((b^2*B - a*(2*A*b + a*B))*Cot[c + d*x])/d + ((a^2*A - A*b^2 - 2*a*b*B)*Cot[c + d*x]^2)/(2*d) - (a*(2*A*b + a*B)*Cot[c + d*x]^3)/(3*d) - (a^2*A*Cot[c + d*x]^4)/(4*d) + ((a^2*A - A*b^2 - 2*a*b*B)*Log[Sin[c + d*x]])/d","A",6,5,31,0.1613,1,"{3604, 3628, 3529, 3531, 3475}"
248,1,201,0,0.3693493,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{b \left(a^2 B+2 a A b-b^2 B\right) \tan (c+d x)}{d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}-\frac{(a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}-\frac{B (a+b \tan (c+d x))^3}{3 d}","-\frac{b \left(a^2 B+2 a A b-b^2 B\right) \tan (c+d x)}{d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}-\frac{(a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}-\frac{B (a+b \tan (c+d x))^3}{3 d}",1,"-((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*x) + ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Log[Cos[c + d*x]])/d - (b*(2*a*A*b + a^2*B - b^2*B)*Tan[c + d*x])/d - ((A*b + a*B)*(a + b*Tan[c + d*x])^2)/(2*d) - (B*(a + b*Tan[c + d*x])^3)/(3*d) + ((5*A*b - a*B)*(a + b*Tan[c + d*x])^4)/(20*b^2*d) + (B*Tan[c + d*x]*(a + b*Tan[c + d*x])^4)/(5*b*d)","A",6,5,31,0.1613,1,"{3607, 3630, 3528, 3525, 3475}"
249,1,165,0,0.193966,"\int \tan (c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{b \left(a^2 A-2 a b B-A b^2\right) \tan (c+d x)}{d}-\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \log (\cos (c+d x))}{d}-x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)+\frac{(a A-b B) (a+b \tan (c+d x))^2}{2 d}+\frac{A (a+b \tan (c+d x))^3}{3 d}+\frac{B (a+b \tan (c+d x))^4}{4 b d}","\frac{b \left(a^2 A-2 a b B-A b^2\right) \tan (c+d x)}{d}-\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \log (\cos (c+d x))}{d}-x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)+\frac{(a A-b B) (a+b \tan (c+d x))^2}{2 d}+\frac{A (a+b \tan (c+d x))^3}{3 d}+\frac{B (a+b \tan (c+d x))^4}{4 b d}",1,"-((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*x) - ((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Log[Cos[c + d*x]])/d + (b*(a^2*A - A*b^2 - 2*a*b*B)*Tan[c + d*x])/d + ((a*A - b*B)*(a + b*Tan[c + d*x])^2)/(2*d) + (A*(a + b*Tan[c + d*x])^3)/(3*d) + (B*(a + b*Tan[c + d*x])^4)/(4*b*d)","A",5,4,29,0.1379,1,"{3592, 3528, 3525, 3475}"
250,1,140,0,0.153958,"\int (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{b \left(a^2 B+2 a A b-b^2 B\right) \tan (c+d x)}{d}-\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}+x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{(a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 d}","\frac{b \left(a^2 B+2 a A b-b^2 B\right) \tan (c+d x)}{d}-\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}+x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{(a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{B (a+b \tan (c+d x))^3}{3 d}",1,"(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*x - ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Log[Cos[c + d*x]])/d + (b*(2*a*A*b + a^2*B - b^2*B)*Tan[c + d*x])/d + ((A*b + a*B)*(a + b*Tan[c + d*x])^2)/(2*d) + (B*(a + b*Tan[c + d*x])^3)/(3*d)","A",4,3,23,0.1304,1,"{3528, 3525, 3475}"
251,1,117,0,0.2701302,"\int \cot (c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{b \left(3 a^2 B+3 a A b-b^2 B\right) \log (\cos (c+d x))}{d}+x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)+\frac{a^3 A \log (\sin (c+d x))}{d}+\frac{b^2 (2 a B+A b) \tan (c+d x)}{d}+\frac{b B (a+b \tan (c+d x))^2}{2 d}","-\frac{b \left(3 a^2 B+3 a A b-b^2 B\right) \log (\cos (c+d x))}{d}+x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)+\frac{a^3 A \log (\sin (c+d x))}{d}+\frac{b^2 (2 a B+A b) \tan (c+d x)}{d}+\frac{b B (a+b \tan (c+d x))^2}{2 d}",1,"(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*x - (b*(3*a*A*b + 3*a^2*B - b^2*B)*Log[Cos[c + d*x]])/d + (a^3*A*Log[Sin[c + d*x]])/d + (b^2*(A*b + 2*a*B)*Tan[c + d*x])/d + (b*B*(a + b*Tan[c + d*x])^2)/(2*d)","A",5,4,29,0.1379,1,"{3607, 3637, 3624, 3475}"
252,1,119,0,0.2629116,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{a^2 (a B+3 A b) \log (\sin (c+d x))}{d}+\frac{b^2 (a A+b B) \tan (c+d x)}{d}-\frac{b^2 (3 a B+A b) \log (\cos (c+d x))}{d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^2}{d}","-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)+\frac{a^2 (a B+3 A b) \log (\sin (c+d x))}{d}+\frac{b^2 (a A+b B) \tan (c+d x)}{d}-\frac{b^2 (3 a B+A b) \log (\cos (c+d x))}{d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^2}{d}",1,"-((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*x) - (b^2*(A*b + 3*a*B)*Log[Cos[c + d*x]])/d + (a^2*(3*A*b + a*B)*Log[Sin[c + d*x]])/d + (b^2*(a*A + b*B)*Tan[c + d*x])/d - (a*A*Cot[c + d*x]*(a + b*Tan[c + d*x])^2)/d","A",5,4,31,0.1290,1,"{3605, 3637, 3624, 3475}"
253,1,127,0,0.2896262,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{a \left(a^2 A-3 a b B-3 A b^2\right) \log (\sin (c+d x))}{d}-x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)-\frac{a^2 (a B+2 A b) \cot (c+d x)}{d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 B \log (\cos (c+d x))}{d}","-\frac{a \left(a^2 A-3 a b B-3 A b^2\right) \log (\sin (c+d x))}{d}-x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)-\frac{a^2 (a B+2 A b) \cot (c+d x)}{d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^3 B \log (\cos (c+d x))}{d}",1,"-((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*x) - (a^2*(2*A*b + a*B)*Cot[c + d*x])/d - (b^3*B*Log[Cos[c + d*x]])/d - (a*(a^2*A - 3*A*b^2 - 3*a*b*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2)/(2*d)","A",5,4,31,0.1290,1,"{3605, 3635, 3624, 3475}"
254,1,154,0,0.364792,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a \left(3 a^2 A-9 a b B-8 A b^2\right) \cot (c+d x)}{3 d}-\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\sin (c+d x))}{d}+x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)-\frac{a^2 (3 a B+5 A b) \cot ^2(c+d x)}{6 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}","\frac{a \left(3 a^2 A-9 a b B-8 A b^2\right) \cot (c+d x)}{3 d}-\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\sin (c+d x))}{d}+x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)-\frac{a^2 (3 a B+5 A b) \cot ^2(c+d x)}{6 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}",1,"(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*x + (a*(3*a^2*A - 8*A*b^2 - 9*a*b*B)*Cot[c + d*x])/(3*d) - (a^2*(5*A*b + 3*a*B)*Cot[c + d*x]^2)/(6*d) - ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2)/(3*d)","A",5,5,31,0.1613,1,"{3605, 3635, 3628, 3531, 3475}"
255,1,191,0,0.4525329,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a \left(2 a^2 A-6 a b B-5 A b^2\right) \cot ^2(c+d x)}{4 d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \cot (c+d x)}{d}+\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \log (\sin (c+d x))}{d}+x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)-\frac{a^2 (2 a B+3 A b) \cot ^3(c+d x)}{6 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}","\frac{a \left(2 a^2 A-6 a b B-5 A b^2\right) \cot ^2(c+d x)}{4 d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \cot (c+d x)}{d}+\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \log (\sin (c+d x))}{d}+x \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)-\frac{a^2 (2 a B+3 A b) \cot ^3(c+d x)}{6 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}",1,"(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*x + ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Cot[c + d*x])/d + (a*(2*a^2*A - 5*A*b^2 - 6*a*b*B)*Cot[c + d*x]^2)/(4*d) - (a^2*(3*A*b + 2*a*B)*Cot[c + d*x]^3)/(6*d) + ((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2)/(4*d)","A",6,6,31,0.1935,1,"{3605, 3635, 3628, 3529, 3531, 3475}"
256,1,233,0,0.4958745,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{a \left(5 a^2 A-15 a b B-12 A b^2\right) \cot ^3(c+d x)}{15 d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \cot ^2(c+d x)}{2 d}-\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \cot (c+d x)}{d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\sin (c+d x))}{d}-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)-\frac{a^2 (5 a B+7 A b) \cot ^4(c+d x)}{20 d}-\frac{a A \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}","\frac{a \left(5 a^2 A-15 a b B-12 A b^2\right) \cot ^3(c+d x)}{15 d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \cot ^2(c+d x)}{2 d}-\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \cot (c+d x)}{d}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \log (\sin (c+d x))}{d}-x \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right)-\frac{a^2 (5 a B+7 A b) \cot ^4(c+d x)}{20 d}-\frac{a A \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}",1,"-((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*x) - ((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Cot[c + d*x])/d + ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Cot[c + d*x]^2)/(2*d) + (a*(5*a^2*A - 12*A*b^2 - 15*a*b*B)*Cot[c + d*x]^3)/(15*d) - (a^2*(7*A*b + 5*a*B)*Cot[c + d*x]^4)/(20*d) + ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Log[Sin[c + d*x]])/d - (a*A*Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2)/(5*d)","A",7,6,31,0.1935,1,"{3605, 3635, 3628, 3529, 3531, 3475}"
257,1,263,0,0.4319178,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 B+2 a A b-b^2 B\right) (a+b \tan (c+d x))^2}{2 d}-\frac{b \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan (c+d x)}{d}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{(6 A b-a B) (a+b \tan (c+d x))^5}{30 b^2 d}-\frac{(a B+A b) (a+b \tan (c+d x))^3}{3 d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^5}{6 b d}-\frac{B (a+b \tan (c+d x))^4}{4 d}","-\frac{\left(a^2 B+2 a A b-b^2 B\right) (a+b \tan (c+d x))^2}{2 d}-\frac{b \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan (c+d x)}{d}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{(6 A b-a B) (a+b \tan (c+d x))^5}{30 b^2 d}-\frac{(a B+A b) (a+b \tan (c+d x))^3}{3 d}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^5}{6 b d}-\frac{B (a+b \tan (c+d x))^4}{4 d}",1,"-((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*x) + ((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*Log[Cos[c + d*x]])/d - (b*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Tan[c + d*x])/d - ((2*a*A*b + a^2*B - b^2*B)*(a + b*Tan[c + d*x])^2)/(2*d) - ((A*b + a*B)*(a + b*Tan[c + d*x])^3)/(3*d) - (B*(a + b*Tan[c + d*x])^4)/(4*d) + ((6*A*b - a*B)*(a + b*Tan[c + d*x])^5)/(30*b^2*d) + (B*Tan[c + d*x]*(a + b*Tan[c + d*x])^5)/(6*b*d)","A",7,5,31,0.1613,1,"{3607, 3630, 3528, 3525, 3475}"
258,1,226,0,0.2732537,"\int \tan (c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 A-2 a b B-A b^2\right) (a+b \tan (c+d x))^2}{2 d}+\frac{b \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \tan (c+d x)}{d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\cos (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)+\frac{(a A-b B) (a+b \tan (c+d x))^3}{3 d}+\frac{A (a+b \tan (c+d x))^4}{4 d}+\frac{B (a+b \tan (c+d x))^5}{5 b d}","\frac{\left(a^2 A-2 a b B-A b^2\right) (a+b \tan (c+d x))^2}{2 d}+\frac{b \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \tan (c+d x)}{d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\cos (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)+\frac{(a A-b B) (a+b \tan (c+d x))^3}{3 d}+\frac{A (a+b \tan (c+d x))^4}{4 d}+\frac{B (a+b \tan (c+d x))^5}{5 b d}",1,"-((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*x) - ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Log[Cos[c + d*x]])/d + (b*(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Tan[c + d*x])/d + ((a^2*A - A*b^2 - 2*a*b*B)*(a + b*Tan[c + d*x])^2)/(2*d) + ((a*A - b*B)*(a + b*Tan[c + d*x])^3)/(3*d) + (A*(a + b*Tan[c + d*x])^4)/(4*d) + (B*(a + b*Tan[c + d*x])^5)/(5*b*d)","A",6,4,29,0.1379,1,"{3592, 3528, 3525, 3475}"
259,1,202,0,0.2300628,"\int (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 B+2 a A b-b^2 B\right) (a+b \tan (c+d x))^2}{2 d}+\frac{b \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan (c+d x)}{d}-\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\cos (c+d x))}{d}+x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{(a B+A b) (a+b \tan (c+d x))^3}{3 d}+\frac{B (a+b \tan (c+d x))^4}{4 d}","\frac{\left(a^2 B+2 a A b-b^2 B\right) (a+b \tan (c+d x))^2}{2 d}+\frac{b \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan (c+d x)}{d}-\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\cos (c+d x))}{d}+x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{(a B+A b) (a+b \tan (c+d x))^3}{3 d}+\frac{B (a+b \tan (c+d x))^4}{4 d}",1,"(a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*x - ((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*Log[Cos[c + d*x]])/d + (b*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Tan[c + d*x])/d + ((2*a*A*b + a^2*B - b^2*B)*(a + b*Tan[c + d*x])^2)/(2*d) + ((A*b + a*B)*(a + b*Tan[c + d*x])^3)/(3*d) + (B*(a + b*Tan[c + d*x])^4)/(4*d)","A",5,3,23,0.1304,1,"{3528, 3525, 3475}"
260,1,172,0,0.4706602,"\int \cot (c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{b^2 \left(3 a^2 B+3 a A b-b^2 B\right) \tan (c+d x)}{d}-\frac{b \left(6 a^2 A b+4 a^3 B-4 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}+x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)+\frac{a^4 A \log (\sin (c+d x))}{d}+\frac{b (2 a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{b B (a+b \tan (c+d x))^3}{3 d}","\frac{b^2 \left(3 a^2 B+3 a A b-b^2 B\right) \tan (c+d x)}{d}-\frac{b \left(6 a^2 A b+4 a^3 B-4 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d}+x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)+\frac{a^4 A \log (\sin (c+d x))}{d}+\frac{b (2 a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac{b B (a+b \tan (c+d x))^3}{3 d}",1,"(4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*x - (b*(6*a^2*A*b - A*b^3 + 4*a^3*B - 4*a*b^2*B)*Log[Cos[c + d*x]])/d + (a^4*A*Log[Sin[c + d*x]])/d + (b^2*(3*a*A*b + 3*a^2*B - b^2*B)*Tan[c + d*x])/d + (b*(A*b + 2*a*B)*(a + b*Tan[c + d*x])^2)/(2*d) + (b*B*(a + b*Tan[c + d*x])^3)/(3*d)","A",6,5,29,0.1724,1,"{3607, 3647, 3637, 3624, 3475}"
261,1,175,0,0.4821516,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{b^2 \left(a^2 A+3 a b B+A b^2\right) \tan (c+d x)}{d}-\frac{b^2 \left(6 a^2 B+4 a A b-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{a^3 (a B+4 A b) \log (\sin (c+d x))}{d}+\frac{b (2 a A+b B) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^3}{d}","\frac{b^2 \left(a^2 A+3 a b B+A b^2\right) \tan (c+d x)}{d}-\frac{b^2 \left(6 a^2 B+4 a A b-b^2 B\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)+\frac{a^3 (a B+4 A b) \log (\sin (c+d x))}{d}+\frac{b (2 a A+b B) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^3}{d}",1,"-((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*x) - (b^2*(4*a*A*b + 6*a^2*B - b^2*B)*Log[Cos[c + d*x]])/d + (a^3*(4*A*b + a*B)*Log[Sin[c + d*x]])/d + (b^2*(a^2*A + A*b^2 + 3*a*b*B)*Tan[c + d*x])/d + (b*(2*a*A + b*B)*(a + b*Tan[c + d*x])^2)/(2*d) - (a*A*Cot[c + d*x]*(a + b*Tan[c + d*x])^3)/d","A",6,5,31,0.1613,1,"{3605, 3647, 3637, 3624, 3475}"
262,1,186,0,0.5054938,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{b^2 \left(a^2 B+3 a A b+b^2 B\right) \tan (c+d x)}{d}-\frac{a^2 \left(a^2 A-4 a b B-6 A b^2\right) \log (\sin (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{b^3 (4 a B+A b) \log (\cos (c+d x))}{d}-\frac{a (2 a B+5 A b) \cot (c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^3}{2 d}","\frac{b^2 \left(a^2 B+3 a A b+b^2 B\right) \tan (c+d x)}{d}-\frac{a^2 \left(a^2 A-4 a b B-6 A b^2\right) \log (\sin (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{b^3 (4 a B+A b) \log (\cos (c+d x))}{d}-\frac{a (2 a B+5 A b) \cot (c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^3}{2 d}",1,"-((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*x) - (b^3*(A*b + 4*a*B)*Log[Cos[c + d*x]])/d - (a^2*(a^2*A - 6*A*b^2 - 4*a*b*B)*Log[Sin[c + d*x]])/d + (b^2*(3*a*A*b + a^2*B + b^2*B)*Tan[c + d*x])/d - (a*(5*A*b + 2*a*B)*Cot[c + d*x]*(a + b*Tan[c + d*x])^2)/(2*d) - (a*A*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^3)/(2*d)","A",6,5,31,0.1613,1,"{3605, 3645, 3637, 3624, 3475}"
263,1,187,0,0.5307049,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^2 \left(a^2 A-3 a b B-3 A b^2\right) \cot (c+d x)}{d}-\frac{a \left(4 a^2 A b+a^3 B-6 a b^2 B-4 A b^3\right) \log (\sin (c+d x))}{d}+x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)-\frac{a (a B+2 A b) \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^3}{3 d}-\frac{b^4 B \log (\cos (c+d x))}{d}","\frac{a^2 \left(a^2 A-3 a b B-3 A b^2\right) \cot (c+d x)}{d}-\frac{a \left(4 a^2 A b+a^3 B-6 a b^2 B-4 A b^3\right) \log (\sin (c+d x))}{d}+x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)-\frac{a (a B+2 A b) \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^3}{3 d}-\frac{b^4 B \log (\cos (c+d x))}{d}",1,"(a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*x + (a^2*(a^2*A - 3*A*b^2 - 3*a*b*B)*Cot[c + d*x])/d - (b^4*B*Log[Cos[c + d*x]])/d - (a*(4*a^2*A*b - 4*A*b^3 + a^3*B - 6*a*b^2*B)*Log[Sin[c + d*x]])/d - (a*(2*A*b + a*B)*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2)/(2*d) - (a*A*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^3)/(3*d)","A",6,5,31,0.1613,1,"{3605, 3645, 3635, 3624, 3475}"
264,1,225,0,0.6448134,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^2 \left(6 a^2 A-16 a b B-13 A b^2\right) \cot ^2(c+d x)}{12 d}+\frac{a \left(24 a^2 A b+6 a^3 B-34 a b^2 B-19 A b^3\right) \cot (c+d x)}{6 d}+\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\sin (c+d x))}{d}+x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{a (4 a B+7 A b) \cot ^3(c+d x) (a+b \tan (c+d x))^2}{12 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^3}{4 d}","\frac{a^2 \left(6 a^2 A-16 a b B-13 A b^2\right) \cot ^2(c+d x)}{12 d}+\frac{a \left(24 a^2 A b+6 a^3 B-34 a b^2 B-19 A b^3\right) \cot (c+d x)}{6 d}+\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\sin (c+d x))}{d}+x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{a (4 a B+7 A b) \cot ^3(c+d x) (a+b \tan (c+d x))^2}{12 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^3}{4 d}",1,"(4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*x + (a*(24*a^2*A*b - 19*A*b^3 + 6*a^3*B - 34*a*b^2*B)*Cot[c + d*x])/(6*d) + (a^2*(6*a^2*A - 13*A*b^2 - 16*a*b*B)*Cot[c + d*x]^2)/(12*d) + ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Log[Sin[c + d*x]])/d - (a*(7*A*b + 4*a*B)*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2)/(12*d) - (a*A*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^3)/(4*d)","A",6,6,31,0.1935,1,"{3605, 3645, 3635, 3628, 3531, 3475}"
265,1,273,0,0.7327608,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^2 \left(10 a^2 A-25 a b B-18 A b^2\right) \cot ^3(c+d x)}{30 d}+\frac{a \left(40 a^2 A b+10 a^3 B-55 a b^2 B-28 A b^3\right) \cot ^2(c+d x)}{20 d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \cot (c+d x)}{d}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\sin (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)-\frac{a (5 a B+8 A b) \cot ^4(c+d x) (a+b \tan (c+d x))^2}{20 d}-\frac{a A \cot ^5(c+d x) (a+b \tan (c+d x))^3}{5 d}","\frac{a^2 \left(10 a^2 A-25 a b B-18 A b^2\right) \cot ^3(c+d x)}{30 d}+\frac{a \left(40 a^2 A b+10 a^3 B-55 a b^2 B-28 A b^3\right) \cot ^2(c+d x)}{20 d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \cot (c+d x)}{d}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \log (\sin (c+d x))}{d}-x \left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right)-\frac{a (5 a B+8 A b) \cot ^4(c+d x) (a+b \tan (c+d x))^2}{20 d}-\frac{a A \cot ^5(c+d x) (a+b \tan (c+d x))^3}{5 d}",1,"-((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*x) - ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Cot[c + d*x])/d + (a*(40*a^2*A*b - 28*A*b^3 + 10*a^3*B - 55*a*b^2*B)*Cot[c + d*x]^2)/(20*d) + (a^2*(10*a^2*A - 18*A*b^2 - 25*a*b*B)*Cot[c + d*x]^3)/(30*d) + ((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*Log[Sin[c + d*x]])/d - (a*(8*A*b + 5*a*B)*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2)/(20*d) - (a*A*Cot[c + d*x]^5*(a + b*Tan[c + d*x])^3)/(5*d)","A",7,7,31,0.2258,1,"{3605, 3645, 3635, 3628, 3529, 3531, 3475}"
266,1,323,0,0.8583791,"\int \cot ^7(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^7*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{a^2 \left(5 a^2 A-12 a b B-8 A b^2\right) \cot ^4(c+d x)}{20 d}+\frac{a \left(20 a^2 A b+5 a^3 B-27 a b^2 B-13 A b^3\right) \cot ^3(c+d x)}{15 d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \cot ^2(c+d x)}{2 d}-\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \cot (c+d x)}{d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\sin (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{a (2 a B+3 A b) \cot ^5(c+d x) (a+b \tan (c+d x))^2}{10 d}-\frac{a A \cot ^6(c+d x) (a+b \tan (c+d x))^3}{6 d}","\frac{a^2 \left(5 a^2 A-12 a b B-8 A b^2\right) \cot ^4(c+d x)}{20 d}+\frac{a \left(20 a^2 A b+5 a^3 B-27 a b^2 B-13 A b^3\right) \cot ^3(c+d x)}{15 d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \cot ^2(c+d x)}{2 d}-\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \cot (c+d x)}{d}-\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \log (\sin (c+d x))}{d}-x \left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right)-\frac{a (2 a B+3 A b) \cot ^5(c+d x) (a+b \tan (c+d x))^2}{10 d}-\frac{a A \cot ^6(c+d x) (a+b \tan (c+d x))^3}{6 d}",1,"-((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*x) - ((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*Cot[c + d*x])/d - ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Cot[c + d*x]^2)/(2*d) + (a*(20*a^2*A*b - 13*A*b^3 + 5*a^3*B - 27*a*b^2*B)*Cot[c + d*x]^3)/(15*d) + (a^2*(5*a^2*A - 8*A*b^2 - 12*a*b*B)*Cot[c + d*x]^4)/(20*d) - ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Log[Sin[c + d*x]])/d - (a*(3*A*b + 2*a*B)*Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2)/(10*d) - (a*A*Cot[c + d*x]^6*(a + b*Tan[c + d*x])^3)/(6*d)","A",8,7,31,0.2258,1,"{3605, 3645, 3635, 3628, 3529, 3531, 3475}"
267,1,127,0,0.3969855,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{a^3 (A b-a B) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{(a A+b B) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (A b-a B)}{a^2+b^2}+\frac{(A b-a B) \tan (c+d x)}{b^2 d}+\frac{B \tan ^2(c+d x)}{2 b d}","-\frac{a^3 (A b-a B) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{(a A+b B) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (A b-a B)}{a^2+b^2}+\frac{(A b-a B) \tan (c+d x)}{b^2 d}+\frac{B \tan ^2(c+d x)}{2 b d}",1,"-(((A*b - a*B)*x)/(a^2 + b^2)) + ((a*A + b*B)*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a^3*(A*b - a*B)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)*d) + ((A*b - a*B)*Tan[c + d*x])/(b^2*d) + (B*Tan[c + d*x]^2)/(2*b*d)","A",6,6,31,0.1935,1,"{3607, 3647, 3626, 3617, 31, 3475}"
268,1,101,0,0.1973705,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{a^2 (A b-a B) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}-\frac{(A b-a B) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (a A+b B)}{a^2+b^2}+\frac{B \tan (c+d x)}{b d}","\frac{a^2 (A b-a B) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}-\frac{(A b-a B) \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{x (a A+b B)}{a^2+b^2}+\frac{B \tan (c+d x)}{b d}",1,"-(((a*A + b*B)*x)/(a^2 + b^2)) - ((A*b - a*B)*Log[Cos[c + d*x]])/((a^2 + b^2)*d) + (a^2*(A*b - a*B)*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) + (B*Tan[c + d*x])/(b*d)","A",5,5,31,0.1613,1,"{3606, 3626, 3617, 31, 3475}"
269,1,80,0,0.1269487,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{a (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}+\frac{x (A b-a B)}{a^2+b^2}-\frac{B \log (\cos (c+d x))}{b d}","-\frac{a (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}+\frac{x (A b-a B)}{a^2+b^2}-\frac{B \log (\cos (c+d x))}{b d}",1,"((A*b - a*B)*x)/(a^2 + b^2) - (B*Log[Cos[c + d*x]])/(b*d) - (a*(A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(b*(a^2 + b^2)*d)","A",5,5,29,0.1724,1,"{3589, 3475, 12, 3531, 3530}"
270,1,58,0,0.0678102,"\int \frac{A+B \tan (c+d x)}{a+b \tan (c+d x)} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x]),x]","\frac{(A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (a A+b B)}{a^2+b^2}","\frac{(A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{x (a A+b B)}{a^2+b^2}",1,"((a*A + b*B)*x)/(a^2 + b^2) + ((A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",2,2,23,0.08696,1,"{3531, 3530}"
271,1,80,0,0.1089936,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{b (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{x (A b-a B)}{a^2+b^2}+\frac{A \log (\sin (c+d x))}{a d}","-\frac{b (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{x (A b-a B)}{a^2+b^2}+\frac{A \log (\sin (c+d x))}{a d}",1,"-(((A*b - a*B)*x)/(a^2 + b^2)) + (A*Log[Sin[c + d*x]])/(a*d) - (b*(A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a*(a^2 + b^2)*d)","A",3,3,29,0.1034,1,"{3611, 3530, 3475}"
272,1,103,0,0.2513841,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{b^2 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{x (a A+b B)}{a^2+b^2}-\frac{(A b-a B) \log (\sin (c+d x))}{a^2 d}-\frac{A \cot (c+d x)}{a d}","\frac{b^2 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{x (a A+b B)}{a^2+b^2}-\frac{(A b-a B) \log (\sin (c+d x))}{a^2 d}-\frac{A \cot (c+d x)}{a d}",1,"-(((a*A + b*B)*x)/(a^2 + b^2)) - (A*Cot[c + d*x])/(a*d) - ((A*b - a*B)*Log[Sin[c + d*x]])/(a^2*d) + (b^2*(A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)*d)","A",4,4,31,0.1290,1,"{3609, 3651, 3530, 3475}"
273,1,137,0,0.5502863,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{\left(a^2 A+a b B-A b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^3 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{x (A b-a B)}{a^2+b^2}+\frac{(A b-a B) \cot (c+d x)}{a^2 d}-\frac{A \cot ^2(c+d x)}{2 a d}","-\frac{\left(a^2 A+a b B-A b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^3 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{x (A b-a B)}{a^2+b^2}+\frac{(A b-a B) \cot (c+d x)}{a^2 d}-\frac{A \cot ^2(c+d x)}{2 a d}",1,"((A*b - a*B)*x)/(a^2 + b^2) + ((A*b - a*B)*Cot[c + d*x])/(a^2*d) - (A*Cot[c + d*x]^2)/(2*a*d) - ((a^2*A - A*b^2 + a*b*B)*Log[Sin[c + d*x]])/(a^3*d) - (b^3*(A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)*d)","A",5,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
274,1,169,0,0.8325765,"\int \frac{\cot ^4(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2 A+a b B-A b^2\right) \cot (c+d x)}{a^3 d}+\frac{\left(a^2-b^2\right) (A b-a B) \log (\sin (c+d x))}{a^4 d}+\frac{b^4 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)}+\frac{x (a A+b B)}{a^2+b^2}+\frac{(A b-a B) \cot ^2(c+d x)}{2 a^2 d}-\frac{A \cot ^3(c+d x)}{3 a d}","\frac{\left(a^2 A+a b B-A b^2\right) \cot (c+d x)}{a^3 d}+\frac{\left(a^2-b^2\right) (A b-a B) \log (\sin (c+d x))}{a^4 d}+\frac{b^4 (A b-a B) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)}+\frac{x (a A+b B)}{a^2+b^2}+\frac{(A b-a B) \cot ^2(c+d x)}{2 a^2 d}-\frac{A \cot ^3(c+d x)}{3 a d}",1,"((a*A + b*B)*x)/(a^2 + b^2) + ((a^2*A - A*b^2 + a*b*B)*Cot[c + d*x])/(a^3*d) + ((A*b - a*B)*Cot[c + d*x]^2)/(2*a^2*d) - (A*Cot[c + d*x]^3)/(3*a*d) + ((a^2 - b^2)*(A*b - a*B)*Log[Sin[c + d*x]])/(a^4*d) + (b^4*(A*b - a*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)*d)","A",6,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
275,1,208,0,0.4548269,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{a (A b-a B) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(-2 a^2 B+a A b-b^2 B\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 \left(a^2 A b-2 a^3 B-4 a b^2 B+3 A b^3\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{\left(a^2 A+2 a b B-A b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}","\frac{a (A b-a B) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(-2 a^2 B+a A b-b^2 B\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 \left(a^2 A b-2 a^3 B-4 a b^2 B+3 A b^3\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{\left(a^2 A+2 a b B-A b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}",1,"-(((2*a*A*b - a^2*B + b^2*B)*x)/(a^2 + b^2)^2) + ((a^2*A - A*b^2 + 2*a*b*B)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) + (a^2*(a^2*A*b + 3*A*b^3 - 2*a^3*B - 4*a*b^2*B)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^2*d) - ((a*A*b - 2*a^2*B - b^2*B)*Tan[c + d*x])/(b^2*(a^2 + b^2)*d) + (a*(A*b - a*B)*Tan[c + d*x]^2)/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",6,6,31,0.1935,1,"{3605, 3647, 3626, 3617, 31, 3475}"
276,1,157,0,0.2733184,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 (A b-a B)}{b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-B)+2 a A b+b^2 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2 (A b-a B)}{b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-B)+2 a A b+b^2 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}",1,"-(((a^2*A - A*b^2 + 2*a*b*B)*x)/(a^2 + b^2)^2) - ((2*a*A*b - a^2*B + b^2*B)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) - (a*(2*A*b^3 - a*(a^2 + 3*b^2)*B)*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)^2*d) - (a^2*(A*b - a*B))/(b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",5,5,31,0.1613,1,"{3604, 3626, 3617, 31, 3475}"
277,1,115,0,0.1592158,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{a (A b-a B)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 A+2 a b B-A b^2\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 A b+b^2 B\right)}{\left(a^2+b^2\right)^2}","\frac{a (A b-a B)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 A+2 a b B-A b^2\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 A b+b^2 B\right)}{\left(a^2+b^2\right)^2}",1,"((2*a*A*b - a^2*B + b^2*B)*x)/(a^2 + b^2)^2 - ((a^2*A - A*b^2 + 2*a*b*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) + (a*(A*b - a*B))/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,29,0.1034,1,"{3591, 3531, 3530}"
278,1,111,0,0.136639,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^2,x]","-\frac{A b-a B}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (-B)+2 a A b+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 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}","-\frac{A b-a B}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (-B)+2 a A b+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 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}",1,"((a^2*A - A*b^2 + 2*a*b*B)*x)/(a^2 + b^2)^2 + ((2*a*A*b - a^2*B + b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) - (A*b - a*B)/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,23,0.1304,1,"{3529, 3531, 3530}"
279,1,137,0,0.3189098,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b (A b-a B)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\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 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}+\frac{A \log (\sin (c+d x))}{a^2 d}","\frac{b (A b-a B)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\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 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}+\frac{A \log (\sin (c+d x))}{a^2 d}",1,"-(((2*a*A*b - a^2*B + b^2*B)*x)/(a^2 + b^2)^2) + (A*Log[Sin[c + d*x]])/(a^2*d) - (b*(3*a^2*A*b + A*b^3 - 2*a^3*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)^2*d) + (b*(A*b - a*B))/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",4,4,29,0.1379,1,"{3609, 3651, 3530, 3475}"
280,1,192,0,0.5411168,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{b \left(a^2 A-a b B+2 A b^2\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b^2 \left(4 a^2 A b-3 a^3 B-a b^2 B+2 A b^3\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 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}-\frac{(2 A b-a B) \log (\sin (c+d x))}{a^3 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))}","-\frac{b \left(a^2 A-a b B+2 A b^2\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{b^2 \left(4 a^2 A b-3 a^3 B-a b^2 B+2 A b^3\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 A+2 a b B-A b^2\right)}{\left(a^2+b^2\right)^2}-\frac{(2 A b-a B) \log (\sin (c+d x))}{a^3 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))}",1,"-(((a^2*A - A*b^2 + 2*a*b*B)*x)/(a^2 + b^2)^2) - ((2*A*b - a*B)*Log[Sin[c + d*x]])/(a^3*d) + (b^2*(4*a^2*A*b + 2*A*b^3 - 3*a^3*B - a*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^2*d) - (b*(a^2*A + 2*A*b^2 - a*b*B))/(a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) - (A*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x]))","A",5,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
281,1,250,0,0.8597156,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b \left(2 a^2 A b+a^3 (-B)-2 a b^2 B+3 A b^3\right)}{a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 A+2 a b B-3 A b^2\right) \log (\sin (c+d x))}{a^4 d}-\frac{b^3 \left(5 a^2 A b-4 a^3 B-2 a b^2 B+3 A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}+\frac{(3 A b-2 a B) \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))}","\frac{b \left(2 a^2 A b+a^3 (-B)-2 a b^2 B+3 A b^3\right)}{a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 A+2 a b B-3 A b^2\right) \log (\sin (c+d x))}{a^4 d}-\frac{b^3 \left(5 a^2 A b-4 a^3 B-2 a b^2 B+3 A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^2}+\frac{x \left(a^2 (-B)+2 a A b+b^2 B\right)}{\left(a^2+b^2\right)^2}+\frac{(3 A b-2 a B) \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))}",1,"((2*a*A*b - a^2*B + b^2*B)*x)/(a^2 + b^2)^2 - ((a^2*A - 3*A*b^2 + 2*a*b*B)*Log[Sin[c + d*x]])/(a^4*d) - (b^3*(5*a^2*A*b + 3*A*b^3 - 4*a^3*B - 2*a*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^2*d) + (b*(2*a^2*A*b + 3*A*b^3 - a^3*B - 2*a*b^2*B))/(a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) + ((3*A*b - 2*a*B)*Cot[c + d*x])/(2*a^2*d*(a + b*Tan[c + d*x])) - (A*Cot[c + d*x]^2)/(2*a*d*(a + b*Tan[c + d*x]))","A",6,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
282,1,331,0,0.7980825,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{a (A b-a B) \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 A b-3 a^3 B-7 a b^2 B+5 A b^3\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(a^3 A b-6 a^2 b^2 B-3 a^4 B+3 a A b^3-b^4 B\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}+\frac{a^2 \left(3 a^2 A b^3+a^4 A b-9 a^3 b^2 B-3 a^5 B-10 a b^4 B+6 A b^5\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}","\frac{a (A b-a B) \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 A b-3 a^3 B-7 a b^2 B+5 A b^3\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(a^3 A b-6 a^2 b^2 B-3 a^4 B+3 a A b^3-b^4 B\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}+\frac{a^2 \left(3 a^2 A b^3+a^4 A b-9 a^3 b^2 B-3 a^5 B-10 a b^4 B+6 A b^5\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*x)/(a^2 + b^2)^3 + ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a^2*(a^4*A*b + 3*a^2*A*b^3 + 6*A*b^5 - 3*a^5*B - 9*a^3*b^2*B - 10*a*b^4*B)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^3*d) - ((a^3*A*b + 3*a*A*b^3 - 3*a^4*B - 6*a^2*b^2*B - b^4*B)*Tan[c + d*x])/(b^3*(a^2 + b^2)^2*d) + (a*(A*b - a*B)*Tan[c + d*x]^3)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(a^2*A*b + 5*A*b^3 - 3*a^3*B - 7*a*b^2*B)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",7,7,31,0.2258,1,"{3605, 3645, 3647, 3626, 3617, 31, 3475}"
283,1,250,0,0.4926493,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{a (A b-a B) \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(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a \left(a^2 A b^3+3 a^3 b^2 B+a^5 B+6 a b^4 B-3 A b^5\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}","\frac{a (A b-a B) \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(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a \left(a^2 A b^3+3 a^3 b^2 B+a^5 B+6 a b^4 B-3 A b^5\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}",1,"-(((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*x)/(a^2 + b^2)^3) + ((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a*(a^2*A*b^3 - 3*A*b^5 + a^5*B + 3*a^3*b^2*B + 6*a*b^4*B)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^3*d) + (a*(A*b - a*B)*Tan[c + d*x]^2)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(2*A*b^3 - a*(a^2 + 3*b^2)*B))/(b^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,6,31,0.1935,1,"{3605, 3635, 3626, 3617, 31, 3475}"
284,1,189,0,0.3716925,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 (A b-a B)}{2 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2 (A b-a B)}{2 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}",1,"-(((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*x)/(a^2 + b^2)^3) - ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - (a^2*(A*b - a*B))/(2*b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(2*A*b^3 - a*(a^2 + 3*b^2)*B))/(b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,31,0.1290,1,"{3604, 3628, 3531, 3530}"
285,1,179,0,0.2747155,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{a (A b-a B)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2 A+2 a b B-A b^2}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-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 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}","\frac{a (A b-a B)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2 A+2 a b B-A b^2}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-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 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}",1,"((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*x)/(a^2 + b^2)^3 - ((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) + (a*(A*b - a*B))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a^2*A - A*b^2 + 2*a*b*B)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,29,0.1379,1,"{3591, 3529, 3531, 3530}"
286,1,175,0,0.2662018,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^3,x]","-\frac{A b-a B}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 (-B)+2 a A b+b^2 B}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}","-\frac{A b-a B}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{a^2 (-B)+2 a A b+b^2 B}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{x \left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*x)/(a^2 + b^2)^3 + ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - (A*b - a*B)/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (2*a*A*b - a^2*B + b^2*B)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,3,23,0.1304,1,"{3529, 3531, 3530}"
287,1,215,0,0.62136,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{b (A b-a B)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2 A b^3+6 a^4 A b+a^3 b^2 B-3 a^5 B+A b^5\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 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}+\frac{A \log (\sin (c+d x))}{a^3 d}","\frac{b (A b-a B)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2 A b^3+6 a^4 A b+a^3 b^2 B-3 a^5 B+A b^5\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 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}+\frac{A \log (\sin (c+d x))}{a^3 d}",1,"-(((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*x)/(a^2 + b^2)^3) + (A*Log[Sin[c + d*x]])/(a^3*d) - (b*(6*a^4*A*b + 3*a^2*A*b^3 + A*b^5 - 3*a^5*B + a^3*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^3*d) + (b*(A*b - a*B))/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b*(3*a^2*A*b + A*b^3 - 2*a^3*B))/(a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",5,5,29,0.1724,1,"{3609, 3649, 3651, 3530, 3475}"
288,1,287,0,0.8823668,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(6 a^2 A b^2+a^4 A-3 a^3 b B-a b^3 B+3 A b^4\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(2 a^2 A-a b B+3 A b^2\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 A b^3+10 a^4 A b-3 a^3 b^2 B-6 a^5 B-a b^4 B+3 A b^5\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(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}-\frac{(3 A b-a B) \log (\sin (c+d x))}{a^4 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^2}","-\frac{b \left(6 a^2 A b^2+a^4 A-3 a^3 b B-a b^3 B+3 A b^4\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(2 a^2 A-a b B+3 A b^2\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 A b^3+10 a^4 A b-3 a^3 b^2 B-6 a^5 B-a b^4 B+3 A b^5\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(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right)}{\left(a^2+b^2\right)^3}-\frac{(3 A b-a B) \log (\sin (c+d x))}{a^4 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^2}",1,"-(((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*x)/(a^2 + b^2)^3) - ((3*A*b - a*B)*Log[Sin[c + d*x]])/(a^4*d) + (b^2*(10*a^4*A*b + 9*a^2*A*b^3 + 3*A*b^5 - 6*a^5*B - 3*a^3*b^2*B - a*b^4*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^3*d) - (b*(2*a^2*A + 3*A*b^2 - a*b*B))/(2*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (A*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x])^2) - (b*(a^4*A + 6*a^2*A*b^2 + 3*A*b^4 - 3*a^3*b*B - a*b^3*B))/(a^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
289,1,352,0,1.2486611,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{b \left(11 a^2 A b^3+3 a^4 A b-6 a^3 b^2 B+a^5 (-B)-3 a b^4 B+6 A b^5\right)}{a^4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b \left(5 a^2 A b-2 a^3 B-3 a b^2 B+6 A b^3\right)}{2 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(a^2 A+3 a b B-6 A b^2\right) \log (\sin (c+d x))}{a^5 d}-\frac{b^3 \left(17 a^2 A b^3+15 a^4 A b-9 a^3 b^2 B-10 a^5 B-3 a b^4 B+6 A b^5\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^5 d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}+\frac{(2 A b-a B) \cot (c+d x)}{a^2 d (a+b \tan (c+d x))^2}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^2}","\frac{b \left(11 a^2 A b^3+3 a^4 A b-6 a^3 b^2 B+a^5 (-B)-3 a b^4 B+6 A b^5\right)}{a^4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b \left(5 a^2 A b-2 a^3 B-3 a b^2 B+6 A b^3\right)}{2 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(a^2 A+3 a b B-6 A b^2\right) \log (\sin (c+d x))}{a^5 d}-\frac{b^3 \left(17 a^2 A b^3+15 a^4 A b-9 a^3 b^2 B-10 a^5 B-3 a b^4 B+6 A b^5\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^5 d \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right)}{\left(a^2+b^2\right)^3}+\frac{(2 A b-a B) \cot (c+d x)}{a^2 d (a+b \tan (c+d x))^2}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^2}",1,"((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*x)/(a^2 + b^2)^3 - ((a^2*A - 6*A*b^2 + 3*a*b*B)*Log[Sin[c + d*x]])/(a^5*d) - (b^3*(15*a^4*A*b + 17*a^2*A*b^3 + 6*A*b^5 - 10*a^5*B - 9*a^3*b^2*B - 3*a*b^4*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^5*(a^2 + b^2)^3*d) + (b*(5*a^2*A*b + 6*A*b^3 - 2*a^3*B - 3*a*b^2*B))/(2*a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + ((2*A*b - a*B)*Cot[c + d*x])/(a^2*d*(a + b*Tan[c + d*x])^2) - (A*Cot[c + d*x]^2)/(2*a*d*(a + b*Tan[c + d*x])^2) + (b*(3*a^4*A*b + 11*a^2*A*b^3 + 6*A*b^5 - a^5*B - 6*a^3*b^2*B - 3*a*b^4*B))/(a^4*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",7,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
290,1,351,0,0.8238858,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","\frac{a (A b-a B) \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{a^2 \left(a^2 A b^3+3 a^3 b^2 B+a^5 B+6 a b^4 B-3 A b^5\right)}{b^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a \left(4 a^2 A b^5+4 a^5 b^2 B+5 a^3 b^4 B+a^7 B+10 a b^6 B-4 A b^7\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^4}+\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}","\frac{a (A b-a B) \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{a^2 \left(a^2 A b^3+3 a^3 b^2 B+a^5 B+6 a b^4 B-3 A b^5\right)}{b^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a \left(4 a^2 A b^5+4 a^5 b^2 B+5 a^3 b^4 B+a^7 B+10 a b^6 B-4 A b^7\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^4}+\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}",1,"((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*x)/(a^2 + b^2)^4 + ((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*Log[Cos[c + d*x]])/((a^2 + b^2)^4*d) + (a*(4*a^2*A*b^5 - 4*A*b^7 + a^7*B + 4*a^5*b^2*B + 5*a^3*b^4*B + 10*a*b^6*B)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^4*d) + (a*(A*b - a*B)*Tan[c + d*x]^3)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a*(2*A*b^3 - a*(a^2 + 3*b^2)*B)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (a^2*(a^2*A*b^3 - 3*A*b^5 + a^5*B + 3*a^3*b^2*B + 6*a*b^4*B))/(b^4*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",7,7,31,0.2258,1,"{3605, 3645, 3635, 3626, 3617, 31, 3475}"
291,1,298,0,0.5722764,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","\frac{a (A b-a B) \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^2 \left(a^2 A b+2 a^3 B+8 a b^2 B-5 A b^3\right)}{6 b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a \left(5 a^2 A b^3+a^4 A b+7 a^3 b^2 B+2 a^5 B+17 a b^4 B-8 A b^5\right)}{3 b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}","\frac{a (A b-a B) \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^2 \left(a^2 A b+2 a^3 B+8 a b^2 B-5 A b^3\right)}{6 b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a \left(5 a^2 A b^3+a^4 A b+7 a^3 b^2 B+2 a^5 B+17 a b^4 B-8 A b^5\right)}{3 b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}",1,"-(((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*x)/(a^2 + b^2)^4) + ((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) + (a*(A*b - a*B)*Tan[c + d*x]^2)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a^2*(a^2*A*b - 5*A*b^3 + 2*a^3*B + 8*a*b^2*B))/(6*b^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (a*(a^4*A*b + 5*a^2*A*b^3 - 8*A*b^5 + 2*a^5*B + 7*a^3*b^2*B + 17*a*b^4*B))/(3*b^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,5,31,0.1613,1,"{3605, 3635, 3628, 3531, 3530}"
292,1,261,0,0.4825992,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 (A b-a B)}{3 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2 (A b-a B)}{3 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}",1,"-(((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*x)/(a^2 + b^2)^4) - ((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - (a^2*(A*b - a*B))/(3*b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a*(2*A*b^3 - a*(a^2 + 3*b^2)*B))/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,5,31,0.1613,1,"{3604, 3628, 3529, 3531, 3530}"
293,1,250,0,0.4275564,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","\frac{a (A b-a B)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 A+3 a^2 b B-3 a A b^2-b^3 B}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a^2 A+2 a b B-A b^2}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}","\frac{a (A b-a B)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 A+3 a^2 b B-3 a A b^2-b^3 B}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a^2 A+2 a b B-A b^2}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}",1,"((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*x)/(a^2 + b^2)^4 - ((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) + (a*(A*b - a*B))/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a^2*A - A*b^2 + 2*a*b*B)/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,4,29,0.1379,1,"{3591, 3529, 3531, 3530}"
294,1,247,0,0.4083876,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^4,x]","-\frac{A b-a B}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{a^2 (-B)+2 a A b+b^2 B}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{A b-a B}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{a^2 (-B)+2 a A b+b^2 B}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}",1,"((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*x)/(a^2 + b^2)^4 + ((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - (A*b - a*B)/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (2*a*A*b - a^2*B + b^2*B)/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,3,23,0.1304,1,"{3529, 3531, 3530}"
295,1,302,0,0.8985866,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","\frac{b (A b-a B)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{b \left(3 a^2 A b^3+6 a^4 A b+a^3 b^2 B-3 a^5 B+A b^5\right)}{a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(5 a^4 A b^3+4 a^2 A b^5+10 a^6 A b+4 a^5 b^2 B-4 a^7 B+A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^4}-\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}+\frac{A \log (\sin (c+d x))}{a^4 d}","\frac{b (A b-a B)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{b \left(3 a^2 A b^3+6 a^4 A b+a^3 b^2 B-3 a^5 B+A b^5\right)}{a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(5 a^4 A b^3+4 a^2 A b^5+10 a^6 A b+4 a^5 b^2 B-4 a^7 B+A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^4}-\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}+\frac{A \log (\sin (c+d x))}{a^4 d}",1,"-(((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*x)/(a^2 + b^2)^4) + (A*Log[Sin[c + d*x]])/(a^4*d) - (b*(10*a^6*A*b + 5*a^4*A*b^3 + 4*a^2*A*b^5 + A*b^7 - 4*a^7*B + 4*a^5*b^2*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^4*d) + (b*(A*b - a*B))/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (b*(3*a^2*A*b + A*b^3 - 2*a^3*B))/(2*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (b*(6*a^4*A*b + 3*a^2*A*b^3 + A*b^5 - 3*a^5*B + a^3*b^2*B))/(a^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",6,5,29,0.1724,1,"{3609, 3649, 3651, 3530, 3475}"
296,1,399,0,1.3207583,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","-\frac{b \left(13 a^4 A b^2+12 a^2 A b^4+a^6 A-3 a^3 b^3 B-6 a^5 b B-a b^5 B+4 A b^6\right)}{a^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{b \left(8 a^2 A b^2+2 a^4 A-3 a^3 b B-a b^3 B+4 A b^4\right)}{2 a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(3 a^2 A-a b B+4 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{b^2 \left(24 a^4 A b^3+16 a^2 A b^5+20 a^6 A b-5 a^5 b^2 B-4 a^3 b^4 B-10 a^7 B-a b^6 B+4 A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^5 d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}-\frac{(4 A b-a B) \log (\sin (c+d x))}{a^5 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^3}","-\frac{b \left(13 a^4 A b^2+12 a^2 A b^4+a^6 A-3 a^3 b^3 B-6 a^5 b B-a b^5 B+4 A b^6\right)}{a^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{b \left(8 a^2 A b^2+2 a^4 A-3 a^3 b B-a b^3 B+4 A b^4\right)}{2 a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(3 a^2 A-a b B+4 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{b^2 \left(24 a^4 A b^3+16 a^2 A b^5+20 a^6 A b-5 a^5 b^2 B-4 a^3 b^4 B-10 a^7 B-a b^6 B+4 A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^5 d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right)}{\left(a^2+b^2\right)^4}-\frac{(4 A b-a B) \log (\sin (c+d x))}{a^5 d}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^3}",1,"-(((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*x)/(a^2 + b^2)^4) - ((4*A*b - a*B)*Log[Sin[c + d*x]])/(a^5*d) + (b^2*(20*a^6*A*b + 24*a^4*A*b^3 + 16*a^2*A*b^5 + 4*A*b^7 - 10*a^7*B - 5*a^5*b^2*B - 4*a^3*b^4*B - a*b^6*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^5*(a^2 + b^2)^4*d) - (b*(3*a^2*A + 4*A*b^2 - a*b*B))/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (A*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x])^3) - (b*(2*a^4*A + 8*a^2*A*b^2 + 4*A*b^4 - 3*a^3*b*B - a*b^3*B))/(2*a^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (b*(a^6*A + 13*a^4*A*b^2 + 12*a^2*A*b^4 + 4*A*b^6 - 6*a^5*b*B - 3*a^3*b^3*B - a*b^5*B))/(a^4*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",7,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
297,1,477,0,1.7383581,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","\frac{b \left(27 a^4 A b^3+29 a^2 A b^5+4 a^6 A b-13 a^5 b^2 B-12 a^3 b^4 B+a^7 (-B)-4 a b^6 B+10 A b^7\right)}{a^5 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(19 a^2 A b^3+7 a^4 A b-8 a^3 b^2 B-2 a^5 B-4 a b^4 B+10 A b^5\right)}{2 a^4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b \left(9 a^2 A b-3 a^3 B-4 a b^2 B+10 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{\left(a^2 A+4 a b B-10 A b^2\right) \log (\sin (c+d x))}{a^6 d}-\frac{b^3 \left(56 a^4 A b^3+39 a^2 A b^5+35 a^6 A b-24 a^5 b^2 B-16 a^3 b^4 B-20 a^7 B-4 a b^6 B+10 A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^6 d \left(a^2+b^2\right)^4}+\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}+\frac{(5 A b-2 a B) \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))^3}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^3}","\frac{b \left(27 a^4 A b^3+29 a^2 A b^5+4 a^6 A b-13 a^5 b^2 B-12 a^3 b^4 B+a^7 (-B)-4 a b^6 B+10 A b^7\right)}{a^5 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(19 a^2 A b^3+7 a^4 A b-8 a^3 b^2 B-2 a^5 B-4 a b^4 B+10 A b^5\right)}{2 a^4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b \left(9 a^2 A b-3 a^3 B-4 a b^2 B+10 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{\left(a^2 A+4 a b B-10 A b^2\right) \log (\sin (c+d x))}{a^6 d}-\frac{b^3 \left(56 a^4 A b^3+39 a^2 A b^5+35 a^6 A b-24 a^5 b^2 B-16 a^3 b^4 B-20 a^7 B-4 a b^6 B+10 A b^7\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^6 d \left(a^2+b^2\right)^4}+\frac{x \left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right)}{\left(a^2+b^2\right)^4}+\frac{(5 A b-2 a B) \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))^3}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^3}",1,"((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*x)/(a^2 + b^2)^4 - ((a^2*A - 10*A*b^2 + 4*a*b*B)*Log[Sin[c + d*x]])/(a^6*d) - (b^3*(35*a^6*A*b + 56*a^4*A*b^3 + 39*a^2*A*b^5 + 10*A*b^7 - 20*a^7*B - 24*a^5*b^2*B - 16*a^3*b^4*B - 4*a*b^6*B)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^6*(a^2 + b^2)^4*d) + (b*(9*a^2*A*b + 10*A*b^3 - 3*a^3*B - 4*a*b^2*B))/(3*a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + ((5*A*b - 2*a*B)*Cot[c + d*x])/(2*a^2*d*(a + b*Tan[c + d*x])^3) - (A*Cot[c + d*x]^2)/(2*a*d*(a + b*Tan[c + d*x])^3) + (b*(7*a^4*A*b + 19*a^2*A*b^3 + 10*A*b^5 - 2*a^5*B - 8*a^3*b^2*B - 4*a*b^4*B))/(2*a^4*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (b*(4*a^6*A*b + 27*a^4*A*b^3 + 29*a^2*A*b^5 + 10*A*b^7 - a^7*B - 13*a^5*b^2*B - 12*a^3*b^4*B - 4*a*b^6*B))/(a^5*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",8,5,31,0.1613,1,"{3609, 3649, 3651, 3530, 3475}"
298,1,29,0,0.0175713,"\int \frac{\tan ^3(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^3*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{B \tan ^2(c+d x)}{2 d}+\frac{B \log (\cos (c+d x))}{d}","\frac{B \tan ^2(c+d x)}{2 d}+\frac{B \log (\cos (c+d x))}{d}",1,"(B*Log[Cos[c + d*x]])/d + (B*Tan[c + d*x]^2)/(2*d)","A",3,3,34,0.08824,1,"{21, 3473, 3475}"
299,1,16,0,0.0116281,"\int \frac{\tan ^2(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^2*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{B \tan (c+d x)}{d}-B x","\frac{B \tan (c+d x)}{d}-B x",1,"-(B*x) + (B*Tan[c + d*x])/d","A",3,3,34,0.08824,1,"{21, 3473, 8}"
300,1,13,0,0.0066428,"\int \frac{\tan (c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \log (\cos (c+d x))}{d}","-\frac{B \log (\cos (c+d x))}{d}",1,"-((B*Log[Cos[c + d*x]])/d)","A",2,2,32,0.06250,1,"{21, 3475}"
301,1,3,0,0.0009798,"\int \frac{a B+b B \tan (c+d x)}{a+b \tan (c+d x)} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(a + b*Tan[c + d*x]),x]","B x","B x",1,"B*x","A",2,2,26,0.07692,1,"{21, 8}"
302,1,12,0,0.0066853,"\int \frac{\cot (c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{B \log (\sin (c+d x))}{d}","\frac{B \log (\sin (c+d x))}{d}",1,"(B*Log[Sin[c + d*x]])/d","A",2,2,32,0.06250,1,"{21, 3475}"
303,1,17,0,0.0114034,"\int \frac{\cot ^2(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^2*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \cot (c+d x)}{d}-B x","-\frac{B \cot (c+d x)}{d}-B x",1,"-(B*x) - (B*Cot[c + d*x])/d","A",3,3,34,0.08824,1,"{21, 3473, 8}"
304,1,30,0,0.0162874,"\int \frac{\cot ^3(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^3*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \cot ^2(c+d x)}{2 d}-\frac{B \log (\sin (c+d x))}{d}","-\frac{B \cot ^2(c+d x)}{2 d}-\frac{B \log (\sin (c+d x))}{d}",1,"-(B*Cot[c + d*x]^2)/(2*d) - (B*Log[Sin[c + d*x]])/d","A",3,3,34,0.08824,1,"{21, 3473, 3475}"
305,1,31,0,0.0257432,"\int \frac{\cot ^4(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^4*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \cot ^3(c+d x)}{3 d}+\frac{B \cot (c+d x)}{d}+B x","-\frac{B \cot ^3(c+d x)}{3 d}+\frac{B \cot (c+d x)}{d}+B x",1,"B*x + (B*Cot[c + d*x])/d - (B*Cot[c + d*x]^3)/(3*d)","A",4,3,34,0.08824,1,"{21, 3473, 8}"
306,1,102,0,0.2906157,"\int \frac{\tan ^4(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^4*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{a^4 B \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{b B \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{a B x}{a^2+b^2}-\frac{a B \tan (c+d x)}{b^2 d}+\frac{B \tan ^2(c+d x)}{2 b d}","\frac{a^4 B \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{b B \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{a B x}{a^2+b^2}-\frac{a B \tan (c+d x)}{b^2 d}+\frac{B \tan ^2(c+d x)}{2 b d}",1,"(a*B*x)/(a^2 + b^2) + (b*B*Log[Cos[c + d*x]])/((a^2 + b^2)*d) + (a^4*B*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)*d) - (a*B*Tan[c + d*x])/(b^2*d) + (B*Tan[c + d*x]^2)/(2*b*d)","A",7,7,34,0.2059,1,"{21, 3566, 3647, 3627, 3617, 31, 3475}"
307,1,83,0,0.1744782,"\int \frac{\tan ^3(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^3*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{a^3 B \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}+\frac{a B \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{b B x}{a^2+b^2}+\frac{B \tan (c+d x)}{b d}","-\frac{a^3 B \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}+\frac{a B \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{b B x}{a^2+b^2}+\frac{B \tan (c+d x)}{b d}",1,"-((b*B*x)/(a^2 + b^2)) + (a*B*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a^3*B*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) + (B*Tan[c + d*x])/(b*d)","A",6,6,34,0.1765,1,"{21, 3566, 3626, 3617, 31, 3475}"
308,1,81,0,0.1157252,"\int \frac{\tan ^2(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^2*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{a^2 B \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}+\frac{a^3 B x}{b^2 \left(a^2+b^2\right)}-\frac{a B x}{b^2}-\frac{B \log (\cos (c+d x))}{b d}","\frac{a^2 B \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}+\frac{a^3 B x}{b^2 \left(a^2+b^2\right)}-\frac{a B x}{b^2}-\frac{B \log (\cos (c+d x))}{b d}",1,"-((a*B*x)/b^2) + (a^3*B*x)/(b^2*(a^2 + b^2)) - (B*Log[Cos[c + d*x]])/(b*d) + (a^2*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(b*(a^2 + b^2)*d)","A",5,5,34,0.1471,1,"{21, 3541, 3475, 3484, 3530}"
309,1,48,0,0.0666127,"\int \frac{\tan (c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b B x}{a^2+b^2}-\frac{a B \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}","\frac{b B x}{a^2+b^2}-\frac{a B \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}",1,"(b*B*x)/(a^2 + b^2) - (a*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",3,3,32,0.09375,1,"{21, 3531, 3530}"
310,1,47,0,0.0540156,"\int \frac{a B+b B \tan (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(a + b*Tan[c + d*x])^2,x]","\frac{b B \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{a B x}{a^2+b^2}","\frac{b B \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{a B x}{a^2+b^2}",1,"(a*B*x)/(a^2 + b^2) + (b*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",3,3,26,0.1154,1,"{21, 3484, 3530}"
311,1,69,0,0.0854284,"\int \frac{\cot (c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{b^2 B \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{b B x}{a^2+b^2}+\frac{B \log (\sin (c+d x))}{a d}","-\frac{b^2 B \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{b B x}{a^2+b^2}+\frac{B \log (\sin (c+d x))}{a d}",1,"-((b*B*x)/(a^2 + b^2)) + (B*Log[Sin[c + d*x]])/(a*d) - (b^2*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a*(a^2 + b^2)*d)","A",4,4,32,0.1250,1,"{21, 3571, 3530, 3475}"
312,1,85,0,0.1823926,"\int \frac{\cot ^2(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^2*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b^3 B \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{a B x}{a^2+b^2}-\frac{b B \log (\sin (c+d x))}{a^2 d}-\frac{B \cot (c+d x)}{a d}","\frac{b^3 B \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{a B x}{a^2+b^2}-\frac{b B \log (\sin (c+d x))}{a^2 d}-\frac{B \cot (c+d x)}{a d}",1,"-((a*B*x)/(a^2 + b^2)) - (B*Cot[c + d*x])/(a*d) - (b*B*Log[Sin[c + d*x]])/(a^2*d) + (b^3*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)*d)","A",5,5,34,0.1471,1,"{21, 3569, 3651, 3530, 3475}"
313,1,112,0,0.324771,"\int \frac{\cot ^3(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^3*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{B \left(a^2-b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^4 B \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{b B x}{a^2+b^2}+\frac{b B \cot (c+d x)}{a^2 d}-\frac{B \cot ^2(c+d x)}{2 a d}","-\frac{B \left(a^2-b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^4 B \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{b B x}{a^2+b^2}+\frac{b B \cot (c+d x)}{a^2 d}-\frac{B \cot ^2(c+d x)}{2 a d}",1,"(b*B*x)/(a^2 + b^2) + (b*B*Cot[c + d*x])/(a^2*d) - (B*Cot[c + d*x]^2)/(2*a*d) - ((a^2 - b^2)*B*Log[Sin[c + d*x]])/(a^3*d) - (b^4*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)*d)","A",6,6,34,0.1765,1,"{21, 3569, 3649, 3652, 3530, 3475}"
314,1,25,0,0.0483056,"\int \frac{3+\tan (c+d x)}{2-\tan (c+d x)} \, dx","Int[(3 + Tan[c + d*x])/(2 - Tan[c + d*x]),x]","x-\frac{\log (2 \cos (c+d x)-\sin (c+d x))}{d}","x-\frac{\log (2 \cos (c+d x)-\sin (c+d x))}{d}",1,"x - Log[2*Cos[c + d*x] - Sin[c + d*x]]/d","A",2,2,21,0.09524,1,"{3531, 3530}"
315,1,58,0,0.0776258,"\int \frac{\frac{b B}{a}+B \tan (c+d x)}{a+b \tan (c+d x)} \, dx","Int[((b*B)/a + B*Tan[c + d*x])/(a + b*Tan[c + d*x]),x]","\frac{2 b B x}{a^2+b^2}-\frac{B \left(a-\frac{b^2}{a}\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}","\frac{2 b B x}{a^2+b^2}-\frac{B \left(a-\frac{b^2}{a}\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}",1,"(2*b*B*x)/(a^2 + b^2) - ((a - b^2/a)*B*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",2,2,28,0.07143,1,"{3531, 3530}"
316,1,101,0,0.1279615,"\int \frac{a+b \tan (c+d x)}{(b+a \tan (c+d x))^2} \, dx","Int[(a + b*Tan[c + d*x])/(b + a*Tan[c + d*x])^2,x]","-\frac{a^2-b^2}{d \left(a^2+b^2\right) (a \tan (c+d x)+b)}+\frac{b \left(3 a^2-b^2\right) \log (a \sin (c+d x)+b \cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2-b^2}{d \left(a^2+b^2\right) (a \tan (c+d x)+b)}+\frac{b \left(3 a^2-b^2\right) \log (a \sin (c+d x)+b \cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^2}",1,"-((a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^2) + (b*(3*a^2 - b^2)*Log[b*Cos[c + d*x] + a*Sin[c + d*x]])/((a^2 + b^2)^2*d) - (a^2 - b^2)/((a^2 + b^2)*d*(b + a*Tan[c + d*x]))","A",3,3,23,0.1304,1,"{3529, 3531, 3530}"
317,1,233,0,0.6295948,"\int \tan ^3(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{2 \left(-8 a^2 B+14 a A b+35 b^2 B\right) (a+b \tan (c+d x))^{3/2}}{105 b^3 d}+\frac{2 (7 A b-4 a B) \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{35 b^2 d}+\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 B \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{7 b d}","-\frac{2 \left(-8 a^2 B+14 a A b+35 b^2 B\right) (a+b \tan (c+d x))^{3/2}}{105 b^3 d}+\frac{2 (7 A b-4 a B) \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{35 b^2 d}+\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 B \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{7 b d}",1,"(Sqrt[a - I*b]*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (Sqrt[a + I*b]*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*A*Sqrt[a + b*Tan[c + d*x]])/d - (2*(14*a*A*b - 8*a^2*B + 35*b^2*B)*(a + b*Tan[c + d*x])^(3/2))/(105*b^3*d) + (2*(7*A*b - 4*a*B)*Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2))/(35*b^2*d) + (2*B*Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2))/(7*b*d)","A",11,8,33,0.2424,1,"{3607, 3647, 3630, 3528, 3539, 3537, 63, 208}"
318,1,186,0,0.4554032,"\int \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{2 (5 A b-2 a B) (a+b \tan (c+d x))^{3/2}}{15 b^2 d}+\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{5 b d}-\frac{2 B \sqrt{a+b \tan (c+d x)}}{d}","\frac{2 (5 A b-2 a B) (a+b \tan (c+d x))^{3/2}}{15 b^2 d}+\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{5 b d}-\frac{2 B \sqrt{a+b \tan (c+d x)}}{d}",1,"(Sqrt[a - I*b]*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (Sqrt[a + I*b]*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*B*Sqrt[a + b*Tan[c + d*x]])/d + (2*(5*A*b - 2*a*B)*(a + b*Tan[c + d*x])^(3/2))/(15*b^2*d) + (2*B*Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2))/(5*b*d)","A",10,7,33,0.2121,1,"{3607, 3630, 3528, 3539, 3537, 63, 208}"
319,1,146,0,0.2785603,"\int \tan (c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 b d}","-\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 b d}",1,"-((Sqrt[a - I*b]*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - (Sqrt[a + I*b]*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*A*Sqrt[a + b*Tan[c + d*x]])/d + (2*B*(a + b*Tan[c + d*x])^(3/2))/(3*b*d)","A",9,6,31,0.1935,1,"{3592, 3528, 3539, 3537, 63, 208}"
320,1,122,0,0.2123573,"\int \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{d}","-\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{d}",1,"-((Sqrt[a - I*b]*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) + (Sqrt[a + I*b]*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*B*Sqrt[a + b*Tan[c + d*x]])/d","A",8,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
321,1,131,0,0.3602482,"\int \cot (c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}","\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{2 \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}",1,"(-2*Sqrt[a]*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + (Sqrt[a - I*b]*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (Sqrt[a + I*b]*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d","A",11,6,31,0.1935,1,"{3612, 3539, 3537, 63, 208, 3634}"
322,1,167,0,0.5163795,"\int \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}","-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}",1,"-(((A*b + 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d)) + (Sqrt[a - I*b]*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (Sqrt[a + I*b]*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (A*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/d","A",12,7,33,0.2121,1,"{3608, 3653, 3539, 3537, 63, 208, 3634}"
323,1,219,0,0.8613362,"\int \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\left(8 a^2 A-4 a b B+A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(4 a B+A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a d}-\frac{A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}","\frac{\left(8 a^2 A-4 a b B+A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{\sqrt{a-i b} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(4 a B+A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a d}-\frac{A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}",1,"((8*a^2*A + A*b^2 - 4*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(3/2)*d) - (Sqrt[a - I*b]*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (Sqrt[a + I*b]*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - ((A*b + 4*a*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*a*d) - (A*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",13,8,33,0.2424,1,"{3608, 3649, 3653, 3539, 3537, 63, 208, 3634}"
324,1,279,0,1.1679261,"\int \cot ^4(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\left(8 a^2 A b+16 a^3 B+2 a b^2 B-A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 a^{5/2} d}+\frac{\left(8 a^2 A-2 a b B+A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 a^2 d}-\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(6 a B+A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 a d}-\frac{A \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}","\frac{\left(8 a^2 A b+16 a^3 B+2 a b^2 B-A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 a^{5/2} d}+\frac{\left(8 a^2 A-2 a b B+A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 a^2 d}-\frac{\sqrt{a-i b} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{\sqrt{a+i b} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(6 a B+A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 a d}-\frac{A \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}",1,"((8*a^2*A*b - A*b^3 + 16*a^3*B + 2*a*b^2*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(8*a^(5/2)*d) - (Sqrt[a - I*b]*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (Sqrt[a + I*b]*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((8*a^2*A + A*b^2 - 2*a*b*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(8*a^2*d) - ((A*b + 6*a*B)*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(12*a*d) - (A*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",14,8,33,0.2424,1,"{3608, 3649, 3653, 3539, 3537, 63, 208, 3634}"
325,1,214,0,0.6233988,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 (7 A b-2 a B) (a+b \tan (c+d x))^{5/2}}{35 b^2 d}-\frac{2 (a B+A b) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{7 b d}-\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 d}","\frac{2 (7 A b-2 a B) (a+b \tan (c+d x))^{5/2}}{35 b^2 d}-\frac{2 (a B+A b) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{7 b d}-\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 d}",1,"((a - I*b)^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(3/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*(A*b + a*B)*Sqrt[a + b*Tan[c + d*x]])/d - (2*B*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*(7*A*b - 2*a*B)*(a + b*Tan[c + d*x])^(5/2))/(35*b^2*d) + (2*B*Tan[c + d*x]*(a + b*Tan[c + d*x])^(5/2))/(7*b*d)","A",11,7,33,0.2121,1,"{3607, 3630, 3528, 3539, 3537, 63, 208}"
326,1,175,0,0.3779473,"\int \tan (c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 (a A-b B) \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 b d}","\frac{2 (a A-b B) \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 b d}",1,"-(((a - I*b)^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - ((a + I*b)^(3/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*(a*A - b*B)*Sqrt[a + b*Tan[c + d*x]])/d + (2*A*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*B*(a + b*Tan[c + d*x])^(5/2))/(5*b*d)","A",10,6,31,0.1935,1,"{3592, 3528, 3539, 3537, 63, 208}"
327,1,150,0,0.3123914,"\int (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 (a B+A b) \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 d}","\frac{2 (a B+A b) \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B (a+b \tan (c+d x))^{3/2}}{3 d}",1,"-(((a - I*b)^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) + ((a + I*b)^(3/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*(A*b + a*B)*Sqrt[a + b*Tan[c + d*x]])/d + (2*B*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",9,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
328,1,152,0,0.6398439,"\int \cot (c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 b B \sqrt{a+b \tan (c+d x)}}{d}","-\frac{2 a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 b B \sqrt{a+b \tan (c+d x)}}{d}",1,"(-2*a^(3/2)*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + ((a - I*b)^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(3/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b*B*Sqrt[a + b*Tan[c + d*x]])/d","A",12,7,31,0.2258,1,"{3607, 3653, 3539, 3537, 63, 208, 3634}"
329,1,169,0,0.634864,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}","\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}",1,"-((Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d) + ((a - I*b)^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(3/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (a*A*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/d","A",12,7,33,0.2121,1,"{3605, 3653, 3539, 3537, 63, 208, 3634}"
330,1,219,0,0.9635408,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(8 a^2 A-12 a b B-3 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(4 a B+5 A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}","\frac{\left(8 a^2 A-12 a b B-3 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{(a-i b)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(4 a B+5 A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}",1,"((8*a^2*A - 3*A*b^2 - 12*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*Sqrt[a]*d) - ((a - I*b)^(3/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(3/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - ((5*A*b + 4*a*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",13,8,33,0.2424,1,"{3605, 3649, 3653, 3539, 3537, 63, 208, 3634}"
331,1,278,0,1.3148863,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(24 a^2 A b+16 a^3 B-6 a b^2 B+A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 a^{3/2} d}+\frac{\left(8 a^2 A-10 a b B-A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 a d}-\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(6 a B+7 A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}-\frac{a A \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}","\frac{\left(24 a^2 A b+16 a^3 B-6 a b^2 B+A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 a^{3/2} d}+\frac{\left(8 a^2 A-10 a b B-A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 a d}-\frac{(a-i b)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{(6 a B+7 A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}-\frac{a A \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}",1,"((24*a^2*A*b + A*b^3 + 16*a^3*B - 6*a*b^2*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(8*a^(3/2)*d) - ((a - I*b)^(3/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(3/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((8*a^2*A - A*b^2 - 10*a*b*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(8*a*d) - ((7*A*b + 6*a*B)*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(12*d) - (a*A*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",14,8,33,0.2424,1,"{3605, 3649, 3653, 3539, 3537, 63, 208, 3634}"
332,1,252,0,0.7691543,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (9 A b-2 a B) (a+b \tan (c+d x))^{7/2}}{63 b^2 d}-\frac{2 (a B+A b) (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{7/2}}{9 b d}-\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 d}","-\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (9 A b-2 a B) (a+b \tan (c+d x))^{7/2}}{63 b^2 d}-\frac{2 (a B+A b) (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B \tan (c+d x) (a+b \tan (c+d x))^{7/2}}{9 b d}-\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 d}",1,"((a - I*b)^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(5/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*(2*a*A*b + a^2*B - b^2*B)*Sqrt[a + b*Tan[c + d*x]])/d - (2*(A*b + a*B)*(a + b*Tan[c + d*x])^(3/2))/(3*d) - (2*B*(a + b*Tan[c + d*x])^(5/2))/(5*d) + (2*(9*A*b - 2*a*B)*(a + b*Tan[c + d*x])^(7/2))/(63*b^2*d) + (2*B*Tan[c + d*x]*(a + b*Tan[c + d*x])^(7/2))/(9*b*d)","A",12,7,33,0.2121,1,"{3607, 3630, 3528, 3539, 3537, 63, 208}"
333,1,213,0,0.5308123,"\int \tan (c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a A-b B) (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{2 B (a+b \tan (c+d x))^{7/2}}{7 b d}","\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a A-b B) (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 A (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{2 B (a+b \tan (c+d x))^{7/2}}{7 b d}",1,"-(((a - I*b)^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - ((a + I*b)^(5/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*(a^2*A - A*b^2 - 2*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/d + (2*(a*A - b*B)*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*A*(a + b*Tan[c + d*x])^(5/2))/(5*d) + (2*B*(a + b*Tan[c + d*x])^(7/2))/(7*b*d)","A",11,6,31,0.1935,1,"{3592, 3528, 3539, 3537, 63, 208}"
334,1,188,0,0.4249735,"\int (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a B+A b) (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 d}","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a B+A b) (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 B (a+b \tan (c+d x))^{5/2}}{5 d}",1,"-(((a - I*b)^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) + ((a + I*b)^(5/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*(2*a*A*b + a^2*B - b^2*B)*Sqrt[a + b*Tan[c + d*x]])/d + (2*(A*b + a*B)*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*B*(a + b*Tan[c + d*x])^(5/2))/(5*d)","A",10,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
335,1,182,0,0.8473297,"\int \cot (c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 b (2 a B+A b) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 b B (a+b \tan (c+d x))^{3/2}}{3 d}","-\frac{2 a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 b (2 a B+A b) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}+\frac{2 b B (a+b \tan (c+d x))^{3/2}}{3 d}",1,"(-2*a^(5/2)*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + ((a - I*b)^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(5/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b*(A*b + 2*a*B)*Sqrt[a + b*Tan[c + d*x]])/d + (2*b*B*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",13,8,31,0.2581,1,"{3607, 3647, 3653, 3539, 3537, 63, 208, 3634}"
336,1,196,0,0.8822019,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{b (a A+2 b B) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^{3/2}}{d}","-\frac{a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{b (a A+2 b B) \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a A \cot (c+d x) (a+b \tan (c+d x))^{3/2}}{d}",1,"-((a^(3/2)*(5*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d) + ((a - I*b)^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(5/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (b*(a*A + 2*b*B)*Sqrt[a + b*Tan[c + d*x]])/d - (a*A*Cot[c + d*x]*(a + b*Tan[c + d*x])^(3/2))/d","A",13,8,33,0.2424,1,"{3605, 3647, 3653, 3539, 3537, 63, 208, 3634}"
337,1,220,0,0.927036,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{a} \left(8 a^2 A-20 a b B-15 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (4 a B+7 A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d}","\frac{\sqrt{a} \left(8 a^2 A-20 a b B-15 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (4 a B+7 A b) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{2 d}",1,"(Sqrt[a]*(8*a^2*A - 15*A*b^2 - 20*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*d) - ((a - I*b)^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(5/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (a*(7*A*b + 4*a*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2))/(2*d)","A",13,8,33,0.2424,1,"{3605, 3645, 3653, 3539, 3537, 63, 208, 3634}"
338,1,277,0,1.3298009,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(40 a^2 A b+16 a^3 B-30 a b^2 B-5 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 \sqrt{a} d}+\frac{\left(8 a^2 A-18 a b B-11 A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 d}-\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (2 a B+3 A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}","\frac{\left(40 a^2 A b+16 a^3 B-30 a b^2 B-5 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 \sqrt{a} d}+\frac{\left(8 a^2 A-18 a b B-11 A b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 d}-\frac{(a-i b)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (2 a B+3 A b) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}-\frac{a A \cot ^3(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}",1,"((40*a^2*A*b - 5*A*b^3 + 16*a^3*B - 30*a*b^2*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(8*Sqrt[a]*d) - ((a - I*b)^(5/2)*(I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(5/2)*(I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((8*a^2*A - 11*A*b^2 - 18*a*b*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(8*d) - (a*(3*A*b + 2*a*B)*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a*A*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",14,9,33,0.2727,1,"{3605, 3645, 3649, 3653, 3539, 3537, 63, 208, 3634}"
339,1,342,0,1.6686768,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{\left(-240 a^2 A b^2+128 a^4 A-320 a^3 b B+40 a b^3 B-5 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{64 a^{3/2} d}+\frac{\left(48 a^2 A-104 a b B-59 A b^2\right) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{96 d}+\frac{\left(144 a^2 A b+64 a^3 B-88 a b^2 B-5 A b^3\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{64 a d}+\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (8 a B+11 A b) \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{24 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}","-\frac{\left(-240 a^2 A b^2+128 a^4 A-320 a^3 b B+40 a b^3 B-5 A b^4\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{64 a^{3/2} d}+\frac{\left(48 a^2 A-104 a b B-59 A b^2\right) \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{96 d}+\frac{\left(144 a^2 A b+64 a^3 B-88 a b^2 B-5 A b^3\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{64 a d}+\frac{(a-i b)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{5/2} (A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a (8 a B+11 A b) \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{24 d}-\frac{a A \cot ^4(c+d x) (a+b \tan (c+d x))^{3/2}}{4 d}",1,"-((128*a^4*A - 240*a^2*A*b^2 - 5*A*b^4 - 320*a^3*b*B + 40*a*b^3*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(64*a^(3/2)*d) + ((a - I*b)^(5/2)*(A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(5/2)*(A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((144*a^2*A*b - 5*A*b^3 + 64*a^3*B - 88*a*b^2*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(64*a*d) + ((48*a^2*A - 59*A*b^2 - 104*a*b*B)*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(96*d) - (a*(11*A*b + 8*a*B)*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(24*d) - (a*A*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^(3/2))/(4*d)","A",15,9,33,0.2727,1,"{3605, 3645, 3649, 3653, 3539, 3537, 63, 208, 3634}"
340,1,151,0,0.2528495,"\int (-a+b \tan (c+d x)) (a+b \tan (c+d x))^{5/2} \, dx","Int[(-a + b*Tan[c + d*x])*(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 b \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{(-b+i a) (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{2 b \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{(-b+i a) (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{5/2} (b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((I*a - b)*(a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(5/2)*(I*a + b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*b*(a^2 + b^2)*Sqrt[a + b*Tan[c + d*x]])/d + (2*b*(a + b*Tan[c + d*x])^(5/2))/(5*d)","A",10,7,27,0.2593,1,"{3528, 12, 3482, 3539, 3537, 63, 208}"
341,1,408,0,0.4730744,"\int (-a+b \tan (c+d x)) (a+b \tan (c+d x))^{3/2} \, dx","Int[(-a + b*Tan[c + d*x])*(a + b*Tan[c + d*x])^(3/2),x]","-\frac{b \left(a^2+b^2\right) \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b \left(a^2+b^2\right) \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \left(a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{b \left(a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{2 b (a+b \tan (c+d x))^{3/2}}{3 d}","-\frac{b \left(a^2+b^2\right) \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b \left(a^2+b^2\right) \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \left(a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{b \left(a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{2 b (a+b \tan (c+d x))^{3/2}}{3 d}",1,"-((b*(a^2 + b^2)*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d)) + (b*(a^2 + b^2)*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) - (b*(a^2 + b^2)*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] - Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) + (b*(a^2 + b^2)*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] + Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) + (2*b*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",13,9,27,0.3333,1,"{3528, 12, 3485, 700, 1129, 634, 618, 206, 628}"
342,1,422,0,0.3945193,"\int (-a+b \tan (c+d x)) \sqrt{a+b \tan (c+d x)} \, dx","Int[(-a + b*Tan[c + d*x])*Sqrt[a + b*Tan[c + d*x]],x]","\frac{b \sqrt{a^2+b^2} \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \sqrt{a^2+b^2} \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}","\frac{b \sqrt{a^2+b^2} \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \sqrt{a^2+b^2} \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}+\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}",1,"-((b*Sqrt[a^2 + b^2]*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d)) + (b*Sqrt[a^2 + b^2]*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) + (b*Sqrt[a^2 + b^2]*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] - Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) - (b*Sqrt[a^2 + b^2]*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] + Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) + (2*b*Sqrt[a + b*Tan[c + d*x]])/d","A",13,9,27,0.3333,1,"{3528, 12, 3485, 708, 1094, 634, 618, 206, 628}"
343,1,213,0,0.5223316,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{2 \left(-8 a^2 B+10 a A b+15 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{15 b^3 d}+\frac{2 (5 A b-4 a B) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{15 b^2 d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b d}","-\frac{2 \left(-8 a^2 B+10 a A b+15 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{15 b^3 d}+\frac{2 (5 A b-4 a B) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{15 b^2 d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b d}",1,"((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d) - (2*(10*a*A*b - 8*a^2*B + 15*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(15*b^3*d) + (2*(5*A*b - 4*a*B)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(15*b^2*d) + (2*B*Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(5*b*d)","A",10,7,33,0.2121,1,"{3607, 3647, 3630, 3539, 3537, 63, 208}"
344,1,166,0,0.3570551,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 (3 A b-2 a B) \sqrt{a+b \tan (c+d x)}}{3 b^2 d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b d}","\frac{2 (3 A b-2 a B) \sqrt{a+b \tan (c+d x)}}{3 b^2 d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b d}",1,"((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d) + (2*(3*A*b - 2*a*B)*Sqrt[a + b*Tan[c + d*x]])/(3*b^2*d) + (2*B*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b*d)","A",9,6,33,0.1818,1,"{3607, 3630, 3539, 3537, 63, 208}"
345,1,124,0,0.2229458,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{b d}","-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{b d}",1,"-(((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d)) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d) + (2*B*Sqrt[a + b*Tan[c + d*x]])/(b*d)","A",8,5,31,0.1613,1,"{3592, 3539, 3537, 63, 208}"
346,1,102,0,0.1507114,"\int \frac{A+B \tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}","\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}",1,"-(((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d)) + ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d)","A",7,4,25,0.1600,1,"{3539, 3537, 63, 208}"
347,1,131,0,0.3397245,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}","\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(-2*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d)","A",11,6,31,0.1935,1,"{3613, 3539, 3537, 63, 208, 3634}"
348,1,169,0,0.5128881,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{a d}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{A \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{a d}",1,"((A*b - 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d) - (A*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(a*d)","A",12,7,33,0.2121,1,"{3609, 3653, 3539, 3537, 63, 208, 3634}"
349,1,224,0,0.8070499,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{\left(8 a^2 A+4 a b B-3 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}+\frac{(3 A b-4 a B) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a^2 d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 a d}","\frac{\left(8 a^2 A+4 a b B-3 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}+\frac{(3 A b-4 a B) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a^2 d}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{A \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 a d}",1,"((8*a^2*A - 3*A*b^2 + 4*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(5/2)*d) - ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d) + ((3*A*b - 4*a*B)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*a^2*d) - (A*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*a*d)","A",13,8,33,0.2424,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
350,1,264,0,0.7239205,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 a (A b-a B) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(-4 a^2 B+3 a A b-b^2 B\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^2 d \left(a^2+b^2\right)}+\frac{2 \left(6 a^2 A b-8 a^3 B-5 a b^2 B+3 A b^3\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","\frac{2 a (A b-a B) \tan ^2(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(-4 a^2 B+3 a A b-b^2 B\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^2 d \left(a^2+b^2\right)}+\frac{2 \left(6 a^2 A b-8 a^3 B-5 a b^2 B+3 A b^3\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (2*a*(A*b - a*B)*Tan[c + d*x]^2)/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + (2*(6*a^2*A*b + 3*A*b^3 - 8*a^3*B - 5*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)*d) - (2*(3*a*A*b - 4*a^2*B - b^2*B)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b^2*(a^2 + b^2)*d)","A",10,7,33,0.2121,1,"{3605, 3647, 3630, 3539, 3537, 63, 208}"
351,1,167,0,0.4431104,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 (A b-a B)}{b^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{b^2 d}","-\frac{2 a^2 (A b-a B)}{b^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}+\frac{2 B \sqrt{a+b \tan (c+d x)}}{b^2 d}",1,"((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*a^2*(A*b - a*B))/(b^2*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + (2*B*Sqrt[a + b*Tan[c + d*x]])/(b^2*d)","A",9,6,33,0.1818,1,"{3604, 3630, 3539, 3537, 63, 208}"
352,1,141,0,0.2809749,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","\frac{2 a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"-(((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d)) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (2*a*(A*b - a*B))/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,31,0.1613,1,"{3591, 3539, 3537, 63, 208}"
353,1,138,0,0.2356501,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 (A b-a B)}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","-\frac{2 (A b-a B)}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"-(((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d)) + ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*(A*b - a*B))/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,25,0.2000,1,"{3529, 3539, 3537, 63, 208}"
354,1,171,0,0.607033,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","\frac{2 b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"(-2*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (2*b*(A*b - a*B))/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",12,7,31,0.2258,1,"{3609, 3653, 3539, 3537, 63, 208, 3634}"
355,1,219,0,0.8578616,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{b \left(a^2 A-2 a b B+3 A b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{A \cot (c+d x)}{a d \sqrt{a+b \tan (c+d x)}}","-\frac{b \left(a^2 A-2 a b B+3 A b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{A \cot (c+d x)}{a d \sqrt{a+b \tan (c+d x)}}",1,"((3*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (b*(a^2*A + 3*A*b^2 - 2*a*b*B))/(a^2*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) - (A*Cot[c + d*x])/(a*d*Sqrt[a + b*Tan[c + d*x]])","A",13,8,33,0.2424,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
356,1,285,0,1.209689,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{b \left(7 a^2 A b-4 a^3 B-12 a b^2 B+15 A b^3\right)}{4 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(8 a^2 A+12 a b B-15 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d}+\frac{(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{A \cot ^2(c+d x)}{2 a d \sqrt{a+b \tan (c+d x)}}","\frac{b \left(7 a^2 A b-4 a^3 B-12 a b^2 B+15 A b^3\right)}{4 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(8 a^2 A+12 a b B-15 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d}+\frac{(5 A b-4 a B) \cot (c+d x)}{4 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{A \cot ^2(c+d x)}{2 a d \sqrt{a+b \tan (c+d x)}}",1,"((8*a^2*A - 15*A*b^2 + 12*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(7/2)*d) - ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (b*(7*a^2*A*b + 15*A*b^3 - 4*a^3*B - 12*a*b^2*B))/(4*a^3*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + ((5*A*b - 4*a*B)*Cot[c + d*x])/(4*a^2*d*Sqrt[a + b*Tan[c + d*x]]) - (A*Cot[c + d*x]^2)/(2*a*d*Sqrt[a + b*Tan[c + d*x]])","A",14,8,33,0.2424,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
357,1,371,0,1.0453609,"\int \frac{\tan ^4(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^4*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a (A b-a B) \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(a^2 A b-2 a^3 B-4 a b^2 B+3 A b^3\right) \tan ^2(c+d x)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(4 a^3 A b-15 a^2 b^2 B-8 a^4 B+10 a A b^3-b^4 B\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)^2}+\frac{2 \left(17 a^2 A b^3+8 a^4 A b-30 a^3 b^2 B-16 a^5 B-8 a b^4 B+3 A b^5\right) \sqrt{a+b \tan (c+d x)}}{3 b^4 d \left(a^2+b^2\right)^2}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","\frac{2 a (A b-a B) \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(a^2 A b-2 a^3 B-4 a b^2 B+3 A b^3\right) \tan ^2(c+d x)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(4 a^3 A b-15 a^2 b^2 B-8 a^4 B+10 a A b^3-b^4 B\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)^2}+\frac{2 \left(17 a^2 A b^3+8 a^4 A b-30 a^3 b^2 B-16 a^5 B-8 a b^4 B+3 A b^5\right) \sqrt{a+b \tan (c+d x)}}{3 b^4 d \left(a^2+b^2\right)^2}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"-(((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d)) + ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (2*a*(A*b - a*B)*Tan[c + d*x]^3)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(a^2*A*b + 3*A*b^3 - 2*a^3*B - 4*a*b^2*B)*Tan[c + d*x]^2)/(b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]]) + (2*(8*a^4*A*b + 17*a^2*A*b^3 + 3*A*b^5 - 16*a^5*B - 30*a^3*b^2*B - 8*a*b^4*B)*Sqrt[a + b*Tan[c + d*x]])/(3*b^4*(a^2 + b^2)^2*d) - (2*(4*a^3*A*b + 10*a*A*b^3 - 8*a^4*B - 15*a^2*b^2*B - b^4*B)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)^2*d)","A",11,8,33,0.2424,1,"{3605, 3645, 3647, 3630, 3539, 3537, 63, 208}"
358,1,261,0,0.7124475,"\int \frac{\tan ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a (A b-a B) \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 a^2 \left(a^2 A b-4 a^3 B-10 a b^2 B+7 A b^3\right)}{3 b^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(-4 a^2 B+a A b-3 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","\frac{2 a (A b-a B) \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 a^2 \left(a^2 A b-4 a^3 B-10 a b^2 B+7 A b^3\right)}{3 b^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 \left(-4 a^2 B+a A b-3 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (2*a*(A*b - a*B)*Tan[c + d*x]^2)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*a^2*(a^2*A*b + 7*A*b^3 - 4*a^3*B - 10*a*b^2*B))/(3*b^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]]) - (2*(a*A*b - 4*a^2*B - 3*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)*d)","A",10,7,33,0.2121,1,"{3605, 3635, 3630, 3539, 3537, 63, 208}"
359,1,198,0,0.529017,"\int \frac{\tan ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 (A b-a B)}{3 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","-\frac{2 a^2 (A b-a B)}{3 b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (2*a^2*(A*b - a*B))/(3*b^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(2*A*b^3 - a*(a^2 + 3*b^2)*B))/(b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,33,0.1818,1,"{3604, 3628, 3539, 3537, 63, 208}"
360,1,188,0,0.400631,"\int \frac{\tan (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(a^2 A+2 a b B-A b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(a^2 A+2 a b B-A b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"-(((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d)) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (2*a*(A*b - a*B))/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*(a^2*A - A*b^2 + 2*a*b*B))/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,31,0.1935,1,"{3591, 3529, 3539, 3537, 63, 208}"
361,1,185,0,0.3642446,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 (A b-a B)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(a^2 (-B)+2 a A b+b^2 B\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","-\frac{2 (A b-a B)}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(a^2 (-B)+2 a A b+b^2 B\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"-(((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d)) + ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (2*(A*b - a*B))/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*(2*a*A*b - a^2*B + b^2*B))/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3529, 3539, 3537, 63, 208}"
362,1,224,0,0.9182386,"\int \frac{\cot (c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b (A b-a B)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","\frac{2 b (A b-a B)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(3 a^2 A b-2 a^3 B+A b^3\right)}{a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"(-2*A*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) + ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (2*b*(A*b - a*B))/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(3*a^2*A*b + A*b^3 - 2*a^3*B))/(a^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",13,8,31,0.2581,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
363,1,289,0,1.2524528,"\int \frac{\cot ^2(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^2*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{b \left(3 a^2 A-2 a b B+5 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{b \left(10 a^2 A b^2+a^4 A-6 a^3 b B-2 a b^3 B+5 A b^4\right)}{a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}","-\frac{b \left(3 a^2 A-2 a b B+5 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{b \left(10 a^2 A b^2+a^4 A-6 a^3 b B-2 a b^3 B+5 A b^4\right)}{a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{A \cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}",1,"((5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(7/2)*d) + ((I*A + B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - ((I*A - B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (b*(3*a^2*A + 5*A*b^2 - 2*a*b*B))/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (A*Cot[c + d*x])/(a*d*(a + b*Tan[c + d*x])^(3/2)) - (b*(a^4*A + 10*a^2*A*b^2 + 5*A*b^4 - 6*a^3*b*B - 2*a*b^3*B))/(a^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",14,8,33,0.2424,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
364,1,364,0,1.6342839,"\int \frac{\cot ^3(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^3*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{b \left(62 a^2 A b^3+11 a^4 A b-40 a^3 b^2 B-4 a^5 B-20 a b^4 B+35 A b^5\right)}{4 a^4 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{b \left(27 a^2 A b-12 a^3 B-20 a b^2 B+35 A b^3\right)}{12 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{\left(8 a^2 A+20 a b B-35 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{9/2} d}+\frac{(7 A b-4 a B) \cot (c+d x)}{4 a^2 d (a+b \tan (c+d x))^{3/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^{3/2}}","\frac{b \left(62 a^2 A b^3+11 a^4 A b-40 a^3 b^2 B-4 a^5 B-20 a b^4 B+35 A b^5\right)}{4 a^4 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{b \left(27 a^2 A b-12 a^3 B-20 a b^2 B+35 A b^3\right)}{12 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{\left(8 a^2 A+20 a b B-35 A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{9/2} d}+\frac{(7 A b-4 a B) \cot (c+d x)}{4 a^2 d (a+b \tan (c+d x))^{3/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(A+i B) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{A \cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))^{3/2}}",1,"((8*a^2*A - 35*A*b^2 + 20*a*b*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(9/2)*d) - ((A - I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - ((A + I*B)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (b*(27*a^2*A*b + 35*A*b^3 - 12*a^3*B - 20*a*b^2*B))/(12*a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + ((7*A*b - 4*a*B)*Cot[c + d*x])/(4*a^2*d*(a + b*Tan[c + d*x])^(3/2)) - (A*Cot[c + d*x]^2)/(2*a*d*(a + b*Tan[c + d*x])^(3/2)) + (b*(11*a^4*A*b + 62*a^2*A*b^3 + 35*A*b^5 - 4*a^5*B - 40*a^3*b^2*B - 20*a*b^4*B))/(4*a^4*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",15,8,33,0.2424,1,"{3609, 3649, 3653, 3539, 3537, 63, 208, 3634}"
365,1,362,0,0.3280086,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/Sqrt[a + b*Tan[c + d*x]],x]","\frac{b B \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b B \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}-\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}","\frac{b B \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}-\frac{b B \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}-\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a-\sqrt{a^2+b^2}}}",1,"(b*B*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) - (b*B*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) + (b*B*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] - Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) - (b*B*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] + Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*d)","A",12,8,28,0.2857,1,"{21, 3485, 700, 1129, 634, 618, 206, 628}"
366,1,406,0,0.334315,"\int \frac{a B+b B \tan (c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{b B \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a^2+b^2} \sqrt{a-\sqrt{a^2+b^2}}}-\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a^2+b^2} \sqrt{a-\sqrt{a^2+b^2}}}","-\frac{b B \log \left(-\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \log \left(\sqrt{2} \sqrt{\sqrt{a^2+b^2}+a} \sqrt{a+b \tan (c+d x)}+\sqrt{a^2+b^2}+a+b \tan (c+d x)\right)}{2 \sqrt{2} d \sqrt{a^2+b^2} \sqrt{\sqrt{a^2+b^2}+a}}+\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}-\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a^2+b^2} \sqrt{a-\sqrt{a^2+b^2}}}-\frac{b B \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a^2+b^2}+a}+\sqrt{2} \sqrt{a+b \tan (c+d x)}}{\sqrt{a-\sqrt{a^2+b^2}}}\right)}{\sqrt{2} d \sqrt{a^2+b^2} \sqrt{a-\sqrt{a^2+b^2}}}",1,"(b*B*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] - Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a^2 + b^2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) - (b*B*ArcTanh[(Sqrt[a + Sqrt[a^2 + b^2]] + Sqrt[2]*Sqrt[a + b*Tan[c + d*x]])/Sqrt[a - Sqrt[a^2 + b^2]]])/(Sqrt[2]*Sqrt[a^2 + b^2]*Sqrt[a - Sqrt[a^2 + b^2]]*d) - (b*B*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] - Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a^2 + b^2]*Sqrt[a + Sqrt[a^2 + b^2]]*d) + (b*B*Log[a + Sqrt[a^2 + b^2] + b*Tan[c + d*x] + Sqrt[2]*Sqrt[a + Sqrt[a^2 + b^2]]*Sqrt[a + b*Tan[c + d*x]]])/(2*Sqrt[2]*Sqrt[a^2 + b^2]*Sqrt[a + Sqrt[a^2 + b^2]]*d)","A",12,8,28,0.2857,1,"{21, 3485, 708, 1094, 634, 618, 206, 628}"
367,1,119,0,0.2804944,"\int \frac{\cot (c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","-\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"(-2*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + (B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) + (B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d)","A",12,7,34,0.2059,1,"{21, 3574, 3539, 3537, 63, 208, 3634}"
368,1,123,0,0.1854769,"\int \frac{a B+b B \tan (c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 b B}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","-\frac{2 b B}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"((-I)*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + (I*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*b*B)/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,28,0.2143,1,"{21, 3483, 3539, 3537, 63, 208}"
369,1,154,0,0.4936707,"\int \frac{\cot (c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b^2 B}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","\frac{2 b^2 B}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"(-2*B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + (B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + (B*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (2*b^2*B)/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",13,8,34,0.2353,1,"{21, 3569, 3653, 3539, 3537, 63, 208, 3634}"
370,1,102,0,0.1492444,"\int \frac{-a+b \tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(-a + b*Tan[c + d*x])/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"((I*a - b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d) - ((I*a + b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d)","A",7,4,27,0.1481,1,"{3539, 3537, 63, 208}"
371,1,132,0,0.2254225,"\int \frac{-a+b \tan (c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(-a + b*Tan[c + d*x])/(a + b*Tan[c + d*x])^(3/2),x]","\frac{4 a b}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}","\frac{4 a b}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"((I*a - b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - ((I*a + b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) + (4*a*b)/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,27,0.1852,1,"{3529, 3539, 3537, 63, 208}"
372,1,174,0,0.3380746,"\int \frac{-a+b \tan (c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(-a + b*Tan[c + d*x])/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{4 a b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","\frac{2 b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{4 a b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"((I*a - b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - ((I*a + b)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) + (4*a*b)/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(3*a^2 - b^2))/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,27,0.1852,1,"{3529, 3539, 3537, 63, 208}"
373,1,45,0,0.0518649,"\int \frac{1+i \tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(1 + I*Tan[c + d*x])/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{2 i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}","-\frac{2 i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}",1,"((-2*I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/(Sqrt[a - I*b]*d)","A",3,3,27,0.1111,1,"{3537, 63, 208}"
374,1,45,0,0.0520216,"\int \frac{1-i \tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(1 - I*Tan[c + d*x])/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","\frac{2 i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"((2*I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/(Sqrt[a + I*b]*d)","A",3,3,27,0.1111,1,"{3537, 63, 208}"
375,1,30,0,0.0306788,"\int \frac{3+\tan (x)}{\sqrt{4+3 \tan (x)}} \, dx","Int[(3 + Tan[x])/Sqrt[4 + 3*Tan[x]],x]","-\sqrt{2} \tan ^{-1}\left(\frac{1-3 \tan (x)}{\sqrt{2} \sqrt{3 \tan (x)+4}}\right)","-\sqrt{2} \tan ^{-1}\left(\frac{1-3 \tan (x)}{\sqrt{2} \sqrt{3 \tan (x)+4}}\right)",1,"-(Sqrt[2]*ArcTan[(1 - 3*Tan[x])/(Sqrt[2]*Sqrt[4 + 3*Tan[x]])])","A",2,2,15,0.1333,1,"{3535, 203}"
376,1,27,0,0.0316424,"\int \frac{1-3 \tan (x)}{\sqrt{4+3 \tan (x)}} \, dx","Int[(1 - 3*Tan[x])/Sqrt[4 + 3*Tan[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\tan (x)+3}{\sqrt{2} \sqrt{3 \tan (x)+4}}\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\tan (x)+3}{\sqrt{2} \sqrt{3 \tan (x)+4}}\right)",1,"Sqrt[2]*ArcTanh[(3 + Tan[x])/(Sqrt[2]*Sqrt[4 + 3*Tan[x]])]","A",2,2,17,0.1176,1,"{3535, 207}"
377,1,85,0,0.1075887,"\int \frac{4-3 \tan (a+b x)}{\sqrt{4+3 \tan (a+b x)}} \, dx","Int[(4 - 3*Tan[a + b*x])/Sqrt[4 + 3*Tan[a + b*x]],x]","\frac{13 \tanh ^{-1}\left(\frac{\tan (a+b x)+3}{\sqrt{2} \sqrt{3 \tan (a+b x)+4}}\right)}{5 \sqrt{2} b}-\frac{9 \tan ^{-1}\left(\frac{1-3 \tan (a+b x)}{\sqrt{2} \sqrt{3 \tan (a+b x)+4}}\right)}{5 \sqrt{2} b}","\frac{13 \tanh ^{-1}\left(\frac{\tan (a+b x)+3}{\sqrt{2} \sqrt{3 \tan (a+b x)+4}}\right)}{5 \sqrt{2} b}-\frac{9 \tan ^{-1}\left(\frac{1-3 \tan (a+b x)}{\sqrt{2} \sqrt{3 \tan (a+b x)+4}}\right)}{5 \sqrt{2} b}",1,"(-9*ArcTan[(1 - 3*Tan[a + b*x])/(Sqrt[2]*Sqrt[4 + 3*Tan[a + b*x]])])/(5*Sqrt[2]*b) + (13*ArcTanh[(3 + Tan[a + b*x])/(Sqrt[2]*Sqrt[4 + 3*Tan[a + b*x]])])/(5*Sqrt[2]*b)","A",5,4,25,0.1600,1,"{3536, 3535, 203, 207}"
378,1,278,0,0.3213369,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 (a B+A b) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 (a A-b B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b) \sqrt{\tan (c+d x)}}{d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{7}{2}}(c+d x)}{7 d}","\frac{2 (a B+A b) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 (a A-b B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b) \sqrt{\tan (c+d x)}}{d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{7}{2}}(c+d x)}{7 d}",1,"((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*(A*b + a*B)*Sqrt[Tan[c + d*x]])/d + (2*(a*A - b*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*(A*b + a*B)*Tan[c + d*x]^(5/2))/(5*d) + (2*b*B*Tan[c + d*x]^(7/2))/(7*d)","A",14,9,31,0.2903,1,"{3592, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
379,1,254,0,0.2630974,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 (a B+A b) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 (a A-b B) \sqrt{\tan (c+d x)}}{d}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x)}{5 d}","\frac{2 (a B+A b) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 (a A-b B) \sqrt{\tan (c+d x)}}{d}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x)}{5 d}",1,"((b*(A - B) + a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a*(A - B) - b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(a*A - b*B)*Sqrt[Tan[c + d*x]])/d + (2*(A*b + a*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*b*B*Tan[c + d*x]^(5/2))/(5*d)","A",13,9,31,0.2903,1,"{3592, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
380,1,229,0,0.2326552,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 (a B+A b) \sqrt{\tan (c+d x)}}{d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x)}{3 d}","-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 (a B+A b) \sqrt{\tan (c+d x)}}{d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x)}{3 d}",1,"-(((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(A*b + a*B)*Sqrt[Tan[c + d*x]])/d + (2*b*B*Tan[c + d*x]^(3/2))/(3*d)","A",12,9,31,0.2903,1,"{3592, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
381,1,205,0,0.1988867,"\int \frac{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \sqrt{\tan (c+d x)}}{d}","-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b B \sqrt{\tan (c+d x)}}{d}",1,"-(((b*(A - B) + a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((b*(A - B) + a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a*(A - B) - b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*B*Sqrt[Tan[c + d*x]])/d","A",11,8,31,0.2581,1,"{3592, 3534, 1168, 1162, 617, 204, 1165, 628}"
382,1,205,0,0.2138306,"\int \frac{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{d \sqrt{\tan (c+d x)}}","\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{d \sqrt{\tan (c+d x)}}",1,"((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a*A)/(d*Sqrt[Tan[c + d*x]])","A",11,8,31,0.2581,1,"{3591, 3534, 1168, 1162, 617, 204, 1165, 628}"
383,1,229,0,0.2278808,"\int \frac{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b)}{d \sqrt{\tan (c+d x)}}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b)}{d \sqrt{\tan (c+d x)}}+\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((b*(A - B) + a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a*(A - B) - b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a*A)/(3*d*Tan[c + d*x]^(3/2)) - (2*(A*b + a*B))/(d*Sqrt[Tan[c + d*x]])","A",12,9,31,0.2903,1,"{3591, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
384,1,254,0,0.2625904,"\int \frac{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b)}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 (a A-b B)}{d \sqrt{\tan (c+d x)}}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{5 d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 (a B+A b)}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 (a A-b B)}{d \sqrt{\tan (c+d x)}}+\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a A}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"-(((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a*A)/(5*d*Tan[c + d*x]^(5/2)) - (2*(A*b + a*B))/(3*d*Tan[c + d*x]^(3/2)) + (2*(a*A - b*B))/(d*Sqrt[Tan[c + d*x]])","A",13,9,31,0.2903,1,"{3591, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
385,1,394,0,0.667325,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{\tan (c+d x)}}{d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (11 a B+9 A b) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{2 b B \tan ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))}{9 d}","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{\tan (c+d x)}}{d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (11 a B+9 A b) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{2 b B \tan ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))}{9 d}",1,"((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*(2*a*A*b + a^2*B - b^2*B)*Sqrt[Tan[c + d*x]])/d + (2*(a^2*A - A*b^2 - 2*a*b*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*(2*a*A*b + a^2*B - b^2*B)*Tan[c + d*x]^(5/2))/(5*d) + (2*b*(9*A*b + 11*a*B)*Tan[c + d*x]^(7/2))/(63*d) + (2*b*B*Tan[c + d*x]^(7/2)*(a + b*Tan[c + d*x]))/(9*d)","A",15,10,33,0.3030,1,"{3607, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
386,1,360,0,0.5827213,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (9 a B+7 A b) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))}{7 d}","\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (9 a B+7 A b) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))}{7 d}",1,"((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(a^2*A - A*b^2 - 2*a*b*B)*Sqrt[Tan[c + d*x]])/d + (2*(2*a*A*b + a^2*B - b^2*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*b*(7*A*b + 9*a*B)*Tan[c + d*x]^(5/2))/(35*d) + (2*b*B*Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x]))/(7*d)","A",14,10,33,0.3030,1,"{3607, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
387,1,326,0,0.5192789,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (7 a B+5 A b) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}{5 d}","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 B+2 a A b-b^2 B\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (7 a B+5 A b) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}{5 d}",1,"-(((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(2*a*A*b + a^2*B - b^2*B)*Sqrt[Tan[c + d*x]])/d + (2*b*(5*A*b + 7*a*B)*Tan[c + d*x]^(3/2))/(15*d) + (2*b*B*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]))/(5*d)","A",13,10,33,0.3030,1,"{3607, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
388,1,294,0,0.4549674,"\int \frac{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (5 a B+3 A b) \sqrt{\tan (c+d x)}}{3 d}+\frac{2 b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}{3 d}","-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b (5 a B+3 A b) \sqrt{\tan (c+d x)}}{3 d}+\frac{2 b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}{3 d}",1,"-(((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*(3*A*b + 5*a*B)*Sqrt[Tan[c + d*x]])/(3*d) + (2*b*B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))/(3*d)","A",12,9,33,0.2727,1,"{3607, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
389,1,276,0,0.3433774,"\int \frac{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{d \sqrt{\tan (c+d x)}}+\frac{2 b^2 B \sqrt{\tan (c+d x)}}{d}","\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{d \sqrt{\tan (c+d x)}}+\frac{2 b^2 B \sqrt{\tan (c+d x)}}{d}",1,"((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2*A)/(d*Sqrt[Tan[c + d*x]]) + (2*b^2*B*Sqrt[Tan[c + d*x]])/d","A",12,9,33,0.2727,1,"{3604, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
390,1,283,0,0.3543126,"\int \frac{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a (a B+2 A b)}{d \sqrt{\tan (c+d x)}}","\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a (a B+2 A b)}{d \sqrt{\tan (c+d x)}}",1,"((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2*A)/(3*d*Tan[c + d*x]^(3/2)) - (2*a*(2*A*b + a*B))/(d*Sqrt[Tan[c + d*x]])","A",12,9,33,0.2727,1,"{3604, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
391,1,317,0,0.4455638,"\int \frac{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a (a B+2 A b)}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2 A-2 a b B-A b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 A}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a (a B+2 A b)}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2*A)/(5*d*Tan[c + d*x]^(5/2)) - (2*a*(2*A*b + a*B))/(3*d*Tan[c + d*x]^(3/2)) + (2*(a^2*A - A*b^2 - 2*a*b*B))/(d*Sqrt[Tan[c + d*x]])","A",13,10,33,0.3030,1,"{3604, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
392,1,463,0,0.9174198,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 b \left(22 a^2 B+27 a A b-9 b^2 B\right) \tan ^{\frac{5}{2}}(c+d x)}{45 d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (13 a B+9 A b) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2}{9 d}","\frac{2 b \left(22 a^2 B+27 a A b-9 b^2 B\right) \tan ^{\frac{5}{2}}(c+d x)}{45 d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (13 a B+9 A b) \tan ^{\frac{7}{2}}(c+d x)}{63 d}+\frac{2 b B \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2}{9 d}",1,"((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Sqrt[Tan[c + d*x]])/d + (2*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Tan[c + d*x]^(3/2))/(3*d) + (2*b*(27*a*A*b + 22*a^2*B - 9*b^2*B)*Tan[c + d*x]^(5/2))/(45*d) + (2*b^2*(9*A*b + 13*a*B)*Tan[c + d*x]^(7/2))/(63*d) + (2*b*B*Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2)/(9*d)","A",15,11,33,0.3333,1,"{3607, 3637, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
393,1,421,0,0.7450426,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 b \left(18 a^2 B+21 a A b-7 b^2 B\right) \tan ^{\frac{3}{2}}(c+d x)}{21 d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (11 a B+7 A b) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2}{7 d}","\frac{2 b \left(18 a^2 B+21 a A b-7 b^2 B\right) \tan ^{\frac{3}{2}}(c+d x)}{21 d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (11 a B+7 A b) \tan ^{\frac{5}{2}}(c+d x)}{35 d}+\frac{2 b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2}{7 d}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Sqrt[Tan[c + d*x]])/d + (2*b*(21*a*A*b + 18*a^2*B - 7*b^2*B)*Tan[c + d*x]^(3/2))/(21*d) + (2*b^2*(7*A*b + 11*a*B)*Tan[c + d*x]^(5/2))/(35*d) + (2*b*B*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2)/(7*d)","A",14,11,33,0.3333,1,"{3607, 3637, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
394,1,380,0,0.666732,"\int \frac{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(14 a^2 B+15 a A b-5 b^2 B\right) \sqrt{\tan (c+d x)}}{5 d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (9 a B+5 A b) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{2 b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2}{5 d}","-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(14 a^2 B+15 a A b-5 b^2 B\right) \sqrt{\tan (c+d x)}}{5 d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (9 a B+5 A b) \tan ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{2 b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2}{5 d}",1,"-(((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*(15*a*A*b + 14*a^2*B - 5*b^2*B)*Sqrt[Tan[c + d*x]])/(5*d) + (2*b^2*(5*A*b + 9*a*B)*Tan[c + d*x]^(3/2))/(15*d) + (2*b*B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2)/(5*d)","A",13,10,33,0.3030,1,"{3607, 3637, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
395,1,374,0,0.6759123,"\int \frac{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(2 a^2 A+3 a b B+A b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (3 a A+b B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 a A (a+b \tan (c+d x))^2}{d \sqrt{\tan (c+d x)}}","\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(2 a^2 A+3 a b B+A b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 (3 a A+b B) \tan ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 a A (a+b \tan (c+d x))^2}{d \sqrt{\tan (c+d x)}}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*(2*a^2*A + A*b^2 + 3*a*b*B)*Sqrt[Tan[c + d*x]])/d + (2*b^2*(3*a*A + b*B)*Tan[c + d*x]^(3/2))/(3*d) - (2*a*A*(a + b*Tan[c + d*x])^2)/(d*Sqrt[Tan[c + d*x]])","A",13,10,33,0.3030,1,"{3605, 3637, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
396,1,372,0,0.6115424,"\int \frac{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 (3 a B+7 A b)}{3 d \sqrt{\tan (c+d x)}}+\frac{2 b^2 (a A+3 b B) \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+b \tan (c+d x))^2}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 (3 a B+7 A b)}{3 d \sqrt{\tan (c+d x)}}+\frac{2 b^2 (a A+3 b B) \sqrt{\tan (c+d x)}}{3 d}-\frac{2 a A (a+b \tan (c+d x))^2}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2*(7*A*b + 3*a*B))/(3*d*Sqrt[Tan[c + d*x]]) + (2*b^2*(a*A + 3*b*B)*Sqrt[Tan[c + d*x]])/(3*d) - (2*a*A*(a + b*Tan[c + d*x])^2)/(3*d*Tan[c + d*x]^(3/2))","A",13,10,33,0.3030,1,"{3605, 3635, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
397,1,380,0,0.6593345,"\int \frac{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(5 a^2 A-15 a b B-14 A b^2\right)}{5 d \sqrt{\tan (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 (5 a B+9 A b)}{15 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a A (a+b \tan (c+d x))^2}{5 d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(5 a^2 A-15 a b B-14 A b^2\right)}{5 d \sqrt{\tan (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2 (5 a B+9 A b)}{15 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a A (a+b \tan (c+d x))^2}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2*(9*A*b + 5*a*B))/(15*d*Tan[c + d*x]^(3/2)) + (2*a*(5*a^2*A - 14*A*b^2 - 15*a*b*B))/(5*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^2)/(5*d*Tan[c + d*x]^(5/2))","A",13,10,33,0.3030,1,"{3605, 3635, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
398,1,325,0,0.9792718,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{2 a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{5/2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{b^2 d}+\frac{2 B \tan ^{\frac{3}{2}}(c+d x)}{3 b d}","-\frac{2 a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{5/2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{b^2 d}+\frac{2 B \tan ^{\frac{3}{2}}(c+d x)}{3 b d}",1,"((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(5/2)*(a^2 + b^2)*d) + ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + (2*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(b^2*d) + (2*B*Tan[c + d*x]^(3/2))/(3*b*d)","A",16,13,33,0.3939,1,"{3607, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
399,1,297,0,0.6536321,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{2 a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B \sqrt{\tan (c+d x)}}{b d}","\frac{2 a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B \sqrt{\tan (c+d x)}}{b d}",1,"-(((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(3/2)*(a^2 + b^2)*d) + ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + (2*B*Sqrt[Tan[c + d*x]])/(b*d)","A",15,12,33,0.3636,1,"{3607, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
400,1,278,0,0.3687436,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}","-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}",1,"-(((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*Sqrt[a]*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[b]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",14,11,33,0.3333,1,"{3612, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
401,1,278,0,0.3606726,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])),x]","\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}","\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}",1,"((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*Sqrt[b]*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[a]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",14,11,33,0.3333,1,"{3613, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
402,1,297,0,0.6369829,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","-\frac{2 b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 A}{a d \sqrt{\tan (c+d x)}}","-\frac{2 b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 A}{a d \sqrt{\tan (c+d x)}}",1,"((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(3/2)*(a^2 + b^2)*d) + ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - (2*A)/(a*d*Sqrt[Tan[c + d*x]])","A",15,12,33,0.3636,1,"{3609, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
403,1,325,0,0.9743892,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","\frac{2 b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B)}{a^2 d \sqrt{\tan (c+d x)}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x)}","\frac{2 b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B)}{a^2 d \sqrt{\tan (c+d x)}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(5/2)*(a^2 + b^2)*d) + ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - (2*A)/(3*a*d*Tan[c + d*x]^(3/2)) + (2*(A*b - a*B))/(a^2*d*Sqrt[Tan[c + d*x]])","A",16,13,33,0.3939,1,"{3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
404,1,436,0,1.1619139,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{a^{3/2} \left(a^2 A b-3 a^3 B-7 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{5/2} d \left(a^2+b^2\right)^2}+\frac{a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(-3 a^2 B+a A b-2 b^2 B\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","\frac{a^{3/2} \left(a^2 A b-3 a^3 B-7 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{5/2} d \left(a^2+b^2\right)^2}+\frac{a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(-3 a^2 B+a A b-2 b^2 B\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (a^(3/2)*(a^2*A*b + 5*A*b^3 - 3*a^3*B - 7*a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(5/2)*(a^2 + b^2)^2*d) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a*A*b - 3*a^2*B - 2*b^2*B)*Sqrt[Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) + (a*(A*b - a*B)*Tan[c + d*x]^(3/2))/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3605, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
405,1,391,0,0.7883642,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\sqrt{a} \left(a^2 A b+a^3 B+5 a b^2 B-3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)^2}+\frac{a (A b-a B) \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\sqrt{a} \left(a^2 A b+a^3 B+5 a b^2 B-3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)^2}+\frac{a (A b-a B) \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"-(((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (Sqrt[a]*(a^2*A*b - 3*A*b^3 + a^3*B + 5*a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(3/2)*(a^2 + b^2)^2*d) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + (a*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,33,0.3636,1,"{3605, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
406,1,391,0,0.81904,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^2}-\frac{(A b-a B) \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^2}-\frac{(A b-a B) \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"-(((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((A*b - a*B)*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,33,0.3636,1,"{3608, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
407,1,391,0,0.8654786,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2),x]","\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\sqrt{b} \left(5 a^2 A b-3 a^3 B+a b^2 B+A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B) \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\sqrt{b} \left(5 a^2 A b-3 a^3 B+a b^2 B+A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B) \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (Sqrt[b]*(5*a^2*A*b + A*b^3 - 3*a^3*B + a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(3/2)*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + (b*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,33,0.3636,1,"{3609, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
408,1,439,0,1.1733112,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2),x]","-\frac{b^{3/2} \left(7 a^2 A b-5 a^3 B-a b^2 B+3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}-\frac{2 a^2 A-a b B+3 A b^2}{a^2 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","-\frac{b^{3/2} \left(7 a^2 A b-5 a^3 B-a b^2 B+3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}-\frac{2 a^2 A-a b B+3 A b^2}{a^2 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (b^(3/2)*(7*a^2*A*b + 3*A*b^3 - 5*a^3*B - a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(5/2)*(a^2 + b^2)^2*d) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - (2*a^2*A + 3*A*b^2 - a*b*B)/(a^2*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]) + (b*(A*b - a*B))/(a*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
409,1,493,0,1.5328586,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2),x]","\frac{b^{5/2} \left(9 a^2 A b-7 a^3 B-3 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B)}{a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{2 a^2 A-3 a b B+5 A b^2}{3 a^2 d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 A b-2 a^3 B-3 a b^2 B+5 A b^3}{a^3 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}","\frac{b^{5/2} \left(9 a^2 A b-7 a^3 B-3 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d \left(a^2+b^2\right)^2}+\frac{b (A b-a B)}{a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{2 a^2 A-3 a b B+5 A b^2}{3 a^2 d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 A b-2 a^3 B-3 a b^2 B+5 A b^3}{a^3 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}",1,"-(((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (b^(5/2)*(9*a^2*A*b + 5*A*b^3 - 7*a^3*B - 3*a*b^2*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(7/2)*(a^2 + b^2)^2*d) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - (2*a^2*A + 5*A*b^2 - 3*a*b*B)/(3*a^2*(a^2 + b^2)*d*Tan[c + d*x]^(3/2)) + (4*a^2*A*b + 5*A*b^3 - 2*a^3*B - 3*a*b^2*B)/(a^3*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]) + (b*(A*b - a*B))/(a*(a^2 + b^2)*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]))","A",17,13,33,0.3939,1,"{3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
410,1,600,0,1.7245193,"\int \frac{\tan ^{\frac{7}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(7/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{a (A b-a B) \tan ^{\frac{5}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2 A b-5 a^3 B-13 a b^2 B+9 A b^3\right) \tan ^{\frac{3}{2}}(c+d x)}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{a^{3/2} \left(6 a^2 A b^3+3 a^4 A b-46 a^3 b^2 B-15 a^5 B-63 a b^4 B+35 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{7/2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^3 A b-31 a^2 b^2 B-15 a^4 B+11 a A b^3-8 b^4 B\right) \sqrt{\tan (c+d x)}}{4 b^3 d \left(a^2+b^2\right)^2}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","\frac{a (A b-a B) \tan ^{\frac{5}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2 A b-5 a^3 B-13 a b^2 B+9 A b^3\right) \tan ^{\frac{3}{2}}(c+d x)}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{a^{3/2} \left(6 a^2 A b^3+3 a^4 A b-46 a^3 b^2 B-15 a^5 B-63 a b^4 B+35 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{7/2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^3 A b-31 a^2 b^2 B-15 a^4 B+11 a A b^3-8 b^4 B\right) \sqrt{\tan (c+d x)}}{4 b^3 d \left(a^2+b^2\right)^2}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (a^(3/2)*(3*a^4*A*b + 6*a^2*A*b^3 + 35*A*b^5 - 15*a^5*B - 46*a^3*b^2*B - 63*a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(7/2)*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^3*A*b + 11*a*A*b^3 - 15*a^4*B - 31*a^2*b^2*B - 8*b^4*B)*Sqrt[Tan[c + d*x]])/(4*b^3*(a^2 + b^2)^2*d) + (a*(A*b - a*B)*Tan[c + d*x]^(5/2))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(a^2*A*b + 9*A*b^3 - 5*a^3*B - 13*a*b^2*B)*Tan[c + d*x]^(3/2))/(4*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",17,14,33,0.4242,1,"{3605, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
411,1,534,0,1.2301779,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\sqrt{a} \left(18 a^2 A b^3+a^4 A b+6 a^3 b^2 B+3 a^5 B+35 a b^4 B-15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{5/2} d \left(a^2+b^2\right)^3}-\frac{a \left(a^2 A b+3 a^3 B+11 a b^2 B-7 A b^3\right) \sqrt{\tan (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","\frac{a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\sqrt{a} \left(18 a^2 A b^3+a^4 A b+6 a^3 b^2 B+3 a^5 B+35 a b^4 B-15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{5/2} d \left(a^2+b^2\right)^3}-\frac{a \left(a^2 A b+3 a^3 B+11 a b^2 B-7 A b^3\right) \sqrt{\tan (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (Sqrt[a]*(a^4*A*b + 18*a^2*A*b^3 - 15*A*b^5 + 3*a^5*B + 6*a^3*b^2*B + 35*a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(5/2)*(a^2 + b^2)^3*d) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + (a*(A*b - a*B)*Tan[c + d*x]^(3/2))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a*(a^2*A*b - 7*A*b^3 + 3*a^3*B + 11*a*b^2*B)*Sqrt[Tan[c + d*x]])/(4*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3605, 3645, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
412,1,533,0,1.2281783,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(-26 a^2 A b^3+3 a^4 A b+18 a^3 b^2 B+a^5 B-15 a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{3/2} d \left(a^2+b^2\right)^3}+\frac{a (A b-a B) \sqrt{\tan (c+d x)}}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2 A b+a^3 B+9 a b^2 B-5 A b^3\right) \sqrt{\tan (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(-26 a^2 A b^3+3 a^4 A b+18 a^3 b^2 B+a^5 B-15 a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{3/2} d \left(a^2+b^2\right)^3}+\frac{a (A b-a B) \sqrt{\tan (c+d x)}}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2 A b+a^3 B+9 a b^2 B-5 A b^3\right) \sqrt{\tan (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + ((3*a^4*A*b - 26*a^2*A*b^3 + 3*A*b^5 + a^5*B + 18*a^3*b^2*B - 15*a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*Sqrt[a]*b^(3/2)*(a^2 + b^2)^3*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + (a*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + ((3*a^2*A*b - 5*A*b^3 + a^3*B + 9*a*b^2*B)*Sqrt[Tan[c + d*x]])/(4*b*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3605, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
413,1,531,0,1.3120534,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(-18 a^2 A b^3+15 a^4 A b+26 a^3 b^2 B-3 a^5 B-3 a b^4 B-A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} d \left(a^2+b^2\right)^3}-\frac{(A b-a B) \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(7 a^2 A b-3 a^3 B+5 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(-18 a^2 A b^3+15 a^4 A b+26 a^3 b^2 B-3 a^5 B-3 a b^4 B-A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} d \left(a^2+b^2\right)^3}-\frac{(A b-a B) \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{\left(7 a^2 A b-3 a^3 B+5 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((15*a^4*A*b - 18*a^2*A*b^3 - A*b^5 - 3*a^5*B + 26*a^3*b^2*B - 3*a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(3/2)*Sqrt[b]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((A*b - a*B)*Sqrt[Tan[c + d*x]])/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - ((7*a^2*A*b - A*b^3 - 3*a^3*B + 5*a*b^2*B)*Sqrt[Tan[c + d*x]])/(4*a*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3608, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
414,1,534,0,1.2497132,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^3),x]","\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\sqrt{b} \left(6 a^2 A b^3+35 a^4 A b+18 a^3 b^2 B-15 a^5 B+a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d \left(a^2+b^2\right)^3}+\frac{b (A b-a B) \sqrt{\tan (c+d x)}}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(11 a^2 A b-7 a^3 B+a b^2 B+3 A b^3\right) \sqrt{\tan (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\sqrt{b} \left(6 a^2 A b^3+35 a^4 A b+18 a^3 b^2 B-15 a^5 B+a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d \left(a^2+b^2\right)^3}+\frac{b (A b-a B) \sqrt{\tan (c+d x)}}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(11 a^2 A b-7 a^3 B+a b^2 B+3 A b^3\right) \sqrt{\tan (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (Sqrt[b]*(35*a^4*A*b + 6*a^2*A*b^3 + 3*A*b^5 - 15*a^5*B + 18*a^3*b^2*B + a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(5/2)*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + (b*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b*(11*a^2*A*b + 3*A*b^3 - 7*a^3*B + a*b^2*B)*Sqrt[Tan[c + d*x]])/(4*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,33,0.3939,1,"{3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
415,1,601,0,1.69065,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{b^{3/2} \left(46 a^2 A b^3+63 a^4 A b-6 a^3 b^2 B-35 a^5 B-3 a b^4 B+15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{b \left(13 a^2 A b-9 a^3 B-a b^2 B+5 A b^3\right)}{4 a^2 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}+\frac{b (A b-a B)}{2 a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2}-\frac{31 a^2 A b^2+8 a^4 A-11 a^3 b B-3 a b^3 B+15 A b^4}{4 a^3 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}","-\frac{b^{3/2} \left(46 a^2 A b^3+63 a^4 A b-6 a^3 b^2 B-35 a^5 B-3 a b^4 B+15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{b \left(13 a^2 A b-9 a^3 B-a b^2 B+5 A b^3\right)}{4 a^2 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}+\frac{b (A b-a B)}{2 a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2}-\frac{31 a^2 A b^2+8 a^4 A-11 a^3 b B-3 a b^3 B+15 A b^4}{4 a^3 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (b^(3/2)*(63*a^4*A*b + 46*a^2*A*b^3 + 15*A*b^5 - 35*a^5*B - 6*a^3*b^2*B - 3*a*b^4*B)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(7/2)*(a^2 + b^2)^3*d) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - (8*a^4*A + 31*a^2*A*b^2 + 15*A*b^4 - 11*a^3*b*B - 3*a*b^3*B)/(4*a^3*(a^2 + b^2)^2*d*Sqrt[Tan[c + d*x]]) + (b*(A*b - a*B))/(2*a*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2) + (b*(13*a^2*A*b + 5*A*b^3 - 9*a^3*B - a*b^2*B))/(4*a^2*(a^2 + b^2)^2*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))","A",17,13,33,0.3939,1,"{3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
416,1,156,0,0.1096195,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(5/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{2 B \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","\frac{2 B \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*B*Tan[c + d*x]^(3/2))/(3*d)","A",13,10,36,0.2778,1,"{21, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
417,1,154,0,0.1043128,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^(3/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 B \sqrt{\tan (c+d x)}}{d}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 B \sqrt{\tan (c+d x)}}{d}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*B*Sqrt[Tan[c + d*x]])/d","A",13,10,36,0.2778,1,"{21, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
418,1,138,0,0.0991125,"\int \frac{\sqrt{\tan (c+d x)} (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Sqrt[Tan[c + d*x]]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,36,0.2500,1,"{21, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
419,1,138,0,0.0960232,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])),x]","-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,36,0.2500,1,"{21, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
420,1,154,0,0.1049381,"\int \frac{a B+b B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 B}{d \sqrt{\tan (c+d x)}}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 B}{d \sqrt{\tan (c+d x)}}-\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*B)/(d*Sqrt[Tan[c + d*x]])","A",13,10,36,0.2778,1,"{21, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
421,1,156,0,0.0989388,"\int \frac{a B+b B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 B}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 B}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{B \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + (B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*B)/(3*d*Tan[c + d*x]^(3/2))","A",13,10,36,0.2778,1,"{21, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
422,1,256,0,0.5262026,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(5/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{2 a^{5/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B \sqrt{\tan (c+d x)}}{b d}","-\frac{2 a^{5/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{3/2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B \sqrt{\tan (c+d x)}}{b d}",1,"((a + b)*B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(5/2)*B*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(3/2)*(a^2 + b^2)*d) - ((a - b)*B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a - b)*B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + (2*B*Sqrt[Tan[c + d*x]])/(b*d)","A",16,13,36,0.3611,1,"{21, 3566, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
423,1,237,0,0.303643,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^(3/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{2 a^{3/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}+\frac{B (a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}","\frac{2 a^{3/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}+\frac{B (a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}",1,"((a - b)*B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(3/2)*B*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[b]*(a^2 + b^2)*d) + ((a + b)*B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,36,0.3333,1,"{21, 3573, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
424,1,237,0,0.2775556,"\int \frac{\sqrt{\tan (c+d x)} (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Sqrt[Tan[c + d*x]]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","-\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{a} \sqrt{b} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}","-\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{a} \sqrt{b} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}",1,"-(((a + b)*B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*Sqrt[a]*Sqrt[b]*B*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/((a^2 + b^2)*d) + ((a - b)*B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,36,0.3333,1,"{21, 3572, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
425,1,237,0,0.2783572,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2),x]","\frac{2 b^{3/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}-\frac{B (a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}","\frac{2 b^{3/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}-\frac{B (a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}",1,"-(((a - b)*B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a - b)*B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(3/2)*B*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[a]*(a^2 + b^2)*d) - ((a + b)*B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a + b)*B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,36,0.3333,1,"{21, 3574, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
426,1,256,0,0.4525958,"\int \frac{a B+b B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2),x]","-\frac{2 b^{5/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 B}{a d \sqrt{\tan (c+d x)}}","-\frac{2 b^{5/2} B \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d \left(a^2+b^2\right)}+\frac{B (a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{B (a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{B (a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 B}{a d \sqrt{\tan (c+d x)}}",1,"((a + b)*B*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*B*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(5/2)*B*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(3/2)*(a^2 + b^2)*d) - ((a - b)*B*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a - b)*B*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - (2*B)/(a*d*Sqrt[Tan[c + d*x]])","A",16,13,36,0.3611,1,"{21, 3569, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
427,1,264,0,1.9125244,"\int \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 (-B)+4 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{3/2} d}+\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(4 A b-a B) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b d}+\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 b d}","\frac{\left(a^2 (-B)+4 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{3/2} d}+\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(4 A b-a B) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b d}+\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 b d}",1,"(Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((4*a*A*b - a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*b^(3/2)*d) + (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((4*A*b - a*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*b*d) + (B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(2*b*d)","A",14,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
428,1,201,0,1.5470866,"\int \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}","\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}",1,"(Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((2*A*b + a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (B*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",13,9,35,0.2571,1,"{3610, 3655, 6725, 63, 217, 206, 93, 205, 208}"
429,1,169,0,0.6439189,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-((Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (2*Sqrt[b]*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d","A",12,9,35,0.2571,1,"{3614, 3616, 3615, 93, 203, 206, 3634, 63, 217}"
430,1,154,0,0.5411646,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","-\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"-((Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*A*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",8,6,35,0.1714,1,"{3608, 3616, 3615, 93, 203, 206}"
431,1,199,0,0.7572536,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+A b) \sqrt{a+b \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+A b) \sqrt{a+b \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"(Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*A*Sqrt[a + b*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (2*(A*b + 3*a*B)*Sqrt[a + b*Tan[c + d*x]])/(3*a*d*Sqrt[Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3608, 3649, 3616, 3615, 93, 203, 206}"
432,1,250,0,1.0580533,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{2 \left(15 a^2 A-5 a b B+2 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \sqrt{\tan (c+d x)}}+\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (5 a B+A b) \sqrt{a+b \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(15 a^2 A-5 a b B+2 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \sqrt{\tan (c+d x)}}+\frac{\sqrt{-b+i a} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (5 a B+A b) \sqrt{a+b \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\sqrt{b+i a} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"(Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*A*Sqrt[a + b*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (2*(A*b + 5*a*B)*Sqrt[a + b*Tan[c + d*x]])/(15*a*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2*A + 2*A*b^2 - 5*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d*Sqrt[Tan[c + d*x]])","A",10,7,35,0.2000,1,"{3608, 3649, 3616, 3615, 93, 203, 206}"
433,1,314,0,1.3428983,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{2 \left(35 a^2 A-7 a b B+4 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(35 a^2 A b+105 a^3 B+14 a b^2 B-8 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a^3 d \sqrt{\tan (c+d x)}}-\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (7 a B+A b) \sqrt{a+b \tan (c+d x)}}{35 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 \left(35 a^2 A-7 a b B+4 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(35 a^2 A b+105 a^3 B+14 a b^2 B-8 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a^3 d \sqrt{\tan (c+d x)}}-\frac{\sqrt{-b+i a} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (7 a B+A b) \sqrt{a+b \tan (c+d x)}}{35 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{\sqrt{b+i a} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"-((Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) - (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*A*Sqrt[a + b*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (2*(A*b + 7*a*B)*Sqrt[a + b*Tan[c + d*x]])/(35*a*d*Tan[c + d*x]^(5/2)) + (2*(35*a^2*A + 4*A*b^2 - 7*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d*Tan[c + d*x]^(3/2)) + (2*(35*a^2*A*b - 8*A*b^3 + 105*a^3*B + 14*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a^3*d*Sqrt[Tan[c + d*x]])","A",11,7,35,0.2000,1,"{3608, 3649, 3616, 3615, 93, 203, 206}"
434,1,323,0,2.5595931,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 (-B)+6 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 b d}+\frac{\left(6 a^2 A b+a^3 (-B)-24 a b^2 B-16 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 b^{3/2} d}+\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(6 A b-a B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{12 b d}+\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{3 b d}","\frac{\left(a^2 (-B)+6 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 b d}+\frac{\left(6 a^2 A b+a^3 (-B)-24 a b^2 B-16 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 b^{3/2} d}+\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(6 A b-a B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{12 b d}+\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{3 b d}",1,"((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((6*a^2*A*b - 16*A*b^3 - a^3*B - 24*a*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(8*b^(3/2)*d) + ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((6*a*A*b - a^2*B - 8*b^2*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(8*b*d) + ((6*A*b - a*B)*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(12*b*d) + (B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2))/(3*b*d)","A",15,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
435,1,268,0,2.406974,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(3 a^2 B+12 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 \sqrt{b} d}+\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(5 a B+4 A b) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}","\frac{\left(3 a^2 B+12 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 \sqrt{b} d}+\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(5 a B+4 A b) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}",1,"((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + ((12*a*A*b + 3*a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*Sqrt[b]*d) + ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((4*A*b + 5*a*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*d) + (b*B*Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",14,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
436,1,204,0,1.7313269,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","-\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b} (3 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}","-\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b} (3 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}",1,"-(((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (Sqrt[b]*(2*A*b + 3*a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (b*B*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",13,9,35,0.2571,1,"{3607, 3655, 6725, 63, 217, 206, 93, 205, 208}"
437,1,209,0,1.6851054,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d)) + (2*b^(3/2)*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",13,9,35,0.2571,1,"{3605, 3655, 6725, 63, 217, 206, 93, 205, 208}"
438,1,196,0,0.8784937,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + b*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (2*(4*A*b + 3*a*B)*Sqrt[a + b*Tan[c + d*x]])/(3*d*Sqrt[Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3605, 3649, 3616, 3615, 93, 203, 206}"
439,1,259,0,1.1528729,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{2 \left(15 a^2 A-20 a b B-3 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a d \sqrt{\tan (c+d x)}}+\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{2 (5 a B+6 A b) \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(15 a^2 A-20 a b B-3 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a d \sqrt{\tan (c+d x)}}+\frac{(a+i b)^2 (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{2 (5 a B+6 A b) \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + b*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (2*(6*A*b + 5*a*B)*Sqrt[a + b*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2*A - 3*A*b^2 - 20*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(15*a*d*Sqrt[Tan[c + d*x]])","A",10,7,35,0.2000,1,"{3605, 3649, 3616, 3615, 93, 203, 206}"
440,1,311,0,1.4772864,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{2 \left(35 a^2 A-42 a b B-3 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(140 a^2 A b+105 a^3 B-21 a b^2 B+6 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (7 a B+8 A b) \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 \left(35 a^2 A-42 a b B-3 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(140 a^2 A b+105 a^3 B-21 a b^2 B+6 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{3/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (7 a B+8 A b) \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{(b+i a)^{3/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"-(((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) - ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + b*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (2*(8*A*b + 7*a*B)*Sqrt[a + b*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (2*(35*a^2*A - 3*A*b^2 - 42*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d*Tan[c + d*x]^(3/2)) + (2*(140*a^2*A*b + 6*A*b^3 + 105*a^3*B - 21*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d*Sqrt[Tan[c + d*x]])","A",11,7,35,0.2000,1,"{3605, 3649, 3616, 3615, 93, 203, 206}"
441,1,382,0,1.8319283,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(11/2),x]","\frac{2 \left(126 a^2 A b+105 a^3 B-9 a b^2 B+4 A b^3\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2 A-24 a b B-A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 \left(-63 a^2 A b^2+315 a^4 A-420 a^3 b B-18 a b^3 B+8 A b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^3 d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{3/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (9 a B+10 A b) \sqrt{a+b \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}","\frac{2 \left(126 a^2 A b+105 a^3 B-9 a b^2 B+4 A b^3\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2 A-24 a b B-A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 \left(-63 a^2 A b^2+315 a^4 A-420 a^3 b B-18 a b^3 B+8 A b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^3 d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{3/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (9 a B+10 A b) \sqrt{a+b \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{3/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{a+b \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}",1,"((I*a - b)^(3/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*A*Sqrt[a + b*Tan[c + d*x]])/(9*d*Tan[c + d*x]^(9/2)) - (2*(10*A*b + 9*a*B)*Sqrt[a + b*Tan[c + d*x]])/(63*d*Tan[c + d*x]^(7/2)) + (2*(21*a^2*A - A*b^2 - 24*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d*Tan[c + d*x]^(5/2)) + (2*(126*a^2*A*b + 4*A*b^3 + 105*a^3*B - 9*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d*Tan[c + d*x]^(3/2)) - (2*(315*a^4*A - 63*a^2*A*b^2 + 8*A*b^4 - 420*a^3*b*B - 18*a*b^3*B)*Sqrt[a + b*Tan[c + d*x]])/(315*a^3*d*Sqrt[Tan[c + d*x]])","A",12,7,35,0.2000,1,"{3605, 3649, 3616, 3615, 93, 203, 206}"
442,1,397,0,3.119688,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(-5 a^2 B+40 a A b-48 b^2 B\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{96 b d}+\frac{\left(40 a^2 A b-5 a^3 B-112 a b^2 B-64 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{64 b d}+\frac{\left(40 a^3 A b-240 a^2 b^2 B-5 a^4 B-320 a A b^3+128 b^4 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{64 b^{3/2} d}-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(8 A b-a B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{24 b d}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{7/2}}{4 b d}","\frac{\left(-5 a^2 B+40 a A b-48 b^2 B\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{96 b d}+\frac{\left(40 a^2 A b-5 a^3 B-112 a b^2 B-64 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{64 b d}+\frac{\left(40 a^3 A b-240 a^2 b^2 B-5 a^4 B-320 a A b^3+128 b^4 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{64 b^{3/2} d}-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(8 A b-a B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{24 b d}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{7/2}}{4 b d}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + ((40*a^3*A*b - 320*a*A*b^3 - 5*a^4*B - 240*a^2*b^2*B + 128*b^4*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(64*b^(3/2)*d) - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((40*a^2*A*b - 64*A*b^3 - 5*a^3*B - 112*a*b^2*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(64*b*d) + ((40*a*A*b - 5*a^2*B - 48*b^2*B)*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(96*b*d) + ((8*A*b - a*B)*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2))/(24*b*d) + (B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(7/2))/(4*b*d)","A",16,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
443,1,316,0,3.0666365,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{\left(5 a^2 B+14 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 d}+\frac{\left(30 a^2 A b+5 a^3 B-40 a b^2 B-16 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 \sqrt{b} d}-\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(3 a B+2 A b) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{4 d}+\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}","\frac{\left(5 a^2 B+14 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 d}+\frac{\left(30 a^2 A b+5 a^3 B-40 a b^2 B-16 A b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 \sqrt{b} d}-\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(3 a B+2 A b) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{4 d}+\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}",1,"-(((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + ((30*a^2*A*b - 16*A*b^3 + 5*a^3*B - 40*a*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(8*Sqrt[b]*d) + ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((14*a*A*b + 5*a^2*B - 8*b^2*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(8*d) + ((2*A*b + 3*a*B)*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(4*d) + (b*B*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",15,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
444,1,260,0,2.3304704,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","\frac{\sqrt{b} \left(15 a^2 B+20 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (7 a B+4 A b) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 d}","\frac{\sqrt{b} \left(15 a^2 B+20 a A b-8 b^2 B\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (7 a B+4 A b) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 d}",1,"((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (Sqrt[b]*(20*a*A*b + 15*a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*d) + ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (b*(4*A*b + 7*a*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*d) + (b*B*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(2*d)","A",14,10,35,0.2857,1,"{3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
445,1,241,0,2.3508044,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","\frac{b^{3/2} (5 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (2 a A+b B) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{d \sqrt{\tan (c+d x)}}","\frac{b^{3/2} (5 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (2 a A+b B) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{d \sqrt{\tan (c+d x)}}",1,"((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (b^(3/2)*(2*A*b + 5*a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (b*(2*a*A + b*B)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(d*Sqrt[Tan[c + d*x]])","A",14,10,35,0.2857,1,"{3605, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
446,1,240,0,2.0164332,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (a B+2 A b) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (a B+2 A b) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (2*b^(5/2)*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*(2*A*b + a*B)*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(3*d*Tan[c + d*x]^(3/2))","A",14,10,35,0.2857,1,"{3605, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
447,1,247,0,1.1702844,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(7/2),x]","\frac{2 \left(15 a^2 A-35 a b B-23 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (5 a B+8 A b) \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(15 a^2 A-35 a b B-23 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (5 a B+8 A b) \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"-(((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*(8*A*b + 5*a*B)*Sqrt[a + b*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2*A - 23*A*b^2 - 35*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(5*d*Tan[c + d*x]^(5/2))","A",10,8,35,0.2286,1,"{3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
448,1,309,0,1.5190946,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(9/2),x]","\frac{2 \left(35 a^2 A-77 a b B-45 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(245 a^2 A b+105 a^3 B-161 a b^2 B-15 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (7 a B+10 A b) \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{7 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 \left(35 a^2 A-77 a b B-45 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(245 a^2 A b+105 a^3 B-161 a b^2 B-15 A b^3\right) \sqrt{a+b \tan (c+d x)}}{105 a d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (7 a B+10 A b) \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{7 d \tan ^{\frac{7}{2}}(c+d x)}",1,"((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*(10*A*b + 7*a*B)*Sqrt[a + b*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (2*(35*a^2*A - 45*A*b^2 - 77*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(3/2)) + (2*(245*a^2*A*b - 15*A*b^3 + 105*a^3*B - 161*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(7*d*Tan[c + d*x]^(7/2))","A",11,8,35,0.2286,1,"{3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
449,1,378,0,1.9113165,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(11/2),x]","\frac{2 \left(231 a^2 A b+105 a^3 B-135 a b^2 B-5 A b^3\right) \sqrt{a+b \tan (c+d x)}}{315 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2 A-45 a b B-25 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 \left(-483 a^2 A b^2+315 a^4 A-735 a^3 b B+45 a b^3 B-10 A b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (3 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{21 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{9 d \tan ^{\frac{9}{2}}(c+d x)}","\frac{2 \left(231 a^2 A b+105 a^3 B-135 a b^2 B-5 A b^3\right) \sqrt{a+b \tan (c+d x)}}{315 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2 A-45 a b B-25 A b^2\right) \sqrt{a+b \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 \left(-483 a^2 A b^2+315 a^4 A-735 a^3 b B+45 a b^3 B-10 A b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \sqrt{\tan (c+d x)}}+\frac{(-b+i a)^{5/2} (A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (3 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{21 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{5/2} (A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{9 d \tan ^{\frac{9}{2}}(c+d x)}",1,"((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*(4*A*b + 3*a*B)*Sqrt[a + b*Tan[c + d*x]])/(21*d*Tan[c + d*x]^(7/2)) + (2*(21*a^2*A - 25*A*b^2 - 45*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(5/2)) + (2*(231*a^2*A*b - 5*A*b^3 + 105*a^3*B - 135*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(315*a*d*Tan[c + d*x]^(3/2)) - (2*(315*a^4*A - 483*a^2*A*b^2 - 10*A*b^4 - 735*a^3*b*B + 45*a*b^3*B)*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(9*d*Tan[c + d*x]^(9/2))","A",12,8,35,0.2286,1,"{3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
450,1,460,0,2.3133643,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\tan ^{\frac{13}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(13/2),x]","-\frac{2 \left(-1485 a^2 A b^2+1155 a^4 A-2541 a^3 b B+55 a b^3 B-20 A b^4\right) \sqrt{a+b \tan (c+d x)}}{3465 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(495 a^2 A b+231 a^3 B-275 a b^2 B-5 A b^3\right) \sqrt{a+b \tan (c+d x)}}{1155 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 \left(99 a^2 A-209 a b B-113 A b^2\right) \sqrt{a+b \tan (c+d x)}}{693 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 \left(-495 a^2 A b^3+8085 a^4 A b-5313 a^3 b^2 B+3465 a^5 B-110 a b^4 B+40 A b^5\right) \sqrt{a+b \tan (c+d x)}}{3465 a^3 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (11 a B+14 A b) \sqrt{a+b \tan (c+d x)}}{99 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{11 d \tan ^{\frac{11}{2}}(c+d x)}","-\frac{2 \left(-1485 a^2 A b^2+1155 a^4 A-2541 a^3 b B+55 a b^3 B-20 A b^4\right) \sqrt{a+b \tan (c+d x)}}{3465 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(495 a^2 A b+231 a^3 B-275 a b^2 B-5 A b^3\right) \sqrt{a+b \tan (c+d x)}}{1155 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 \left(99 a^2 A-209 a b B-113 A b^2\right) \sqrt{a+b \tan (c+d x)}}{693 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 \left(-495 a^2 A b^3+8085 a^4 A b-5313 a^3 b^2 B+3465 a^5 B-110 a b^4 B+40 A b^5\right) \sqrt{a+b \tan (c+d x)}}{3465 a^3 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{5/2} (-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (11 a B+14 A b) \sqrt{a+b \tan (c+d x)}}{99 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{(b+i a)^{5/2} (B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A (a+b \tan (c+d x))^{3/2}}{11 d \tan ^{\frac{11}{2}}(c+d x)}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a*(14*A*b + 11*a*B)*Sqrt[a + b*Tan[c + d*x]])/(99*d*Tan[c + d*x]^(9/2)) + (2*(99*a^2*A - 113*A*b^2 - 209*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(693*d*Tan[c + d*x]^(7/2)) + (2*(495*a^2*A*b - 5*A*b^3 + 231*a^3*B - 275*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(1155*a*d*Tan[c + d*x]^(5/2)) - (2*(1155*a^4*A - 1485*a^2*A*b^2 - 20*A*b^4 - 2541*a^3*b*B + 55*a*b^3*B)*Sqrt[a + b*Tan[c + d*x]])/(3465*a^2*d*Tan[c + d*x]^(3/2)) - (2*(8085*a^4*A*b - 495*a^2*A*b^3 + 40*A*b^5 + 3465*a^5*B - 5313*a^3*b^2*B - 110*a*b^4*B)*Sqrt[a + b*Tan[c + d*x]])/(3465*a^3*d*Sqrt[Tan[c + d*x]]) - (2*a*A*(a + b*Tan[c + d*x])^(3/2))/(11*d*Tan[c + d*x]^(11/2))","A",13,8,35,0.2286,1,"{3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
451,1,253,0,2.4564818,"\int \frac{(a+b \tan (c+d x))^{5/2} \left(\frac{3 b B}{2 a}+B \tan (c+d x)\right)}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*((3*b*B)/(2*a) + B*Tan[c + d*x]))/Tan[c + d*x]^(5/2),x]","-\frac{2 B \left(a^2+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (2 a-3 i b) (-b+i a)^{5/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{2 a d}-\frac{b B (a+b \tan (c+d x))^{3/2}}{d \tan ^{\frac{3}{2}}(c+d x)}-\frac{B (2 a+3 i b) (b+i a)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{2 a d}","-\frac{2 B \left(a^2+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (2 a-3 i b) (-b+i a)^{5/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{2 a d}-\frac{b B (a+b \tan (c+d x))^{3/2}}{d \tan ^{\frac{3}{2}}(c+d x)}-\frac{B (2 a+3 i b) (b+i a)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{2 a d}",1,"((I*a - b)^(5/2)*(2*a - (3*I)*b)*B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(2*a*d) + (2*b^(5/2)*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((2*a + (3*I)*b)*(I*a + b)^(5/2)*B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(2*a*d) - (2*(a^2 + 3*b^2)*B*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (b*B*(a + b*Tan[c + d*x])^(3/2))/(d*Tan[c + d*x]^(3/2))","A",14,10,43,0.2326,1,"{3605, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
452,1,206,0,1.3683654,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b d}","\frac{(2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{B \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b d}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d)) + ((2*A*b - a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(3/2)*d) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) + (B*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(b*d)","A",13,9,35,0.2571,1,"{3607, 3655, 6725, 63, 217, 206, 93, 205, 208}"
453,1,168,0,0.6080691,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}","\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",12,9,35,0.2571,1,"{3614, 3616, 3615, 93, 203, 206, 3634, 63, 217}"
454,1,123,0,0.3693045,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",7,5,35,0.1429,1,"{3616, 3615, 93, 203, 206}"
455,1,159,0,0.5346628,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]),x]","-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}","-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d)) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*A*Sqrt[a + b*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",8,6,35,0.1714,1,"{3609, 3616, 3615, 93, 203, 206}"
456,1,203,0,0.7417038,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{2 (2 A b-3 a B) \sqrt{a+b \tan (c+d x)}}{3 a^2 d \sqrt{\tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}","\frac{2 (2 A b-3 a B) \sqrt{a+b \tan (c+d x)}}{3 a^2 d \sqrt{\tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d)) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*A*Sqrt[a + b*Tan[c + d*x]])/(3*a*d*Tan[c + d*x]^(3/2)) + (2*(2*A*b - 3*a*B)*Sqrt[a + b*Tan[c + d*x]])/(3*a^2*d*Sqrt[Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
457,1,256,0,1.0620632,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{2 \left(15 a^2 A+10 a b B-8 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^3 d \sqrt{\tan (c+d x)}}+\frac{2 (4 A b-5 a B) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(15 a^2 A+10 a b B-8 A b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^3 d \sqrt{\tan (c+d x)}}+\frac{2 (4 A b-5 a B) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{a+b \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*A*Sqrt[a + b*Tan[c + d*x]])/(5*a*d*Tan[c + d*x]^(5/2)) + (2*(4*A*b - 5*a*B)*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2*A - 8*A*b^2 + 10*a*b*B)*Sqrt[a + b*Tan[c + d*x]])/(15*a^3*d*Sqrt[Tan[c + d*x]])","A",10,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
458,1,219,0,1.7696229,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 a (A b-a B) \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}","\frac{2 a (A b-a B) \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d)) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(3/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) + (2*a*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",13,9,35,0.2571,1,"{3605, 3655, 6725, 63, 217, 206, 93, 205, 208}"
459,1,170,0,0.6045694,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}","-\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d)) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) - (2*(A*b - a*B)*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,6,35,0.1714,1,"{3608, 3616, 3615, 93, 203, 206}"
460,1,175,0,0.5776956,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 b (A b-a B) \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}","\frac{2 b (A b-a B) \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) + (2*b*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,6,35,0.1714,1,"{3609, 3616, 3615, 93, 203, 206}"
461,1,216,0,0.8474687,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 b \left(a^2 A-a b B+2 A b^2\right) \sqrt{\tan (c+d x)}}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A}{a d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}","-\frac{2 b \left(a^2 A-a b B+2 A b^2\right) \sqrt{\tan (c+d x)}}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A}{a d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) - (2*A)/(a*d*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) - (2*b*(a^2*A + 2*A*b^2 - a*b*B)*Sqrt[Tan[c + d*x]])/(a^2*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
462,1,276,0,1.1597301,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 b \left(5 a^2 A b-3 a^3 B-6 a b^2 B+8 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 (4 A b-3 a B)}{3 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}","\frac{2 b \left(5 a^2 A b-3 a^3 B-6 a b^2 B+8 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 (4 A b-3 a B)}{3 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d)) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) - (2*A)/(3*a*d*Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]) + (2*(4*A*b - 3*a*B))/(3*a^2*d*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) + (2*b*(5*a^2*A*b + 8*A*b^3 - 3*a^3*B - 6*a*b^2*B)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",10,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
463,1,282,0,2.4781066,"\int \frac{\tan ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}","\frac{2 a (A b-a B) \tan ^{\frac{3}{2}}(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(5/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) + (2*a*(A*b - a*B)*Tan[c + d*x]^(3/2))/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(2*A*b^3 - a*(a^2 + 3*b^2)*B)*Sqrt[Tan[c + d*x]])/(b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",14,10,35,0.2857,1,"{3605, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
464,1,244,0,0.9892441,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a (A b-a B) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(2 a^2 A b+a^3 B+7 a b^2 B-4 A b^3\right) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","\frac{2 a (A b-a B) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(2 a^2 A b+a^3 B+7 a b^2 B-4 A b^3\right) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) + (2*a*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*(2*a^2*A*b - 4*A*b^3 + a^3*B + 7*a*b^2*B)*Sqrt[Tan[c + d*x]])/(3*b*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3605, 3649, 3616, 3615, 93, 203, 206}"
465,1,244,0,1.0087605,"\int \frac{\sqrt{\tan (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(5 a^2 A b-2 a^3 B+4 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","-\frac{2 (A b-a B) \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(5 a^2 A b-2 a^3 B+4 a b^2 B-A b^3\right) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d)) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) - (2*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*(5*a^2*A*b - A*b^3 - 2*a^3*B + 4*a*b^2*B)*Sqrt[Tan[c + d*x]])/(3*a*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3608, 3649, 3616, 3615, 93, 203, 206}"
466,1,247,0,0.9273659,"\int \frac{A+B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{2 b (A b-a B) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(8 a^2 A b-5 a^3 B+a b^2 B+2 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","\frac{2 b (A b-a B) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(8 a^2 A b-5 a^3 B+a b^2 B+2 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d)) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) + (2*b*(A*b - a*B)*Sqrt[Tan[c + d*x]])/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(8*a^2*A*b + 2*A*b^3 - 5*a^3*B + a*b^2*B)*Sqrt[Tan[c + d*x]])/(3*a^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
467,1,301,0,1.1903559,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)),x]","-\frac{2 b \left(17 a^2 A b^2+3 a^4 A-8 a^3 b B-2 a b^3 B+8 A b^4\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b \left(3 a^2 A-a b B+4 A b^2\right) \sqrt{\tan (c+d x)}}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A}{a d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}","-\frac{2 b \left(17 a^2 A b^2+3 a^4 A-8 a^3 b B-2 a b^3 B+8 A b^4\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b \left(3 a^2 A-a b B+4 A b^2\right) \sqrt{\tan (c+d x)}}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{(-B+i A) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A}{a d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) - (2*A)/(a*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^2*A + 4*A*b^2 - a*b*B)*Sqrt[Tan[c + d*x]])/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^4*A + 17*a^2*A*b^2 + 8*A*b^4 - 8*a^3*b*B - 2*a*b^3*B)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",10,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
468,1,359,0,1.6423487,"\int \frac{A+B \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{2 b \left(30 a^2 A b^3+8 a^4 A b-17 a^3 b^2 B-3 a^5 B-8 a b^4 B+16 A b^5\right) \sqrt{\tan (c+d x)}}{3 a^4 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 b \left(7 a^2 A b-3 a^3 B-4 a b^2 B+8 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 (2 A b-a B)}{a^2 d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}","\frac{2 b \left(30 a^2 A b^3+8 a^4 A b-17 a^3 b^2 B-3 a^5 B-8 a b^4 B+16 A b^5\right) \sqrt{\tan (c+d x)}}{3 a^4 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 b \left(7 a^2 A b-3 a^3 B-4 a b^2 B+8 A b^3\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 (2 A b-a B)}{a^2 d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{(A+i B) \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A}{3 a d \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(5/2)*d) - (2*A)/(3*a*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)) + (2*(2*A*b - a*B))/(a^2*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(7*a^2*A*b + 8*A*b^3 - 3*a^3*B - 4*a*b^2*B)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(8*a^4*A*b + 30*a^2*A*b^3 + 16*A*b^5 - 3*a^5*B - 17*a^3*b^2*B - 8*a*b^4*B)*Sqrt[Tan[c + d*x]])/(3*a^4*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",11,7,35,0.2000,1,"{3609, 3649, 3616, 3615, 93, 203, 206}"
469,1,155,0,0.2002259,"\int \frac{\tan ^{\frac{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^(3/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","-\frac{B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"-((B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d)) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - (B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",13,10,38,0.2632,1,"{21, 3575, 910, 63, 217, 206, 912, 93, 205, 208}"
470,1,117,0,0.1432094,"\int \frac{\sqrt{\tan (c+d x)} (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Tan[c + d*x]]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{i B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{i B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{i B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{i B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"(I*B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) - (I*B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",8,6,38,0.1579,1,"{21, 3575, 910, 93, 205, 208}"
471,1,111,0,0.1366933,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"(B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + (B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",8,6,38,0.1579,1,"{21, 3575, 912, 93, 205, 208}"
472,1,150,0,0.2215009,"\int \frac{a B+b B \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{i B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{2 B \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{i B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","-\frac{i B \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{2 B \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{i B \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"((-I)*B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + (I*B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*B*Sqrt[a + b*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",10,8,38,0.2105,1,"{21, 3569, 12, 3575, 910, 93, 205, 208}"
473,1,379,0,0.4402364,"\int (a+b \tan (c+d x))^{2/3} (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^(2/3)*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{3} (a-i b)^{2/3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d}-\frac{\sqrt{3} (a+i b)^{2/3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d}+\frac{3 (a-i b)^{2/3} (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 (a+i b)^{2/3} (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}-\frac{(a+i b)^{2/3} (-B+i A) \log (\cos (c+d x))}{4 d}+\frac{(a-i b)^{2/3} (B+i A) \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{2/3} (A-i B)-\frac{1}{4} x (a+i b)^{2/3} (A+i B)+\frac{3 B (a+b \tan (c+d x))^{2/3}}{2 d}","\frac{\sqrt{3} (a-i b)^{2/3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d}-\frac{\sqrt{3} (a+i b)^{2/3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d}+\frac{3 (a-i b)^{2/3} (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 (a+i b)^{2/3} (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}-\frac{(a+i b)^{2/3} (-B+i A) \log (\cos (c+d x))}{4 d}+\frac{(a-i b)^{2/3} (B+i A) \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{2/3} (A-i B)-\frac{1}{4} x (a+i b)^{2/3} (A+i B)+\frac{3 B (a+b \tan (c+d x))^{2/3}}{2 d}",1,"-((a - I*b)^(2/3)*(A - I*B)*x)/4 - ((a + I*b)^(2/3)*(A + I*B)*x)/4 + (Sqrt[3]*(a - I*b)^(2/3)*(I*A + B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/(2*d) - (Sqrt[3]*(a + I*b)^(2/3)*(I*A - B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/(2*d) - ((a + I*b)^(2/3)*(I*A - B)*Log[Cos[c + d*x]])/(4*d) + ((a - I*b)^(2/3)*(I*A + B)*Log[Cos[c + d*x]])/(4*d) + (3*(a - I*b)^(2/3)*(I*A + B)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*d) - (3*(a + I*b)^(2/3)*(I*A - B)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*d) + (3*B*(a + b*Tan[c + d*x])^(2/3))/(2*d)","A",12,7,25,0.2800,1,"{3528, 3539, 3537, 55, 617, 204, 31}"
474,1,377,0,0.4060384,"\int \sqrt[3]{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^(1/3)*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{3} \sqrt[3]{a-i b} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d}+\frac{\sqrt{3} \sqrt[3]{a+i b} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d}+\frac{3 \sqrt[3]{a-i b} (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 \sqrt[3]{a+i b} (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}-\frac{\sqrt[3]{a+i b} (-B+i A) \log (\cos (c+d x))}{4 d}+\frac{\sqrt[3]{a-i b} (B+i A) \log (\cos (c+d x))}{4 d}-\frac{1}{4} x \sqrt[3]{a-i b} (A-i B)-\frac{1}{4} x \sqrt[3]{a+i b} (A+i B)+\frac{3 B \sqrt[3]{a+b \tan (c+d x)}}{d}","-\frac{\sqrt{3} \sqrt[3]{a-i b} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d}+\frac{\sqrt{3} \sqrt[3]{a+i b} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d}+\frac{3 \sqrt[3]{a-i b} (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 \sqrt[3]{a+i b} (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}-\frac{\sqrt[3]{a+i b} (-B+i A) \log (\cos (c+d x))}{4 d}+\frac{\sqrt[3]{a-i b} (B+i A) \log (\cos (c+d x))}{4 d}-\frac{1}{4} x \sqrt[3]{a-i b} (A-i B)-\frac{1}{4} x \sqrt[3]{a+i b} (A+i B)+\frac{3 B \sqrt[3]{a+b \tan (c+d x)}}{d}",1,"-((a - I*b)^(1/3)*(A - I*B)*x)/4 - ((a + I*b)^(1/3)*(A + I*B)*x)/4 - (Sqrt[3]*(a - I*b)^(1/3)*(I*A + B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/(2*d) + (Sqrt[3]*(a + I*b)^(1/3)*(I*A - B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/(2*d) - ((a + I*b)^(1/3)*(I*A - B)*Log[Cos[c + d*x]])/(4*d) + ((a - I*b)^(1/3)*(I*A + B)*Log[Cos[c + d*x]])/(4*d) + (3*(a - I*b)^(1/3)*(I*A + B)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*d) - (3*(a + I*b)^(1/3)*(I*A - B)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*d) + (3*B*(a + b*Tan[c + d*x])^(1/3))/d","A",12,7,25,0.2800,1,"{3528, 3539, 3537, 57, 617, 204, 31}"
475,1,357,0,0.2783173,"\int \frac{A+B \tan (c+d x)}{\sqrt[3]{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(1/3),x]","\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d \sqrt[3]{a-i b}}-\frac{\sqrt{3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d \sqrt[3]{a+i b}}+\frac{3 (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d \sqrt[3]{a-i b}}-\frac{3 (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d \sqrt[3]{a+i b}}-\frac{(-B+i A) \log (\cos (c+d x))}{4 d \sqrt[3]{a+i b}}+\frac{(B+i A) \log (\cos (c+d x))}{4 d \sqrt[3]{a-i b}}-\frac{x (A-i B)}{4 \sqrt[3]{a-i b}}-\frac{x (A+i B)}{4 \sqrt[3]{a+i b}}","\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d \sqrt[3]{a-i b}}-\frac{\sqrt{3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d \sqrt[3]{a+i b}}+\frac{3 (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d \sqrt[3]{a-i b}}-\frac{3 (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d \sqrt[3]{a+i b}}-\frac{(-B+i A) \log (\cos (c+d x))}{4 d \sqrt[3]{a+i b}}+\frac{(B+i A) \log (\cos (c+d x))}{4 d \sqrt[3]{a-i b}}-\frac{x (A-i B)}{4 \sqrt[3]{a-i b}}-\frac{x (A+i B)}{4 \sqrt[3]{a+i b}}",1,"-((A - I*B)*x)/(4*(a - I*b)^(1/3)) - ((A + I*B)*x)/(4*(a + I*b)^(1/3)) + (Sqrt[3]*(I*A + B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/(2*(a - I*b)^(1/3)*d) - (Sqrt[3]*(I*A - B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/(2*(a + I*b)^(1/3)*d) - ((I*A - B)*Log[Cos[c + d*x]])/(4*(a + I*b)^(1/3)*d) + ((I*A + B)*Log[Cos[c + d*x]])/(4*(a - I*b)^(1/3)*d) + (3*(I*A + B)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*(a - I*b)^(1/3)*d) - (3*(I*A - B)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*(a + I*b)^(1/3)*d)","A",11,6,25,0.2400,1,"{3539, 3537, 55, 617, 204, 31}"
476,1,357,0,0.2838259,"\int \frac{A+B \tan (c+d x)}{(a+b \tan (c+d x))^{2/3}} \, dx","Int[(A + B*Tan[c + d*x])/(a + b*Tan[c + d*x])^(2/3),x]","-\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d (a-i b)^{2/3}}+\frac{\sqrt{3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d (a+i b)^{2/3}}+\frac{3 (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{2/3}}-\frac{3 (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{2/3}}-\frac{(-B+i A) \log (\cos (c+d x))}{4 d (a+i b)^{2/3}}+\frac{(B+i A) \log (\cos (c+d x))}{4 d (a-i b)^{2/3}}-\frac{x (A-i B)}{4 (a-i b)^{2/3}}-\frac{x (A+i B)}{4 (a+i b)^{2/3}}","-\frac{\sqrt{3} (B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-i b}}}{\sqrt{3}}\right)}{2 d (a-i b)^{2/3}}+\frac{\sqrt{3} (-B+i A) \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+i b}}}{\sqrt{3}}\right)}{2 d (a+i b)^{2/3}}+\frac{3 (B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{2/3}}-\frac{3 (-B+i A) \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{2/3}}-\frac{(-B+i A) \log (\cos (c+d x))}{4 d (a+i b)^{2/3}}+\frac{(B+i A) \log (\cos (c+d x))}{4 d (a-i b)^{2/3}}-\frac{x (A-i B)}{4 (a-i b)^{2/3}}-\frac{x (A+i B)}{4 (a+i b)^{2/3}}",1,"-((A - I*B)*x)/(4*(a - I*b)^(2/3)) - ((A + I*B)*x)/(4*(a + I*b)^(2/3)) - (Sqrt[3]*(I*A + B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/(2*(a - I*b)^(2/3)*d) + (Sqrt[3]*(I*A - B)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/(2*(a + I*b)^(2/3)*d) - ((I*A - B)*Log[Cos[c + d*x]])/(4*(a + I*b)^(2/3)*d) + ((I*A + B)*Log[Cos[c + d*x]])/(4*(a - I*b)^(2/3)*d) + (3*(I*A + B)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*(a - I*b)^(2/3)*d) - (3*(I*A - B)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*(a + I*b)^(2/3)*d)","A",11,6,25,0.2400,1,"{3539, 3537, 57, 617, 204, 31}"
477,1,148,0,0.1255315,"\int \frac{i-\tan (e+f x)}{\sqrt[3]{c+d \tan (e+f x)}} \, dx","Int[(I - Tan[e + f*x])/(c + d*Tan[e + f*x])^(1/3),x]","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-i d}}}{\sqrt{3}}\right)}{f \sqrt[3]{c-i d}}-\frac{3 \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c-i d}\right)}{2 f \sqrt[3]{c-i d}}-\frac{\log (\cos (e+f x))}{2 f \sqrt[3]{c-i d}}-\frac{i x}{2 \sqrt[3]{c-i d}}","-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-i d}}}{\sqrt{3}}\right)}{f \sqrt[3]{c-i d}}-\frac{3 \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c-i d}\right)}{2 f \sqrt[3]{c-i d}}-\frac{\log (\cos (e+f x))}{2 f \sqrt[3]{c-i d}}-\frac{i x}{2 \sqrt[3]{c-i d}}",1,"((-I/2)*x)/(c - I*d)^(1/3) - (Sqrt[3]*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - I*d)^(1/3))/Sqrt[3]])/((c - I*d)^(1/3)*f) - Log[Cos[e + f*x]]/(2*(c - I*d)^(1/3)*f) - (3*Log[(c - I*d)^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(2*(c - I*d)^(1/3)*f)","A",5,5,27,0.1852,1,"{3537, 55, 617, 204, 31}"
478,1,299,0,0.344992,"\int \frac{d-c \tan (e+f x)}{(c+d \tan (e+f x))^{2/3}} \, dx","Int[(d - c*Tan[e + f*x])/(c + d*Tan[e + f*x])^(2/3),x]","\frac{\sqrt{3} \sqrt[3]{c-i d} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-i d}}}{\sqrt{3}}\right)}{2 f}+\frac{\sqrt{3} \sqrt[3]{c+i d} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+i d}}}{\sqrt{3}}\right)}{2 f}-\frac{3 \sqrt[3]{c-i d} \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c-i d}\right)}{4 f}-\frac{3 \sqrt[3]{c+i d} \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c+i d}\right)}{4 f}-\frac{\sqrt[3]{c-i d} \log (\cos (e+f x))}{4 f}-\frac{\sqrt[3]{c+i d} \log (\cos (e+f x))}{4 f}-\frac{1}{4} i x \sqrt[3]{c-i d}+\frac{1}{4} i x \sqrt[3]{c+i d}","\frac{\sqrt{3} \sqrt[3]{c-i d} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-i d}}}{\sqrt{3}}\right)}{2 f}+\frac{\sqrt{3} \sqrt[3]{c+i d} \tan ^{-1}\left(\frac{1+\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+i d}}}{\sqrt{3}}\right)}{2 f}-\frac{3 \sqrt[3]{c-i d} \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c-i d}\right)}{4 f}-\frac{3 \sqrt[3]{c+i d} \log \left(-\sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c+i d}\right)}{4 f}-\frac{\sqrt[3]{c-i d} \log (\cos (e+f x))}{4 f}-\frac{\sqrt[3]{c+i d} \log (\cos (e+f x))}{4 f}-\frac{1}{4} i x \sqrt[3]{c-i d}+\frac{1}{4} i x \sqrt[3]{c+i d}",1,"(-I/4)*(c - I*d)^(1/3)*x + (I/4)*(c + I*d)^(1/3)*x + (Sqrt[3]*(c - I*d)^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - I*d)^(1/3))/Sqrt[3]])/(2*f) + (Sqrt[3]*(c + I*d)^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c + I*d)^(1/3))/Sqrt[3]])/(2*f) - ((c - I*d)^(1/3)*Log[Cos[e + f*x]])/(4*f) - ((c + I*d)^(1/3)*Log[Cos[e + f*x]])/(4*f) - (3*(c - I*d)^(1/3)*Log[(c - I*d)^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*f) - (3*(c + I*d)^(1/3)*Log[(c + I*d)^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*f)","A",11,6,26,0.2308,1,"{3539, 3537, 57, 617, 204, 31}"
479,1,403,0,1.3283354,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^4 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^4*(A + B*Tan[c + d*x]),x]","\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}-\frac{b \left(-a^2 A b \left(5 m^2+37 m+68\right)-2 a^3 B \left(m^2+8 m+19\right)+4 a b^2 B \left(m^2+7 m+12\right)+A b^3 \left(m^2+7 m+12\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+3) (m+4)}+\frac{b^2 \left(a^2 B \left(m^2+9 m+26\right)+2 a A b (m+4)^2-b^2 B \left(m^2+7 m+12\right)\right) \tan ^{m+2}(c+d x)}{d (m+2) (m+3) (m+4)}+\frac{b (a B (m+7)+A b (m+4)) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^2}{d (m+3) (m+4)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^3}{d (m+4)}","\frac{\left(-6 a^2 A b^2+a^4 A-4 a^3 b B+4 a b^3 B+A b^4\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(4 a^3 A b-6 a^2 b^2 B+a^4 B-4 a A b^3+b^4 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}-\frac{b \left(-a^2 A b \left(5 m^2+37 m+68\right)-2 a^3 B \left(m^2+8 m+19\right)+4 a b^2 B \left(m^2+7 m+12\right)+A b^3 \left(m^2+7 m+12\right)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+3) (m+4)}+\frac{b^2 \left(a^2 B \left(m^2+9 m+26\right)+2 a A b (m+4)^2-b^2 B \left(m^2+7 m+12\right)\right) \tan ^{m+2}(c+d x)}{d (m+2) (m+3) (m+4)}+\frac{b (a B (m+7)+A b (m+4)) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^2}{d (m+3) (m+4)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^3}{d (m+4)}",1,"-((b*(A*b^3*(12 + 7*m + m^2) + 4*a*b^2*B*(12 + 7*m + m^2) - 2*a^3*B*(19 + 8*m + m^2) - a^2*A*b*(68 + 37*m + 5*m^2))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(3 + m)*(4 + m))) + ((a^4*A - 6*a^2*A*b^2 + A*b^4 - 4*a^3*b*B + 4*a*b^3*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (b^2*(2*a*A*b*(4 + m)^2 - b^2*B*(12 + 7*m + m^2) + a^2*B*(26 + 9*m + m^2))*Tan[c + d*x]^(2 + m))/(d*(2 + m)*(3 + m)*(4 + m)) + ((4*a^3*A*b - 4*a*A*b^3 + a^4*B - 6*a^2*b^2*B + b^4*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(d*(2 + m)) + (b*(A*b*(4 + m) + a*B*(7 + m))*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x])^2)/(d*(3 + m)*(4 + m)) + (b*B*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x])^3)/(d*(4 + m))","A",9,7,31,0.2258,1,"{3607, 3647, 3637, 3630, 3538, 3476, 364}"
480,1,267,0,0.6905493,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b \left(2 a^2 B (m+4)+3 a A b (m+3)-b^2 B (m+3)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+3)}+\frac{b^2 (a B (m+5)+A b (m+3)) \tan ^{m+2}(c+d x)}{d (m+2) (m+3)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^2}{d (m+3)}","\frac{\left(a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b \left(2 a^2 B (m+4)+3 a A b (m+3)-b^2 B (m+3)\right) \tan ^{m+1}(c+d x)}{d (m+1) (m+3)}+\frac{b^2 (a B (m+5)+A b (m+3)) \tan ^{m+2}(c+d x)}{d (m+2) (m+3)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^2}{d (m+3)}",1,"(b*(3*a*A*b*(3 + m) - b^2*B*(3 + m) + 2*a^2*B*(4 + m))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(3 + m)) + ((a^3*A - 3*a*A*b^2 - 3*a^2*b*B + b^3*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + (b^2*(A*b*(3 + m) + a*B*(5 + m))*Tan[c + d*x]^(2 + m))/(d*(2 + m)*(3 + m)) + ((3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(d*(2 + m)) + (b*B*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x])^2)/(d*(3 + m))","A",8,6,31,0.1935,1,"{3607, 3637, 3630, 3538, 3476, 364}"
481,1,194,0,0.3324911,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 A-2 a b B-A b^2\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(a^2 B+2 a A b-b^2 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b (a B (m+3)+A b (m+2)) \tan ^{m+1}(c+d x)}{d (m+1) (m+2)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))}{d (m+2)}","\frac{\left(a^2 A-2 a b B-A b^2\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{\left(a^2 B+2 a A b-b^2 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b (a B (m+3)+A b (m+2)) \tan ^{m+1}(c+d x)}{d (m+1) (m+2)}+\frac{b B \tan ^{m+1}(c+d x) (a+b \tan (c+d x))}{d (m+2)}",1,"(b*(A*b*(2 + m) + a*B*(3 + m))*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(2 + m)) + ((a^2*A - A*b^2 - 2*a*b*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + ((2*a*A*b + a^2*B - b^2*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(d*(2 + m)) + (b*B*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x]))/(d*(2 + m))","A",7,5,31,0.1613,1,"{3607, 3630, 3538, 3476, 364}"
482,1,127,0,0.1392037,"\int \tan ^m(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{(a A-b B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{(a B+A b) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b B \tan ^{m+1}(c+d x)}{d (m+1)}","\frac{(a A-b B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1)}+\frac{(a B+A b) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2)}+\frac{b B \tan ^{m+1}(c+d x)}{d (m+1)}",1,"(b*B*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + ((a*A - b*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/(d*(1 + m)) + ((A*b + a*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/(d*(2 + m))","A",6,4,29,0.1379,1,"{3592, 3538, 3476, 364}"
483,1,185,0,0.3128909,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{(a A+b B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)}+\frac{b (A b-a B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{a d (m+1) \left(a^2+b^2\right)}-\frac{(A b-a B) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)}","\frac{(a A+b B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)}+\frac{b (A b-a B) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{a d (m+1) \left(a^2+b^2\right)}-\frac{(A b-a B) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)}",1,"((a*A + b*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/((a^2 + b^2)*d*(1 + m)) + (b*(A*b - a*B)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1 + m))/(a*(a^2 + b^2)*d*(1 + m)) - ((A*b - a*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/((a^2 + b^2)*d*(2 + m))","A",8,6,31,0.1935,1,"{3613, 3538, 3476, 364, 3634, 64}"
484,1,282,0,0.7038141,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2 A+2 a b B-A b^2\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^2}+\frac{b \left(a^2 A b (2-m)+a^3 (-(B-B m))+a b^2 B (m+1)-A b^3 m\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{a^2 d (m+1) \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-B)+2 a A b+b^2 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^2}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}","\frac{\left(a^2 A+2 a b B-A b^2\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^2}+\frac{b \left(a^2 A b (2-m)+a^3 (-(B-B m))+a b^2 B (m+1)-A b^3 m\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{a^2 d (m+1) \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-B)+2 a A b+b^2 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^2}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}",1,"((a^2*A - A*b^2 + 2*a*b*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/((a^2 + b^2)^2*d*(1 + m)) + (b*(a^2*A*b*(2 - m) - A*b^3*m + a*b^2*B*(1 + m) - a^3*(B - B*m))*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1 + m))/(a^2*(a^2 + b^2)^2*d*(1 + m)) - ((2*a*A*b - a^2*B + b^2*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/((a^2 + b^2)^2*d*(2 + m)) + (b*(A*b - a*B)*Tan[c + d*x]^(1 + m))/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",9,7,31,0.2258,1,"{3609, 3653, 3538, 3476, 364, 3634, 64}"
485,1,438,0,1.2848547,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(2 a^2 A b^3 \left(-m^2+3 m+1\right)-a^4 A b \left(m^2-5 m+6\right)-2 a^3 b^2 B \left(-m^2+m+3\right)+a^5 B \left(m^2-3 m+2\right)+a b^4 B m (m+1)+A b^5 (1-m) m\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{2 a^3 d (m+1) \left(a^2+b^2\right)^3}+\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^3}+\frac{b \left(a^2 A b (5-m)+a^3 (-B) (3-m)+a b^2 B (m+1)+A b^3 (1-m)\right) \tan ^{m+1}(c+d x)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}","-\frac{b \left(2 a^2 A b^3 \left(-m^2+3 m+1\right)-a^4 A b \left(m^2-5 m+6\right)-2 a^3 b^2 B \left(-m^2+m+3\right)+a^5 B \left(m^2-3 m+2\right)+a b^4 B m (m+1)+A b^5 (1-m) m\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{2 a^3 d (m+1) \left(a^2+b^2\right)^3}+\frac{\left(a^3 A+3 a^2 b B-3 a A b^2-b^3 B\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^3}+\frac{b \left(a^2 A b (5-m)+a^3 (-B) (3-m)+a b^2 B (m+1)+A b^3 (1-m)\right) \tan ^{m+1}(c+d x)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}",1,"((a^3*A - 3*a*A*b^2 + 3*a^2*b*B - b^3*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/((a^2 + b^2)^3*d*(1 + m)) - (b*(A*b^5*(1 - m)*m + a*b^4*B*m*(1 + m) - 2*a^3*b^2*B*(3 + m - m^2) + 2*a^2*A*b^3*(1 + 3*m - m^2) - a^4*A*b*(6 - 5*m + m^2) + a^5*B*(2 - 3*m + m^2))*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1 + m))/(2*a^3*(a^2 + b^2)^3*d*(1 + m)) - ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/((a^2 + b^2)^3*d*(2 + m)) + (b*(A*b - a*B)*Tan[c + d*x]^(1 + m))/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b*(A*b^3*(1 - m) - a^3*B*(3 - m) + a^2*A*b*(5 - m) + a*b^2*B*(1 + m))*Tan[c + d*x]^(1 + m))/(2*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",10,8,31,0.2581,1,"{3609, 3649, 3653, 3538, 3476, 364, 3634, 64}"
486,1,659,0,2.4473603,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^4} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^4,x]","-\frac{b \left(3 a^4 A b^3 \left(m^3-7 m^2+10 m+8\right)+3 a^2 A b^5 m \left(m^2-5 m+2\right)-a^6 A b \left(-m^3+9 m^2-26 m+24\right)-3 a^5 b^2 B \left(m^3-4 m^2-m+12\right)+3 a^3 b^4 B \left(-m^3+2 m^2+5 m+2\right)+a^7 B \left(-m^3+6 m^2-11 m+6\right)+a b^6 B m \left(1-m^2\right)+A b^7 m \left(m^2-3 m+2\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{6 a^4 d (m+1) \left(a^2+b^2\right)^4}+\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^4}-\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^4}+\frac{b \left(2 a^2 A b^3 \left(m^2-6 m+2\right)+a^4 A b \left(m^2-9 m+26\right)+2 a^3 b^2 B \left(-m^2+3 m+7\right)+a^5 (-B) \left(m^2-6 m+11\right)+a b^4 B \left(1-m^2\right)+A b^5 \left(m^2-3 m+2\right)\right) \tan ^{m+1}(c+d x)}{6 a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(a^2 A b (8-m)+a^3 (-B) (5-m)+a b^2 B (m+1)+A b^3 (2-m)\right) \tan ^{m+1}(c+d x)}{6 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}","-\frac{b \left(3 a^4 A b^3 \left(m^3-7 m^2+10 m+8\right)+3 a^2 A b^5 m \left(m^2-5 m+2\right)-a^6 A b \left(-m^3+9 m^2-26 m+24\right)-3 a^5 b^2 B \left(m^3-4 m^2-m+12\right)+3 a^3 b^4 B \left(-m^3+2 m^2+5 m+2\right)+a^7 B \left(-m^3+6 m^2-11 m+6\right)+a b^6 B m \left(1-m^2\right)+A b^7 m \left(m^2-3 m+2\right)\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,m+1;m+2;-\frac{b \tan (c+d x)}{a}\right)}{6 a^4 d (m+1) \left(a^2+b^2\right)^4}+\frac{\left(-6 a^2 A b^2+a^4 A+4 a^3 b B-4 a b^3 B+A b^4\right) \tan ^{m+1}(c+d x) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\tan ^2(c+d x)\right)}{d (m+1) \left(a^2+b^2\right)^4}-\frac{\left(4 a^3 A b+6 a^2 b^2 B+a^4 (-B)-4 a A b^3-b^4 B\right) \tan ^{m+2}(c+d x) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\tan ^2(c+d x)\right)}{d (m+2) \left(a^2+b^2\right)^4}+\frac{b \left(2 a^2 A b^3 \left(m^2-6 m+2\right)+a^4 A b \left(m^2-9 m+26\right)+2 a^3 b^2 B \left(-m^2+3 m+7\right)+a^5 (-B) \left(m^2-6 m+11\right)+a b^4 B \left(1-m^2\right)+A b^5 \left(m^2-3 m+2\right)\right) \tan ^{m+1}(c+d x)}{6 a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b \left(a^2 A b (8-m)+a^3 (-B) (5-m)+a b^2 B (m+1)+A b^3 (2-m)\right) \tan ^{m+1}(c+d x)}{6 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b (A b-a B) \tan ^{m+1}(c+d x)}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}",1,"((a^4*A - 6*a^2*A*b^2 + A*b^4 + 4*a^3*b*B - 4*a*b^3*B)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(1 + m))/((a^2 + b^2)^4*d*(1 + m)) - (b*(a*b^6*B*m*(1 - m^2) + 3*a^2*A*b^5*m*(2 - 5*m + m^2) + A*b^7*m*(2 - 3*m + m^2) + 3*a^3*b^4*B*(2 + 5*m + 2*m^2 - m^3) + a^7*B*(6 - 11*m + 6*m^2 - m^3) - a^6*A*b*(24 - 26*m + 9*m^2 - m^3) + 3*a^4*A*b^3*(8 + 10*m - 7*m^2 + m^3) - 3*a^5*b^2*B*(12 - m - 4*m^2 + m^3))*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1 + m))/(6*a^4*(a^2 + b^2)^4*d*(1 + m)) - ((4*a^3*A*b - 4*a*A*b^3 - a^4*B + 6*a^2*b^2*B - b^4*B)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -Tan[c + d*x]^2]*Tan[c + d*x]^(2 + m))/((a^2 + b^2)^4*d*(2 + m)) + (b*(A*b - a*B)*Tan[c + d*x]^(1 + m))/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (b*(A*b^3*(2 - m) - a^3*B*(5 - m) + a^2*A*b*(8 - m) + a*b^2*B*(1 + m))*Tan[c + d*x]^(1 + m))/(6*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (b*(a*b^4*B*(1 - m^2) + 2*a^3*b^2*B*(7 + 3*m - m^2) + a^4*A*b*(26 - 9*m + m^2) + 2*a^2*A*b^3*(2 - 6*m + m^2) - a^5*B*(11 - 6*m + m^2) + A*b^5*(2 - 3*m + m^2))*Tan[c + d*x]^(1 + m))/(6*a^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",11,8,31,0.2581,1,"{3609, 3649, 3653, 3538, 3476, 364, 3634, 64}"
487,1,193,0,0.4516466,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{a^2 (A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{a^2 (A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}","\frac{a^2 (A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{a^2 (A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}",1,"(a^2*(A + I*B)*AppellF1[1 + m, -5/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a]) + (a^2*(A - I*B)*AppellF1[1 + m, -5/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
488,1,189,0,0.4549368,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{a (A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{a (A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}","\frac{a (A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{a (A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}",1,"(a*(A + I*B)*AppellF1[1 + m, -3/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a]) + (a*(A - I*B)*AppellF1[1 + m, -3/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
489,1,187,0,0.3978574,"\int \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{a+b \tan (c+d x)} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{\frac{b \tan (c+d x)}{a}+1}}",1,"((A + I*B)*AppellF1[1 + m, -1/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a]) + ((A - I*B)*AppellF1[1 + m, -1/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[a + b*Tan[c + d*x]])/(2*d*(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
490,1,187,0,0.4093175,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+b \tan (c+d x)}}","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1) \sqrt{a+b \tan (c+d x)}}",1,"((A + I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 1/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
491,1,193,0,0.45469,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 a d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 a d (m+1) \sqrt{a+b \tan (c+d x)}}","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 a d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 a d (m+1) \sqrt{a+b \tan (c+d x)}}",1,"((A + I*B)*AppellF1[1 + m, 3/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*a*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 3/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*a*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
492,1,193,0,0.4568349,"\int \frac{\tan ^m(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Tan[c + d*x]^m*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 a^2 d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 a^2 d (m+1) \sqrt{a+b \tan (c+d x)}}","\frac{(A+i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 a^2 d (m+1) \sqrt{a+b \tan (c+d x)}}+\frac{(A-i B) \tan ^{m+1}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 a^2 d (m+1) \sqrt{a+b \tan (c+d x)}}",1,"((A + I*B)*AppellF1[1 + m, 5/2, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*a^2*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]]) + ((A - I*B)*AppellF1[1 + m, 5/2, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*a^2*d*(1 + m)*Sqrt[a + b*Tan[c + d*x]])","A",7,4,33,0.1212,1,"{3603, 3602, 135, 133}"
493,1,183,0,0.3137768,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1)}+\frac{(A-i B) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1)}","\frac{(A+i B) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (m+1)}+\frac{(A-i B) \tan ^{m+1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (m+1)}",1,"((A + I*B)*AppellF1[1 + m, -n, 1, 2 + m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x])^n)/(2*d*(1 + m)*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[1 + m, -n, 1, 2 + m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Tan[c + d*x]^(1 + m)*(a + b*Tan[c + d*x])^n)/(2*d*(1 + m)*(1 + (b*Tan[c + d*x])/a)^n)","A",7,4,31,0.1290,1,"{3603, 3602, 135, 133}"
494,1,385,0,1.0510746,"\int \tan ^4(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^4*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{\left(-2 a^2 A b (n+4)+6 a^3 B-a b^2 B (n+3) (n+4)+A b^3 (n+2) (n+3) (n+4)\right) (a+b \tan (c+d x))^{n+1}}{b^4 d (n+1) (n+2) (n+3) (n+4)}+\frac{\tan (c+d x) \left(6 a^2 B-2 a A b (n+4)-b^2 B (n+3) (n+4)\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+2) (n+3) (n+4)}-\frac{\tan ^2(c+d x) (3 a B-A b (n+4)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+3) (n+4)}+\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}+\frac{B \tan ^3(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+4)}","-\frac{\tan ^2(c+d x) (3 a B-A b (n+4)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+3) (n+4)}-\frac{\left(A b^3 (n+2) (n+3) (n+4)-a \left(b^2 B (n+3) (n+4)-2 a (3 a B-A b (n+4))\right)\right) (a+b \tan (c+d x))^{n+1}}{b^4 d (n+1) (n+2) (n+3) (n+4)}-\frac{\tan (c+d x) \left(b^2 B (n+3) (n+4)-2 a (3 a B-A b (n+4))\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+2) (n+3) (n+4)}+\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}+\frac{B \tan ^3(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+4)}",1,"-(((6*a^3*B - 2*a^2*A*b*(4 + n) - a*b^2*B*(3 + n)*(4 + n) + A*b^3*(2 + n)*(3 + n)*(4 + n))*(a + b*Tan[c + d*x])^(1 + n))/(b^4*d*(1 + n)*(2 + n)*(3 + n)*(4 + n))) + ((A - I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) - ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a - b)*d*(1 + n)) + ((6*a^2*B - 2*a*A*b*(4 + n) - b^2*B*(3 + n)*(4 + n))*Tan[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b^3*d*(2 + n)*(3 + n)*(4 + n)) - ((3*a*B - A*b*(4 + n))*Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n))/(b^2*d*(3 + n)*(4 + n)) + (B*Tan[c + d*x]^3*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(4 + n))","A",9,6,31,0.1935,1,"{3607, 3647, 3630, 3539, 3537, 68}"
495,1,289,0,0.5839635,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{\left(2 a^2 B-a A b (n+3)-b^2 B (n+2) (n+3)\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1) (n+2) (n+3)}-\frac{\tan (c+d x) (2 a B-A b (n+3)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+2) (n+3)}+\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}+\frac{B \tan ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+3)}","\frac{\left(2 a^2 B-a A b (n+3)-b^2 B \left(n^2+5 n+6\right)\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1) (n+2) (n+3)}-\frac{\tan (c+d x) (2 a B-A b (n+3)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+2) (n+3)}+\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}+\frac{B \tan ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+3)}",1,"((2*a^2*B - a*A*b*(3 + n) - b^2*B*(2 + n)*(3 + n))*(a + b*Tan[c + d*x])^(1 + n))/(b^3*d*(1 + n)*(2 + n)*(3 + n)) + ((I*A + B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) + ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a + I*b)*d*(1 + n)) - ((2*a*B - A*b*(3 + n))*Tan[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b^2*d*(2 + n)*(3 + n)) + (B*Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(3 + n))","A",8,6,31,0.1935,1,"{3607, 3647, 3630, 3539, 3537, 68}"
496,1,219,0,0.3530106,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{(a B-A b (n+2)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+1) (n+2)}+\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (a-i b)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+2)}","-\frac{(a B-A b (n+2)) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+1) (n+2)}+\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (a-i b)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}+\frac{B \tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+2)}",1,"-(((a*B - A*b*(2 + n))*(a + b*Tan[c + d*x])^(1 + n))/(b^2*d*(1 + n)*(2 + n))) + ((I*A + B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a - I*b)*d*(1 + n)) + ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a - b)*d*(1 + n)) + (B*Tan[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(2 + n))","A",7,5,31,0.1613,1,"{3607, 3630, 3539, 3537, 68}"
497,1,168,0,0.1779362,"\int \tan (c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (a-i b)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}+\frac{B (a+b \tan (c+d x))^{n+1}}{b d (n+1)}","-\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (a-i b)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}+\frac{B (a+b \tan (c+d x))^{n+1}}{b d (n+1)}",1,"(B*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(1 + n)) - ((A - I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a - I*b)*d*(1 + n)) - ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a + I*b)*d*(1 + n))","A",6,4,29,0.1379,1,"{3592, 3539, 3537, 68}"
498,1,143,0,0.1302051,"\int (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(-B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}","\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(-B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}",1,"((A - I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) + ((I*A - B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a + I*b)*d*(1 + n))","A",5,3,23,0.1304,1,"{3539, 3537, 68}"
499,1,190,0,0.2733559,"\int \cot (c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}-\frac{A (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{a d (n+1)}","\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}-\frac{A (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{a d (n+1)}",1,"((I*A + B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) + ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a + I*b)*d*(1 + n)) - (A*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*Tan[c + d*x])/a]*(a + b*Tan[c + d*x])^(1 + n))/(a*d*(1 + n))","A",8,6,29,0.2069,1,"{3613, 3539, 3537, 68, 3634, 65}"
500,1,228,0,0.4473537,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{(a B+A b n) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{a^2 d (n+1)}-\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}-\frac{A \cot (c+d x) (a+b \tan (c+d x))^{n+1}}{a d}","-\frac{(a B+A b n) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{a^2 d (n+1)}-\frac{(A-i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}+\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (-b+i a)}-\frac{A \cot (c+d x) (a+b \tan (c+d x))^{n+1}}{a d}",1,"-((A*Cot[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(a*d)) - ((A - I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) + ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a - b)*d*(1 + n)) - ((a*B + A*b*n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*Tan[c + d*x])/a]*(a + b*Tan[c + d*x])^(1 + n))/(a^2*d*(1 + n))","A",9,7,31,0.2258,1,"{3609, 3653, 3539, 3537, 68, 3634, 65}"
501,1,292,0,0.8056425,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{\left(2 a^2 A-2 a b B n+A b^2 (1-n) n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{2 a^3 d (n+1)}-\frac{\cot (c+d x) (2 a B-A b (1-n)) (a+b \tan (c+d x))^{n+1}}{2 a^2 d}-\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}-\frac{A \cot ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{2 a d}","\frac{\left(2 a^2 A-2 a b B n+A b^2 (1-n) n\right) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b \tan (c+d x)}{a}+1\right)}{2 a^3 d (n+1)}-\frac{\cot (c+d x) (2 a B-A b (1-n)) (a+b \tan (c+d x))^{n+1}}{2 a^2 d}-\frac{(B+i A) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-i b}\right)}{2 d (n+1) (b+i a)}-\frac{(A+i B) (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+i b}\right)}{2 d (n+1) (a+i b)}-\frac{A \cot ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{2 a d}",1,"-((2*a*B - A*b*(1 - n))*Cot[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(2*a^2*d) - (A*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n))/(2*a*d) - ((I*A + B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(I*a + b)*d*(1 + n)) - ((A + I*B)*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + I*b)]*(a + b*Tan[c + d*x])^(1 + n))/(2*(a + I*b)*d*(1 + n)) + ((2*a^2*A - 2*a*b*B*n + A*b^2*(1 - n)*n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*Tan[c + d*x])/a]*(a + b*Tan[c + d*x])^(1 + n))/(2*a^3*d*(1 + n))","A",10,8,31,0.2581,1,"{3609, 3649, 3653, 3539, 3537, 68, 3634, 65}"
502,1,103,0,0.2359645,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{2 a (B+i A) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 a (A-i B) \sqrt{\cot (c+d x)}}{d}+\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x)}{5 d}","-\frac{2 a (B+i A) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 a (A-i B) \sqrt{\cot (c+d x)}}{d}+\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x)}{5 d}",1,"(2*(-1)^(1/4)*a*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (2*a*(A - I*B)*Sqrt[Cot[c + d*x]])/d - (2*a*(I*A + B)*Cot[c + d*x]^(3/2))/(3*d) - (2*a*A*Cot[c + d*x]^(5/2))/(5*d)","A",6,5,34,0.1471,1,"{3581, 3592, 3528, 3533, 208}"
503,1,78,0,0.1916672,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{2 a (B+i A) \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x)}{3 d}","-\frac{2 a (B+i A) \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x)}{3 d}",1,"(-2*(-1)^(1/4)*a*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a*(I*A + B)*Sqrt[Cot[c + d*x]])/d - (2*a*A*Cot[c + d*x]^(3/2))/(3*d)","A",5,5,34,0.1471,1,"{3581, 3592, 3528, 3533, 208}"
504,1,53,0,0.1507647,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{2 a A \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a A \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-2*(-1)^(1/4)*a*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a*A*Sqrt[Cot[c + d*x]])/d","A",4,4,34,0.1176,1,"{3581, 3592, 3533, 208}"
505,1,55,0,0.1515348,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{d \sqrt{\cot (c+d x)}}","\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{d \sqrt{\cot (c+d x)}}",1,"(2*(-1)^(1/4)*a*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + ((2*I)*a*B)/(d*Sqrt[Cot[c + d*x]])","A",4,4,34,0.1176,1,"{3581, 3591, 3533, 208}"
506,1,80,0,0.1876181,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{2 a (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{2 a (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{2 \sqrt[4]{-1} a (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"(2*(-1)^(1/4)*a*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (((2*I)/3)*a*B)/(d*Cot[c + d*x]^(3/2)) + (2*a*(I*A + B))/(d*Sqrt[Cot[c + d*x]])","A",5,5,34,0.1471,1,"{3581, 3591, 3529, 3533, 208}"
507,1,105,0,0.2263743,"\int \frac{(a+i a \tan (c+d x)) (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","\frac{2 a (B+i A)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a (A-i B)}{d \sqrt{\cot (c+d x)}}-\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 a (B+i A)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a (A-i B)}{d \sqrt{\cot (c+d x)}}-\frac{2 \sqrt[4]{-1} a (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"(-2*(-1)^(1/4)*a*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (((2*I)/5)*a*B)/(d*Cot[c + d*x]^(5/2)) + (2*a*(I*A + B))/(3*d*Cot[c + d*x]^(3/2)) + (2*a*(A - I*B))/(d*Sqrt[Cot[c + d*x]])","A",6,5,34,0.1471,1,"{3581, 3591, 3529, 3533, 208}"
508,1,128,0,0.3601646,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (5 B+7 i A) \cot ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{4 a^2 (A-i B) \sqrt{\cot (c+d x)}}{d}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \left(a^2 \cot (c+d x)+i a^2\right)}{5 d}","-\frac{2 a^2 (5 B+7 i A) \cot ^{\frac{3}{2}}(c+d x)}{15 d}+\frac{4 a^2 (A-i B) \sqrt{\cot (c+d x)}}{d}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \left(a^2 \cot (c+d x)+i a^2\right)}{5 d}",1,"(4*(-1)^(1/4)*a^2*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (4*a^2*(A - I*B)*Sqrt[Cot[c + d*x]])/d - (2*a^2*((7*I)*A + 5*B)*Cot[c + d*x]^(3/2))/(15*d) - (2*A*Cot[c + d*x]^(3/2)*(I*a^2 + a^2*Cot[c + d*x]))/(5*d)","A",6,6,36,0.1667,1,"{3581, 3594, 3592, 3528, 3533, 208}"
509,1,103,0,0.3257297,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (3 B+5 i A) \sqrt{\cot (c+d x)}}{3 d}-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \left(a^2 \cot (c+d x)+i a^2\right)}{3 d}","-\frac{2 a^2 (3 B+5 i A) \sqrt{\cot (c+d x)}}{3 d}-\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \left(a^2 \cot (c+d x)+i a^2\right)}{3 d}",1,"(-4*(-1)^(1/4)*a^2*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2*((5*I)*A + 3*B)*Sqrt[Cot[c + d*x]])/(3*d) - (2*A*Sqrt[Cot[c + d*x]]*(I*a^2 + a^2*Cot[c + d*x]))/(3*d)","A",5,5,36,0.1389,1,"{3581, 3594, 3592, 3533, 208}"
510,1,99,0,0.3167394,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (A+i B) \sqrt{\cot (c+d x)}}{d}-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{d \sqrt{\cot (c+d x)}}","-\frac{2 a^2 (A+i B) \sqrt{\cot (c+d x)}}{d}-\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{d \sqrt{\cot (c+d x)}}",1,"(-4*(-1)^(1/4)*a^2*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2*(A + I*B)*Sqrt[Cot[c + d*x]])/d + ((2*I)*B*(I*a^2 + a^2*Cot[c + d*x]))/(d*Sqrt[Cot[c + d*x]])","A",5,5,36,0.1389,1,"{3581, 3593, 3592, 3533, 208}"
511,1,105,0,0.3255419,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (3 A-5 i B)}{3 d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{2 a^2 (3 A-5 i B)}{3 d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"(4*(-1)^(1/4)*a^2*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2*(3*A - (5*I)*B))/(3*d*Sqrt[Cot[c + d*x]]) + (((2*I)/3)*B*(I*a^2 + a^2*Cot[c + d*x]))/(d*Cot[c + d*x]^(3/2))","A",5,5,36,0.1389,1,"{3581, 3593, 3591, 3533, 208}"
512,1,130,0,0.3715074,"\int \frac{(a+i a \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{2 a^2 (5 A-7 i B)}{15 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}","-\frac{2 a^2 (5 A-7 i B)}{15 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{4 a^2 (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i B \left(a^2 \cot (c+d x)+i a^2\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"(4*(-1)^(1/4)*a^2*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2*(5*A - (7*I)*B))/(15*d*Cot[c + d*x]^(3/2)) + (4*a^2*(I*A + B))/(d*Sqrt[Cot[c + d*x]]) + (((2*I)/5)*B*(I*a^2 + a^2*Cot[c + d*x]))/(d*Cot[c + d*x]^(5/2))","A",6,6,36,0.1667,1,"{3581, 3593, 3591, 3529, 3533, 208}"
513,1,171,0,0.5281058,"\int \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{8 a^3 (23 A-21 i B) \cot ^{\frac{3}{2}}(c+d x)}{105 d}-\frac{2 (7 B+11 i A) \cot ^{\frac{3}{2}}(c+d x) \left(a^3 \cot (c+d x)+i a^3\right)}{35 d}+\frac{8 a^3 (B+i A) \sqrt{\cot (c+d x)}}{d}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+i a)^2}{7 d}","\frac{8 a^3 (23 A-21 i B) \cot ^{\frac{3}{2}}(c+d x)}{105 d}-\frac{2 (7 B+11 i A) \cot ^{\frac{3}{2}}(c+d x) \left(a^3 \cot (c+d x)+i a^3\right)}{35 d}+\frac{8 a^3 (B+i A) \sqrt{\cot (c+d x)}}{d}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+i a)^2}{7 d}",1,"(8*(-1)^(1/4)*a^3*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (8*a^3*(I*A + B)*Sqrt[Cot[c + d*x]])/d + (8*a^3*(23*A - (21*I)*B)*Cot[c + d*x]^(3/2))/(105*d) - (2*a*A*Cot[c + d*x]^(3/2)*(I*a + a*Cot[c + d*x])^2)/(7*d) - (2*((11*I)*A + 7*B)*Cot[c + d*x]^(3/2)*(I*a^3 + a^3*Cot[c + d*x]))/(35*d)","A",7,6,36,0.1667,1,"{3581, 3594, 3592, 3528, 3533, 208}"
514,1,146,0,0.488346,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{16 a^3 (6 A-5 i B) \sqrt{\cot (c+d x)}}{15 d}-\frac{2 (5 B+9 i A) \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{15 d}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}{5 d}","\frac{16 a^3 (6 A-5 i B) \sqrt{\cot (c+d x)}}{15 d}-\frac{2 (5 B+9 i A) \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{15 d}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}{5 d}",1,"(8*(-1)^(1/4)*a^3*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (16*a^3*(6*A - (5*I)*B)*Sqrt[Cot[c + d*x]])/(15*d) - (2*a*A*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])^2)/(5*d) - (2*((9*I)*A + 5*B)*Sqrt[Cot[c + d*x]]*(I*a^3 + a^3*Cot[c + d*x]))/(15*d)","A",6,5,36,0.1389,1,"{3581, 3594, 3592, 3533, 208}"
515,1,138,0,0.4574952,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{2 (A+3 i B) \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{3 d}-\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{16 i a^3 A \sqrt{\cot (c+d x)}}{3 d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{d \sqrt{\cot (c+d x)}}","-\frac{2 (A+3 i B) \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{3 d}-\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{16 i a^3 A \sqrt{\cot (c+d x)}}{3 d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{d \sqrt{\cot (c+d x)}}",1,"(-8*(-1)^(1/4)*a^3*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (((16*I)/3)*a^3*A*Sqrt[Cot[c + d*x]])/d + ((2*I)*a*B*(I*a + a*Cot[c + d*x])^2)/(d*Sqrt[Cot[c + d*x]]) - (2*(A + (3*I)*B)*Sqrt[Cot[c + d*x]]*(I*a^3 + a^3*Cot[c + d*x]))/(3*d)","A",6,6,36,0.1667,1,"{3581, 3593, 3594, 3592, 3533, 208}"
516,1,142,0,0.4709699,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{2 (3 A-7 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{3 d \sqrt{\cot (c+d x)}}-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{16 i a^3 B \sqrt{\cot (c+d x)}}{3 d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{2 (3 A-7 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{3 d \sqrt{\cot (c+d x)}}-\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{16 i a^3 B \sqrt{\cot (c+d x)}}{3 d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"(-8*(-1)^(1/4)*a^3*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (((16*I)/3)*a^3*B*Sqrt[Cot[c + d*x]])/d + (((2*I)/3)*a*B*(I*a + a*Cot[c + d*x])^2)/(d*Cot[c + d*x]^(3/2)) - (2*(3*A - (7*I)*B)*(I*a^3 + a^3*Cot[c + d*x]))/(3*d*Sqrt[Cot[c + d*x]])","A",6,5,36,0.1389,1,"{3581, 3593, 3592, 3533, 208}"
517,1,148,0,0.4915508,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{2 (5 A-9 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{15 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{16 a^3 (5 A-6 i B)}{15 d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}","-\frac{2 (5 A-9 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{15 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{16 a^3 (5 A-6 i B)}{15 d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 (B+i A) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"(8*(-1)^(1/4)*a^3*(I*A + B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (16*a^3*(5*A - (6*I)*B))/(15*d*Sqrt[Cot[c + d*x]]) + (((2*I)/5)*a*B*(I*a + a*Cot[c + d*x])^2)/(d*Cot[c + d*x]^(5/2)) - (2*(5*A - (9*I)*B)*(I*a^3 + a^3*Cot[c + d*x]))/(15*d*Cot[c + d*x]^(3/2))","A",6,5,36,0.1389,1,"{3581, 3593, 3591, 3533, 208}"
518,1,173,0,0.5422783,"\int \frac{(a+i a \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{8 a^3 (21 A-23 i B)}{105 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 A-11 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{35 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 a^3 (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}","-\frac{8 a^3 (21 A-23 i B)}{105 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 (7 A-11 i B) \left(a^3 \cot (c+d x)+i a^3\right)}{35 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 a^3 (B+i A)}{d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 (A-i B) \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a B (a \cot (c+d x)+i a)^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}",1,"(8*(-1)^(1/4)*a^3*(A - I*B)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (8*a^3*(21*A - (23*I)*B))/(105*d*Cot[c + d*x]^(3/2)) + (8*a^3*(I*A + B))/(d*Sqrt[Cot[c + d*x]]) + (((2*I)/7)*a*B*(I*a + a*Cot[c + d*x])^2)/(d*Cot[c + d*x]^(7/2)) - (2*(7*A - (11*I)*B)*(I*a^3 + a^3*Cot[c + d*x]))/(35*d*Cot[c + d*x]^(5/2))","A",7,6,36,0.1667,1,"{3581, 3593, 3591, 3529, 3533, 208}"
519,1,297,0,0.5175929,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{(7 A+3 i B) \cot ^{\frac{3}{2}}(c+d x)}{6 a d}+\frac{5 (-B+i A) \sqrt{\cot (c+d x)}}{2 a d}+\frac{((7+5 i) A-(5-3 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((5-3 i) B-(7+5 i) A) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) ((6+i) A+(1+4 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}+\frac{((7-5 i) A+(5+3 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{4 \sqrt{2} a d}","\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{(7 A+3 i B) \cot ^{\frac{3}{2}}(c+d x)}{6 a d}+\frac{5 (-B+i A) \sqrt{\cot (c+d x)}}{2 a d}+\frac{((7+5 i) A-(5-3 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((5-3 i) B-(7+5 i) A) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) ((6+i) A+(1+4 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}+\frac{((7-5 i) A+(5+3 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{4 \sqrt{2} a d}",1,"((-1/4 + I/4)*((6 + I)*A + (1 + 4*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) + (((7 - 5*I)*A + (5 + 3*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(4*Sqrt[2]*a*d) + (5*(I*A - B)*Sqrt[Cot[c + d*x]])/(2*a*d) - ((7*A + (3*I)*B)*Cot[c + d*x]^(3/2))/(6*a*d) + ((A + I*B)*Cot[c + d*x]^(5/2))/(2*d*(I*a + a*Cot[c + d*x])) + (((7 + 5*I)*A - (5 - 3*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d) + (((-7 - 5*I)*A + (5 - 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d)","A",14,10,36,0.2778,1,"{3581, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
520,1,268,0,0.4591418,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{(5 A+i B) \sqrt{\cot (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) ((4+i) A+(1+2 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((5-3 i) A+(3+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3-i) B-(5+3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{((5+3 i) A-(3-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{4 \sqrt{2} a d}","\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{(5 A+i B) \sqrt{\cot (c+d x)}}{2 a d}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) ((4+i) A+(1+2 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((5-3 i) A+(3+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3-i) B-(5+3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{((5+3 i) A-(3-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{4 \sqrt{2} a d}",1,"(((-5 - 3*I)*A + (3 - I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(4*Sqrt[2]*a*d) + (((5 + 3*I)*A - (3 - I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(4*Sqrt[2]*a*d) - ((5*A + I*B)*Sqrt[Cot[c + d*x]])/(2*a*d) + ((A + I*B)*Cot[c + d*x]^(3/2))/(2*d*(I*a + a*Cot[c + d*x])) - ((1/8 - I/8)*((4 + I)*A + (1 + 2*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) + (((5 - 3*I)*A + (3 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d)","A",13,10,36,0.2778,1,"{3581, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
521,1,235,0,0.3785196,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{a+i a \tan (c+d x)} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x]),x]","\frac{(A+i B) \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{((3+i) A-(1+i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3+i) A-(1+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{(A+i B) \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{((3+i) A-(1+i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{((3+i) A-(1+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (B+(2+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((1/4 - I/4)*((2 + I)*A + B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((1/4 - I/4)*((2 + I)*A + B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(2*d*(I*a + a*Cot[c + d*x])) - (((3 + I)*A - (1 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d) + (((3 + I)*A - (1 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d)","A",12,9,36,0.2500,1,"{3581, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
522,1,237,0,0.3903934,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])),x]","\frac{(-B+i A) \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{(-B+i A) \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-(2+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A+(2-i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((1/4 - I/4)*(A + (2 - I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((1/4 - I/4)*(A + (2 - I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) + ((I*A - B)*Sqrt[Cot[c + d*x]])/(2*d*(I*a + a*Cot[c + d*x])) + ((1/8 + I/8)*(A - (2 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) - ((1/8 + I/8)*(A - (2 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",12,9,36,0.2500,1,"{3581, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
523,1,276,0,0.4565151,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])),x]","\frac{-B+i A}{2 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)}-\frac{A+5 i B}{2 a d \sqrt{\cot (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((1-3 i) A+(3+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((1+2 i) A-(4+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{-B+i A}{2 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)}-\frac{A+5 i B}{2 a d \sqrt{\cot (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((2+i) A+(1+4 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{((1-3 i) A+(3+5 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{4 \sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((1+2 i) A-(4+i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"(((1 - 3*I)*A + (3 + 5*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(4*Sqrt[2]*a*d) + ((1/4 + I/4)*((1 + 2*I)*A - (4 + I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - (A + (5*I)*B)/(2*a*d*Sqrt[Cot[c + d*x]]) + (I*A - B)/(2*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])) - ((1/8 + I/8)*((2 + I)*A + (1 + 4*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) + ((1/8 + I/8)*((2 + I)*A + (1 + 4*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",13,10,36,0.2778,1,"{3581, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
524,1,307,0,0.5131839,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])),x]","\frac{-B+i A}{2 d \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+i a)}-\frac{3 A+7 i B}{6 a d \cot ^{\frac{3}{2}}(c+d x)}-\frac{5 (-B+i A)}{2 a d \sqrt{\cot (c+d x)}}+\frac{((3-5 i) A+(5+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((1+4 i) A-(6+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{-B+i A}{2 d \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+i a)}-\frac{3 A+7 i B}{6 a d \cot ^{\frac{3}{2}}(c+d x)}-\frac{5 (-B+i A)}{2 a d \sqrt{\cot (c+d x)}}+\frac{((3-5 i) A+(5+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a d}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) ((1+4 i) A-(6+i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) ((4+i) A+(1+6 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((1/4 + I/4)*((4 + I)*A + (1 + 6*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((1/4 + I/4)*((4 + I)*A + (1 + 6*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - (3*A + (7*I)*B)/(6*a*d*Cot[c + d*x]^(3/2)) - (5*(I*A - B))/(2*a*d*Sqrt[Cot[c + d*x]]) + (I*A - B)/(2*d*Cot[c + d*x]^(3/2)*(I*a + a*Cot[c + d*x])) + (((3 - 5*I)*A + (5 + 7*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(8*Sqrt[2]*a*d) + ((1/8 + I/8)*((1 + 4*I)*A - (6 + I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",14,10,36,0.2778,1,"{3581, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
525,1,317,0,0.6849938,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{(7 A+3 i B) \cot ^{\frac{3}{2}}(c+d x)}{8 a^2 d (\cot (c+d x)+i)}-\frac{5 (5 A+i B) \sqrt{\cot (c+d x)}}{8 a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+23 i) A-(7+2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((25+21 i) A-(9-5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}","\frac{(7 A+3 i B) \cot ^{\frac{3}{2}}(c+d x)}{8 a^2 d (\cot (c+d x)+i)}-\frac{5 (5 A+i B) \sqrt{\cot (c+d x)}}{8 a^2 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((23+2 i) A+(2+7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+23 i) A-(7+2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((25+21 i) A-(9-5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}",1,"((-1/16 + I/16)*((2 + 23*I)*A - (7 + 2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (((25 + 21*I)*A - (9 - 5*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) - (5*(5*A + I*B)*Sqrt[Cot[c + d*x]])/(8*a^2*d) + ((7*A + (3*I)*B)*Cot[c + d*x]^(3/2))/(8*a^2*d*(I + Cot[c + d*x])) + ((A + I*B)*Cot[c + d*x]^(5/2))/(4*d*(I*a + a*Cot[c + d*x])^2) - ((1/32 - I/32)*((23 + 2*I)*A + (2 + 7*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((1/32 - I/32)*((23 + 2*I)*A + (2 + 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",14,10,36,0.2778,1,"{3581, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
526,1,284,0,0.61032,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^2} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^2,x]","\frac{(5 A+i B) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((2+i) B-(7-2 i) A) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(1+3 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{((9-5 i) A+(1-3 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^2 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+2 i) B-(2-7 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}","\frac{(5 A+i B) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((2+i) B-(7-2 i) A) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(1+3 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{((9-5 i) A+(1-3 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^2 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+2 i) B-(2-7 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}",1,"(((9 - 5*I)*A + (1 - 3*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) + ((1/16 + I/16)*((-2 + 7*I)*A + (1 + 2*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + ((5*A + I*B)*Sqrt[Cot[c + d*x]])/(8*a^2*d*(I + Cot[c + d*x])) + ((A + I*B)*Cot[c + d*x]^(3/2))/(4*d*(I*a + a*Cot[c + d*x])^2) + ((1/32 + I/32)*((-7 + 2*I)*A + (2 + I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + (((9 + 5*I)*A - (1 + 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^2*d)","A",13,9,36,0.2500,1,"{3581, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
527,1,274,0,0.5759726,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^2),x]","\frac{(B+3 i A) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{((1+3 i) A+(1-3 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(1-3 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^2 d}+\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}","\frac{(B+3 i A) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{((1+3 i) A+(1-3 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) A+(1-3 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}-\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^2 d}+\frac{((1+3 i) B-(1-3 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}",1,"-(((-1 + 3*I)*A + (1 + 3*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) + (((-1 + 3*I)*A + (1 + 3*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) + (((3*I)*A + B)*Sqrt[Cot[c + d*x]])/(8*a^2*d*(I + Cot[c + d*x])) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(4*d*(I*a + a*Cot[c + d*x])^2) + (((1 + 3*I)*A + (1 - 3*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^2*d) - (((1 + 3*I)*A + (1 - 3*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^2*d)","A",13,10,36,0.2778,1,"{3581, 3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
528,1,284,0,0.6009841,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{(A+5 i B) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{((1-3 i) A-(9-5 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((1+2 i) A+(2-7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((2+i) A+(7-2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(-B+i A) \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}","\frac{(A+5 i B) \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{((1-3 i) A-(9-5 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((1+2 i) A+(2-7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((2+i) A+(7-2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((1+3 i) A+(9+5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{(-B+i A) \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}",1,"((-1/16 - I/16)*((2 + I)*A + (7 - 2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (((1 + 3*I)*A + (9 + 5*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) + ((A + (5*I)*B)*Sqrt[Cot[c + d*x]])/(8*a^2*d*(I + Cot[c + d*x])) + ((I*A - B)*Sqrt[Cot[c + d*x]])/(4*d*(I*a + a*Cot[c + d*x])^2) + (((1 - 3*I)*A - (9 - 5*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^2*d) + ((1/32 + I/32)*((1 + 2*I)*A + (2 - 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",13,9,36,0.2500,1,"{3581, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
529,1,319,0,0.6802884,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{5 (-5 B+i A)}{8 a^2 d \sqrt{\cot (c+d x)}}+\frac{3 A+7 i B}{8 a^2 d \sqrt{\cot (c+d x)} (\cot (c+d x)+i)}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+7 i) A-(23+2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{-B+i A}{4 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}","\frac{5 (-5 B+i A)}{8 a^2 d \sqrt{\cot (c+d x)}}+\frac{3 A+7 i B}{8 a^2 d \sqrt{\cot (c+d x)} (\cot (c+d x)+i)}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((7+2 i) A+(2+23 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((2+7 i) A-(23+2 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{((9+5 i) A-(25-21 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^2 d}+\frac{-B+i A}{4 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}",1,"((-1/16 + I/16)*((2 + 7*I)*A - (23 + 2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (((9 + 5*I)*A - (25 - 21*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^2*d) + (5*(I*A - 5*B))/(8*a^2*d*Sqrt[Cot[c + d*x]]) + (3*A + (7*I)*B)/(8*a^2*d*Sqrt[Cot[c + d*x]]*(I + Cot[c + d*x])) + (I*A - B)/(4*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])^2) - ((1/32 - I/32)*((7 + 2*I)*A + (2 + 23*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((1/32 - I/32)*((7 + 2*I)*A + (2 + 23*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",14,10,36,0.2778,1,"{3581, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
530,1,367,0,0.918336,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","\frac{7 (4 A+i B) \cot ^{\frac{3}{2}}(c+d x)}{24 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{5 (6 A+i B) \sqrt{\cot (c+d x)}}{8 a^3 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((1+29 i) A-(6+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{((30+28 i) A-(7-5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{(A+i B) \cot ^{\frac{7}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{(5 A+2 i B) \cot ^{\frac{5}{2}}(c+d x)}{12 a d (a \cot (c+d x)+i a)^2}","\frac{7 (4 A+i B) \cot ^{\frac{3}{2}}(c+d x)}{24 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{5 (6 A+i B) \sqrt{\cot (c+d x)}}{8 a^3 d}-\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{32}-\frac{i}{32}\right) ((29+i) A+(1+6 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}-\frac{i}{16}\right) ((1+29 i) A-(6+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{((30+28 i) A-(7-5 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{(A+i B) \cot ^{\frac{7}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{(5 A+2 i B) \cot ^{\frac{5}{2}}(c+d x)}{12 a d (a \cot (c+d x)+i a)^2}",1,"((-1/16 + I/16)*((1 + 29*I)*A - (6 + I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + (((30 + 28*I)*A - (7 - 5*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) - (5*(6*A + I*B)*Sqrt[Cot[c + d*x]])/(8*a^3*d) + ((A + I*B)*Cot[c + d*x]^(7/2))/(6*d*(I*a + a*Cot[c + d*x])^3) + ((5*A + (2*I)*B)*Cot[c + d*x]^(5/2))/(12*a*d*(I*a + a*Cot[c + d*x])^2) + (7*(4*A + I*B)*Cot[c + d*x]^(3/2))/(24*d*(I*a^3 + a^3*Cot[c + d*x])) - ((1/32 - I/32)*((29 + I)*A + (1 + 6*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d) + ((1/32 - I/32)*((29 + I)*A + (1 + 6*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d)","A",15,10,36,0.2778,1,"{3581, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
531,1,318,0,0.7748285,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^3} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^3,x]","-\frac{((7+5 i) A-2 i B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{((7+5 i) A-2 i B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i B-(7-5 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 i B-(7-5 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 A \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{(4 A+i B) \cot ^{\frac{3}{2}}(c+d x)}{12 a d (a \cot (c+d x)+i a)^2}","-\frac{((7+5 i) A-2 i B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{((7+5 i) A-2 i B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i B-(7-5 i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 i B-(7-5 i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 A \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(A+i B) \cot ^{\frac{5}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{(4 A+i B) \cot ^{\frac{3}{2}}(c+d x)}{12 a d (a \cot (c+d x)+i a)^2}",1,"-(((-7 + 5*I)*A + (2*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + (((-7 + 5*I)*A + (2*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + ((A + I*B)*Cot[c + d*x]^(5/2))/(6*d*(I*a + a*Cot[c + d*x])^3) + ((4*A + I*B)*Cot[c + d*x]^(3/2))/(12*a*d*(I*a + a*Cot[c + d*x])^2) + (5*A*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) - (((7 + 5*I)*A - (2*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d) + (((7 + 5*I)*A - (2*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d)","A",14,9,36,0.2500,1,"{3581, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
532,1,316,0,0.7613678,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^3),x]","\frac{(B+2 i A) \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(2 i A+(1-i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i A+(1-i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{A \sqrt{\cot (c+d x)}}{4 a d (a \cot (c+d x)+i a)^2}","\frac{(B+2 i A) \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(2 i A+(1-i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 i A+(1-i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) (B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{A \sqrt{\cot (c+d x)}}{4 a d (a \cot (c+d x)+i a)^2}",1,"((-1/16 - I/16)*((1 + I)*A + B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + ((1/16 + I/16)*((1 + I)*A + B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + ((A + I*B)*Cot[c + d*x]^(3/2))/(6*d*(I*a + a*Cot[c + d*x])^3) + (A*Sqrt[Cot[c + d*x]])/(4*a*d*(I*a + a*Cot[c + d*x])^2) + (((2*I)*A + B)*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) + (((2*I)*A + (1 - I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d) - (((2*I)*A + (1 - I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d)","A",14,10,36,0.2778,1,"{3581, 3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
533,1,308,0,0.7252256,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3),x]","-\frac{(2 B-(1-i) A) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 B-(1-i) A) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{A \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(B+2 i A) \sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}","-\frac{(2 B-(1-i) A) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 B-(1-i) A) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 B+(1+i) A) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 B+(1+i) A) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{A \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(B+2 i A) \sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}",1,"-(((1 + I)*A + 2*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + (((1 + I)*A + 2*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(6*d*(I*a + a*Cot[c + d*x])^3) + (((2*I)*A + B)*Sqrt[Cot[c + d*x]])/(12*a*d*(I*a + a*Cot[c + d*x])^2) + (A*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) - (((-1 + I)*A + 2*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d) + (((-1 + I)*A + 2*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d)","A",14,10,36,0.2778,1,"{3581, 3595, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
534,1,310,0,0.7568258,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^3),x]","-\frac{(2 A-(5+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 A-(5+7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 B \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(-B+i A) \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}+\frac{(A+4 i B) \sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}","-\frac{(2 A-(5+7 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}+\frac{(2 A-(5+7 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{32 \sqrt{2} a^3 d}-\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{16 \sqrt{2} a^3 d}+\frac{(2 A+(5-7 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{5 B \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{(-B+i A) \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}+\frac{(A+4 i B) \sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}",1,"-((2*A + (5 - 7*I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + ((2*A + (5 - 7*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + ((I*A - B)*Sqrt[Cot[c + d*x]])/(6*d*(I*a + a*Cot[c + d*x])^3) + ((A + (4*I)*B)*Sqrt[Cot[c + d*x]])/(12*a*d*(I*a + a*Cot[c + d*x])^2) + (5*B*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) - ((2*A - (5 + 7*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d) + ((2*A - (5 + 7*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(32*Sqrt[2]*a^3*d)","A",14,9,36,0.2500,1,"{3581, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
535,1,367,0,0.9255659,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^3),x]","-\frac{7 (-4 B+i A)}{24 d \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{5 (A+6 i B)}{8 a^3 d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+6 i) A-(29+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{((5-7 i) A+(28+30 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{2 A+5 i B}{12 a d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}+\frac{-B+i A}{6 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^3}","-\frac{7 (-4 B+i A)}{24 d \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{5 (A+6 i B)}{8 a^3 d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{1}{32}+\frac{i}{32}\right) ((6+i) A+(1+29 i) B) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{1}{16}+\frac{i}{16}\right) ((1+6 i) A-(29+i) B) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{((5-7 i) A+(28+30 i) B) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{2 A+5 i B}{12 a d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}+\frac{-B+i A}{6 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^3}",1,"((1/16 + I/16)*((1 + 6*I)*A - (29 + I)*B)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + (((5 - 7*I)*A + (28 + 30*I)*B)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(16*Sqrt[2]*a^3*d) + (5*(A + (6*I)*B))/(8*a^3*d*Sqrt[Cot[c + d*x]]) + (I*A - B)/(6*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])^3) + (2*A + (5*I)*B)/(12*a*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])^2) - (7*(I*A - 4*B))/(24*d*Sqrt[Cot[c + d*x]]*(I*a^3 + a^3*Cot[c + d*x])) + ((1/32 + I/32)*((6 + I)*A + (1 + 29*I)*B)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d) - ((1/32 + I/32)*((6 + I)*A + (1 + 29*I)*B)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d)","A",15,10,36,0.2778,1,"{3581, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
536,1,198,0,0.6680293,"\int \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{2 (5 B+i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 (13 A-5 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}","-\frac{2 (5 B+i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 (13 A-5 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}",1,"((-1 - I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(13*A - (5*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*(I*A + 5*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*A*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(5*d)","A",7,5,38,0.1316,1,"{4241, 3598, 12, 3544, 205}"
537,1,155,0,0.4797587,"\int \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{2 (3 B+i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{(1+i) \sqrt{a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","-\frac{2 (3 B+i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{(1+i) \sqrt{a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"((1 + I)*Sqrt[a]*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(I*A + 3*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(3*d) - (2*A*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",6,5,38,0.1316,1,"{4241, 3598, 12, 3544, 205}"
538,1,110,0,0.314343,"\int \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"((1 + I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*A*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",5,5,38,0.1316,1,"{4241, 3598, 12, 3544, 205}"
539,1,152,0,0.4584746,"\int \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{(1-i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 (-1)^{3/4} \sqrt{a} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","\frac{(1-i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 (-1)^{3/4} \sqrt{a} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-2*(-1)^(3/4)*Sqrt[a]*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((1 - I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d","A",8,8,38,0.2105,1,"{4241, 3601, 3544, 205, 3599, 63, 217, 203}"
540,1,192,0,0.6144323,"\int \frac{\sqrt{a+i a \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[(Sqrt[a + I*a*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{(-1)^{3/4} \sqrt{a} (2 A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}","-\frac{(-1)^{3/4} \sqrt{a} (2 A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{(1+i) \sqrt{a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}",1,"-(((-1)^(3/4)*Sqrt[a]*(2*A - I*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) - ((1 + I)*Sqrt[a]*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (B*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",9,9,38,0.2368,1,"{4241, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
541,1,245,0,0.8936196,"\int \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(2-2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (7 B+8 i A) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{4 a (19 A-21 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 a (63 B+67 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}","\frac{(2-2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (7 B+8 i A) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{4 a (19 A-21 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 a (63 B+67 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}",1,"((2 - 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (4*a*((67*I)*A + 63*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) + (4*a*(19*A - (21*I)*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) - (2*a*((8*I)*A + 7*B)*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) - (2*a*A*Cot[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]])/(7*d)","A",8,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
542,1,201,0,0.7102949,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (5 B+6 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{4 a (9 A-10 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}","-\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (5 B+6 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{4 a (9 A-10 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}",1,"((-2 - 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (4*a*(9*A - (10*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*a*((6*I)*A + 5*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*a*A*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(5*d)","A",7,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
543,1,157,0,0.511212,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(2+2 i) a^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (3 B+4 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}","\frac{(2+2 i) a^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a (3 B+4 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}",1,"((2 + 2*I)*a^(3/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*a*((4*I)*A + 3*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(3*d) - (2*a*A*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",6,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
544,1,186,0,0.6337728,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt[4]{-1} a^{3/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt[4]{-1} a^{3/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"(2*(-1)^(1/4)*a^(3/2)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((2 + 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*a*A*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",9,9,38,0.2368,1,"{4241, 3593, 3601, 3544, 205, 3599, 63, 217, 203}"
545,1,196,0,0.6539572,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-1)^{3/4} a^{3/2} (3 B+2 i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{(2-2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}","-\frac{(-1)^{3/4} a^{3/2} (3 B+2 i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{(2-2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}",1,"-(((-1)^(3/4)*a^(3/2)*((2*I)*A + 3*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + ((2 - 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (I*a*B*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",9,9,38,0.2368,1,"{4241, 3594, 3601, 3544, 205, 3599, 63, 217, 203}"
546,1,244,0,0.8577986,"\int \frac{(a+i a \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{(-1)^{3/4} a^{3/2} (12 A-11 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (5 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{i a B \sqrt{a+i a \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{(-1)^{3/4} a^{3/2} (12 A-11 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{(2+2 i) a^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a (5 B+4 i A) \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{i a B \sqrt{a+i a \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}",1,"-((-1)^(3/4)*a^(3/2)*(12*A - (11*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(4*d) - ((2 + 2*I)*a^(3/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((I/2)*a*B*Sqrt[a + I*a*Tan[c + d*x]])/(d*Cot[c + d*x]^(3/2)) + (a*((4*I)*A + 5*B)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]])","A",10,10,38,0.2632,1,"{4241, 3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
547,1,297,0,1.1288011,"\int \cot ^{\frac{11}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(11/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (3 B+4 i A) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 a^2 (46 A-45 i B) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{8 a^2 (60 B+59 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{315 d}-\frac{8 a^2 (197 A-195 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{315 d}+\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}","-\frac{2 a^2 (3 B+4 i A) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{2 a^2 (46 A-45 i B) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{8 a^2 (60 B+59 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{315 d}-\frac{8 a^2 (197 A-195 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{315 d}+\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{9 d}",1,"((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (8*a^2*(197*A - (195*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(315*d) + (8*a^2*((59*I)*A + 60*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(315*d) + (2*a^2*(46*A - (45*I)*B)*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) - (2*a^2*((4*I)*A + 3*B)*Cot[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]])/(21*d) - (2*a*A*Cot[c + d*x]^(9/2)*(a + I*a*Tan[c + d*x])^(3/2))/(9*d)","A",9,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
548,1,251,0,0.9460503,"\int \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (7 B+10 i A) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{2 a^2 (80 A-77 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 a^2 (133 B+130 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{(4-4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{7 d}","-\frac{2 a^2 (7 B+10 i A) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{2 a^2 (80 A-77 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 a^2 (133 B+130 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{(4-4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{7 d}",1,"((4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (4*a^2*((130*I)*A + 133*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) + (2*a^2*(80*A - (77*I)*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) - (2*a^2*((10*I)*A + 7*B)*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) - (2*a*A*Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(3/2))/(7*d)","A",8,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
549,1,205,0,0.7358294,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (5 B+8 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 a^2 (38 A-35 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}","-\frac{2 a^2 (5 B+8 i A) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{2 a^2 (38 A-35 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{5 d}",1,"((-4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*a^2*(38*A - (35*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*a^2*((8*I)*A + 5*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (2*a*A*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2))/(5*d)","A",7,6,38,0.1579,1,"{4241, 3593, 3598, 12, 3544, 205}"
550,1,230,0,0.8287886,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{2 a^2 (B+2 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{2 a^2 (B+2 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{2 (-1)^{3/4} a^{5/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(2*(-1)^(3/4)*a^(5/2)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((4 + 4*I)*a^(5/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*a^2*((2*I)*A + B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*a*A*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",10,9,38,0.2368,1,"{4241, 3593, 3601, 3544, 205, 3599, 63, 217, 203}"
551,1,236,0,0.8572089,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{(-1)^{3/4} a^{5/2} (2 A-5 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a^2 (-B+2 i A) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}{d}","\frac{(-1)^{3/4} a^{5/2} (2 A-5 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{a^2 (-B+2 i A) \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}{d}",1,"((-1)^(3/4)*a^(5/2)*(2*A - (5*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (a^2*((2*I)*A - B)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]]) - (2*a*A*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2))/d","A",10,10,38,0.2632,1,"{4241, 3593, 3594, 3601, 3544, 205, 3599, 63, 217, 203}"
552,1,246,0,0.8819141,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-1)^{3/4} a^{5/2} (23 B+20 i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{a^2 (4 A-7 i B) \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(4-4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B (a+i a \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}","-\frac{(-1)^{3/4} a^{5/2} (23 B+20 i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 d}-\frac{a^2 (4 A-7 i B) \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(4-4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B (a+i a \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}",1,"-((-1)^(3/4)*a^(5/2)*((20*I)*A + 23*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(4*d) + ((4 - 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (a^2*(4*A - (7*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]]) + ((I/2)*a*B*(a + I*a*Tan[c + d*x])^(3/2))/(d*Sqrt[Cot[c + d*x]])","A",10,9,38,0.2368,1,"{4241, 3594, 3601, 3544, 205, 3599, 63, 217, 203}"
553,1,292,0,1.0864128,"\int \frac{(a+i a \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{a^2 (2 A-3 i B) \sqrt{a+i a \tan (c+d x)}}{4 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{(-1)^{3/4} a^{5/2} (46 A-45 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}+\frac{a^2 (19 B+18 i A) \sqrt{a+i a \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}-\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B (a+i a \tan (c+d x))^{3/2}}{3 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{a^2 (2 A-3 i B) \sqrt{a+i a \tan (c+d x)}}{4 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{(-1)^{3/4} a^{5/2} (46 A-45 i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{8 d}+\frac{a^2 (19 B+18 i A) \sqrt{a+i a \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}-\frac{(4+4 i) a^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{i a B (a+i a \tan (c+d x))^{3/2}}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"-((-1)^(3/4)*a^(5/2)*(46*A - (45*I)*B)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(8*d) - ((4 + 4*I)*a^(5/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (a^2*(2*A - (3*I)*B)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d*Cot[c + d*x]^(3/2)) + (a^2*((18*I)*A + 19*B)*Sqrt[a + I*a*Tan[c + d*x]])/(8*d*Sqrt[Cot[c + d*x]]) + ((I/3)*a*B*(a + I*a*Tan[c + d*x])^(3/2))/(d*Cot[c + d*x]^(3/2))","A",11,10,38,0.2632,1,"{4241, 3594, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
554,1,211,0,0.6969778,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{(5 A+3 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-9 B+7 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","-\frac{(5 A+3 i B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{(A+i B) \cot ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{(-9 B+7 i A) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 + I/2)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[a]*d) + ((A + I*B)*Cot[c + d*x]^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((7*I)*A - 9*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d) - ((5*A + (3*I)*B)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d)","A",7,6,38,0.1579,1,"{4241, 3596, 3598, 12, 3544, 205}"
555,1,163,0,0.4958126,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(A+i B) \sqrt{\cot (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(3 A+i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{(A+i B) \sqrt{\cot (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(3 A+i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 + I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[a]*d) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((3*A + I*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",6,6,38,0.1579,1,"{4241, 3596, 3598, 12, 3544, 205}"
556,1,119,0,0.3212068,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{A+i B}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{A+i B}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"((1/2 - I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[a]*d) + (A + I*B)/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,38,0.1316,1,"{4241, 3596, 12, 3544, 205}"
557,1,196,0,0.6145834,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{-B+i A}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{2 \sqrt[4]{-1} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}","\frac{-B+i A}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}-\frac{2 \sqrt[4]{-1} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{\sqrt{a} d}",1,"(-2*(-1)^(1/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[a]*d) - ((1/2 + I/2)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[a]*d) + (I*A - B)/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",9,9,38,0.2368,1,"{4241, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
558,1,214,0,0.725347,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{(25 A+7 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{6 a^2 d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(11 A+5 i B) \sqrt{\cot (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{(25 A+7 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{6 a^2 d}+\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{(11 A+5 i B) \sqrt{\cot (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"((1/4 + I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(3/2)*d) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((11*A + (5*I)*B)*Sqrt[Cot[c + d*x]])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - ((25*A + (7*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d)","A",7,6,38,0.1579,1,"{4241, 3596, 3598, 12, 3544, 205}"
559,1,168,0,0.5312704,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{7 A+i B}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{A+i B}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{7 A+i B}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((1/4 - I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(3/2)*d) + (A + I*B)/(3*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (7*A + I*B)/(6*a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,38,0.1316,1,"{4241, 3596, 12, 3544, 205}"
560,1,170,0,0.5318157,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{-B+i A}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{5 B+i A}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{-B+i A}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{5 B+i A}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 - I/4)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(3/2)*d) + (I*A - B)/(3*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (I*A + 5*B)/(6*a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",6,6,38,0.1579,1,"{4241, 3595, 3596, 12, 3544, 205}"
561,1,243,0,0.8250997,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{2 (-1)^{3/4} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{-B+i A}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{A+3 i B}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{2 (-1)^{3/4} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{3/2} d}+\frac{-B+i A}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{A+3 i B}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"(2*(-1)^(3/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(3/2)*d) + ((1/4 + I/4)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(3/2)*d) + (I*A - B)/(3*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + (A + (3*I)*B)/(2*a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",10,9,38,0.2368,1,"{4241, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
562,1,260,0,0.96579,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{(317 A+67 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{(151 A+41 i B) \sqrt{\cot (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(17 A+7 i B) \sqrt{\cot (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{(317 A+67 i B) \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{(151 A+41 i B) \sqrt{\cot (c+d x)}}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{(A+i B) \sqrt{\cot (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{(17 A+7 i B) \sqrt{\cot (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 + I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + ((A + I*B)*Sqrt[Cot[c + d*x]])/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((17*A + (7*I)*B)*Sqrt[Cot[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((151*A + (41*I)*B)*Sqrt[Cot[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - ((317*A + (67*I)*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d)","A",8,6,38,0.1579,1,"{4241, 3596, 3598, 12, 3544, 205}"
563,1,214,0,0.7474591,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{67 A-3 i B}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}+\frac{13 A+3 i B}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}","\frac{67 A-3 i B}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+i B}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}+\frac{13 A+3 i B}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 - I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + (A + I*B)/(5*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + (13*A + (3*I)*B)/(30*a*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (67*A - (3*I)*B)/(60*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",7,5,38,0.1316,1,"{4241, 3596, 12, 3544, 205}"
564,1,216,0,0.7471814,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{-13 B+3 i A}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{7 B+3 i A}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{-B+i A}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}","-\frac{-13 B+3 i A}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{7 B+3 i A}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{-B+i A}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 - I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + (I*A - B)/(5*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + ((3*I)*A + 7*B)/(30*a*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) - ((3*I)*A - 13*B)/(60*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",7,6,38,0.1579,1,"{4241, 3595, 3596, 12, 3544, 205}"
565,1,214,0,0.7573655,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{13 A-37 i B}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{-B+i A}{5 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}+\frac{A+11 i B}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}","\frac{13 A-37 i B}{60 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{-B+i A}{5 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}+\frac{A+11 i B}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 + I/8)*(I*A + B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + (I*A - B)/(5*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)) + (A + (11*I)*B)/(30*a*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + (13*A - (37*I)*B)/(60*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",7,6,38,0.1579,1,"{4241, 3595, 3596, 12, 3544, 205}"
566,1,289,0,1.0315981,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{-7 B+i A}{4 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{2 \sqrt[4]{-1} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+3 i B}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{-B+i A}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","-\frac{-7 B+i A}{4 a^2 d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{8}+\frac{i}{8}\right) (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{2 \sqrt[4]{-1} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{a^{5/2} d}+\frac{A+3 i B}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{-B+i A}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"(2*(-1)^(1/4)*B*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + ((1/8 + I/8)*(A - I*B)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(a^(5/2)*d) + (I*A - B)/(5*d*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)) + (A + (3*I)*B)/(6*a*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) - (I*A - 7*B)/(4*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",11,9,38,0.2368,1,"{4241, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
567,1,179,0,0.4289082,"\int \cot ^m(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^m*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A-i B) \cot ^{m-1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1(1-m;1-n,1;2-m;-i \tan (c+d x),i \tan (c+d x))}{d (1-m)}+\frac{i B \cot ^{m-1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1(1-m,1-n;2-m;-i \tan (c+d x))}{d (1-m)}","\frac{(A-i B) \cot ^{m-1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1(1-m;1-n,1;2-m;-i \tan (c+d x),i \tan (c+d x))}{d (1-m)}+\frac{i B \cot ^{m-1}(c+d x) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1(1-m,1-n;2-m;-i \tan (c+d x))}{d (1-m)}",1,"((A - I*B)*AppellF1[1 - m, 1 - n, 1, 2 - m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Cot[c + d*x]^(-1 + m)*(a + I*a*Tan[c + d*x])^n)/(d*(1 - m)*(1 + I*Tan[c + d*x])^n) + (I*B*Cot[c + d*x]^(-1 + m)*Hypergeometric2F1[1 - m, 1 - n, 2 - m, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 - m)*(1 + I*Tan[c + d*x])^n)","A",8,8,34,0.2353,1,"{4241, 3601, 3564, 135, 133, 3599, 66, 64}"
568,1,247,0,0.8267631,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 (1-2 n) (-2 A n+3 i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{3 d \sqrt{\cot (c+d x)}}-\frac{2 (3 B+2 i A n) \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n}{3 d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{3 d}","-\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 (1-2 n) (-2 A n+3 i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{3 d \sqrt{\cot (c+d x)}}-\frac{2 (3 B+2 i A n) \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n}{3 d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n}{3 d}",1,"(-2*(3*B + (2*I)*A*n)*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(3*d) - (2*A*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n)/(3*d) - (2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) - (2*(1 - 2*n)*((3*I)*B - 2*A*n)*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(3*d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",11,10,36,0.2778,1,"{4241, 3598, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
569,1,194,0,0.5933999,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 i A (1-2 n) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 A \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n}{d}","\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 i A (1-2 n) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 A \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n}{d}",1,"(-2*A*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/d + (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) - ((2*I)*A*(1 - 2*n)*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",10,10,36,0.2778,1,"{4241, 3598, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
570,1,158,0,0.3914093,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 i B (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}","\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 i B (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}",1,"(2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) + ((2*I)*B*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",9,9,36,0.2500,1,"{4241, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
571,1,215,0,0.5981588,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","-\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 (2 B n+i A (2 n+1)) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) \sqrt{\cot (c+d x)}}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+1) \sqrt{\cot (c+d x)}}","-\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 (2 B n+i A (2 n+1)) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) \sqrt{\cot (c+d x)}}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+1) \sqrt{\cot (c+d x)}}",1,"(2*B*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*Sqrt[Cot[c + d*x]]) - (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) + (2*(2*B*n + I*A*(1 + 2*n))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",10,10,36,0.2778,1,"{4241, 3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
572,1,291,0,0.8953614,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","-\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 \left(2 A n (2 n+3)-i B \left(4 n^2+6 n+3\right)\right) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\cot (c+d x)}}-\frac{2 (-A (2 n+3)+2 i B n) (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) \sqrt{\cot (c+d x)}}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+3) \cot ^{\frac{3}{2}}(c+d x)}","-\frac{2 (A-i B) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}+\frac{2 \left(2 A n (2 n+3)-i B \left(4 n^2+6 n+3\right)\right) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) \sqrt{\cot (c+d x)}}-\frac{2 (-A (2 n+3)+2 i B n) (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) \sqrt{\cot (c+d x)}}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+3) \cot ^{\frac{3}{2}}(c+d x)}",1,"(2*B*(a + I*a*Tan[c + d*x])^n)/(d*(3 + 2*n)*Cot[c + d*x]^(3/2)) - (2*((2*I)*B*n - A*(3 + 2*n))*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*Sqrt[Cot[c + d*x]]) - (2*(A - I*B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) + (2*(2*A*n*(3 + 2*n) - I*B*(3 + 6*n + 4*n^2))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",11,10,36,0.2778,1,"{4241, 3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
573,1,383,0,1.2637865,"\int \frac{(a+i a \tan (c+d x))^n (A+B \tan (c+d x))}{\cot ^{\frac{5}{2}}(c+d x)} \, dx","Int[((a + I*a*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(5/2),x]","\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 \left(4 B n \left(2 n^2+8 n+9\right)+i A \left(8 n^3+32 n^2+36 n+15\right)\right) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) (2 n+5) \sqrt{\cot (c+d x)}}-\frac{2 \left(B \left(4 n^2+10 n+15\right)+2 i A n (2 n+5)\right) (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) (2 n+5) \sqrt{\cot (c+d x)}}-\frac{2 (-A (2 n+5)+2 i B n) (a+i a \tan (c+d x))^n}{d (2 n+3) (2 n+5) \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+5) \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 (B+i A) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{1}{2};1-n,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\cot (c+d x)}}-\frac{2 \left(4 B n \left(2 n^2+8 n+9\right)+i A \left(8 n^3+32 n^2+36 n+15\right)\right) (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n \, _2F_1\left(\frac{1}{2},1-n;\frac{3}{2};-i \tan (c+d x)\right)}{d (2 n+1) (2 n+3) (2 n+5) \sqrt{\cot (c+d x)}}-\frac{2 \left(B \left(4 n^2+10 n+15\right)+2 i A n (2 n+5)\right) (a+i a \tan (c+d x))^n}{d (2 n+1) (2 n+3) (2 n+5) \sqrt{\cot (c+d x)}}-\frac{2 (-A (2 n+5)+2 i B n) (a+i a \tan (c+d x))^n}{d (2 n+3) (2 n+5) \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 B (a+i a \tan (c+d x))^n}{d (2 n+5) \cot ^{\frac{5}{2}}(c+d x)}",1,"(2*B*(a + I*a*Tan[c + d*x])^n)/(d*(5 + 2*n)*Cot[c + d*x]^(5/2)) - (2*((2*I)*B*n - A*(5 + 2*n))*(a + I*a*Tan[c + d*x])^n)/(d*(3 + 2*n)*(5 + 2*n)*Cot[c + d*x]^(3/2)) - (2*((2*I)*A*n*(5 + 2*n) + B*(15 + 10*n + 4*n^2))*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*Sqrt[Cot[c + d*x]]) + (2*(I*A + B)*AppellF1[1/2, 1 - n, 1, 3/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n) - (2*(4*B*n*(9 + 8*n + 2*n^2) + I*A*(15 + 36*n + 32*n^2 + 8*n^3))*Hypergeometric2F1[1/2, 1 - n, 3/2, (-I)*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*Sqrt[Cot[c + d*x]]*(1 + I*Tan[c + d*x])^n)","A",12,10,36,0.2778,1,"{4241, 3597, 3601, 3564, 130, 430, 429, 3599, 66, 64}"
574,1,229,0,0.300146,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{2 (a B+A b) \sqrt{\cot (c+d x)}}{d}+\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x)}{3 d}","-\frac{2 (a B+A b) \sqrt{\cot (c+d x)}}{d}+\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x)}{3 d}",1,"-(((b*(A - B) + a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((b*(A - B) + a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*(A*b + a*B)*Sqrt[Cot[c + d*x]])/d - (2*a*A*Cot[c + d*x]^(3/2))/(3*d) + ((a*(A - B) - b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,31,0.3226,1,"{3581, 3592, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
575,1,205,0,0.242498,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a A \sqrt{\cot (c+d x)}}{d}","-\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a A \sqrt{\cot (c+d x)}}{d}",1,"-(((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a*A*Sqrt[Cot[c + d*x]])/d - ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,31,0.2903,1,"{3581, 3592, 3534, 1168, 1162, 617, 204, 1165, 628}"
576,1,205,0,0.2416806,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x)) (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]),x]","-\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b B}{d \sqrt{\cot (c+d x)}}","-\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b B}{d \sqrt{\cot (c+d x)}}",1,"((b*(A - B) + a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b*B)/(d*Sqrt[Cot[c + d*x]]) - ((a*(A - B) - b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a*(A - B) - b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,31,0.2903,1,"{3581, 3591, 3534, 1168, 1162, 617, 204, 1165, 628}"
577,1,229,0,0.2833492,"\int \frac{(a+b \tan (c+d x)) (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{2 (a B+A b)}{d \sqrt{\cot (c+d x)}}+\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b B}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{2 (a B+A b)}{d \sqrt{\cot (c+d x)}}+\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a (A+B)+b (A-B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a (A-B)-b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b B}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((a*(A - B) - b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a*(A - B) - b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b*B)/(3*d*Cot[c + d*x]^(3/2)) + (2*(A*b + a*B))/(d*Sqrt[Cot[c + d*x]]) + ((b*(A - B) + a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((b*(A - B) + a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,31,0.3226,1,"{3581, 3591, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
578,1,326,0,0.6139945,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a (5 a B+7 A b) \cot ^{\frac{3}{2}}(c+d x)}{15 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)}{5 d}","\frac{2 \left(a^2 A-2 a b B-A b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a (5 a B+7 A b) \cot ^{\frac{3}{2}}(c+d x)}{15 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)}{5 d}",1,"((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*(a^2*A - A*b^2 - 2*a*b*B)*Sqrt[Cot[c + d*x]])/d - (2*a*(7*A*b + 5*a*B)*Cot[c + d*x]^(3/2))/(15*d) - (2*a*A*Cot[c + d*x]^(3/2)*(b + a*Cot[c + d*x]))/(5*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3607, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
579,1,294,0,0.5459084,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a (3 a B+5 A b) \sqrt{\cot (c+d x)}}{3 d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}{3 d}","\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a (3 a B+5 A b) \sqrt{\cot (c+d x)}}{3 d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}{3 d}",1,"-(((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a*(5*A*b + 3*a*B)*Sqrt[Cot[c + d*x]])/(3*d) - (2*a*A*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x]))/(3*d) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,33,0.3030,1,"{3581, 3607, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
580,1,276,0,0.4428298,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 A \sqrt{\cot (c+d x)}}{d}+\frac{2 b^2 B}{d \sqrt{\cot (c+d x)}}","-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 A \sqrt{\cot (c+d x)}}{d}+\frac{2 b^2 B}{d \sqrt{\cot (c+d x)}}",1,"-(((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*B)/(d*Sqrt[Cot[c + d*x]]) - (2*a^2*A*Sqrt[Cot[c + d*x]])/d - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,33,0.3030,1,"{3581, 3604, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
581,1,283,0,0.433677,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^2 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]),x]","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b (2 a B+A b)}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2 B}{3 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b (2 a B+A b)}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2 B}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*B)/(3*d*Cot[c + d*x]^(3/2)) + (2*b*(A*b + 2*a*B))/(d*Sqrt[Cot[c + d*x]]) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,33,0.3030,1,"{3581, 3604, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
582,1,317,0,0.4887668,"\int \frac{(a+b \tan (c+d x))^2 (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^2*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{2 \left(a^2 B+2 a A b-b^2 B\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b (2 a B+A b)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b^2 B}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(a^2 B+2 a A b-b^2 B\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2 (A+B)+2 a b (A-B)-b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2 (A-B)-2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b (2 a B+A b)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b^2 B}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2*(A - B) - b^2*(A - B) - 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*B)/(5*d*Cot[c + d*x]^(5/2)) + (2*b*(A*b + 2*a*B))/(3*d*Cot[c + d*x]^(3/2)) + (2*(2*a*A*b + a^2*B - b^2*B))/(d*Sqrt[Cot[c + d*x]]) + ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((2*a*b*(A - B) + a^2*(A + B) - b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3604, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
583,1,421,0,0.8617242,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 a \left(7 a^2 A-21 a b B-18 A b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{21 d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \sqrt{\cot (c+d x)}}{d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (7 a B+11 A b) \cot ^{\frac{5}{2}}(c+d x)}{35 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)^2}{7 d}","\frac{2 a \left(7 a^2 A-21 a b B-18 A b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{21 d}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right) \sqrt{\cot (c+d x)}}{d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (7 a B+11 A b) \cot ^{\frac{5}{2}}(c+d x)}{35 d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)^2}{7 d}",1,"((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B)*Sqrt[Cot[c + d*x]])/d + (2*a*(7*a^2*A - 18*A*b^2 - 21*a*b*B)*Cot[c + d*x]^(3/2))/(21*d) - (2*a^2*(11*A*b + 7*a*B)*Cot[c + d*x]^(5/2))/(35*d) - (2*a*A*Cot[c + d*x]^(3/2)*(b + a*Cot[c + d*x])^2)/(7*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,12,33,0.3636,1,"{3581, 3607, 3637, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
584,1,380,0,0.7691565,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 a \left(5 a^2 A-15 a b B-14 A b^2\right) \sqrt{\cot (c+d x)}}{5 d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (5 a B+9 A b) \cot ^{\frac{3}{2}}(c+d x)}{15 d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)^2}{5 d}","\frac{2 a \left(5 a^2 A-15 a b B-14 A b^2\right) \sqrt{\cot (c+d x)}}{5 d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (5 a B+9 A b) \cot ^{\frac{3}{2}}(c+d x)}{15 d}-\frac{2 a A \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)^2}{5 d}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*a*(5*a^2*A - 14*A*b^2 - 15*a*b*B)*Sqrt[Cot[c + d*x]])/(5*d) - (2*a^2*(9*A*b + 5*a*B)*Cot[c + d*x]^(3/2))/(15*d) - (2*a*A*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x])^2)/(5*d) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3607, 3637, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
585,1,374,0,0.7697157,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{2 a \left(a^2 B+3 a A b+2 b^2 B\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (a A+3 b B) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b B (a \cot (c+d x)+b)^2}{d \sqrt{\cot (c+d x)}}","-\frac{2 a \left(a^2 B+3 a A b+2 b^2 B\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (a A+3 b B) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b B (a \cot (c+d x)+b)^2}{d \sqrt{\cot (c+d x)}}",1,"-(((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a*(3*a*A*b + a^2*B + 2*b^2*B)*Sqrt[Cot[c + d*x]])/d - (2*a^2*(a*A + 3*b*B)*Cot[c + d*x]^(3/2))/(3*d) + (2*b*B*(b + a*Cot[c + d*x])^2)/(d*Sqrt[Cot[c + d*x]]) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3605, 3637, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
586,1,372,0,0.6947685,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (3 a A+b B) \sqrt{\cot (c+d x)}}{3 d}+\frac{2 b^2 (7 a B+3 A b)}{3 d \sqrt{\cot (c+d x)}}+\frac{2 b B (a \cot (c+d x)+b)^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}","-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 (3 a A+b B) \sqrt{\cot (c+d x)}}{3 d}+\frac{2 b^2 (7 a B+3 A b)}{3 d \sqrt{\cot (c+d x)}}+\frac{2 b B (a \cot (c+d x)+b)^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*(3*A*b + 7*a*B))/(3*d*Sqrt[Cot[c + d*x]]) - (2*a^2*(3*a*A + b*B)*Sqrt[Cot[c + d*x]])/(3*d) + (2*b*B*(b + a*Cot[c + d*x])^2)/(3*d*Cot[c + d*x]^(3/2)) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3605, 3635, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
587,1,380,0,0.7141319,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]),x]","\frac{2 b \left(14 a^2 B+15 a A b-5 b^2 B\right)}{5 d \sqrt{\cot (c+d x)}}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (9 a B+5 A b)}{15 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b B (a \cot (c+d x)+b)^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 b \left(14 a^2 B+15 a A b-5 b^2 B\right)}{5 d \sqrt{\cot (c+d x)}}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (9 a B+5 A b)}{15 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b B (a \cot (c+d x)+b)^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*(5*A*b + 9*a*B))/(15*d*Cot[c + d*x]^(3/2)) + (2*b*(15*a*A*b + 14*a^2*B - 5*b^2*B))/(5*d*Sqrt[Cot[c + d*x]]) + (2*b*B*(b + a*Cot[c + d*x])^2)/(5*d*Cot[c + d*x]^(5/2)) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,33,0.3333,1,"{3581, 3605, 3635, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
588,1,421,0,0.782665,"\int \frac{(a+b \tan (c+d x))^3 (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^3*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{2 b \left(18 a^2 B+21 a A b-7 b^2 B\right)}{21 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (11 a B+7 A b)}{35 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{2 b B (a \cot (c+d x)+b)^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}","\frac{2 b \left(18 a^2 B+21 a A b-7 b^2 B\right)}{21 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(3 a^2 A b+a^3 B-3 a b^2 B-A b^3\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(3 a^2 b (A-B)+a^3 (A+B)-3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(-3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)+b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (11 a B+7 A b)}{35 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{2 b B (a \cot (c+d x)+b)^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) - 3*a^2*b*(A + B) + b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2*(7*A*b + 11*a*B))/(35*d*Cot[c + d*x]^(5/2)) + (2*b*(21*a*A*b + 18*a^2*B - 7*b^2*B))/(21*d*Cot[c + d*x]^(3/2)) + (2*(3*a^2*A*b - A*b^3 + a^3*B - 3*a*b^2*B))/(d*Sqrt[Cot[c + d*x]]) + (2*b*B*(b + a*Cot[c + d*x])^2)/(7*d*Cot[c + d*x]^(7/2)) + ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((3*a^2*b*(A - B) - b^3*(A - B) + a^3*(A + B) - 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,12,33,0.3636,1,"{3581, 3605, 3635, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
589,1,325,0,1.1291417,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{5/2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B) \sqrt{\cot (c+d x)}}{a^2 d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d}","\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{5/2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B) \sqrt{\cot (c+d x)}}{a^2 d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d}",1,"((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(5/2)*(a^2 + b^2)*d) + (2*(A*b - a*B)*Sqrt[Cot[c + d*x]])/(a^2*d) - (2*A*Cot[c + d*x]^(3/2))/(3*a*d) + ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",17,14,33,0.4242,1,"{3581, 3607, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
590,1,297,0,0.7710077,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{3/2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 A \sqrt{\cot (c+d x)}}{a d}","\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{3/2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 A \sqrt{\cot (c+d x)}}{a d}",1,"-(((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(3/2)*(a^2 + b^2)*d) - (2*A*Sqrt[Cot[c + d*x]])/(a*d) + ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",16,13,33,0.3939,1,"{3581, 3607, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
591,1,278,0,0.4597715,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}","-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{2 \sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} d \left(a^2+b^2\right)}",1,"-(((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*Sqrt[b]*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[a]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,33,0.3636,1,"{3581, 3612, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
592,1,278,0,0.4629795,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])),x]","-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}","-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}",1,"((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*Sqrt[a]*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[b]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,33,0.3636,1,"{3581, 3613, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
593,1,297,0,0.7604637,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B}{b d \sqrt{\cot (c+d x)}}","\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{2 a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d \left(a^2+b^2\right)}+\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 B}{b d \sqrt{\cot (c+d x)}}",1,"((b*(A - B) - a*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(3/2)*(a^2 + b^2)*d) + (2*B)/(b*d*Sqrt[Cot[c + d*x]]) + ((a*(A - B) + b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a*(A - B) + b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",16,13,33,0.3939,1,"{3581, 3609, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
594,1,325,0,1.0903921,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B)}{b^2 d \sqrt{\cot (c+d x)}}+\frac{2 B}{3 b d \cot ^{\frac{3}{2}}(c+d x)}","\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}-\frac{(b (A-B)-a (A+B)) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)}+\frac{2 a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d \left(a^2+b^2\right)}-\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(a (A-B)+b (A+B)) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 (A b-a B)}{b^2 d \sqrt{\cot (c+d x)}}+\frac{2 B}{3 b d \cot ^{\frac{3}{2}}(c+d x)}",1,"-(((a*(A - B) + b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a*(A - B) + b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(5/2)*(a^2 + b^2)*d) + (2*B)/(3*b*d*Cot[c + d*x]^(3/2)) + (2*(A*b - a*B))/(b^2*d*Sqrt[Cot[c + d*x]]) + ((b*(A - B) - a*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((b*(A - B) - a*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",17,14,33,0.4242,1,"{3581, 3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
595,1,438,0,1.2983607,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b (A b-a B) \cot ^{\frac{3}{2}}(c+d x)}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(2 a^2 A-a b B+3 A b^2\right) \sqrt{\cot (c+d x)}}{a^2 d \left(a^2+b^2\right)}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{b^{3/2} \left(7 a^2 A b-5 a^3 B-a b^2 B+3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{5/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}","\frac{b (A b-a B) \cot ^{\frac{3}{2}}(c+d x)}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(2 a^2 A-a b B+3 A b^2\right) \sqrt{\cot (c+d x)}}{a^2 d \left(a^2+b^2\right)}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{b^{3/2} \left(7 a^2 A b-5 a^3 B-a b^2 B+3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{5/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}",1,"-(((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (b^(3/2)*(7*a^2*A*b + 3*A*b^3 - 5*a^3*B - a*b^2*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(5/2)*(a^2 + b^2)^2*d) - ((2*a^2*A + 3*A*b^2 - a*b*B)*Sqrt[Cot[c + d*x]])/(a^2*(a^2 + b^2)*d) + (b*(A*b - a*B)*Cot[c + d*x]^(3/2))/(a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",17,14,33,0.4242,1,"{3581, 3605, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
596,1,392,0,0.9401414,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^2} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^2,x]","\frac{b (A b-a B) \sqrt{\cot (c+d x)}}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\sqrt{b} \left(5 a^2 A b-3 a^3 B+a b^2 B+A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{3/2} d \left(a^2+b^2\right)^2}","\frac{b (A b-a B) \sqrt{\cot (c+d x)}}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\sqrt{b} \left(5 a^2 A b-3 a^3 B+a b^2 B+A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{3/2} d \left(a^2+b^2\right)^2}",1,"-(((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (Sqrt[b]*(5*a^2*A*b + A*b^3 - 3*a^3*B + a*b^2*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(3/2)*(a^2 + b^2)^2*d) + (b*(A*b - a*B)*Sqrt[Cot[c + d*x]])/(a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,33,0.3939,1,"{3581, 3605, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
597,1,390,0,0.9201001,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^2),x]","-\frac{(A b-a B) \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^2}","-\frac{(A b-a B) \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(3 a^2 A b+a^3 (-B)+3 a b^2 B-A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^2}",1,"((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + ((3*a^2*A*b - A*b^3 - a^3*B + 3*a*b^2*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*(a^2 + b^2)^2*d) - ((A*b - a*B)*Sqrt[Cot[c + d*x]])/((a^2 + b^2)*d*(b + a*Cot[c + d*x])) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,33,0.3939,1,"{3581, 3608, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
598,1,392,0,0.9160945,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2),x]","\frac{a (A b-a B) \sqrt{\cot (c+d x)}}{b d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\sqrt{a} \left(a^2 A b+a^3 B+5 a b^2 B-3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d \left(a^2+b^2\right)^2}","\frac{a (A b-a B) \sqrt{\cot (c+d x)}}{b d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\sqrt{a} \left(a^2 A b+a^3 B+5 a b^2 B-3 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d \left(a^2+b^2\right)^2}",1,"((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (Sqrt[a]*(a^2*A*b - 3*A*b^3 + a^3*B + 5*a*b^2*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(3/2)*(a^2 + b^2)^2*d) + (a*(A*b - a*B)*Sqrt[Cot[c + d*x]])/(b*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,33,0.3939,1,"{3581, 3609, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
599,1,437,0,1.281648,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2),x]","\frac{a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}-\frac{-3 a^2 B+a A b-2 b^2 B}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a^{3/2} \left(a^2 A b-3 a^3 B-7 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}","\frac{a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}-\frac{-3 a^2 B+a A b-2 b^2 B}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}+\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (-(A+B))+2 a b (A-B)+b^2 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a^{3/2} \left(a^2 A b-3 a^3 B-7 a b^2 B+5 A b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{\left(a^2 (A-B)+2 a b (A+B)-b^2 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}",1,"-(((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2*(A - B) - b^2*(A - B) + 2*a*b*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (a^(3/2)*(a^2*A*b + 5*A*b^3 - 3*a^3*B - 7*a*b^2*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(5/2)*(a^2 + b^2)^2*d) - (a*A*b - 3*a^2*B - 2*b^2*B)/(b^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]) + (a*(A*b - a*B))/(b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x])) + ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((2*a*b*(A - B) - a^2*(A + B) + b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",17,14,33,0.4242,1,"{3581, 3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
600,1,601,0,1.8449657,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{b (A b-a B) \cot ^{\frac{5}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{b \left(13 a^2 A b-9 a^3 B-a b^2 B+5 A b^3\right) \cot ^{\frac{3}{2}}(c+d x)}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(31 a^2 A b^2+8 a^4 A-11 a^3 b B-3 a b^3 B+15 A b^4\right) \sqrt{\cot (c+d x)}}{4 a^3 d \left(a^2+b^2\right)^2}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{b^{3/2} \left(46 a^2 A b^3+63 a^4 A b-6 a^3 b^2 B-35 a^5 B-3 a b^4 B+15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{7/2} d \left(a^2+b^2\right)^3}","\frac{b (A b-a B) \cot ^{\frac{5}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{b \left(13 a^2 A b-9 a^3 B-a b^2 B+5 A b^3\right) \cot ^{\frac{3}{2}}(c+d x)}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(31 a^2 A b^2+8 a^4 A-11 a^3 b B-3 a b^3 B+15 A b^4\right) \sqrt{\cot (c+d x)}}{4 a^3 d \left(a^2+b^2\right)^2}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{b^{3/2} \left(46 a^2 A b^3+63 a^4 A b-6 a^3 b^2 B-35 a^5 B-3 a b^4 B+15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{7/2} d \left(a^2+b^2\right)^3}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (b^(3/2)*(63*a^4*A*b + 46*a^2*A*b^3 + 15*A*b^5 - 35*a^5*B - 6*a^3*b^2*B - 3*a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(7/2)*(a^2 + b^2)^3*d) - ((8*a^4*A + 31*a^2*A*b^2 + 15*A*b^4 - 11*a^3*b*B - 3*a*b^3*B)*Sqrt[Cot[c + d*x]])/(4*a^3*(a^2 + b^2)^2*d) + (b*(A*b - a*B)*Cot[c + d*x]^(5/2))/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + (b*(13*a^2*A*b + 5*A*b^3 - 9*a^3*B - a*b^2*B)*Cot[c + d*x]^(3/2))/(4*a^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",18,15,33,0.4545,1,"{3581, 3605, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
601,1,534,0,1.3650054,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^3} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^3,x]","\frac{b (A b-a B) \cot ^{\frac{3}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{b \left(11 a^2 A b-7 a^3 B+a b^2 B+3 A b^3\right) \sqrt{\cot (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\sqrt{b} \left(6 a^2 A b^3+35 a^4 A b+18 a^3 b^2 B-15 a^5 B+a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{5/2} d \left(a^2+b^2\right)^3}","\frac{b (A b-a B) \cot ^{\frac{3}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{b \left(11 a^2 A b-7 a^3 B+a b^2 B+3 A b^3\right) \sqrt{\cot (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\sqrt{b} \left(6 a^2 A b^3+35 a^4 A b+18 a^3 b^2 B-15 a^5 B+a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{5/2} d \left(a^2+b^2\right)^3}",1,"-(((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (Sqrt[b]*(35*a^4*A*b + 6*a^2*A*b^3 + 3*A*b^5 - 15*a^5*B + 18*a^3*b^2*B + a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(5/2)*(a^2 + b^2)^3*d) + (b*(A*b - a*B)*Cot[c + d*x]^(3/2))/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + (b*(11*a^2*A*b + 3*A*b^3 - 7*a^3*B + a*b^2*B)*Sqrt[Cot[c + d*x]])/(4*a^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,33,0.4242,1,"{3581, 3605, 3645, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
602,1,534,0,1.3878475,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^3),x]","\frac{b (A b-a B) \sqrt{\cot (c+d x)}}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(9 a^2 A b-5 a^3 B+3 a b^2 B+A b^3\right) \sqrt{\cot (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(-18 a^2 A b^3+15 a^4 A b+26 a^3 b^2 B-3 a^5 B-3 a b^4 B-A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{3/2} \sqrt{b} d \left(a^2+b^2\right)^3}","\frac{b (A b-a B) \sqrt{\cot (c+d x)}}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(9 a^2 A b-5 a^3 B+3 a b^2 B+A b^3\right) \sqrt{\cot (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(-18 a^2 A b^3+15 a^4 A b+26 a^3 b^2 B-3 a^5 B-3 a b^4 B-A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{3/2} \sqrt{b} d \left(a^2+b^2\right)^3}",1,"((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + ((15*a^4*A*b - 18*a^2*A*b^3 - A*b^5 - 3*a^5*B + 26*a^3*b^2*B - 3*a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(3/2)*Sqrt[b]*(a^2 + b^2)^3*d) + (b*(A*b - a*B)*Sqrt[Cot[c + d*x]])/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) - ((9*a^2*A*b + A*b^3 - 5*a^3*B + 3*a*b^2*B)*Sqrt[Cot[c + d*x]])/(4*a*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,33,0.4242,1,"{3581, 3605, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
603,1,530,0,1.42535,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{(A b-a B) \sqrt{\cot (c+d x)}}{2 d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{\left(5 a^2 A b+a^3 (-B)+7 a b^2 B-3 A b^3\right) \sqrt{\cot (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(-26 a^2 A b^3+3 a^4 A b+18 a^3 b^2 B+a^5 B-15 a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{a} b^{3/2} d \left(a^2+b^2\right)^3}","-\frac{(A b-a B) \sqrt{\cot (c+d x)}}{2 d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}+\frac{\left(5 a^2 A b+a^3 (-B)+7 a b^2 B-3 A b^3\right) \sqrt{\cot (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(-26 a^2 A b^3+3 a^4 A b+18 a^3 b^2 B+a^5 B-15 a b^4 B+3 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{a} b^{3/2} d \left(a^2+b^2\right)^3}",1,"((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^4*A*b - 26*a^2*A*b^3 + 3*A*b^5 + a^5*B + 18*a^3*b^2*B - 15*a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*Sqrt[a]*b^(3/2)*(a^2 + b^2)^3*d) - ((A*b - a*B)*Sqrt[Cot[c + d*x]])/(2*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + ((5*a^2*A*b - 3*A*b^3 - a^3*B + 7*a*b^2*B)*Sqrt[Cot[c + d*x]])/(4*b*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,33,0.4242,1,"{3581, 3608, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
604,1,534,0,1.3787782,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3),x]","\frac{a (A b-a B) \sqrt{\cot (c+d x)}}{2 b d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{a \left(a^2 A b+3 a^3 B+11 a b^2 B-7 A b^3\right) \sqrt{\cot (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\sqrt{a} \left(18 a^2 A b^3+a^4 A b+6 a^3 b^2 B+3 a^5 B+35 a b^4 B-15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{5/2} d \left(a^2+b^2\right)^3}","\frac{a (A b-a B) \sqrt{\cot (c+d x)}}{2 b d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{a \left(a^2 A b+3 a^3 B+11 a b^2 B-7 A b^3\right) \sqrt{\cot (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{\sqrt{a} \left(18 a^2 A b^3+a^4 A b+6 a^3 b^2 B+3 a^5 B+35 a b^4 B-15 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{5/2} d \left(a^2+b^2\right)^3}",1,"-(((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (Sqrt[a]*(a^4*A*b + 18*a^2*A*b^3 - 15*A*b^5 + 3*a^5*B + 6*a^3*b^2*B + 35*a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*b^(5/2)*(a^2 + b^2)^3*d) + (a*(A*b - a*B)*Sqrt[Cot[c + d*x]])/(2*b*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) - (a*(a^2*A*b - 7*A*b^3 + 3*a^3*B + 11*a*b^2*B)*Sqrt[Cot[c + d*x]])/(4*b^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,33,0.4242,1,"{3581, 3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
605,1,600,0,1.8246523,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^3),x]","\frac{a \left(a^2 A b-5 a^3 B-13 a b^2 B+9 A b^3\right)}{4 b^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}+\frac{a (A b-a B)}{2 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)^2}-\frac{3 a^3 A b-31 a^2 b^2 B-15 a^4 B+11 a A b^3-8 b^4 B}{4 b^3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)}}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{a^{3/2} \left(6 a^2 A b^3+3 a^4 A b-46 a^3 b^2 B-15 a^5 B-63 a b^4 B+35 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{7/2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}","\frac{a \left(a^2 A b-5 a^3 B-13 a b^2 B+9 A b^3\right)}{4 b^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}+\frac{a (A b-a B)}{2 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)^2}-\frac{3 a^3 A b-31 a^2 b^2 B-15 a^4 B+11 a A b^3-8 b^4 B}{4 b^3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)}}-\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A+B)+a^3 (A-B)-3 a b^2 (A-B)-b^3 (A+B)\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^2+b^2\right)^3}-\frac{a^{3/2} \left(6 a^2 A b^3+3 a^4 A b-46 a^3 b^2 B-15 a^5 B-63 a b^4 B+35 A b^5\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{7/2} d \left(a^2+b^2\right)^3}-\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{\left(3 a^2 b (A-B)+a^3 (-(A+B))+3 a b^2 (A+B)-b^3 (A-B)\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((3*a^2*b*(A - B) - b^3*(A - B) - a^3*(A + B) + 3*a*b^2*(A + B))*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (a^(3/2)*(3*a^4*A*b + 6*a^2*A*b^3 + 35*A*b^5 - 15*a^5*B - 46*a^3*b^2*B - 63*a*b^4*B)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*b^(7/2)*(a^2 + b^2)^3*d) - (3*a^3*A*b + 11*a*A*b^3 - 15*a^4*B - 31*a^2*b^2*B - 8*b^4*B)/(4*b^3*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]) + (a*(A*b - a*B))/(2*b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x])^2) + (a*(a^2*A*b + 9*A*b^3 - 5*a^3*B - 13*a*b^2*B))/(4*b^2*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x])) - ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a^3*(A - B) - 3*a*b^2*(A - B) + 3*a^2*b*(A + B) - b^3*(A + B))*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",18,14,33,0.4242,1,"{3581, 3609, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
606,1,156,0,0.1053832,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(5/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{2 B \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","-\frac{2 B \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*B*Cot[c + d*x]^(3/2))/(3*d) + (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,36,0.2778,1,"{21, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
607,1,154,0,0.1033124,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Cot[c + d*x]^(3/2)*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{2 B \sqrt{\cot (c+d x)}}{d}-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","-\frac{2 B \sqrt{\cot (c+d x)}}{d}-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*B*Sqrt[Cot[c + d*x]])/d - (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,36,0.2778,1,"{21, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
608,1,138,0,0.0966662,"\int \frac{\sqrt{\cot (c+d x)} (a B+b B \tan (c+d x))}{a+b \tan (c+d x)} \, dx","Int[(Sqrt[Cot[c + d*x]]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x]),x]","-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,36,0.2500,1,"{21, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
609,1,138,0,0.0922854,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])),x]","\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"(B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,36,0.2500,1,"{21, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
610,1,154,0,0.1022616,"\int \frac{a B+b B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","\frac{2 B}{d \sqrt{\cot (c+d x)}}+\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","\frac{2 B}{d \sqrt{\cot (c+d x)}}+\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*B)/(d*Sqrt[Cot[c + d*x]]) + (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,36,0.2778,1,"{21, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
611,1,156,0,0.101635,"\int \frac{a B+b B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","\frac{2 B}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","\frac{2 B}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{B \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{B \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{B \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{B \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"-((B*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + (B*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*B)/(3*d*Cot[c + d*x]^(3/2)) - (B*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + (B*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,36,0.2778,1,"{21, 3474, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
612,1,354,0,1.4877414,"\int \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{2 \left(35 a^2 A-7 a b B+4 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a^2 d}+\frac{2 \left(35 a^2 A b+105 a^3 B+14 a b^2 B-8 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^3 d}-\frac{2 (7 a B+A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 a d}-\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}","\frac{2 \left(35 a^2 A-7 a b B+4 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a^2 d}+\frac{2 \left(35 a^2 A b+105 a^3 B+14 a b^2 B-8 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^3 d}-\frac{2 (7 a B+A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 a d}-\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}",1,"-((Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) - (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(35*a^2*A*b - 8*A*b^3 + 105*a^3*B + 14*a*b^2*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(105*a^3*d) + (2*(35*a^2*A + 4*A*b^2 - 7*a*b*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d) - (2*(A*b + 7*a*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(35*a*d) - (2*A*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(7*d)","A",12,8,35,0.2286,1,"{4241, 3608, 3649, 3616, 3615, 93, 203, 206}"
613,1,290,0,1.1874424,"\int \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{2 \left(15 a^2 A-5 a b B+2 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^2 d}-\frac{2 (5 a B+A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a d}+\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}","\frac{2 \left(15 a^2 A-5 a b B+2 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^2 d}-\frac{2 (5 a B+A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a d}+\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}",1,"(Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(15*a^2*A + 2*A*b^2 - 5*a*b*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d) - (2*(A*b + 5*a*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*a*d) - (2*A*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d)","A",11,8,35,0.2286,1,"{4241, 3608, 3649, 3616, 3615, 93, 203, 206}"
614,1,239,0,0.8866438,"\int \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a d}+\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}","\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a d}+\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}",1,"(Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(A*b + 3*a*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*a*d) - (2*A*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",10,8,35,0.2286,1,"{4241, 3608, 3649, 3616, 3615, 93, 203, 206}"
615,1,194,0,0.6636339,"\int \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}","-\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}",1,"-((Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*A*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",9,7,35,0.2000,1,"{4241, 3608, 3616, 3615, 93, 203, 206}"
616,1,229,0,0.7344316,"\int \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]),x]","-\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt{b} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{2 \sqrt{b} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-((Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + (2*Sqrt[b]*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d","A",13,10,35,0.2857,1,"{4241, 3614, 3616, 3615, 93, 203, 206, 3634, 63, 217}"
617,1,261,0,1.5111551,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}","\frac{\sqrt{-b+i a} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\sqrt{b+i a} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}",1,"(Sqrt[I*a - b]*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((2*A*b + a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[b]*d) - (Sqrt[I*a + b]*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (B*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",14,10,35,0.2857,1,"{4241, 3610, 3655, 6725, 63, 217, 206, 93, 205, 208}"
618,1,324,0,1.9914454,"\int \frac{\sqrt{a+b \tan (c+d x)} (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(Sqrt[a + b*Tan[c + d*x]]*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","\frac{\left(a^2 (-B)+4 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{3/2} d}+\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(4 A b-a B) \sqrt{a+b \tan (c+d x)}}{4 b d \sqrt{\cot (c+d x)}}+\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{3/2}}{2 b d \sqrt{\cot (c+d x)}}","\frac{\left(a^2 (-B)+4 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{3/2} d}+\frac{\sqrt{-b+i a} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(4 A b-a B) \sqrt{a+b \tan (c+d x)}}{4 b d \sqrt{\cot (c+d x)}}+\frac{\sqrt{b+i a} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{3/2}}{2 b d \sqrt{\cot (c+d x)}}",1,"(Sqrt[I*a - b]*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((4*a*A*b - a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(4*b^(3/2)*d) + (Sqrt[I*a + b]*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((4*A*b - a*B)*Sqrt[a + b*Tan[c + d*x]])/(4*b*d*Sqrt[Cot[c + d*x]]) + (B*(a + b*Tan[c + d*x])^(3/2))/(2*b*d*Sqrt[Cot[c + d*x]])","A",15,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
619,1,422,0,2.0245223,"\int \cot ^{\frac{11}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(11/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(21 a^2 A-24 a b B-A b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{2 \left(126 a^2 A b+105 a^3 B-9 a b^2 B+4 A b^3\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 \left(-63 a^2 A b^2+315 a^4 A-420 a^3 b B-18 a b^3 B+8 A b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^3 d}-\frac{2 (9 a B+10 A b) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{63 d}+\frac{(-b+i a)^{3/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{9 d}","\frac{2 \left(21 a^2 A-24 a b B-A b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{2 \left(126 a^2 A b+105 a^3 B-9 a b^2 B+4 A b^3\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 \left(-63 a^2 A b^2+315 a^4 A-420 a^3 b B-18 a b^3 B+8 A b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^3 d}-\frac{2 (9 a B+10 A b) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{63 d}+\frac{(-b+i a)^{3/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{9 d}",1,"((I*a - b)^(3/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(315*a^4*A - 63*a^2*A*b^2 + 8*A*b^4 - 420*a^3*b*B - 18*a*b^3*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(315*a^3*d) + (2*(126*a^2*A*b + 4*A*b^3 + 105*a^3*B - 9*a*b^2*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d) + (2*(21*a^2*A - A*b^2 - 24*a*b*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d) - (2*(10*A*b + 9*a*B)*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(63*d) - (2*a*A*Cot[c + d*x]^(9/2)*Sqrt[a + b*Tan[c + d*x]])/(9*d)","A",13,8,35,0.2286,1,"{4241, 3605, 3649, 3616, 3615, 93, 203, 206}"
620,1,351,0,1.6441689,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(35 a^2 A-42 a b B-3 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{2 \left(140 a^2 A b+105 a^3 B-21 a b^2 B+6 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^2 d}-\frac{2 (7 a B+8 A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}-\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}","\frac{2 \left(35 a^2 A-42 a b B-3 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{2 \left(140 a^2 A b+105 a^3 B-21 a b^2 B+6 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^2 d}-\frac{2 (7 a B+8 A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}-\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}",1,"-(((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) - ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(140*a^2*A*b + 6*A*b^3 + 105*a^3*B - 21*a*b^2*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d) + (2*(35*a^2*A - 3*A*b^2 - 42*a*b*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d) - (2*(8*A*b + 7*a*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(35*d) - (2*a*A*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(7*d)","A",12,8,35,0.2286,1,"{4241, 3605, 3649, 3616, 3615, 93, 203, 206}"
621,1,299,0,1.3053068,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(15 a^2 A-20 a b B-3 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a d}-\frac{2 (5 a B+6 A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}+\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}","\frac{2 \left(15 a^2 A-20 a b B-3 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a d}-\frac{2 (5 a B+6 A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}+\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}",1,"((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) + ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(15*a^2*A - 3*A*b^2 - 20*a*b*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*a*d) - (2*(6*A*b + 5*a*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*d) - (2*a*A*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d)","A",11,8,35,0.2286,1,"{4241, 3605, 3649, 3616, 3615, 93, 203, 206}"
622,1,236,0,1.0974895,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+4 A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}","\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 (3 a B+4 A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}",1,"((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(4*A*b + 3*a*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*d) - (2*a*A*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",10,8,35,0.2286,1,"{4241, 3605, 3649, 3616, 3615, 93, 203, 206}"
623,1,269,0,1.8629992,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b^{3/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b^{3/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d)) + (2*b^(3/2)*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*a*A*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",14,10,35,0.2857,1,"{4241, 3605, 3655, 6725, 63, 217, 206, 93, 205, 208}"
624,1,264,0,1.8374743,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b} (3 a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}","-\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{b} (3 a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}",1,"-(((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + (Sqrt[b]*(2*A*b + 3*a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (b*B*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",14,10,35,0.2857,1,"{4241, 3607, 3655, 6725, 63, 217, 206, 93, 205, 208}"
625,1,328,0,2.3928909,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{\left(3 a^2 B+12 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 \sqrt{b} d}+\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(5 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{a+b \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{\left(3 a^2 B+12 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 \sqrt{b} d}+\frac{(a+i b)^2 (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(5 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B \sqrt{a+b \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((a + I*b)^2*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) + ((12*a*A*b + 3*a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(4*Sqrt[b]*d) + ((I*a + b)^(3/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (b*B*Sqrt[a + b*Tan[c + d*x]])/(2*d*Cot[c + d*x]^(3/2)) + ((4*A*b + 5*a*B)*Sqrt[a + b*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]])","A",15,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
626,1,383,0,2.5324775,"\int \frac{(a+b \tan (c+d x))^{3/2} (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(3/2)*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","\frac{\left(a^2 (-B)+6 a A b-8 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{8 b d \sqrt{\cot (c+d x)}}+\frac{\left(6 a^2 A b+a^3 (-B)-24 a b^2 B-16 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 b^{3/2} d}+\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(6 A b-a B) (a+b \tan (c+d x))^{3/2}}{12 b d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{5/2}}{3 b d \sqrt{\cot (c+d x)}}","\frac{\left(a^2 (-B)+6 a A b-8 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{8 b d \sqrt{\cot (c+d x)}}+\frac{\left(6 a^2 A b+a^3 (-B)-24 a b^2 B-16 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 b^{3/2} d}+\frac{(-b+i a)^{3/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(6 A b-a B) (a+b \tan (c+d x))^{3/2}}{12 b d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{5/2}}{3 b d \sqrt{\cot (c+d x)}}",1,"((I*a - b)^(3/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((6*a^2*A*b - 16*A*b^3 - a^3*B - 24*a*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(8*b^(3/2)*d) + ((I*a + b)^(3/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((6*a*A*b - a^2*B - 8*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(8*b*d*Sqrt[Cot[c + d*x]]) + ((6*A*b - a*B)*(a + b*Tan[c + d*x])^(3/2))/(12*b*d*Sqrt[Cot[c + d*x]]) + (B*(a + b*Tan[c + d*x])^(5/2))/(3*b*d*Sqrt[Cot[c + d*x]])","A",16,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
627,1,500,0,2.4704325,"\int \cot ^{\frac{13}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(13/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(99 a^2 A-209 a b B-113 A b^2\right) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{693 d}+\frac{2 \left(495 a^2 A b+231 a^3 B-275 a b^2 B-5 A b^3\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{1155 a d}-\frac{2 \left(-1485 a^2 A b^2+1155 a^4 A-2541 a^3 b B+55 a b^3 B-20 A b^4\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3465 a^2 d}-\frac{2 \left(-495 a^2 A b^3+8085 a^4 A b-5313 a^3 b^2 B+3465 a^5 B-110 a b^4 B+40 A b^5\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3465 a^3 d}-\frac{2 a (11 a B+14 A b) \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{99 d}-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{11}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{11 d}","\frac{2 \left(99 a^2 A-209 a b B-113 A b^2\right) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{693 d}+\frac{2 \left(495 a^2 A b+231 a^3 B-275 a b^2 B-5 A b^3\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{1155 a d}-\frac{2 \left(-1485 a^2 A b^2+1155 a^4 A-2541 a^3 b B+55 a b^3 B-20 A b^4\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3465 a^2 d}-\frac{2 \left(-495 a^2 A b^3+8085 a^4 A b-5313 a^3 b^2 B+3465 a^5 B-110 a b^4 B+40 A b^5\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3465 a^3 d}-\frac{2 a (11 a B+14 A b) \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{99 d}-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{11}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{11 d}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(8085*a^4*A*b - 495*a^2*A*b^3 + 40*A*b^5 + 3465*a^5*B - 5313*a^3*b^2*B - 110*a*b^4*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3465*a^3*d) - (2*(1155*a^4*A - 1485*a^2*A*b^2 - 20*A*b^4 - 2541*a^3*b*B + 55*a*b^3*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3465*a^2*d) + (2*(495*a^2*A*b - 5*A*b^3 + 231*a^3*B - 275*a*b^2*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(1155*a*d) + (2*(99*a^2*A - 113*A*b^2 - 209*a*b*B)*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(693*d) - (2*a*(14*A*b + 11*a*B)*Cot[c + d*x]^(9/2)*Sqrt[a + b*Tan[c + d*x]])/(99*d) - (2*a*A*Cot[c + d*x]^(11/2)*(a + b*Tan[c + d*x])^(3/2))/(11*d)","A",14,9,35,0.2571,1,"{4241, 3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
628,1,418,0,2.034523,"\int \cot ^{\frac{11}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(11/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(21 a^2 A-45 a b B-25 A b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 \left(231 a^2 A b+105 a^3 B-135 a b^2 B-5 A b^3\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a d}-\frac{2 \left(-483 a^2 A b^2+315 a^4 A-735 a^3 b B+45 a b^3 B-10 A b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 a (3 a B+4 A b) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{21 d}+\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{9 d}","\frac{2 \left(21 a^2 A-45 a b B-25 A b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 \left(231 a^2 A b+105 a^3 B-135 a b^2 B-5 A b^3\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a d}-\frac{2 \left(-483 a^2 A b^2+315 a^4 A-735 a^3 b B+45 a b^3 B-10 A b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 a (3 a B+4 A b) \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{21 d}+\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{9 d}",1,"((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*(315*a^4*A - 483*a^2*A*b^2 - 10*A*b^4 - 735*a^3*b*B + 45*a*b^3*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d) + (2*(231*a^2*A*b - 5*A*b^3 + 105*a^3*B - 135*a*b^2*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(315*a*d) + (2*(21*a^2*A - 25*A*b^2 - 45*a*b*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(105*d) - (2*a*(4*A*b + 3*a*B)*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(21*d) - (2*a*A*Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^(3/2))/(9*d)","A",13,9,35,0.2571,1,"{4241, 3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
629,1,349,0,1.6526689,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(35 a^2 A-77 a b B-45 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 \left(245 a^2 A b+105 a^3 B-161 a b^2 B-15 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a d}-\frac{2 a (7 a B+10 A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}+\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{7 d}","\frac{2 \left(35 a^2 A-77 a b B-45 A b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 \left(245 a^2 A b+105 a^3 B-161 a b^2 B-15 A b^3\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a d}-\frac{2 a (7 a B+10 A b) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}+\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{7 d}",1,"((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(245*a^2*A*b - 15*A*b^3 + 105*a^3*B - 161*a*b^2*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(105*a*d) + (2*(35*a^2*A - 45*A*b^2 - 77*a*b*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(105*d) - (2*a*(10*A*b + 7*a*B)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(35*d) - (2*a*A*Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(3/2))/(7*d)","A",12,9,35,0.2571,1,"{4241, 3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
630,1,287,0,1.3052802,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{2 \left(15 a^2 A-35 a b B-23 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{2 a (5 a B+8 A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{5 d}","\frac{2 \left(15 a^2 A-35 a b B-23 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{2 a (5 a B+8 A b) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{5 d}",1,"-(((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (2*(15*a^2*A - 23*A*b^2 - 35*a*b*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*d) - (2*a*(8*A*b + 5*a*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*d) - (2*a*A*Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2))/(5*d)","A",11,9,35,0.2571,1,"{4241, 3605, 3645, 3649, 3616, 3615, 93, 203, 206}"
631,1,300,0,2.2885532,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (a B+2 A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 b^{5/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a (a B+2 A b) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 b^{5/2} B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + (2*b^(5/2)*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - (2*a*(2*A*b + a*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d - (2*a*A*Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",15,11,35,0.3143,1,"{4241, 3605, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
632,1,301,0,2.4463241,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{b^{3/2} (5 a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (2 a A+b B) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}-\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}{d}","\frac{b^{3/2} (5 a B+2 A b) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (2 a A+b B) \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}-\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{2 a A \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}{d}",1,"((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (b^(3/2)*(2*A*b + 5*a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d - ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (b*(2*a*A + b*B)*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]]) - (2*a*A*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/d","A",15,11,35,0.3143,1,"{4241, 3605, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
633,1,320,0,2.175324,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]),x]","\frac{\sqrt{b} \left(15 a^2 B+20 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (7 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B (a+b \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}","\frac{\sqrt{b} \left(15 a^2 B+20 a A b-8 b^2 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b (7 a B+4 A b) \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B (a+b \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}",1,"((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (Sqrt[b]*(20*a*A*b + 15*a^2*B - 8*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(4*d) + ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + (b*(4*A*b + 7*a*B)*Sqrt[a + b*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]]) + (b*B*(a + b*Tan[c + d*x])^(3/2))/(2*d*Sqrt[Cot[c + d*x]])","A",15,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
634,1,376,0,2.9698407,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{\left(5 a^2 B+14 a A b-8 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}+\frac{\left(30 a^2 A b+5 a^3 B-40 a b^2 B-16 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 \sqrt{b} d}-\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(3 a B+2 A b) (a+b \tan (c+d x))^{3/2}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B (a+b \tan (c+d x))^{3/2}}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{\left(5 a^2 B+14 a A b-8 b^2 B\right) \sqrt{a+b \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}+\frac{\left(30 a^2 A b+5 a^3 B-40 a b^2 B-16 A b^3\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{8 \sqrt{b} d}-\frac{(-b+i a)^{5/2} (A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(3 a B+2 A b) (a+b \tan (c+d x))^{3/2}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} (A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{b B (a+b \tan (c+d x))^{3/2}}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"-(((I*a - b)^(5/2)*(A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + ((30*a^2*A*b - 16*A*b^3 + 5*a^3*B - 40*a*b^2*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(8*Sqrt[b]*d) + ((I*a + b)^(5/2)*(A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((14*a*A*b + 5*a^2*B - 8*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(8*d*Sqrt[Cot[c + d*x]]) + (b*B*(a + b*Tan[c + d*x])^(3/2))/(3*d*Cot[c + d*x]^(3/2)) + ((2*A*b + 3*a*B)*(a + b*Tan[c + d*x])^(3/2))/(4*d*Sqrt[Cot[c + d*x]])","A",16,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
635,1,457,0,3.0109765,"\int \frac{(a+b \tan (c+d x))^{5/2} (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^(5/2)*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","\frac{\left(-5 a^2 B+40 a A b-48 b^2 B\right) (a+b \tan (c+d x))^{3/2}}{96 b d \sqrt{\cot (c+d x)}}+\frac{\left(40 a^2 A b-5 a^3 B-112 a b^2 B-64 A b^3\right) \sqrt{a+b \tan (c+d x)}}{64 b d \sqrt{\cot (c+d x)}}+\frac{\left(40 a^3 A b-240 a^2 b^2 B-5 a^4 B-320 a A b^3+128 b^4 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{64 b^{3/2} d}-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(8 A b-a B) (a+b \tan (c+d x))^{5/2}}{24 b d \sqrt{\cot (c+d x)}}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{7/2}}{4 b d \sqrt{\cot (c+d x)}}","\frac{\left(-5 a^2 B+40 a A b-48 b^2 B\right) (a+b \tan (c+d x))^{3/2}}{96 b d \sqrt{\cot (c+d x)}}+\frac{\left(40 a^2 A b-5 a^3 B-112 a b^2 B-64 A b^3\right) \sqrt{a+b \tan (c+d x)}}{64 b d \sqrt{\cot (c+d x)}}+\frac{\left(40 a^3 A b-240 a^2 b^2 B-5 a^4 B-320 a A b^3+128 b^4 B\right) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{64 b^{3/2} d}-\frac{(-b+i a)^{5/2} (-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{(8 A b-a B) (a+b \tan (c+d x))^{5/2}}{24 b d \sqrt{\cot (c+d x)}}-\frac{(b+i a)^{5/2} (B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{B (a+b \tan (c+d x))^{7/2}}{4 b d \sqrt{\cot (c+d x)}}",1,"-(((I*a - b)^(5/2)*(I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d) + ((40*a^3*A*b - 320*a*A*b^3 - 5*a^4*B - 240*a^2*b^2*B + 128*b^4*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(64*b^(3/2)*d) - ((I*a + b)^(5/2)*(I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/d + ((40*a^2*A*b - 64*A*b^3 - 5*a^3*B - 112*a*b^2*B)*Sqrt[a + b*Tan[c + d*x]])/(64*b*d*Sqrt[Cot[c + d*x]]) + ((40*a*A*b - 5*a^2*B - 48*b^2*B)*(a + b*Tan[c + d*x])^(3/2))/(96*b*d*Sqrt[Cot[c + d*x]]) + ((8*A*b - a*B)*(a + b*Tan[c + d*x])^(5/2))/(24*b*d*Sqrt[Cot[c + d*x]]) + (B*(a + b*Tan[c + d*x])^(7/2))/(4*b*d*Sqrt[Cot[c + d*x]])","A",17,11,35,0.3143,1,"{4241, 3607, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
636,1,296,0,1.1566084,"\int \frac{\cot ^{\frac{7}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^(7/2)*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \left(15 a^2 A+10 a b B-8 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^3 d}+\frac{2 (4 A b-5 a B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a^2 d}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 a d}","\frac{2 \left(15 a^2 A+10 a b B-8 A b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^3 d}+\frac{2 (4 A b-5 a B) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a^2 d}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 a d}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d) + (2*(15*a^2*A - 8*A*b^2 + 10*a*b*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*a^3*d) + (2*(4*A*b - 5*a*B)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d) - (2*A*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*a*d)","A",11,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
637,1,243,0,0.8620462,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 (2 A b-3 a B) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a^2 d}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 a d}","\frac{2 (2 A b-3 a B) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a^2 d}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 a d}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d)) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d) + (2*(2*A*b - 3*a*B)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*a^2*d) - (2*A*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*a*d)","A",10,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
638,1,199,0,0.6303306,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{a d}","-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}-\frac{2 A \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{a d}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d)) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d) - (2*A*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(a*d)","A",9,7,35,0.2000,1,"{4241, 3609, 3616, 3615, 93, 203, 206}"
639,1,163,0,0.4800173,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/Sqrt[a + b*Tan[c + d*x]],x]","\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d)","A",8,6,35,0.1714,1,"{4241, 3616, 3615, 93, 203, 206}"
640,1,228,0,0.6999103,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}","\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[b]*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d)","A",13,10,35,0.2857,1,"{4241, 3614, 3616, 3615, 93, 203, 206, 3634, 63, 217}"
641,1,266,0,1.4614927,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{(2 A b-a B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{B \sqrt{a+b \tan (c+d x)}}{b d \sqrt{\cot (c+d x)}}","\frac{(2 A b-a B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}+\frac{B \sqrt{a+b \tan (c+d x)}}{b d \sqrt{\cot (c+d x)}}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d)) + ((2*A*b - a*B)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(b^(3/2)*d) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d) + (B*Sqrt[a + b*Tan[c + d*x]])/(b*d*Sqrt[Cot[c + d*x]])","A",14,10,35,0.2857,1,"{4241, 3607, 3655, 6725, 63, 217, 206, 93, 205, 208}"
642,1,316,0,1.3177043,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b \left(5 a^2 A b-3 a^3 B-6 a b^2 B+8 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 (4 A b-3 a B) \sqrt{\cot (c+d x)}}{3 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d \sqrt{a+b \tan (c+d x)}}","\frac{2 b \left(5 a^2 A b-3 a^3 B-6 a b^2 B+8 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 (4 A b-3 a B) \sqrt{\cot (c+d x)}}{3 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d \sqrt{a+b \tan (c+d x)}}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(3/2)*d)) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(3/2)*d) + (2*b*(5*a^2*A*b + 8*A*b^3 - 3*a^3*B - 6*a*b^2*B))/(3*a^3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) + (2*(4*A*b - 3*a*B)*Sqrt[Cot[c + d*x]])/(3*a^2*d*Sqrt[a + b*Tan[c + d*x]]) - (2*A*Cot[c + d*x]^(3/2))/(3*a*d*Sqrt[a + b*Tan[c + d*x]])","A",11,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
643,1,256,0,0.9700648,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 b \left(a^2 A-a b B+2 A b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A \sqrt{\cot (c+d x)}}{a d \sqrt{a+b \tan (c+d x)}}","-\frac{2 b \left(a^2 A-a b B+2 A b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}-\frac{2 A \sqrt{\cot (c+d x)}}{a d \sqrt{a+b \tan (c+d x)}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(3/2)*d) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(3/2)*d) - (2*b*(a^2*A + 2*A*b^2 - a*b*B))/(a^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) - (2*A*Sqrt[Cot[c + d*x]])/(a*d*Sqrt[a + b*Tan[c + d*x]])","A",10,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
644,1,215,0,0.7157136,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}","\frac{2 b (A b-a B)}{a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(3/2)*d) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(3/2)*d) + (2*b*(A*b - a*B))/(a*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{4241, 3609, 3616, 3615, 93, 203, 206}"
645,1,210,0,0.7424421,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 (A b-a B)}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}","-\frac{2 (A b-a B)}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(3/2)*d)) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(3/2)*d) - (2*(A*b - a*B))/((a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",9,7,35,0.2000,1,"{4241, 3608, 3616, 3615, 93, 203, 206}"
646,1,279,0,1.9048775,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}","\frac{2 a (A b-a B)}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{3/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{3/2}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(3/2)*d)) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(b^(3/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(3/2)*d) + (2*a*(A*b - a*B))/(b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",14,10,35,0.2857,1,"{4241, 3605, 3655, 6725, 63, 217, 206, 93, 205, 208}"
647,1,399,0,1.7450966,"\int \frac{\cot ^{\frac{5}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^(5/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b \left(30 a^2 A b^3+8 a^4 A b-17 a^3 b^2 B-3 a^5 B-8 a b^4 B+16 A b^5\right)}{3 a^4 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 b \left(7 a^2 A b-3 a^3 B-4 a b^2 B+8 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 (2 A b-a B) \sqrt{\cot (c+d x)}}{a^2 d (a+b \tan (c+d x))^{3/2}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d (a+b \tan (c+d x))^{3/2}}","\frac{2 b \left(30 a^2 A b^3+8 a^4 A b-17 a^3 b^2 B-3 a^5 B-8 a b^4 B+16 A b^5\right)}{3 a^4 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 b \left(7 a^2 A b-3 a^3 B-4 a b^2 B+8 A b^3\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 (2 A b-a B) \sqrt{\cot (c+d x)}}{a^2 d (a+b \tan (c+d x))^{3/2}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A \cot ^{\frac{3}{2}}(c+d x)}{3 a d (a+b \tan (c+d x))^{3/2}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) + (2*b*(7*a^2*A*b + 8*A*b^3 - 3*a^3*B - 4*a*b^2*B))/(3*a^3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*(2*A*b - a*B)*Sqrt[Cot[c + d*x]])/(a^2*d*(a + b*Tan[c + d*x])^(3/2)) - (2*A*Cot[c + d*x]^(3/2))/(3*a*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(8*a^4*A*b + 30*a^2*A*b^3 + 16*A*b^5 - 3*a^5*B - 17*a^3*b^2*B - 8*a*b^4*B))/(3*a^4*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",12,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
648,1,341,0,1.3354821,"\int \frac{\cot ^{\frac{3}{2}}(c+d x) (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Cot[c + d*x]^(3/2)*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 b \left(17 a^2 A b^2+3 a^4 A-8 a^3 b B-2 a b^3 B+8 A b^4\right)}{3 a^3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{2 b \left(3 a^2 A-a b B+4 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A \sqrt{\cot (c+d x)}}{a d (a+b \tan (c+d x))^{3/2}}","-\frac{2 b \left(17 a^2 A b^2+3 a^4 A-8 a^3 b B-2 a b^3 B+8 A b^4\right)}{3 a^3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{2 b \left(3 a^2 A-a b B+4 A b^2\right)}{3 a^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}-\frac{2 A \sqrt{\cot (c+d x)}}{a d (a+b \tan (c+d x))^{3/2}}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) - (2*b*(3*a^2*A + 4*A*b^2 - a*b*B))/(3*a^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*A*Sqrt[Cot[c + d*x]])/(a*d*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^4*A + 17*a^2*A*b^2 + 8*A*b^4 - 8*a^3*b*B - 2*a*b^3*B))/(3*a^3*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",11,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
649,1,287,0,1.0764778,"\int \frac{\sqrt{\cot (c+d x)} (A+B \tan (c+d x))}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(A + B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b (A b-a B)}{3 a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(8 a^2 A b-5 a^3 B+a b^2 B+2 A b^3\right)}{3 a^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","\frac{2 b (A b-a B)}{3 a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 b \left(8 a^2 A b-5 a^3 B+a b^2 B+2 A b^3\right)}{3 a^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"-(((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d)) - ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) + (2*b*(A*b - a*B))/(3*a*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*b*(8*a^2*A*b + 2*A*b^3 - 5*a^3*B + a*b^2*B))/(3*a^2*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,35,0.2286,1,"{4241, 3609, 3649, 3616, 3615, 93, 203, 206}"
650,1,284,0,1.1252103,"\int \frac{A+B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)),x]","-\frac{2 (A b-a B)}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(5 a^2 A b-2 a^3 B+4 a b^2 B-A b^3\right)}{3 a d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","-\frac{2 (A b-a B)}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{2 \left(5 a^2 A b-2 a^3 B+4 a b^2 B-A b^3\right)}{3 a d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"-(((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d)) + ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) - (2*(A*b - a*B))/(3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*(5*a^2*A*b - A*b^3 - 2*a^3*B + 4*a*b^2*B))/(3*a*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,35,0.2286,1,"{4241, 3608, 3649, 3616, 3615, 93, 203, 206}"
651,1,284,0,1.1157335,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(2 a^2 A b+a^3 B+7 a b^2 B-4 A b^3\right)}{3 b d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(2 a^2 A b+a^3 B+7 a b^2 B-4 A b^3\right)}{3 b d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(A+i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}+\frac{(A-i B) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}",1,"((A + I*B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d) + ((A - I*B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) + (2*a*(A*b - a*B))/(3*b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*(2*a^2*A*b - 4*A*b^3 + a^3*B + 7*a*b^2*B))/(3*b*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,35,0.2286,1,"{4241, 3605, 3649, 3616, 3615, 93, 203, 206}"
652,1,342,0,2.4578457,"\int \frac{A+B \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[(A + B*Tan[c + d*x])/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}","\frac{2 a (A b-a B)}{3 b d \left(a^2+b^2\right) \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(2 A b^3-a B \left(a^2+3 b^2\right)\right)}{b^2 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{(-B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (-b+i a)^{5/2}}-\frac{(B+i A) \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d (b+i a)^{5/2}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}",1,"((I*A - B)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a - b)^(5/2)*d) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(b^(5/2)*d) - ((I*A + B)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/((I*a + b)^(5/2)*d) + (2*a*(A*b - a*B))/(3*b*(a^2 + b^2)*d*Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(2*A*b^3 - a*(a^2 + 3*b^2)*B))/(b^2*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",15,11,35,0.3143,1,"{4241, 3605, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
653,1,151,0,0.2147532,"\int \frac{\sqrt{\cot (c+d x)} (a B+b B \tan (c+d x))}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(Sqrt[Cot[c + d*x]]*(a*B + b*B*Tan[c + d*x]))/(a + b*Tan[c + d*x])^(3/2),x]","\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"(B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) + (B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d)","A",9,7,38,0.1842,1,"{21, 4241, 3575, 912, 93, 205, 208}"
654,1,157,0,0.2178491,"\int \frac{a B+b B \tan (c+d x)}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{i B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{i B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","\frac{i B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}-\frac{i B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"(I*B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d) - (I*B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d)","A",9,7,38,0.1842,1,"{21, 4241, 3575, 910, 93, 205, 208}"
655,1,215,0,0.2594545,"\int \frac{a B+b B \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[(a*B + b*B*Tan[c + d*x])/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}","-\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{-b+i a}}+\frac{2 B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{B \sqrt{\tan (c+d x)} \sqrt{\cot (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d \sqrt{b+i a}}",1,"-((B*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a - b]*d)) + (2*B*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[b]*d) - (B*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]*Sqrt[Cot[c + d*x]]*Sqrt[Tan[c + d*x]])/(Sqrt[I*a + b]*d)","A",14,11,38,0.2895,1,"{21, 4241, 3575, 910, 63, 217, 206, 912, 93, 205, 208}"
656,1,195,0,0.4401666,"\int \cot ^m(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^m*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) \cot ^{m-1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(1-m;-n,1;2-m;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (1-m)}+\frac{(A-i B) \cot ^{m-1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(1-m;-n,1;2-m;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (1-m)}","\frac{(A+i B) \cot ^{m-1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(1-m;-n,1;2-m;-\frac{b \tan (c+d x)}{a},-i \tan (c+d x)\right)}{2 d (1-m)}+\frac{(A-i B) \cot ^{m-1}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(1-m;-n,1;2-m;-\frac{b \tan (c+d x)}{a},i \tan (c+d x)\right)}{2 d (1-m)}",1,"((A + I*B)*AppellF1[1 - m, -n, 1, 2 - m, -((b*Tan[c + d*x])/a), (-I)*Tan[c + d*x]]*Cot[c + d*x]^(-1 + m)*(a + b*Tan[c + d*x])^n)/(2*d*(1 - m)*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[1 - m, -n, 1, 2 - m, -((b*Tan[c + d*x])/a), I*Tan[c + d*x]]*Cot[c + d*x]^(-1 + m)*(a + b*Tan[c + d*x])^n)/(2*d*(1 - m)*(1 + (b*Tan[c + d*x])/a)^n)","A",8,5,31,0.1613,1,"{4241, 3603, 3602, 135, 133}"
657,1,169,0,0.4876558,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","-\frac{(A+i B) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}-\frac{(A-i B) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}","-\frac{(A+i B) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}-\frac{(A-i B) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}",1,"-(((A + I*B)*AppellF1[-1/2, 1, -n, 1/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^n)/(d*(1 + (b*Tan[c + d*x])/a)^n)) - ((A - I*B)*AppellF1[-1/2, 1, -n, 1/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^n)/(d*(1 + (b*Tan[c + d*x])/a)^n)","A",10,6,33,0.1818,1,"{4241, 3603, 3602, 130, 511, 510}"
658,1,167,0,0.432217,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\cot (c+d x)}}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\cot (c+d x)}}","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\cot (c+d x)}}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\cot (c+d x)}}",1,"((A + I*B)*AppellF1[1/2, 1, -n, 3/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[1/2, 1, -n, 3/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(d*Sqrt[Cot[c + d*x]]*(1 + (b*Tan[c + d*x])/a)^n)","A",10,6,33,0.1818,1,"{4241, 3603, 3602, 130, 430, 429}"
659,1,173,0,0.4633241,"\int \frac{(a+b \tan (c+d x))^n (A+B \tan (c+d x))}{\sqrt{\cot (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Sqrt[Cot[c + d*x]],x]","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((A + I*B)*AppellF1[3/2, 1, -n, 5/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(3*d*Cot[c + d*x]^(3/2)*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[3/2, 1, -n, 5/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(3*d*Cot[c + d*x]^(3/2)*(1 + (b*Tan[c + d*x])/a)^n)","A",10,6,33,0.1818,1,"{4241, 3603, 3602, 130, 511, 510}"
660,1,173,0,0.4623797,"\int \frac{(a+b \tan (c+d x))^n (A+B \tan (c+d x))}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Cot[c + d*x]^(3/2),x]","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"((A + I*B)*AppellF1[5/2, 1, -n, 7/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(5*d*Cot[c + d*x]^(5/2)*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[5/2, 1, -n, 7/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(5*d*Cot[c + d*x]^(5/2)*(1 + (b*Tan[c + d*x])/a)^n)","A",10,6,33,0.1818,1,"{4241, 3603, 3602, 130, 511, 510}"
661,1,173,0,0.3669156,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d}+\frac{(A-i B) \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d}","\frac{(A+i B) \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d}+\frac{(A-i B) \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{5}{2};1,-n;\frac{7}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{5 d}",1,"((A + I*B)*AppellF1[5/2, 1, -n, 7/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^n)/(5*d*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[5/2, 1, -n, 7/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^n)/(5*d*(1 + (b*Tan[c + d*x])/a)^n)","A",9,5,33,0.1515,1,"{3603, 3602, 130, 511, 510}"
662,1,173,0,0.3634229,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n (A+B \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]),x]","\frac{(A+i B) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d}+\frac{(A-i B) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d}","\frac{(A+i B) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d}+\frac{(A-i B) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{3}{2};1,-n;\frac{5}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{3 d}",1,"((A + I*B)*AppellF1[3/2, 1, -n, 5/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n)/(3*d*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[3/2, 1, -n, 5/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n)/(3*d*(1 + (b*Tan[c + d*x])/a)^n)","A",9,5,33,0.1515,1,"{3603, 3602, 130, 511, 510}"
663,1,167,0,0.3310036,"\int \frac{(a+b \tan (c+d x))^n (A+B \tan (c+d x))}{\sqrt{\tan (c+d x)}} \, dx","Int[((a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Sqrt[Tan[c + d*x]],x]","\frac{(A+i B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}+\frac{(A-i B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}","\frac{(A+i B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}+\frac{(A-i B) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(\frac{1}{2};1,-n;\frac{3}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d}",1,"((A + I*B)*AppellF1[1/2, 1, -n, 3/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^n)/(d*(1 + (b*Tan[c + d*x])/a)^n) + ((A - I*B)*AppellF1[1/2, 1, -n, 3/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^n)/(d*(1 + (b*Tan[c + d*x])/a)^n)","A",9,5,33,0.1515,1,"{3603, 3602, 130, 430, 429}"
664,1,169,0,0.3751585,"\int \frac{(a+b \tan (c+d x))^n (A+B \tan (c+d x))}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[((a + b*Tan[c + d*x])^n*(A + B*Tan[c + d*x]))/Tan[c + d*x]^(3/2),x]","-\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\tan (c+d x)}}-\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\tan (c+d x)}}","-\frac{(A+i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\tan (c+d x)}}-\frac{(A-i B) (a+b \tan (c+d x))^n \left(\frac{b \tan (c+d x)}{a}+1\right)^{-n} F_1\left(-\frac{1}{2};1,-n;\frac{1}{2};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{d \sqrt{\tan (c+d x)}}",1,"-(((A + I*B)*AppellF1[-1/2, 1, -n, 1/2, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(d*Sqrt[Tan[c + d*x]]*(1 + (b*Tan[c + d*x])/a)^n)) - ((A - I*B)*AppellF1[-1/2, 1, -n, 1/2, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*(a + b*Tan[c + d*x])^n)/(d*Sqrt[Tan[c + d*x]]*(1 + (b*Tan[c + d*x])/a)^n)","A",9,5,33,0.1515,1,"{3603, 3602, 130, 511, 510}"
665,1,63,0,0.0944794,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n,x]","\frac{a (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{a B (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}","\frac{a (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{a B (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}",1,"(a*(I*A + B)*(c - I*c*Tan[e + f*x])^n)/(f*n) - (a*B*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n))","A",3,2,39,0.05128,1,"{3588, 43}"
666,1,59,0,0.0835138,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4,x]","\frac{a c^4 (B+i A) (1-i \tan (e+f x))^4}{4 f}-\frac{a B c^4 (1-i \tan (e+f x))^5}{5 f}","\frac{a c^4 (B+i A) (1-i \tan (e+f x))^4}{4 f}-\frac{a B c^4 (1-i \tan (e+f x))^5}{5 f}",1,"(a*(I*A + B)*c^4*(1 - I*Tan[e + f*x])^4)/(4*f) - (a*B*c^4*(1 - I*Tan[e + f*x])^5)/(5*f)","A",3,2,39,0.05128,1,"{3588, 43}"
667,1,59,0,0.0932845,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3,x]","\frac{a c^3 (B+i A) (1-i \tan (e+f x))^3}{3 f}-\frac{a B c^3 (1-i \tan (e+f x))^4}{4 f}","\frac{a c^3 (B+i A) (1-i \tan (e+f x))^3}{3 f}-\frac{a B c^3 (1-i \tan (e+f x))^4}{4 f}",1,"(a*(I*A + B)*c^3*(1 - I*Tan[e + f*x])^3)/(3*f) - (a*B*c^3*(1 - I*Tan[e + f*x])^4)/(4*f)","A",3,2,39,0.05128,1,"{3588, 43}"
668,1,66,0,0.0852537,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2,x]","-\frac{a c^2 (-B+i A) \tan ^2(e+f x)}{2 f}+\frac{a A c^2 \tan (e+f x)}{f}-\frac{i a B c^2 \tan ^3(e+f x)}{3 f}","-\frac{a c^2 (-B+i A) \tan ^2(e+f x)}{2 f}+\frac{a A c^2 \tan (e+f x)}{f}-\frac{i a B c^2 \tan ^3(e+f x)}{3 f}",1,"(a*A*c^2*Tan[e + f*x])/f - (a*(I*A - B)*c^2*Tan[e + f*x]^2)/(2*f) - ((I/3)*a*B*c^2*Tan[e + f*x]^3)/f","A",3,2,39,0.05128,1,"{3588, 43}"
669,1,32,0,0.0398157,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]),x]","\frac{a A c \tan (e+f x)}{f}+\frac{a B c \tan ^2(e+f x)}{2 f}","\frac{a A c \tan (e+f x)}{f}+\frac{a B c \tan ^2(e+f x)}{2 f}",1,"(a*A*c*Tan[e + f*x])/f + (a*B*c*Tan[e + f*x]^2)/(2*f)","A",2,1,37,0.02703,1,"{3588}"
670,1,46,0,0.0308762,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]),x]","-\frac{a (B+i A) \log (\cos (e+f x))}{f}+a x (A-i B)+\frac{i a B \tan (e+f x)}{f}","-\frac{a (B+i A) \log (\cos (e+f x))}{f}+a x (A-i B)+\frac{i a B \tan (e+f x)}{f}",1,"a*(A - I*B)*x - (a*(I*A + B)*Log[Cos[e + f*x]])/f + (I*a*B*Tan[e + f*x])/f","A",2,2,24,0.08333,1,"{3525, 3475}"
671,1,54,0,0.0880086,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{c-i c \tan (e+f x)} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x]),x]","\frac{a (A-i B)}{c f (\tan (e+f x)+i)}+\frac{a B \log (\cos (e+f x))}{c f}+\frac{i a B x}{c}","\frac{a (A-i B)}{c f (\tan (e+f x)+i)}+\frac{a B \log (\cos (e+f x))}{c f}+\frac{i a B x}{c}",1,"(I*a*B*x)/c + (a*B*Log[Cos[e + f*x]])/(c*f) + (a*(A - I*B))/(c*f*(I + Tan[e + f*x]))","A",3,2,39,0.05128,1,"{3588, 43}"
672,1,46,0,0.0752459,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^2} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^2,x]","\frac{a (A+B \tan (e+f x))^2}{2 c^2 f (B+i A) (1-i \tan (e+f x))^2}","\frac{a (A+B \tan (e+f x))^2}{2 c^2 f (B+i A) (1-i \tan (e+f x))^2}",1,"(a*(A + B*Tan[e + f*x])^2)/(2*(I*A + B)*c^2*f*(1 - I*Tan[e + f*x])^2)","A",2,2,39,0.05128,1,"{3588, 37}"
673,1,55,0,0.0867701,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^3} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^3,x]","-\frac{a (A-i B)}{3 c^3 f (\tan (e+f x)+i)^3}-\frac{a B}{2 c^3 f (\tan (e+f x)+i)^2}","-\frac{a (A-i B)}{3 c^3 f (\tan (e+f x)+i)^3}-\frac{a B}{2 c^3 f (\tan (e+f x)+i)^2}",1,"-(a*(A - I*B))/(3*c^3*f*(I + Tan[e + f*x])^3) - (a*B)/(2*c^3*f*(I + Tan[e + f*x])^2)","A",3,2,39,0.05128,1,"{3588, 43}"
674,1,57,0,0.0878122,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^4} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^4,x]","-\frac{a (B+i A)}{4 c^4 f (\tan (e+f x)+i)^4}-\frac{i a B}{3 c^4 f (\tan (e+f x)+i)^3}","-\frac{a (B+i A)}{4 c^4 f (\tan (e+f x)+i)^4}-\frac{i a B}{3 c^4 f (\tan (e+f x)+i)^3}",1,"-(a*(I*A + B))/(4*c^4*f*(I + Tan[e + f*x])^4) - ((I/3)*a*B)/(c^4*f*(I + Tan[e + f*x])^3)","A",3,2,39,0.05128,1,"{3588, 43}"
675,1,55,0,0.0889989,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^5} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^5,x]","\frac{a (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}+\frac{a B}{4 c^5 f (\tan (e+f x)+i)^4}","\frac{a (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}+\frac{a B}{4 c^5 f (\tan (e+f x)+i)^4}",1,"(a*(A - I*B))/(5*c^5*f*(I + Tan[e + f*x])^5) + (a*B)/(4*c^5*f*(I + Tan[e + f*x])^4)","A",3,2,39,0.05128,1,"{3588, 43}"
676,1,109,0,0.1636572,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n,x]","\frac{2 a^2 (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{a^2 (3 B+i A) (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}+\frac{a^2 B (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}","\frac{2 a^2 (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{a^2 (3 B+i A) (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}+\frac{a^2 B (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}",1,"(2*a^2*(I*A + B)*(c - I*c*Tan[e + f*x])^n)/(f*n) - (a^2*(I*A + 3*B)*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n)) + (a^2*B*(c - I*c*Tan[e + f*x])^(2 + n))/(c^2*f*(2 + n))","A",3,2,41,0.04878,1,"{3588, 77}"
677,1,99,0,0.1677183,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^5 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^5,x]","-\frac{a^2 c^5 (3 B+i A) (1-i \tan (e+f x))^6}{6 f}+\frac{2 a^2 c^5 (B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^2 B c^5 (1-i \tan (e+f x))^7}{7 f}","-\frac{a^2 c^5 (3 B+i A) (1-i \tan (e+f x))^6}{6 f}+\frac{2 a^2 c^5 (B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^2 B c^5 (1-i \tan (e+f x))^7}{7 f}",1,"(2*a^2*(I*A + B)*c^5*(1 - I*Tan[e + f*x])^5)/(5*f) - (a^2*(I*A + 3*B)*c^5*(1 - I*Tan[e + f*x])^6)/(6*f) + (a^2*B*c^5*(1 - I*Tan[e + f*x])^7)/(7*f)","A",3,2,41,0.04878,1,"{3588, 77}"
678,1,99,0,0.1551219,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4,x]","-\frac{a^2 c^4 (3 B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^2 c^4 (B+i A) (1-i \tan (e+f x))^4}{2 f}+\frac{a^2 B c^4 (1-i \tan (e+f x))^6}{6 f}","-\frac{a^2 c^4 (3 B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^2 c^4 (B+i A) (1-i \tan (e+f x))^4}{2 f}+\frac{a^2 B c^4 (1-i \tan (e+f x))^6}{6 f}",1,"(a^2*(I*A + B)*c^4*(1 - I*Tan[e + f*x])^4)/(2*f) - (a^2*(I*A + 3*B)*c^4*(1 - I*Tan[e + f*x])^5)/(5*f) + (a^2*B*c^4*(1 - I*Tan[e + f*x])^6)/(6*f)","A",3,2,41,0.04878,1,"{3588, 77}"
679,1,99,0,0.150024,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3,x]","-\frac{a^2 c^3 (3 B+i A) (1-i \tan (e+f x))^4}{4 f}+\frac{2 a^2 c^3 (B+i A) (1-i \tan (e+f x))^3}{3 f}+\frac{a^2 B c^3 (1-i \tan (e+f x))^5}{5 f}","-\frac{a^2 c^3 (3 B+i A) (1-i \tan (e+f x))^4}{4 f}+\frac{2 a^2 c^3 (B+i A) (1-i \tan (e+f x))^3}{3 f}+\frac{a^2 B c^3 (1-i \tan (e+f x))^5}{5 f}",1,"(2*a^2*(I*A + B)*c^3*(1 - I*Tan[e + f*x])^3)/(3*f) - (a^2*(I*A + 3*B)*c^3*(1 - I*Tan[e + f*x])^4)/(4*f) + (a^2*B*c^3*(1 - I*Tan[e + f*x])^5)/(5*f)","A",3,2,41,0.04878,1,"{3588, 77}"
680,1,62,0,0.1090284,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2,x]","\frac{a^2 A c^2 \tan ^3(e+f x)}{3 f}+\frac{a^2 A c^2 \tan (e+f x)}{f}+\frac{a^2 B c^2 \sec ^4(e+f x)}{4 f}","\frac{a^2 A c^2 \tan ^3(e+f x)}{3 f}+\frac{a^2 A c^2 \tan (e+f x)}{f}+\frac{a^2 B c^2 \sec ^4(e+f x)}{4 f}",1,"(a^2*B*c^2*Sec[e + f*x]^4)/(4*f) + (a^2*A*c^2*Tan[e + f*x])/f + (a^2*A*c^2*Tan[e + f*x]^3)/(3*f)","A",4,3,41,0.07317,1,"{3588, 73, 641}"
681,1,64,0,0.0823462,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]),x]","\frac{a^2 c (B+i A) \tan ^2(e+f x)}{2 f}+\frac{a^2 A c \tan (e+f x)}{f}+\frac{i a^2 B c \tan ^3(e+f x)}{3 f}","\frac{a^2 c (B+i A) \tan ^2(e+f x)}{2 f}+\frac{a^2 A c \tan (e+f x)}{f}+\frac{i a^2 B c \tan ^3(e+f x)}{3 f}",1,"(a^2*A*c*Tan[e + f*x])/f + (a^2*(I*A + B)*c*Tan[e + f*x]^2)/(2*f) + ((I/3)*a^2*B*c*Tan[e + f*x]^3)/f","A",3,2,39,0.05128,1,"{3588, 43}"
682,1,80,0,0.0696908,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]),x]","-\frac{a^2 (A-i B) \tan (e+f x)}{f}-\frac{2 a^2 (B+i A) \log (\cos (e+f x))}{f}+2 a^2 x (A-i B)+\frac{B (a+i a \tan (e+f x))^2}{2 f}","-\frac{a^2 (A-i B) \tan (e+f x)}{f}-\frac{2 a^2 (B+i A) \log (\cos (e+f x))}{f}+2 a^2 x (A-i B)+\frac{B (a+i a \tan (e+f x))^2}{2 f}",1,"2*a^2*(A - I*B)*x - (2*a^2*(I*A + B)*Log[Cos[e + f*x]])/f - (a^2*(A - I*B)*Tan[e + f*x])/f + (B*(a + I*a*Tan[e + f*x])^2)/(2*f)","A",3,3,26,0.1154,1,"{3527, 3477, 3475}"
683,1,93,0,0.1555552,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{c-i c \tan (e+f x)} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x]),x]","\frac{2 a^2 (A-i B)}{c f (\tan (e+f x)+i)}+\frac{a^2 (3 B+i A) \log (\cos (e+f x))}{c f}-\frac{a^2 x (A-3 i B)}{c}-\frac{i a^2 B \tan (e+f x)}{c f}","\frac{2 a^2 (A-i B)}{c f (\tan (e+f x)+i)}+\frac{a^2 (3 B+i A) \log (\cos (e+f x))}{c f}-\frac{a^2 x (A-3 i B)}{c}-\frac{i a^2 B \tan (e+f x)}{c f}",1,"-((a^2*(A - (3*I)*B)*x)/c) + (a^2*(I*A + 3*B)*Log[Cos[e + f*x]])/(c*f) - (I*a^2*B*Tan[e + f*x])/(c*f) + (2*a^2*(A - I*B))/(c*f*(I + Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
684,1,91,0,0.1513588,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^2} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^2,x]","-\frac{a^2 (A-3 i B)}{c^2 f (\tan (e+f x)+i)}+\frac{a^2 (B+i A)}{c^2 f (\tan (e+f x)+i)^2}-\frac{a^2 B \log (\cos (e+f x))}{c^2 f}-\frac{i a^2 B x}{c^2}","-\frac{a^2 (A-3 i B)}{c^2 f (\tan (e+f x)+i)}+\frac{a^2 (B+i A)}{c^2 f (\tan (e+f x)+i)^2}-\frac{a^2 B \log (\cos (e+f x))}{c^2 f}-\frac{i a^2 B x}{c^2}",1,"((-I)*a^2*B*x)/c^2 - (a^2*B*Log[Cos[e + f*x]])/(c^2*f) + (a^2*(I*A + B))/(c^2*f*(I + Tan[e + f*x])^2) - (a^2*(A - (3*I)*B))/(c^2*f*(I + Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
685,1,93,0,0.1523208,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^3} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^3,x]","-\frac{a^2 (3 B+i A)}{2 c^3 f (\tan (e+f x)+i)^2}-\frac{2 a^2 (A-i B)}{3 c^3 f (\tan (e+f x)+i)^3}-\frac{i a^2 B}{c^3 f (\tan (e+f x)+i)}","-\frac{a^2 (3 B+i A)}{2 c^3 f (\tan (e+f x)+i)^2}-\frac{2 a^2 (A-i B)}{3 c^3 f (\tan (e+f x)+i)^3}-\frac{i a^2 B}{c^3 f (\tan (e+f x)+i)}",1,"(-2*a^2*(A - I*B))/(3*c^3*f*(I + Tan[e + f*x])^3) - (a^2*(I*A + 3*B))/(2*c^3*f*(I + Tan[e + f*x])^2) - (I*a^2*B)/(c^3*f*(I + Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
686,1,91,0,0.1496922,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^4} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^4,x]","\frac{a^2 (A-3 i B)}{3 c^4 f (\tan (e+f x)+i)^3}-\frac{a^2 (B+i A)}{2 c^4 f (\tan (e+f x)+i)^4}+\frac{a^2 B}{2 c^4 f (\tan (e+f x)+i)^2}","\frac{a^2 (A-3 i B)}{3 c^4 f (\tan (e+f x)+i)^3}-\frac{a^2 (B+i A)}{2 c^4 f (\tan (e+f x)+i)^4}+\frac{a^2 B}{2 c^4 f (\tan (e+f x)+i)^2}",1,"-(a^2*(I*A + B))/(2*c^4*f*(I + Tan[e + f*x])^4) + (a^2*(A - (3*I)*B))/(3*c^4*f*(I + Tan[e + f*x])^3) + (a^2*B)/(2*c^4*f*(I + Tan[e + f*x])^2)","A",3,2,41,0.04878,1,"{3588, 77}"
687,1,95,0,0.1522853,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^5} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^5,x]","\frac{a^2 (3 B+i A)}{4 c^5 f (\tan (e+f x)+i)^4}+\frac{2 a^2 (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}+\frac{i a^2 B}{3 c^5 f (\tan (e+f x)+i)^3}","\frac{a^2 (3 B+i A)}{4 c^5 f (\tan (e+f x)+i)^4}+\frac{2 a^2 (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}+\frac{i a^2 B}{3 c^5 f (\tan (e+f x)+i)^3}",1,"(2*a^2*(A - I*B))/(5*c^5*f*(I + Tan[e + f*x])^5) + (a^2*(I*A + 3*B))/(4*c^5*f*(I + Tan[e + f*x])^4) + ((I/3)*a^2*B)/(c^5*f*(I + Tan[e + f*x])^3)","A",3,2,41,0.04878,1,"{3588, 77}"
688,1,91,0,0.1495889,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^6} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^6,x]","-\frac{a^2 (A-3 i B)}{5 c^6 f (\tan (e+f x)+i)^5}+\frac{a^2 (B+i A)}{3 c^6 f (\tan (e+f x)+i)^6}-\frac{a^2 B}{4 c^6 f (\tan (e+f x)+i)^4}","-\frac{a^2 (A-3 i B)}{5 c^6 f (\tan (e+f x)+i)^5}+\frac{a^2 (B+i A)}{3 c^6 f (\tan (e+f x)+i)^6}-\frac{a^2 B}{4 c^6 f (\tan (e+f x)+i)^4}",1,"(a^2*(I*A + B))/(3*c^6*f*(I + Tan[e + f*x])^6) - (a^2*(A - (3*I)*B))/(5*c^6*f*(I + Tan[e + f*x])^5) - (a^2*B)/(4*c^6*f*(I + Tan[e + f*x])^4)","A",3,2,41,0.04878,1,"{3588, 77}"
689,1,151,0,0.190707,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n,x]","\frac{a^3 (5 B+i A) (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}+\frac{4 a^3 (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{4 a^3 (2 B+i A) (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}-\frac{a^3 B (c-i c \tan (e+f x))^{n+3}}{c^3 f (n+3)}","\frac{a^3 (5 B+i A) (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}+\frac{4 a^3 (B+i A) (c-i c \tan (e+f x))^n}{f n}-\frac{4 a^3 (2 B+i A) (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}-\frac{a^3 B (c-i c \tan (e+f x))^{n+3}}{c^3 f (n+3)}",1,"(4*a^3*(I*A + B)*(c - I*c*Tan[e + f*x])^n)/(f*n) - (4*a^3*(I*A + 2*B)*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n)) + (a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(2 + n))/(c^2*f*(2 + n)) - (a^3*B*(c - I*c*Tan[e + f*x])^(3 + n))/(c^3*f*(3 + n))","A",3,2,41,0.04878,1,"{3588, 77}"
690,1,135,0,0.2025435,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^6 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^6,x]","\frac{a^3 c^6 (5 B+i A) (1-i \tan (e+f x))^8}{8 f}-\frac{4 a^3 c^6 (2 B+i A) (1-i \tan (e+f x))^7}{7 f}+\frac{2 a^3 c^6 (B+i A) (1-i \tan (e+f x))^6}{3 f}-\frac{a^3 B c^6 (1-i \tan (e+f x))^9}{9 f}","\frac{a^3 c^6 (5 B+i A) (1-i \tan (e+f x))^8}{8 f}-\frac{4 a^3 c^6 (2 B+i A) (1-i \tan (e+f x))^7}{7 f}+\frac{2 a^3 c^6 (B+i A) (1-i \tan (e+f x))^6}{3 f}-\frac{a^3 B c^6 (1-i \tan (e+f x))^9}{9 f}",1,"(2*a^3*(I*A + B)*c^6*(1 - I*Tan[e + f*x])^6)/(3*f) - (4*a^3*(I*A + 2*B)*c^6*(1 - I*Tan[e + f*x])^7)/(7*f) + (a^3*(I*A + 5*B)*c^6*(1 - I*Tan[e + f*x])^8)/(8*f) - (a^3*B*c^6*(1 - I*Tan[e + f*x])^9)/(9*f)","A",3,2,41,0.04878,1,"{3588, 77}"
691,1,135,0,0.190149,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^5 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^5,x]","\frac{a^3 c^5 (5 B+i A) (1-i \tan (e+f x))^7}{7 f}-\frac{2 a^3 c^5 (2 B+i A) (1-i \tan (e+f x))^6}{3 f}+\frac{4 a^3 c^5 (B+i A) (1-i \tan (e+f x))^5}{5 f}-\frac{a^3 B c^5 (1-i \tan (e+f x))^8}{8 f}","\frac{a^3 c^5 (5 B+i A) (1-i \tan (e+f x))^7}{7 f}-\frac{2 a^3 c^5 (2 B+i A) (1-i \tan (e+f x))^6}{3 f}+\frac{4 a^3 c^5 (B+i A) (1-i \tan (e+f x))^5}{5 f}-\frac{a^3 B c^5 (1-i \tan (e+f x))^8}{8 f}",1,"(4*a^3*(I*A + B)*c^5*(1 - I*Tan[e + f*x])^5)/(5*f) - (2*a^3*(I*A + 2*B)*c^5*(1 - I*Tan[e + f*x])^6)/(3*f) + (a^3*(I*A + 5*B)*c^5*(1 - I*Tan[e + f*x])^7)/(7*f) - (a^3*B*c^5*(1 - I*Tan[e + f*x])^8)/(8*f)","A",3,2,41,0.04878,1,"{3588, 77}"
692,1,132,0,0.1780583,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4,x]","\frac{a^3 c^4 (5 B+i A) (1-i \tan (e+f x))^6}{6 f}-\frac{4 a^3 c^4 (2 B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^3 c^4 (B+i A) (1-i \tan (e+f x))^4}{f}-\frac{a^3 B c^4 (1-i \tan (e+f x))^7}{7 f}","\frac{a^3 c^4 (5 B+i A) (1-i \tan (e+f x))^6}{6 f}-\frac{4 a^3 c^4 (2 B+i A) (1-i \tan (e+f x))^5}{5 f}+\frac{a^3 c^4 (B+i A) (1-i \tan (e+f x))^4}{f}-\frac{a^3 B c^4 (1-i \tan (e+f x))^7}{7 f}",1,"(a^3*(I*A + B)*c^4*(1 - I*Tan[e + f*x])^4)/f - (4*a^3*(I*A + 2*B)*c^4*(1 - I*Tan[e + f*x])^5)/(5*f) + (a^3*(I*A + 5*B)*c^4*(1 - I*Tan[e + f*x])^6)/(6*f) - (a^3*B*c^4*(1 - I*Tan[e + f*x])^7)/(7*f)","A",3,2,41,0.04878,1,"{3588, 77}"
693,1,84,0,0.1258897,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3,x]","\frac{a^3 A c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 A c^3 \tan ^3(e+f x)}{3 f}+\frac{a^3 A c^3 \tan (e+f x)}{f}+\frac{a^3 B c^3 \sec ^6(e+f x)}{6 f}","\frac{a^3 A c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 A c^3 \tan ^3(e+f x)}{3 f}+\frac{a^3 A c^3 \tan (e+f x)}{f}+\frac{a^3 B c^3 \sec ^6(e+f x)}{6 f}",1,"(a^3*B*c^3*Sec[e + f*x]^6)/(6*f) + (a^3*A*c^3*Tan[e + f*x])/f + (2*a^3*A*c^3*Tan[e + f*x]^3)/(3*f) + (a^3*A*c^3*Tan[e + f*x]^5)/(5*f)","A",5,4,41,0.09756,1,"{3588, 73, 641, 194}"
694,1,101,0,0.1484418,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2,x]","\frac{a^3 c^2 (-3 B+i A) (1+i \tan (e+f x))^4}{4 f}-\frac{2 a^3 c^2 (-B+i A) (1+i \tan (e+f x))^3}{3 f}+\frac{a^3 B c^2 (1+i \tan (e+f x))^5}{5 f}","\frac{a^3 c^2 (-3 B+i A) (1+i \tan (e+f x))^4}{4 f}-\frac{2 a^3 c^2 (-B+i A) (1+i \tan (e+f x))^3}{3 f}+\frac{a^3 B c^2 (1+i \tan (e+f x))^5}{5 f}",1,"(-2*a^3*(I*A - B)*c^2*(1 + I*Tan[e + f*x])^3)/(3*f) + (a^3*(I*A - 3*B)*c^2*(1 + I*Tan[e + f*x])^4)/(4*f) + (a^3*B*c^2*(1 + I*Tan[e + f*x])^5)/(5*f)","A",3,2,41,0.04878,1,"{3588, 77}"
695,1,61,0,0.0874857,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]),x]","-\frac{a^3 c (-B+i A) (1+i \tan (e+f x))^3}{3 f}-\frac{a^3 B c (1+i \tan (e+f x))^4}{4 f}","-\frac{a^3 c (-B+i A) (1+i \tan (e+f x))^3}{3 f}-\frac{a^3 B c (1+i \tan (e+f x))^4}{4 f}",1,"-(a^3*(I*A - B)*c*(1 + I*Tan[e + f*x])^3)/(3*f) - (a^3*B*c*(1 + I*Tan[e + f*x])^4)/(4*f)","A",3,2,39,0.05128,1,"{3588, 43}"
696,1,110,0,0.093102,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]),x]","-\frac{2 a^3 (A-i B) \tan (e+f x)}{f}-\frac{4 a^3 (B+i A) \log (\cos (e+f x))}{f}+4 a^3 x (A-i B)+\frac{a (B+i A) (a+i a \tan (e+f x))^2}{2 f}+\frac{B (a+i a \tan (e+f x))^3}{3 f}","-\frac{2 a^3 (A-i B) \tan (e+f x)}{f}-\frac{4 a^3 (B+i A) \log (\cos (e+f x))}{f}+4 a^3 x (A-i B)+\frac{a (B+i A) (a+i a \tan (e+f x))^2}{2 f}+\frac{B (a+i a \tan (e+f x))^3}{3 f}",1,"4*a^3*(A - I*B)*x - (4*a^3*(I*A + B)*Log[Cos[e + f*x]])/f - (2*a^3*(A - I*B)*Tan[e + f*x])/f + (a*(I*A + B)*(a + I*a*Tan[e + f*x])^2)/(2*f) + (B*(a + I*a*Tan[e + f*x])^3)/(3*f)","A",4,4,26,0.1538,1,"{3527, 3478, 3477, 3475}"
697,1,119,0,0.1719204,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{c-i c \tan (e+f x)} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x]),x]","\frac{a^3 (A-4 i B) \tan (e+f x)}{c f}+\frac{4 a^3 (A-i B)}{c f (\tan (e+f x)+i)}+\frac{4 a^3 (2 B+i A) \log (\cos (e+f x))}{c f}-\frac{4 a^3 x (A-2 i B)}{c}+\frac{a^3 B \tan ^2(e+f x)}{2 c f}","\frac{a^3 (A-4 i B) \tan (e+f x)}{c f}+\frac{4 a^3 (A-i B)}{c f (\tan (e+f x)+i)}+\frac{4 a^3 (2 B+i A) \log (\cos (e+f x))}{c f}-\frac{4 a^3 x (A-2 i B)}{c}+\frac{a^3 B \tan ^2(e+f x)}{2 c f}",1,"(-4*a^3*(A - (2*I)*B)*x)/c + (4*a^3*(I*A + 2*B)*Log[Cos[e + f*x]])/(c*f) + (a^3*(A - (4*I)*B)*Tan[e + f*x])/(c*f) + (a^3*B*Tan[e + f*x]^2)/(2*c*f) + (4*a^3*(A - I*B))/(c*f*(I + Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
698,1,123,0,0.1782713,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^2} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^2,x]","-\frac{4 a^3 (A-2 i B)}{c^2 f (\tan (e+f x)+i)}+\frac{2 a^3 (B+i A)}{c^2 f (\tan (e+f x)+i)^2}-\frac{a^3 (5 B+i A) \log (\cos (e+f x))}{c^2 f}+\frac{a^3 x (A-5 i B)}{c^2}+\frac{i a^3 B \tan (e+f x)}{c^2 f}","-\frac{4 a^3 (A-2 i B)}{c^2 f (\tan (e+f x)+i)}+\frac{2 a^3 (B+i A)}{c^2 f (\tan (e+f x)+i)^2}-\frac{a^3 (5 B+i A) \log (\cos (e+f x))}{c^2 f}+\frac{a^3 x (A-5 i B)}{c^2}+\frac{i a^3 B \tan (e+f x)}{c^2 f}",1,"(a^3*(A - (5*I)*B)*x)/c^2 - (a^3*(I*A + 5*B)*Log[Cos[e + f*x]])/(c^2*f) + (I*a^3*B*Tan[e + f*x])/(c^2*f) + (2*a^3*(I*A + B))/(c^2*f*(I + Tan[e + f*x])^2) - (4*a^3*(A - (2*I)*B))/(c^2*f*(I + Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
699,1,129,0,0.1538664,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^3} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^3,x]","-\frac{a^3 (B+i A) (1+i \tan (e+f x))^3}{6 c^3 f (1-i \tan (e+f x))^3}-\frac{4 i a^3 B}{c^3 f (\tan (e+f x)+i)}-\frac{2 a^3 B}{c^3 f (\tan (e+f x)+i)^2}+\frac{a^3 B \log (\cos (e+f x))}{c^3 f}+\frac{i a^3 B x}{c^3}","-\frac{a^3 (B+i A) (1+i \tan (e+f x))^3}{6 c^3 f (1-i \tan (e+f x))^3}-\frac{4 i a^3 B}{c^3 f (\tan (e+f x)+i)}-\frac{2 a^3 B}{c^3 f (\tan (e+f x)+i)^2}+\frac{a^3 B \log (\cos (e+f x))}{c^3 f}+\frac{i a^3 B x}{c^3}",1,"(I*a^3*B*x)/c^3 + (a^3*B*Log[Cos[e + f*x]])/(c^3*f) - (a^3*(I*A + B)*(1 + I*Tan[e + f*x])^3)/(6*c^3*f*(1 - I*Tan[e + f*x])^3) - (2*a^3*B)/(c^3*f*(I + Tan[e + f*x])^2) - ((4*I)*a^3*B)/(c^3*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 78, 43}"
700,1,99,0,0.1384708,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^4} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^4,x]","-\frac{a^3 (-7 B+i A) (1+i \tan (e+f x))^3}{48 c^4 f (1-i \tan (e+f x))^3}-\frac{a^3 (B+i A) (1+i \tan (e+f x))^3}{8 c^4 f (1-i \tan (e+f x))^4}","-\frac{a^3 (-7 B+i A) (1+i \tan (e+f x))^3}{48 c^4 f (1-i \tan (e+f x))^3}-\frac{a^3 (B+i A) (1+i \tan (e+f x))^3}{8 c^4 f (1-i \tan (e+f x))^4}",1,"-(a^3*(I*A + B)*(1 + I*Tan[e + f*x])^3)/(8*c^4*f*(1 - I*Tan[e + f*x])^4) - (a^3*(I*A - 7*B)*(1 + I*Tan[e + f*x])^3)/(48*c^4*f*(1 - I*Tan[e + f*x])^3)","A",3,3,41,0.07317,1,"{3588, 78, 37}"
701,1,122,0,0.1752107,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^5} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^5,x]","-\frac{a^3 (A-5 i B)}{3 c^5 f (\tan (e+f x)+i)^3}+\frac{a^3 (2 B+i A)}{c^5 f (\tan (e+f x)+i)^4}+\frac{4 a^3 (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}-\frac{a^3 B}{2 c^5 f (\tan (e+f x)+i)^2}","-\frac{a^3 (A-5 i B)}{3 c^5 f (\tan (e+f x)+i)^3}+\frac{a^3 (2 B+i A)}{c^5 f (\tan (e+f x)+i)^4}+\frac{4 a^3 (A-i B)}{5 c^5 f (\tan (e+f x)+i)^5}-\frac{a^3 B}{2 c^5 f (\tan (e+f x)+i)^2}",1,"(4*a^3*(A - I*B))/(5*c^5*f*(I + Tan[e + f*x])^5) + (a^3*(I*A + 2*B))/(c^5*f*(I + Tan[e + f*x])^4) - (a^3*(A - (5*I)*B))/(3*c^5*f*(I + Tan[e + f*x])^3) - (a^3*B)/(2*c^5*f*(I + Tan[e + f*x])^2)","A",3,2,41,0.04878,1,"{3588, 77}"
702,1,127,0,0.1764726,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^6} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^6,x]","-\frac{a^3 (5 B+i A)}{4 c^6 f (\tan (e+f x)+i)^4}-\frac{4 a^3 (A-2 i B)}{5 c^6 f (\tan (e+f x)+i)^5}+\frac{2 a^3 (B+i A)}{3 c^6 f (\tan (e+f x)+i)^6}-\frac{i a^3 B}{3 c^6 f (\tan (e+f x)+i)^3}","-\frac{a^3 (5 B+i A)}{4 c^6 f (\tan (e+f x)+i)^4}-\frac{4 a^3 (A-2 i B)}{5 c^6 f (\tan (e+f x)+i)^5}+\frac{2 a^3 (B+i A)}{3 c^6 f (\tan (e+f x)+i)^6}-\frac{i a^3 B}{3 c^6 f (\tan (e+f x)+i)^3}",1,"(2*a^3*(I*A + B))/(3*c^6*f*(I + Tan[e + f*x])^6) - (4*a^3*(A - (2*I)*B))/(5*c^6*f*(I + Tan[e + f*x])^5) - (a^3*(I*A + 5*B))/(4*c^6*f*(I + Tan[e + f*x])^4) - ((I/3)*a^3*B)/(c^6*f*(I + Tan[e + f*x])^3)","A",3,2,41,0.04878,1,"{3588, 77}"
703,1,125,0,0.1744682,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^7} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^7,x]","\frac{a^3 (A-5 i B)}{5 c^7 f (\tan (e+f x)+i)^5}-\frac{2 a^3 (2 B+i A)}{3 c^7 f (\tan (e+f x)+i)^6}-\frac{4 a^3 (A-i B)}{7 c^7 f (\tan (e+f x)+i)^7}+\frac{a^3 B}{4 c^7 f (\tan (e+f x)+i)^4}","\frac{a^3 (A-5 i B)}{5 c^7 f (\tan (e+f x)+i)^5}-\frac{2 a^3 (2 B+i A)}{3 c^7 f (\tan (e+f x)+i)^6}-\frac{4 a^3 (A-i B)}{7 c^7 f (\tan (e+f x)+i)^7}+\frac{a^3 B}{4 c^7 f (\tan (e+f x)+i)^4}",1,"(-4*a^3*(A - I*B))/(7*c^7*f*(I + Tan[e + f*x])^7) - (2*a^3*(I*A + 2*B))/(3*c^7*f*(I + Tan[e + f*x])^6) + (a^3*(A - (5*I)*B))/(5*c^7*f*(I + Tan[e + f*x])^5) + (a^3*B)/(4*c^7*f*(I + Tan[e + f*x])^4)","A",3,2,41,0.04878,1,"{3588, 77}"
704,1,127,0,0.1821773,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^8} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^8,x]","\frac{a^3 (5 B+i A)}{6 c^8 f (\tan (e+f x)+i)^6}+\frac{4 a^3 (A-2 i B)}{7 c^8 f (\tan (e+f x)+i)^7}-\frac{a^3 (B+i A)}{2 c^8 f (\tan (e+f x)+i)^8}+\frac{i a^3 B}{5 c^8 f (\tan (e+f x)+i)^5}","\frac{a^3 (5 B+i A)}{6 c^8 f (\tan (e+f x)+i)^6}+\frac{4 a^3 (A-2 i B)}{7 c^8 f (\tan (e+f x)+i)^7}-\frac{a^3 (B+i A)}{2 c^8 f (\tan (e+f x)+i)^8}+\frac{i a^3 B}{5 c^8 f (\tan (e+f x)+i)^5}",1,"-(a^3*(I*A + B))/(2*c^8*f*(I + Tan[e + f*x])^8) + (4*a^3*(A - (2*I)*B))/(7*c^8*f*(I + Tan[e + f*x])^7) + (a^3*(I*A + 5*B))/(6*c^8*f*(I + Tan[e + f*x])^6) + ((I/5)*a^3*B)/(c^8*f*(I + Tan[e + f*x])^5)","A",3,2,41,0.04878,1,"{3588, 77}"
705,1,115,0,0.1790903,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^n}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n)/(a + I*a*Tan[e + f*x]),x]","\frac{(B (n+1)+i A (1-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{4 a f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{2 a f (1+i \tan (e+f x))}","\frac{(B (n+1)+i A (1-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(1,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{4 a f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{2 a f (1+i \tan (e+f x))}",1,"((I*A*(1 - n) + B*(1 + n))*Hypergeometric2F1[1, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(4*a*f*n) + ((I*A - B)*(c - I*c*Tan[e + f*x])^n)/(2*a*f*(1 + I*Tan[e + f*x]))","A",3,3,41,0.07317,1,"{3588, 78, 68}"
706,1,157,0,0.2159322,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^4}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4)/(a + I*a*Tan[e + f*x]),x]","-\frac{c^4 (-5 B+i A) \tan ^2(e+f x)}{2 a f}+\frac{c^4 (5 A+12 i B) \tan (e+f x)}{a f}-\frac{8 c^4 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{4 c^4 (-5 B+3 i A) \log (\cos (e+f x))}{a f}-\frac{4 c^4 x (3 A+5 i B)}{a}-\frac{i B c^4 \tan ^3(e+f x)}{3 a f}","-\frac{c^4 (-5 B+i A) \tan ^2(e+f x)}{2 a f}+\frac{c^4 (5 A+12 i B) \tan (e+f x)}{a f}-\frac{8 c^4 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{4 c^4 (-5 B+3 i A) \log (\cos (e+f x))}{a f}-\frac{4 c^4 x (3 A+5 i B)}{a}-\frac{i B c^4 \tan ^3(e+f x)}{3 a f}",1,"(-4*(3*A + (5*I)*B)*c^4*x)/a - (4*((3*I)*A - 5*B)*c^4*Log[Cos[e + f*x]])/(a*f) - (8*(A + I*B)*c^4)/(a*f*(I - Tan[e + f*x])) + ((5*A + (12*I)*B)*c^4*Tan[e + f*x])/(a*f) - ((I*A - 5*B)*c^4*Tan[e + f*x]^2)/(2*a*f) - ((I/3)*B*c^4*Tan[e + f*x]^3)/(a*f)","A",3,2,41,0.04878,1,"{3588, 77}"
707,1,121,0,0.1827698,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^3}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3)/(a + I*a*Tan[e + f*x]),x]","\frac{c^3 (A+4 i B) \tan (e+f x)}{a f}-\frac{4 c^3 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{4 c^3 (-2 B+i A) \log (\cos (e+f x))}{a f}-\frac{4 c^3 x (A+2 i B)}{a}+\frac{B c^3 \tan ^2(e+f x)}{2 a f}","\frac{c^3 (A+4 i B) \tan (e+f x)}{a f}-\frac{4 c^3 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{4 c^3 (-2 B+i A) \log (\cos (e+f x))}{a f}-\frac{4 c^3 x (A+2 i B)}{a}+\frac{B c^3 \tan ^2(e+f x)}{2 a f}",1,"(-4*(A + (2*I)*B)*c^3*x)/a - (4*(I*A - 2*B)*c^3*Log[Cos[e + f*x]])/(a*f) - (4*(A + I*B)*c^3)/(a*f*(I - Tan[e + f*x])) + ((A + (4*I)*B)*c^3*Tan[e + f*x])/(a*f) + (B*c^3*Tan[e + f*x]^2)/(2*a*f)","A",3,2,41,0.04878,1,"{3588, 77}"
708,1,96,0,0.1593171,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^2}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2)/(a + I*a*Tan[e + f*x]),x]","-\frac{2 c^2 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{c^2 (-3 B+i A) \log (\cos (e+f x))}{a f}-\frac{c^2 x (A+3 i B)}{a}+\frac{i B c^2 \tan (e+f x)}{a f}","-\frac{2 c^2 (A+i B)}{a f (-\tan (e+f x)+i)}-\frac{c^2 (-3 B+i A) \log (\cos (e+f x))}{a f}-\frac{c^2 x (A+3 i B)}{a}+\frac{i B c^2 \tan (e+f x)}{a f}",1,"-(((A + (3*I)*B)*c^2*x)/a) - ((I*A - 3*B)*c^2*Log[Cos[e + f*x]])/(a*f) - (2*(A + I*B)*c^2)/(a*f*(I - Tan[e + f*x])) + (I*B*c^2*Tan[e + f*x])/(a*f)","A",3,2,41,0.04878,1,"{3588, 77}"
709,1,57,0,0.090516,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]))/(a + I*a*Tan[e + f*x]),x]","-\frac{c (A+i B)}{a f (-\tan (e+f x)+i)}+\frac{B c \log (\cos (e+f x))}{a f}-\frac{i B c x}{a}","-\frac{c (A+i B)}{a f (-\tan (e+f x)+i)}+\frac{B c \log (\cos (e+f x))}{a f}-\frac{i B c x}{a}",1,"((-I)*B*c*x)/a + (B*c*Log[Cos[e + f*x]])/(a*f) - ((A + I*B)*c)/(a*f*(I - Tan[e + f*x]))","A",3,2,39,0.05128,1,"{3588, 43}"
710,1,47,0,0.0451566,"\int \frac{A+B \tan (e+f x)}{a+i a \tan (e+f x)} \, dx","Int[(A + B*Tan[e + f*x])/(a + I*a*Tan[e + f*x]),x]","\frac{-B+i A}{2 f (a+i a \tan (e+f x))}+\frac{x (A-i B)}{2 a}","\frac{-B+i A}{2 f (a+i a \tan (e+f x))}+\frac{x (A-i B)}{2 a}",1,"((A - I*B)*x)/(2*a) + (I*A - B)/(2*f*(a + I*a*Tan[e + f*x]))","A",2,2,26,0.07692,1,"{3526, 8}"
711,1,45,0,0.1275541,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])),x]","\frac{A x}{2 a c}-\frac{\cos ^2(e+f x) (B-A \tan (e+f x))}{2 a c f}","\frac{A x}{2 a c}-\frac{\cos ^2(e+f x) (B-A \tan (e+f x))}{2 a c f}",1,"(A*x)/(2*a*c) - (Cos[e + f*x]^2*(B - A*Tan[e + f*x]))/(2*a*c*f)","A",4,4,41,0.09756,1,"{3588, 73, 639, 205}"
712,1,113,0,0.189822,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2),x]","-\frac{A+i B}{8 a c^2 f (-\tan (e+f x)+i)}+\frac{B+i A}{8 a c^2 f (\tan (e+f x)+i)^2}+\frac{x (3 A+i B)}{8 a c^2}+\frac{A}{4 a c^2 f (\tan (e+f x)+i)}","-\frac{A+i B}{8 a c^2 f (-\tan (e+f x)+i)}+\frac{B+i A}{8 a c^2 f (\tan (e+f x)+i)^2}+\frac{x (3 A+i B)}{8 a c^2}+\frac{A}{4 a c^2 f (\tan (e+f x)+i)}",1,"((3*A + I*B)*x)/(8*a*c^2) - (A + I*B)/(8*a*c^2*f*(I - Tan[e + f*x])) + (I*A + B)/(8*a*c^2*f*(I + Tan[e + f*x])^2) + A/(4*a*c^2*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
713,1,149,0,0.2159356,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3),x]","-\frac{A+i B}{16 a c^3 f (-\tan (e+f x)+i)}+\frac{3 A+i B}{16 a c^3 f (\tan (e+f x)+i)}-\frac{A-i B}{12 a c^3 f (\tan (e+f x)+i)^3}+\frac{x (2 A+i B)}{8 a c^3}+\frac{i A}{8 a c^3 f (\tan (e+f x)+i)^2}","-\frac{A+i B}{16 a c^3 f (-\tan (e+f x)+i)}+\frac{3 A+i B}{16 a c^3 f (\tan (e+f x)+i)}-\frac{A-i B}{12 a c^3 f (\tan (e+f x)+i)^3}+\frac{x (2 A+i B)}{8 a c^3}+\frac{i A}{8 a c^3 f (\tan (e+f x)+i)^2}",1,"((2*A + I*B)*x)/(8*a*c^3) - (A + I*B)/(16*a*c^3*f*(I - Tan[e + f*x])) - (A - I*B)/(12*a*c^3*f*(I + Tan[e + f*x])^3) + ((I/8)*A)/(a*c^3*f*(I + Tan[e + f*x])^2) + (3*A + I*B)/(16*a*c^3*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
714,1,181,0,0.2401965,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^4} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4),x]","-\frac{A+i B}{32 a c^4 f (-\tan (e+f x)+i)}+\frac{2 A+i B}{16 a c^4 f (\tan (e+f x)+i)}+\frac{-B+3 i A}{32 a c^4 f (\tan (e+f x)+i)^2}-\frac{B+i A}{16 a c^4 f (\tan (e+f x)+i)^4}+\frac{x (5 A+3 i B)}{32 a c^4}-\frac{A}{12 a c^4 f (\tan (e+f x)+i)^3}","-\frac{A+i B}{32 a c^4 f (-\tan (e+f x)+i)}+\frac{2 A+i B}{16 a c^4 f (\tan (e+f x)+i)}+\frac{-B+3 i A}{32 a c^4 f (\tan (e+f x)+i)^2}-\frac{B+i A}{16 a c^4 f (\tan (e+f x)+i)^4}+\frac{x (5 A+3 i B)}{32 a c^4}-\frac{A}{12 a c^4 f (\tan (e+f x)+i)^3}",1,"((5*A + (3*I)*B)*x)/(32*a*c^4) - (A + I*B)/(32*a*c^4*f*(I - Tan[e + f*x])) - (I*A + B)/(16*a*c^4*f*(I + Tan[e + f*x])^4) - A/(12*a*c^4*f*(I + Tan[e + f*x])^3) + ((3*I)*A - B)/(32*a*c^4*f*(I + Tan[e + f*x])^2) + (2*A + I*B)/(16*a*c^4*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
715,1,115,0,0.1734198,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n)/(a + I*a*Tan[e + f*x])^2,x]","\frac{(B (n+2)+i A (2-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(2,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{16 a^2 f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{4 a^2 f (1+i \tan (e+f x))^2}","\frac{(B (n+2)+i A (2-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(2,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{16 a^2 f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{4 a^2 f (1+i \tan (e+f x))^2}",1,"((I*A*(2 - n) + B*(2 + n))*Hypergeometric2F1[2, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(16*a^2*f*n) + ((I*A - B)*(c - I*c*Tan[e + f*x])^n)/(4*a^2*f*(1 + I*Tan[e + f*x])^2)","A",3,3,41,0.07317,1,"{3588, 78, 68}"
716,1,194,0,0.2489146,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^5}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^5)/(a + I*a*Tan[e + f*x])^2,x]","\frac{c^5 (-7 B+i A) \tan ^2(e+f x)}{2 a^2 f}-\frac{c^5 (7 A+24 i B) \tan (e+f x)}{a^2 f}+\frac{16 c^5 (2 A+3 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{8 c^5 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{8 c^5 (-7 B+3 i A) \log (\cos (e+f x))}{a^2 f}+\frac{8 c^5 x (3 A+7 i B)}{a^2}+\frac{i B c^5 \tan ^3(e+f x)}{3 a^2 f}","\frac{c^5 (-7 B+i A) \tan ^2(e+f x)}{2 a^2 f}-\frac{c^5 (7 A+24 i B) \tan (e+f x)}{a^2 f}+\frac{16 c^5 (2 A+3 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{8 c^5 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{8 c^5 (-7 B+3 i A) \log (\cos (e+f x))}{a^2 f}+\frac{8 c^5 x (3 A+7 i B)}{a^2}+\frac{i B c^5 \tan ^3(e+f x)}{3 a^2 f}",1,"(8*(3*A + (7*I)*B)*c^5*x)/a^2 + (8*((3*I)*A - 7*B)*c^5*Log[Cos[e + f*x]])/(a^2*f) - (8*(I*A - B)*c^5)/(a^2*f*(I - Tan[e + f*x])^2) + (16*(2*A + (3*I)*B)*c^5)/(a^2*f*(I - Tan[e + f*x])) - ((7*A + (24*I)*B)*c^5*Tan[e + f*x])/(a^2*f) + ((I*A - 7*B)*c^5*Tan[e + f*x]^2)/(2*a^2*f) + ((I/3)*B*c^5*Tan[e + f*x]^3)/(a^2*f)","A",3,2,41,0.04878,1,"{3588, 77}"
717,1,158,0,0.2100528,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4)/(a + I*a*Tan[e + f*x])^2,x]","-\frac{c^4 (A+6 i B) \tan (e+f x)}{a^2 f}+\frac{4 c^4 (3 A+5 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{4 c^4 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{6 c^4 (-3 B+i A) \log (\cos (e+f x))}{a^2 f}+\frac{6 c^4 x (A+3 i B)}{a^2}-\frac{B c^4 \tan ^2(e+f x)}{2 a^2 f}","-\frac{c^4 (A+6 i B) \tan (e+f x)}{a^2 f}+\frac{4 c^4 (3 A+5 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{4 c^4 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{6 c^4 (-3 B+i A) \log (\cos (e+f x))}{a^2 f}+\frac{6 c^4 x (A+3 i B)}{a^2}-\frac{B c^4 \tan ^2(e+f x)}{2 a^2 f}",1,"(6*(A + (3*I)*B)*c^4*x)/a^2 + (6*(I*A - 3*B)*c^4*Log[Cos[e + f*x]])/(a^2*f) - (4*(I*A - B)*c^4)/(a^2*f*(I - Tan[e + f*x])^2) + (4*(3*A + (5*I)*B)*c^4)/(a^2*f*(I - Tan[e + f*x])) - ((A + (6*I)*B)*c^4*Tan[e + f*x])/(a^2*f) - (B*c^4*Tan[e + f*x]^2)/(2*a^2*f)","A",3,2,41,0.04878,1,"{3588, 77}"
718,1,128,0,0.1801172,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3)/(a + I*a*Tan[e + f*x])^2,x]","\frac{4 c^3 (A+2 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{2 c^3 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{c^3 (-5 B+i A) \log (\cos (e+f x))}{a^2 f}+\frac{c^3 x (A+5 i B)}{a^2}-\frac{i B c^3 \tan (e+f x)}{a^2 f}","\frac{4 c^3 (A+2 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{2 c^3 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}+\frac{c^3 (-5 B+i A) \log (\cos (e+f x))}{a^2 f}+\frac{c^3 x (A+5 i B)}{a^2}-\frac{i B c^3 \tan (e+f x)}{a^2 f}",1,"((A + (5*I)*B)*c^3*x)/a^2 + ((I*A - 5*B)*c^3*Log[Cos[e + f*x]])/(a^2*f) - (2*(I*A - B)*c^3)/(a^2*f*(I - Tan[e + f*x])^2) + (4*(A + (2*I)*B)*c^3)/(a^2*f*(I - Tan[e + f*x])) - (I*B*c^3*Tan[e + f*x])/(a^2*f)","A",3,2,41,0.04878,1,"{3588, 77}"
719,1,97,0,0.1517587,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^2}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{c^2 (A+3 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{c^2 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}-\frac{B c^2 \log (\cos (e+f x))}{a^2 f}+\frac{i B c^2 x}{a^2}","\frac{c^2 (A+3 i B)}{a^2 f (-\tan (e+f x)+i)}-\frac{c^2 (-B+i A)}{a^2 f (-\tan (e+f x)+i)^2}-\frac{B c^2 \log (\cos (e+f x))}{a^2 f}+\frac{i B c^2 x}{a^2}",1,"(I*B*c^2*x)/a^2 - (B*c^2*Log[Cos[e + f*x]])/(a^2*f) - ((I*A - B)*c^2)/(a^2*f*(I - Tan[e + f*x])^2) + ((A + (3*I)*B)*c^2)/(a^2*f*(I - Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
720,1,48,0,0.0813494,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]))/(a + I*a*Tan[e + f*x])^2,x]","-\frac{c (A+B \tan (e+f x))^2}{2 a^2 f (-B+i A) (1+i \tan (e+f x))^2}","-\frac{c (A+B \tan (e+f x))^2}{2 a^2 f (-B+i A) (1+i \tan (e+f x))^2}",1,"-(c*(A + B*Tan[e + f*x])^2)/(2*a^2*(I*A - B)*f*(1 + I*Tan[e + f*x])^2)","A",2,2,39,0.05128,1,"{3588, 37}"
721,1,80,0,0.0653431,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^2,x]","\frac{B+i A}{4 f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{x (A-i B)}{4 a^2}+\frac{-B+i A}{4 f (a+i a \tan (e+f x))^2}","\frac{B+i A}{4 f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{x (A-i B)}{4 a^2}+\frac{-B+i A}{4 f (a+i a \tan (e+f x))^2}",1,"((A - I*B)*x)/(4*a^2) + (I*A - B)/(4*f*(a + I*a*Tan[e + f*x])^2) + (I*A + B)/(4*f*(a^2 + I*a^2*Tan[e + f*x]))","A",3,3,26,0.1154,1,"{3526, 3479, 8}"
722,1,117,0,0.1868119,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])),x]","\frac{A-i B}{8 a^2 c f (\tan (e+f x)+i)}-\frac{-B+i A}{8 a^2 c f (-\tan (e+f x)+i)^2}+\frac{x (3 A-i B)}{8 a^2 c}-\frac{A}{4 a^2 c f (-\tan (e+f x)+i)}","\frac{A-i B}{8 a^2 c f (\tan (e+f x)+i)}-\frac{-B+i A}{8 a^2 c f (-\tan (e+f x)+i)^2}+\frac{x (3 A-i B)}{8 a^2 c}-\frac{A}{4 a^2 c f (-\tan (e+f x)+i)}",1,"((3*A - I*B)*x)/(8*a^2*c) - (I*A - B)/(8*a^2*c*f*(I - Tan[e + f*x])^2) - A/(4*a^2*c*f*(I - Tan[e + f*x])) + (A - I*B)/(8*a^2*c*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
723,1,71,0,0.138077,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^2),x]","-\frac{\cos ^4(e+f x) (B-A \tan (e+f x))}{4 a^2 c^2 f}+\frac{3 A \sin (e+f x) \cos (e+f x)}{8 a^2 c^2 f}+\frac{3 A x}{8 a^2 c^2}","-\frac{\cos ^4(e+f x) (B-A \tan (e+f x))}{4 a^2 c^2 f}+\frac{3 A \sin (e+f x) \cos (e+f x)}{8 a^2 c^2 f}+\frac{3 A x}{8 a^2 c^2}",1,"(3*A*x)/(8*a^2*c^2) + (3*A*Cos[e + f*x]*Sin[e + f*x])/(8*a^2*c^2*f) - (Cos[e + f*x]^4*(B - A*Tan[e + f*x]))/(4*a^2*c^2*f)","A",5,5,41,0.1220,1,"{3588, 73, 639, 199, 205}"
724,1,183,0,0.2388822,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^3),x]","-\frac{2 A+i B}{16 a^2 c^3 f (-\tan (e+f x)+i)}-\frac{-B+i A}{32 a^2 c^3 f (-\tan (e+f x)+i)^2}+\frac{B+3 i A}{32 a^2 c^3 f (\tan (e+f x)+i)^2}-\frac{A-i B}{24 a^2 c^3 f (\tan (e+f x)+i)^3}+\frac{x (5 A+i B)}{16 a^2 c^3}+\frac{3 A}{16 a^2 c^3 f (\tan (e+f x)+i)}","-\frac{2 A+i B}{16 a^2 c^3 f (-\tan (e+f x)+i)}-\frac{-B+i A}{32 a^2 c^3 f (-\tan (e+f x)+i)^2}+\frac{B+3 i A}{32 a^2 c^3 f (\tan (e+f x)+i)^2}-\frac{A-i B}{24 a^2 c^3 f (\tan (e+f x)+i)^3}+\frac{x (5 A+i B)}{16 a^2 c^3}+\frac{3 A}{16 a^2 c^3 f (\tan (e+f x)+i)}",1,"((5*A + I*B)*x)/(16*a^2*c^3) - (I*A - B)/(32*a^2*c^3*f*(I - Tan[e + f*x])^2) - (2*A + I*B)/(16*a^2*c^3*f*(I - Tan[e + f*x])) - (A - I*B)/(24*a^2*c^3*f*(I + Tan[e + f*x])^3) + ((3*I)*A + B)/(32*a^2*c^3*f*(I + Tan[e + f*x])^2) + (3*A)/(16*a^2*c^3*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
725,1,221,0,0.2678896,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^4} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^4),x]","-\frac{5 A+3 i B}{64 a^2 c^4 f (-\tan (e+f x)+i)}+\frac{5 A+i B}{32 a^2 c^4 f (\tan (e+f x)+i)}-\frac{-B+i A}{64 a^2 c^4 f (-\tan (e+f x)+i)^2}-\frac{3 A-i B}{48 a^2 c^4 f (\tan (e+f x)+i)^3}-\frac{B+i A}{32 a^2 c^4 f (\tan (e+f x)+i)^4}+\frac{5 x (3 A+i B)}{64 a^2 c^4}+\frac{3 i A}{32 a^2 c^4 f (\tan (e+f x)+i)^2}","-\frac{5 A+3 i B}{64 a^2 c^4 f (-\tan (e+f x)+i)}+\frac{5 A+i B}{32 a^2 c^4 f (\tan (e+f x)+i)}-\frac{-B+i A}{64 a^2 c^4 f (-\tan (e+f x)+i)^2}-\frac{3 A-i B}{48 a^2 c^4 f (\tan (e+f x)+i)^3}-\frac{B+i A}{32 a^2 c^4 f (\tan (e+f x)+i)^4}+\frac{5 x (3 A+i B)}{64 a^2 c^4}+\frac{3 i A}{32 a^2 c^4 f (\tan (e+f x)+i)^2}",1,"(5*(3*A + I*B)*x)/(64*a^2*c^4) - (I*A - B)/(64*a^2*c^4*f*(I - Tan[e + f*x])^2) - (5*A + (3*I)*B)/(64*a^2*c^4*f*(I - Tan[e + f*x])) - (I*A + B)/(32*a^2*c^4*f*(I + Tan[e + f*x])^4) - (3*A - I*B)/(48*a^2*c^4*f*(I + Tan[e + f*x])^3) + (((3*I)/32)*A)/(a^2*c^4*f*(I + Tan[e + f*x])^2) + (5*A + I*B)/(32*a^2*c^4*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
726,1,251,0,0.3046167,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^5} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^5),x]","-\frac{3 A+2 i B}{64 a^2 c^5 f (-\tan (e+f x)+i)}+\frac{5 (3 A+i B)}{128 a^2 c^5 f (\tan (e+f x)+i)}-\frac{-B+i A}{128 a^2 c^5 f (-\tan (e+f x)+i)^2}+\frac{-B+5 i A}{64 a^2 c^5 f (\tan (e+f x)+i)^2}-\frac{B+3 i A}{64 a^2 c^5 f (\tan (e+f x)+i)^4}+\frac{A-i B}{40 a^2 c^5 f (\tan (e+f x)+i)^5}+\frac{3 x (7 A+3 i B)}{128 a^2 c^5}-\frac{A}{16 a^2 c^5 f (\tan (e+f x)+i)^3}","-\frac{3 A+2 i B}{64 a^2 c^5 f (-\tan (e+f x)+i)}+\frac{5 (3 A+i B)}{128 a^2 c^5 f (\tan (e+f x)+i)}-\frac{-B+i A}{128 a^2 c^5 f (-\tan (e+f x)+i)^2}+\frac{-B+5 i A}{64 a^2 c^5 f (\tan (e+f x)+i)^2}-\frac{B+3 i A}{64 a^2 c^5 f (\tan (e+f x)+i)^4}+\frac{A-i B}{40 a^2 c^5 f (\tan (e+f x)+i)^5}+\frac{3 x (7 A+3 i B)}{128 a^2 c^5}-\frac{A}{16 a^2 c^5 f (\tan (e+f x)+i)^3}",1,"(3*(7*A + (3*I)*B)*x)/(128*a^2*c^5) - (I*A - B)/(128*a^2*c^5*f*(I - Tan[e + f*x])^2) - (3*A + (2*I)*B)/(64*a^2*c^5*f*(I - Tan[e + f*x])) + (A - I*B)/(40*a^2*c^5*f*(I + Tan[e + f*x])^5) - ((3*I)*A + B)/(64*a^2*c^5*f*(I + Tan[e + f*x])^4) - A/(16*a^2*c^5*f*(I + Tan[e + f*x])^3) + ((5*I)*A - B)/(64*a^2*c^5*f*(I + Tan[e + f*x])^2) + (5*(3*A + I*B))/(128*a^2*c^5*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
727,1,115,0,0.1706649,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^n}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n)/(a + I*a*Tan[e + f*x])^3,x]","\frac{(B (n+3)+i A (3-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(3,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{48 a^3 f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{6 a^3 f (1+i \tan (e+f x))^3}","\frac{(B (n+3)+i A (3-n)) (c-i c \tan (e+f x))^n \, _2F_1\left(3,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{48 a^3 f n}+\frac{(-B+i A) (c-i c \tan (e+f x))^n}{6 a^3 f (1+i \tan (e+f x))^3}",1,"((I*A*(3 - n) + B*(3 + n))*Hypergeometric2F1[3, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(48*a^3*f*n) + ((I*A - B)*(c - I*c*Tan[e + f*x])^n)/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",3,3,41,0.07317,1,"{3588, 78, 68}"
728,1,191,0,0.2445384,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^5}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^5)/(a + I*a*Tan[e + f*x])^3,x]","\frac{c^5 (A+8 i B) \tan (e+f x)}{a^3 f}-\frac{8 c^5 (3 A+7 i B)}{a^3 f (-\tan (e+f x)+i)}+\frac{8 c^5 (-3 B+2 i A)}{a^3 f (-\tan (e+f x)+i)^2}+\frac{16 c^5 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{8 c^5 (-4 B+i A) \log (\cos (e+f x))}{a^3 f}-\frac{8 c^5 x (A+4 i B)}{a^3}+\frac{B c^5 \tan ^2(e+f x)}{2 a^3 f}","\frac{c^5 (A+8 i B) \tan (e+f x)}{a^3 f}-\frac{8 c^5 (3 A+7 i B)}{a^3 f (-\tan (e+f x)+i)}+\frac{8 c^5 (-3 B+2 i A)}{a^3 f (-\tan (e+f x)+i)^2}+\frac{16 c^5 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{8 c^5 (-4 B+i A) \log (\cos (e+f x))}{a^3 f}-\frac{8 c^5 x (A+4 i B)}{a^3}+\frac{B c^5 \tan ^2(e+f x)}{2 a^3 f}",1,"(-8*(A + (4*I)*B)*c^5*x)/a^3 - (8*(I*A - 4*B)*c^5*Log[Cos[e + f*x]])/(a^3*f) + (16*(A + I*B)*c^5)/(3*a^3*f*(I - Tan[e + f*x])^3) + (8*((2*I)*A - 3*B)*c^5)/(a^3*f*(I - Tan[e + f*x])^2) - (8*(3*A + (7*I)*B)*c^5)/(a^3*f*(I - Tan[e + f*x])) + ((A + (8*I)*B)*c^5*Tan[e + f*x])/(a^3*f) + (B*c^5*Tan[e + f*x]^2)/(2*a^3*f)","A",3,2,41,0.04878,1,"{3588, 77}"
729,1,164,0,0.2096339,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4)/(a + I*a*Tan[e + f*x])^3,x]","-\frac{6 c^4 (A+3 i B)}{a^3 f (-\tan (e+f x)+i)}+\frac{2 c^4 (-5 B+3 i A)}{a^3 f (-\tan (e+f x)+i)^2}+\frac{8 c^4 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{c^4 (-7 B+i A) \log (\cos (e+f x))}{a^3 f}-\frac{c^4 x (A+7 i B)}{a^3}+\frac{i B c^4 \tan (e+f x)}{a^3 f}","-\frac{6 c^4 (A+3 i B)}{a^3 f (-\tan (e+f x)+i)}+\frac{2 c^4 (-5 B+3 i A)}{a^3 f (-\tan (e+f x)+i)^2}+\frac{8 c^4 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{c^4 (-7 B+i A) \log (\cos (e+f x))}{a^3 f}-\frac{c^4 x (A+7 i B)}{a^3}+\frac{i B c^4 \tan (e+f x)}{a^3 f}",1,"-(((A + (7*I)*B)*c^4*x)/a^3) - ((I*A - 7*B)*c^4*Log[Cos[e + f*x]])/(a^3*f) + (8*(A + I*B)*c^4)/(3*a^3*f*(I - Tan[e + f*x])^3) + (2*((3*I)*A - 5*B)*c^4)/(a^3*f*(I - Tan[e + f*x])^2) - (6*(A + (3*I)*B)*c^4)/(a^3*f*(I - Tan[e + f*x])) + (I*B*c^4*Tan[e + f*x])/(a^3*f)","A",3,2,41,0.04878,1,"{3588, 77}"
730,1,135,0,0.1568342,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3)/(a + I*a*Tan[e + f*x])^3,x]","\frac{c^3 (-B+i A) (1-i \tan (e+f x))^3}{6 a^3 f (1+i \tan (e+f x))^3}-\frac{4 i B c^3}{a^3 f (-\tan (e+f x)+i)}-\frac{2 B c^3}{a^3 f (-\tan (e+f x)+i)^2}+\frac{B c^3 \log (\cos (e+f x))}{a^3 f}-\frac{i B c^3 x}{a^3}","\frac{c^3 (-B+i A) (1-i \tan (e+f x))^3}{6 a^3 f (1+i \tan (e+f x))^3}-\frac{4 i B c^3}{a^3 f (-\tan (e+f x)+i)}-\frac{2 B c^3}{a^3 f (-\tan (e+f x)+i)^2}+\frac{B c^3 \log (\cos (e+f x))}{a^3 f}-\frac{i B c^3 x}{a^3}",1,"((-I)*B*c^3*x)/a^3 + (B*c^3*Log[Cos[e + f*x]])/(a^3*f) - (2*B*c^3)/(a^3*f*(I - Tan[e + f*x])^2) - ((4*I)*B*c^3)/(a^3*f*(I - Tan[e + f*x])) + ((I*A - B)*c^3*(1 - I*Tan[e + f*x])^3)/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",4,3,41,0.07317,1,"{3588, 78, 43}"
731,1,99,0,0.1569428,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^2}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{c^2 (-3 B+i A)}{2 a^3 f (-\tan (e+f x)+i)^2}+\frac{2 c^2 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{i B c^2}{a^3 f (-\tan (e+f x)+i)}","\frac{c^2 (-3 B+i A)}{2 a^3 f (-\tan (e+f x)+i)^2}+\frac{2 c^2 (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{i B c^2}{a^3 f (-\tan (e+f x)+i)}",1,"(2*(A + I*B)*c^2)/(3*a^3*f*(I - Tan[e + f*x])^3) + ((I*A - 3*B)*c^2)/(2*a^3*f*(I - Tan[e + f*x])^2) - (I*B*c^2)/(a^3*f*(I - Tan[e + f*x]))","A",3,2,41,0.04878,1,"{3588, 77}"
732,1,59,0,0.0884157,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x]))/(a + I*a*Tan[e + f*x])^3,x]","\frac{c (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{B c}{2 a^3 f (-\tan (e+f x)+i)^2}","\frac{c (A+i B)}{3 a^3 f (-\tan (e+f x)+i)^3}-\frac{B c}{2 a^3 f (-\tan (e+f x)+i)^2}",1,"((A + I*B)*c)/(3*a^3*f*(I - Tan[e + f*x])^3) - (B*c)/(2*a^3*f*(I - Tan[e + f*x])^2)","A",3,2,39,0.05128,1,"{3588, 43}"
733,1,112,0,0.0850948,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^3,x]","\frac{B+i A}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (A-i B)}{8 a^3}+\frac{-B+i A}{6 f (a+i a \tan (e+f x))^3}+\frac{B+i A}{8 a f (a+i a \tan (e+f x))^2}","\frac{B+i A}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (A-i B)}{8 a^3}+\frac{-B+i A}{6 f (a+i a \tan (e+f x))^3}+\frac{B+i A}{8 a f (a+i a \tan (e+f x))^2}",1,"((A - I*B)*x)/(8*a^3) + (I*A - B)/(6*f*(a + I*a*Tan[e + f*x])^3) + (I*A + B)/(8*a*f*(a + I*a*Tan[e + f*x])^2) + (I*A + B)/(8*f*(a^3 + I*a^3*Tan[e + f*x]))","A",4,3,26,0.1154,1,"{3526, 3479, 8}"
734,1,153,0,0.2134716,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])),x]","-\frac{3 A-i B}{16 a^3 c f (-\tan (e+f x)+i)}+\frac{A-i B}{16 a^3 c f (\tan (e+f x)+i)}+\frac{A+i B}{12 a^3 c f (-\tan (e+f x)+i)^3}+\frac{x (2 A-i B)}{8 a^3 c}-\frac{i A}{8 a^3 c f (-\tan (e+f x)+i)^2}","-\frac{3 A-i B}{16 a^3 c f (-\tan (e+f x)+i)}+\frac{A-i B}{16 a^3 c f (\tan (e+f x)+i)}+\frac{A+i B}{12 a^3 c f (-\tan (e+f x)+i)^3}+\frac{x (2 A-i B)}{8 a^3 c}-\frac{i A}{8 a^3 c f (-\tan (e+f x)+i)^2}",1,"((2*A - I*B)*x)/(8*a^3*c) + (A + I*B)/(12*a^3*c*f*(I - Tan[e + f*x])^3) - ((I/8)*A)/(a^3*c*f*(I - Tan[e + f*x])^2) - (3*A - I*B)/(16*a^3*c*f*(I - Tan[e + f*x])) + (A - I*B)/(16*a^3*c*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
735,1,185,0,0.2392471,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^2} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^2),x]","\frac{2 A-i B}{16 a^3 c^2 f (\tan (e+f x)+i)}-\frac{-B+3 i A}{32 a^3 c^2 f (-\tan (e+f x)+i)^2}+\frac{B+i A}{32 a^3 c^2 f (\tan (e+f x)+i)^2}+\frac{A+i B}{24 a^3 c^2 f (-\tan (e+f x)+i)^3}+\frac{x (5 A-i B)}{16 a^3 c^2}-\frac{3 A}{16 a^3 c^2 f (-\tan (e+f x)+i)}","\frac{2 A-i B}{16 a^3 c^2 f (\tan (e+f x)+i)}-\frac{-B+3 i A}{32 a^3 c^2 f (-\tan (e+f x)+i)^2}+\frac{B+i A}{32 a^3 c^2 f (\tan (e+f x)+i)^2}+\frac{A+i B}{24 a^3 c^2 f (-\tan (e+f x)+i)^3}+\frac{x (5 A-i B)}{16 a^3 c^2}-\frac{3 A}{16 a^3 c^2 f (-\tan (e+f x)+i)}",1,"((5*A - I*B)*x)/(16*a^3*c^2) + (A + I*B)/(24*a^3*c^2*f*(I - Tan[e + f*x])^3) - ((3*I)*A - B)/(32*a^3*c^2*f*(I - Tan[e + f*x])^2) - (3*A)/(16*a^3*c^2*f*(I - Tan[e + f*x])) + (I*A + B)/(32*a^3*c^2*f*(I + Tan[e + f*x])^2) + (2*A - I*B)/(16*a^3*c^2*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
736,1,99,0,0.1458604,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^3} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^3),x]","-\frac{\cos ^6(e+f x) (B-A \tan (e+f x))}{6 a^3 c^3 f}+\frac{5 A \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^3 f}+\frac{5 A \sin (e+f x) \cos (e+f x)}{16 a^3 c^3 f}+\frac{5 A x}{16 a^3 c^3}","-\frac{\cos ^6(e+f x) (B-A \tan (e+f x))}{6 a^3 c^3 f}+\frac{5 A \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^3 f}+\frac{5 A \sin (e+f x) \cos (e+f x)}{16 a^3 c^3 f}+\frac{5 A x}{16 a^3 c^3}",1,"(5*A*x)/(16*a^3*c^3) + (5*A*Cos[e + f*x]*Sin[e + f*x])/(16*a^3*c^3*f) + (5*A*Cos[e + f*x]^3*Sin[e + f*x])/(24*a^3*c^3*f) - (Cos[e + f*x]^6*(B - A*Tan[e + f*x]))/(6*a^3*c^3*f)","A",6,5,41,0.1220,1,"{3588, 73, 639, 199, 205}"
737,1,251,0,0.3062396,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^4} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^4),x]","-\frac{5 (3 A+i B)}{128 a^3 c^4 f (-\tan (e+f x)+i)}-\frac{-3 B+5 i A}{128 a^3 c^4 f (-\tan (e+f x)+i)^2}+\frac{B+5 i A}{64 a^3 c^4 f (\tan (e+f x)+i)^2}+\frac{A+i B}{96 a^3 c^4 f (-\tan (e+f x)+i)^3}-\frac{2 A-i B}{48 a^3 c^4 f (\tan (e+f x)+i)^3}-\frac{B+i A}{64 a^3 c^4 f (\tan (e+f x)+i)^4}+\frac{5 x (7 A+i B)}{128 a^3 c^4}+\frac{5 A}{32 a^3 c^4 f (\tan (e+f x)+i)}","-\frac{5 (3 A+i B)}{128 a^3 c^4 f (-\tan (e+f x)+i)}-\frac{-3 B+5 i A}{128 a^3 c^4 f (-\tan (e+f x)+i)^2}+\frac{B+5 i A}{64 a^3 c^4 f (\tan (e+f x)+i)^2}+\frac{A+i B}{96 a^3 c^4 f (-\tan (e+f x)+i)^3}-\frac{2 A-i B}{48 a^3 c^4 f (\tan (e+f x)+i)^3}-\frac{B+i A}{64 a^3 c^4 f (\tan (e+f x)+i)^4}+\frac{5 x (7 A+i B)}{128 a^3 c^4}+\frac{5 A}{32 a^3 c^4 f (\tan (e+f x)+i)}",1,"(5*(7*A + I*B)*x)/(128*a^3*c^4) + (A + I*B)/(96*a^3*c^4*f*(I - Tan[e + f*x])^3) - ((5*I)*A - 3*B)/(128*a^3*c^4*f*(I - Tan[e + f*x])^2) - (5*(3*A + I*B))/(128*a^3*c^4*f*(I - Tan[e + f*x])) - (I*A + B)/(64*a^3*c^4*f*(I + Tan[e + f*x])^4) - (2*A - I*B)/(48*a^3*c^4*f*(I + Tan[e + f*x])^3) + ((5*I)*A + B)/(64*a^3*c^4*f*(I + Tan[e + f*x])^2) + (5*A)/(32*a^3*c^4*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
738,1,287,0,0.3379374,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^5} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^5),x]","-\frac{3 (7 A+3 i B)}{256 a^3 c^5 f (-\tan (e+f x)+i)}+\frac{5 (7 A+i B)}{256 a^3 c^5 f (\tan (e+f x)+i)}-\frac{-2 B+3 i A}{128 a^3 c^5 f (-\tan (e+f x)+i)^2}+\frac{A+i B}{192 a^3 c^5 f (-\tan (e+f x)+i)^3}-\frac{5 A-i B}{96 a^3 c^5 f (\tan (e+f x)+i)^3}-\frac{B+2 i A}{64 a^3 c^5 f (\tan (e+f x)+i)^4}+\frac{A-i B}{80 a^3 c^5 f (\tan (e+f x)+i)^5}+\frac{7 x (4 A+i B)}{128 a^3 c^5}+\frac{5 i A}{64 a^3 c^5 f (\tan (e+f x)+i)^2}","-\frac{3 (7 A+3 i B)}{256 a^3 c^5 f (-\tan (e+f x)+i)}+\frac{5 (7 A+i B)}{256 a^3 c^5 f (\tan (e+f x)+i)}-\frac{-2 B+3 i A}{128 a^3 c^5 f (-\tan (e+f x)+i)^2}+\frac{A+i B}{192 a^3 c^5 f (-\tan (e+f x)+i)^3}-\frac{5 A-i B}{96 a^3 c^5 f (\tan (e+f x)+i)^3}-\frac{B+2 i A}{64 a^3 c^5 f (\tan (e+f x)+i)^4}+\frac{A-i B}{80 a^3 c^5 f (\tan (e+f x)+i)^5}+\frac{7 x (4 A+i B)}{128 a^3 c^5}+\frac{5 i A}{64 a^3 c^5 f (\tan (e+f x)+i)^2}",1,"(7*(4*A + I*B)*x)/(128*a^3*c^5) + (A + I*B)/(192*a^3*c^5*f*(I - Tan[e + f*x])^3) - ((3*I)*A - 2*B)/(128*a^3*c^5*f*(I - Tan[e + f*x])^2) - (3*(7*A + (3*I)*B))/(256*a^3*c^5*f*(I - Tan[e + f*x])) + (A - I*B)/(80*a^3*c^5*f*(I + Tan[e + f*x])^5) - ((2*I)*A + B)/(64*a^3*c^5*f*(I + Tan[e + f*x])^4) - (5*A - I*B)/(96*a^3*c^5*f*(I + Tan[e + f*x])^3) + (((5*I)/64)*A)/(a^3*c^5*f*(I + Tan[e + f*x])^2) + (5*(7*A + I*B))/(256*a^3*c^5*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
739,1,319,0,0.3802214,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^6} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^6),x]","-\frac{7 (2 A+i B)}{256 a^3 c^6 f (-\tan (e+f x)+i)}+\frac{7 (4 A+i B)}{256 a^3 c^6 f (\tan (e+f x)+i)}-\frac{-5 B+7 i A}{512 a^3 c^6 f (-\tan (e+f x)+i)^2}+\frac{5 (-B+7 i A)}{512 a^3 c^6 f (\tan (e+f x)+i)^2}+\frac{A+i B}{384 a^3 c^6 f (-\tan (e+f x)+i)^3}-\frac{B+5 i A}{128 a^3 c^6 f (\tan (e+f x)+i)^4}+\frac{2 A-i B}{80 a^3 c^6 f (\tan (e+f x)+i)^5}+\frac{B+i A}{96 a^3 c^6 f (\tan (e+f x)+i)^6}+\frac{7 x (3 A+i B)}{128 a^3 c^6}-\frac{5 A}{96 a^3 c^6 f (\tan (e+f x)+i)^3}","-\frac{7 (2 A+i B)}{256 a^3 c^6 f (-\tan (e+f x)+i)}+\frac{7 (4 A+i B)}{256 a^3 c^6 f (\tan (e+f x)+i)}-\frac{-5 B+7 i A}{512 a^3 c^6 f (-\tan (e+f x)+i)^2}+\frac{5 (-B+7 i A)}{512 a^3 c^6 f (\tan (e+f x)+i)^2}+\frac{A+i B}{384 a^3 c^6 f (-\tan (e+f x)+i)^3}-\frac{B+5 i A}{128 a^3 c^6 f (\tan (e+f x)+i)^4}+\frac{2 A-i B}{80 a^3 c^6 f (\tan (e+f x)+i)^5}+\frac{B+i A}{96 a^3 c^6 f (\tan (e+f x)+i)^6}+\frac{7 x (3 A+i B)}{128 a^3 c^6}-\frac{5 A}{96 a^3 c^6 f (\tan (e+f x)+i)^3}",1,"(7*(3*A + I*B)*x)/(128*a^3*c^6) + (A + I*B)/(384*a^3*c^6*f*(I - Tan[e + f*x])^3) - ((7*I)*A - 5*B)/(512*a^3*c^6*f*(I - Tan[e + f*x])^2) - (7*(2*A + I*B))/(256*a^3*c^6*f*(I - Tan[e + f*x])) + (I*A + B)/(96*a^3*c^6*f*(I + Tan[e + f*x])^6) + (2*A - I*B)/(80*a^3*c^6*f*(I + Tan[e + f*x])^5) - ((5*I)*A + B)/(128*a^3*c^6*f*(I + Tan[e + f*x])^4) - (5*A)/(96*a^3*c^6*f*(I + Tan[e + f*x])^3) + (5*((7*I)*A - B))/(512*a^3*c^6*f*(I + Tan[e + f*x])^2) + (7*(4*A + I*B))/(256*a^3*c^6*f*(I + Tan[e + f*x]))","A",4,3,41,0.07317,1,"{3588, 77, 203}"
740,1,62,0,0.1065254,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}-\frac{2 a B (c-i c \tan (e+f x))^{9/2}}{9 c f}","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}-\frac{2 a B (c-i c \tan (e+f x))^{9/2}}{9 c f}",1,"(2*a*(I*A + B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*f) - (2*a*B*(c - I*c*Tan[e + f*x])^(9/2))/(9*c*f)","A",3,2,41,0.04878,1,"{3588, 43}"
741,1,62,0,0.1077914,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 a B (c-i c \tan (e+f x))^{7/2}}{7 c f}","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 a B (c-i c \tan (e+f x))^{7/2}}{7 c f}",1,"(2*a*(I*A + B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*f) - (2*a*B*(c - I*c*Tan[e + f*x])^(7/2))/(7*c*f)","A",3,2,41,0.04878,1,"{3588, 43}"
742,1,62,0,0.1065424,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 a B (c-i c \tan (e+f x))^{5/2}}{5 c f}","\frac{2 a (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 a B (c-i c \tan (e+f x))^{5/2}}{5 c f}",1,"(2*a*(I*A + B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*f) - (2*a*B*(c - I*c*Tan[e + f*x])^(5/2))/(5*c*f)","A",3,2,41,0.04878,1,"{3588, 43}"
743,1,60,0,0.0989737,"\int (a+i a \tan (e+f x)) (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 a (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 a B (c-i c \tan (e+f x))^{3/2}}{3 c f}","\frac{2 a (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 a B (c-i c \tan (e+f x))^{3/2}}{3 c f}",1,"(2*a*(I*A + B)*Sqrt[c - I*c*Tan[e + f*x]])/f - (2*a*B*(c - I*c*Tan[e + f*x])^(3/2))/(3*c*f)","A",3,2,41,0.04878,1,"{3588, 43}"
744,1,58,0,0.1000293,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 a (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a B \sqrt{c-i c \tan (e+f x)}}{c f}","-\frac{2 a (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a B \sqrt{c-i c \tan (e+f x)}}{c f}",1,"(-2*a*(I*A + B))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (2*a*B*Sqrt[c - I*c*Tan[e + f*x]])/(c*f)","A",3,2,41,0.04878,1,"{3588, 43}"
745,1,60,0,0.1071259,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 a B}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}","\frac{2 a B}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(-2*a*(I*A + B))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a*B)/(c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,2,41,0.04878,1,"{3588, 43}"
746,1,62,0,0.1055021,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a B}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 a (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{2 a B}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 a (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"(-2*a*(I*A + B))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) + (2*a*B)/(3*c*f*(c - I*c*Tan[e + f*x])^(3/2))","A",3,2,41,0.04878,1,"{3588, 43}"
747,1,62,0,0.1039323,"\int \frac{(a+i a \tan (e+f x)) (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","\frac{2 a B}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}","\frac{2 a B}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}",1,"(-2*a*(I*A + B))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) + (2*a*B)/(5*c*f*(c - I*c*Tan[e + f*x])^(5/2))","A",3,2,41,0.04878,1,"{3588, 43}"
748,1,105,0,0.1832023,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{11/2}}{11 c^2 f}","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{11/2}}{11 c^2 f}",1,"(4*a^2*(I*A + B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*f) - (2*a^2*(I*A + 3*B)*(c - I*c*Tan[e + f*x])^(9/2))/(9*c*f) + (2*a^2*B*(c - I*c*Tan[e + f*x])^(11/2))/(11*c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
749,1,105,0,0.1808872,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}",1,"(4*a^2*(I*A + B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*f) - (2*a^2*(I*A + 3*B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*c*f) + (2*a^2*B*(c - I*c*Tan[e + f*x])^(9/2))/(9*c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
750,1,105,0,0.1812518,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{4 a^2 (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}",1,"(4*a^2*(I*A + B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*f) - (2*a^2*(I*A + 3*B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*c*f) + (2*a^2*B*(c - I*c*Tan[e + f*x])^(7/2))/(7*c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
751,1,103,0,0.1636026,"\int (a+i a \tan (e+f x))^2 (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{4 a^2 (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}","-\frac{2 a^2 (3 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{4 a^2 (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}+\frac{2 a^2 B (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}",1,"(4*a^2*(I*A + B)*Sqrt[c - I*c*Tan[e + f*x]])/f - (2*a^2*(I*A + 3*B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*c*f) + (2*a^2*B*(c - I*c*Tan[e + f*x])^(5/2))/(5*c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
752,1,101,0,0.168383,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 a^2 (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{4 a^2 (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}+\frac{2 a^2 B (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}","-\frac{2 a^2 (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{4 a^2 (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}+\frac{2 a^2 B (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}",1,"(-4*a^2*(I*A + B))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (2*a^2*(I*A + 3*B)*Sqrt[c - I*c*Tan[e + f*x]])/(c*f) + (2*a^2*B*(c - I*c*Tan[e + f*x])^(3/2))/(3*c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
753,1,101,0,0.1800323,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 a^2 (3 B+i A)}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{4 a^2 (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}+\frac{2 a^2 B \sqrt{c-i c \tan (e+f x)}}{c^2 f}","\frac{2 a^2 (3 B+i A)}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{4 a^2 (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}+\frac{2 a^2 B \sqrt{c-i c \tan (e+f x)}}{c^2 f}",1,"(-4*a^2*(I*A + B))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a^2*(I*A + 3*B))/(c*f*Sqrt[c - I*c*Tan[e + f*x]]) + (2*a^2*B*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f)","A",3,2,43,0.04651,1,"{3588, 77}"
754,1,103,0,0.1794484,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a^2 (3 B+i A)}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 a^2 (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a^2 B}{c^2 f \sqrt{c-i c \tan (e+f x)}}","\frac{2 a^2 (3 B+i A)}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 a^2 (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a^2 B}{c^2 f \sqrt{c-i c \tan (e+f x)}}",1,"(-4*a^2*(I*A + B))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) + (2*a^2*(I*A + 3*B))/(3*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*a^2*B)/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,2,43,0.04651,1,"{3588, 77}"
755,1,105,0,0.1858564,"\int \frac{(a+i a \tan (e+f x))^2 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^2*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","\frac{2 a^2 (3 B+i A)}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{4 a^2 (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 a^2 B}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}","\frac{2 a^2 (3 B+i A)}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{4 a^2 (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 a^2 B}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}",1,"(-4*a^2*(I*A + B))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) + (2*a^2*(I*A + 3*B))/(5*c*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*a^2*B)/(3*c^2*f*(c - I*c*Tan[e + f*x])^(3/2))","A",3,2,43,0.04651,1,"{3588, 77}"
756,1,144,0,0.2101946,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{11/2}}{11 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{13/2}}{13 c^3 f}","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{11/2}}{11 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{7/2}}{7 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{13/2}}{13 c^3 f}",1,"(8*a^3*(I*A + B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*f) - (8*a^3*(I*A + 2*B)*(c - I*c*Tan[e + f*x])^(9/2))/(9*c*f) + (2*a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(11/2))/(11*c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(13/2))/(13*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
757,1,144,0,0.2003004,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{11/2}}{11 c^3 f}","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{11/2}}{11 c^3 f}",1,"(8*a^3*(I*A + B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*f) - (8*a^3*(I*A + 2*B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*c*f) + (2*a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(9/2))/(9*c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(11/2))/(11*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
758,1,144,0,0.2004472,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{9/2}}{9 c^3 f}","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{8 a^3 (B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{9/2}}{9 c^3 f}",1,"(8*a^3*(I*A + B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*f) - (8*a^3*(I*A + 2*B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*c*f) + (2*a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(7/2))/(7*c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(9/2))/(9*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
759,1,142,0,0.1817024,"\int (a+i a \tan (e+f x))^3 (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{8 a^3 (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{7/2}}{7 c^3 f}","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}-\frac{8 a^3 (2 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{8 a^3 (B+i A) \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 a^3 B (c-i c \tan (e+f x))^{7/2}}{7 c^3 f}",1,"(8*a^3*(I*A + B)*Sqrt[c - I*c*Tan[e + f*x]])/f - (8*a^3*(I*A + 2*B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*c*f) + (2*a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(7/2))/(7*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
760,1,140,0,0.1850849,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}-\frac{8 a^3 (2 B+i A) \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{8 a^3 (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a^3 B (c-i c \tan (e+f x))^{5/2}}{5 c^3 f}","\frac{2 a^3 (5 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}-\frac{8 a^3 (2 B+i A) \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{8 a^3 (B+i A)}{f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a^3 B (c-i c \tan (e+f x))^{5/2}}{5 c^3 f}",1,"(-8*a^3*(I*A + B))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (8*a^3*(I*A + 2*B)*Sqrt[c - I*c*Tan[e + f*x]])/(c*f) + (2*a^3*(I*A + 5*B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(5/2))/(5*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
761,1,140,0,0.1985867,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 a^3 (5 B+i A) \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{8 a^3 (2 B+i A)}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{8 a^3 (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 a^3 B (c-i c \tan (e+f x))^{3/2}}{3 c^3 f}","\frac{2 a^3 (5 B+i A) \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{8 a^3 (2 B+i A)}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{8 a^3 (B+i A)}{3 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 a^3 B (c-i c \tan (e+f x))^{3/2}}{3 c^3 f}",1,"(-8*a^3*(I*A + B))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (8*a^3*(I*A + 2*B))/(c*f*Sqrt[c - I*c*Tan[e + f*x]]) + (2*a^3*(I*A + 5*B)*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f) - (2*a^3*B*(c - I*c*Tan[e + f*x])^(3/2))/(3*c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
762,1,140,0,0.2013669,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{2 a^3 (5 B+i A)}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{8 a^3 (2 B+i A)}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{8 a^3 (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a^3 B \sqrt{c-i c \tan (e+f x)}}{c^3 f}","-\frac{2 a^3 (5 B+i A)}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{8 a^3 (2 B+i A)}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{8 a^3 (B+i A)}{5 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 a^3 B \sqrt{c-i c \tan (e+f x)}}{c^3 f}",1,"(-8*a^3*(I*A + B))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) + (8*a^3*(I*A + 2*B))/(3*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*a^3*(I*A + 5*B))/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]]) - (2*a^3*B*Sqrt[c - I*c*Tan[e + f*x]])/(c^3*f)","A",3,2,43,0.04651,1,"{3588, 77}"
763,1,142,0,0.2051216,"\int \frac{(a+i a \tan (e+f x))^3 (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^3*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{2 a^3 (5 B+i A)}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{8 a^3 (2 B+i A)}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{8 a^3 (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}+\frac{2 a^3 B}{c^3 f \sqrt{c-i c \tan (e+f x)}}","-\frac{2 a^3 (5 B+i A)}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{8 a^3 (2 B+i A)}{5 c f (c-i c \tan (e+f x))^{5/2}}-\frac{8 a^3 (B+i A)}{7 f (c-i c \tan (e+f x))^{7/2}}+\frac{2 a^3 B}{c^3 f \sqrt{c-i c \tan (e+f x)}}",1,"(-8*a^3*(I*A + B))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) + (8*a^3*(I*A + 2*B))/(5*c*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*a^3*(I*A + 5*B))/(3*c^2*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a^3*B)/(c^3*f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,2,43,0.04651,1,"{3588, 77}"
764,1,220,0,0.2755517,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2))/(a + I*a*Tan[e + f*x]),x]","\frac{2 c^3 (-9 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{c^2 (-9 B+5 i A) (c-i c \tan (e+f x))^{3/2}}{3 a f}-\frac{2 \sqrt{2} c^{7/2} (-9 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}+\frac{c (-9 B+5 i A) (c-i c \tan (e+f x))^{5/2}}{10 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{2 a f (1+i \tan (e+f x))}","\frac{2 c^3 (-9 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{c^2 (-9 B+5 i A) (c-i c \tan (e+f x))^{3/2}}{3 a f}-\frac{2 \sqrt{2} c^{7/2} (-9 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}+\frac{c (-9 B+5 i A) (c-i c \tan (e+f x))^{5/2}}{10 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{2 a f (1+i \tan (e+f x))}",1,"(-2*Sqrt[2]*((5*I)*A - 9*B)*c^(7/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(a*f) + (2*((5*I)*A - 9*B)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(a*f) + (((5*I)*A - 9*B)*c^2*(c - I*c*Tan[e + f*x])^(3/2))/(3*a*f) + (((5*I)*A - 9*B)*c*(c - I*c*Tan[e + f*x])^(5/2))/(10*a*f) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(7/2))/(2*a*f*(1 + I*Tan[e + f*x]))","A",7,5,43,0.1163,1,"{3588, 78, 50, 63, 208}"
765,1,180,0,0.239907,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/(a + I*a*Tan[e + f*x]),x]","\frac{c^2 (-7 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{a f}-\frac{\sqrt{2} c^{5/2} (-7 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}+\frac{c (-7 B+3 i A) (c-i c \tan (e+f x))^{3/2}}{6 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{2 a f (1+i \tan (e+f x))}","\frac{c^2 (-7 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{a f}-\frac{\sqrt{2} c^{5/2} (-7 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}+\frac{c (-7 B+3 i A) (c-i c \tan (e+f x))^{3/2}}{6 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{2 a f (1+i \tan (e+f x))}",1,"-((Sqrt[2]*((3*I)*A - 7*B)*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(a*f)) + (((3*I)*A - 7*B)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a*f) + (((3*I)*A - 7*B)*c*(c - I*c*Tan[e + f*x])^(3/2))/(6*a*f) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(2*a*f*(1 + I*Tan[e + f*x]))","A",6,5,43,0.1163,1,"{3588, 78, 50, 63, 208}"
766,1,144,0,0.2203483,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/(a + I*a*Tan[e + f*x]),x]","-\frac{c^{3/2} (-5 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a f}+\frac{c (-5 B+i A) \sqrt{c-i c \tan (e+f x)}}{2 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{2 a f (1+i \tan (e+f x))}","-\frac{c^{3/2} (-5 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a f}+\frac{c (-5 B+i A) \sqrt{c-i c \tan (e+f x)}}{2 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{2 a f (1+i \tan (e+f x))}",1,"-(((I*A - 5*B)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*f)) + ((I*A - 5*B)*c*Sqrt[c - I*c*Tan[e + f*x]])/(2*a*f) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(2*a*f*(1 + I*Tan[e + f*x]))","A",5,5,43,0.1163,1,"{3588, 78, 50, 63, 208}"
767,1,109,0,0.1852134,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{a+i a \tan (e+f x)} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/(a + I*a*Tan[e + f*x]),x]","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{2 a f (1+i \tan (e+f x))}+\frac{\sqrt{c} (3 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a f}","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{2 a f (1+i \tan (e+f x))}+\frac{\sqrt{c} (3 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a f}",1,"((I*A + 3*B)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(2*Sqrt[2]*a*f) + ((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(2*a*f*(1 + I*Tan[e + f*x]))","A",4,4,43,0.09302,1,"{3588, 78, 63, 208}"
768,1,141,0,0.2194544,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{-B+i A}{2 a f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}-\frac{B+3 i A}{4 a f \sqrt{c-i c \tan (e+f x)}}+\frac{(B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a \sqrt{c} f}","\frac{-B+i A}{2 a f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}-\frac{B+3 i A}{4 a f \sqrt{c-i c \tan (e+f x)}}+\frac{(B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a \sqrt{c} f}",1,"(((3*I)*A + B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(4*Sqrt[2]*a*Sqrt[c]*f) - ((3*I)*A + B)/(4*a*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I*A - B)/(2*a*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",5,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
769,1,184,0,0.2675804,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{(-B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a c^{3/2} f}+\frac{-B+i A}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}-\frac{-B+5 i A}{8 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{-B+5 i A}{12 a f (c-i c \tan (e+f x))^{3/2}}","\frac{(-B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a c^{3/2} f}+\frac{-B+i A}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}-\frac{-B+5 i A}{8 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{-B+5 i A}{12 a f (c-i c \tan (e+f x))^{3/2}}",1,"(((5*I)*A - B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(8*Sqrt[2]*a*c^(3/2)*f) - ((5*I)*A - B)/(12*a*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I*A - B)/(2*a*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - ((5*I)*A - B)/(8*a*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",6,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
770,1,223,0,0.2886169,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{-3 B+7 i A}{16 a c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{(-3 B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a c^{5/2} f}-\frac{-3 B+7 i A}{24 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{-3 B+7 i A}{20 a f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}","-\frac{-3 B+7 i A}{16 a c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{(-3 B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a c^{5/2} f}-\frac{-3 B+7 i A}{24 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{-3 B+7 i A}{20 a f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}",1,"(((7*I)*A - 3*B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(16*Sqrt[2]*a*c^(5/2)*f) - ((7*I)*A - 3*B)/(20*a*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I*A - B)/(2*a*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - ((7*I)*A - 3*B)/(24*a*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((7*I)*A - 3*B)/(16*a*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
771,1,275,0,0.3011717,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(9/2))/(a + I*a*Tan[e + f*x])^2,x]","-\frac{7 c^4 (-13 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{2 a^2 f}-\frac{7 c^3 (-13 B+5 i A) (c-i c \tan (e+f x))^{3/2}}{12 a^2 f}-\frac{7 c^2 (-13 B+5 i A) (c-i c \tan (e+f x))^{5/2}}{40 a^2 f}+\frac{7 c^{9/2} (-13 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a^2 f}-\frac{c (-13 B+5 i A) (c-i c \tan (e+f x))^{7/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{4 a^2 f (1+i \tan (e+f x))^2}","-\frac{7 c^4 (-13 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{2 a^2 f}-\frac{7 c^3 (-13 B+5 i A) (c-i c \tan (e+f x))^{3/2}}{12 a^2 f}-\frac{7 c^2 (-13 B+5 i A) (c-i c \tan (e+f x))^{5/2}}{40 a^2 f}+\frac{7 c^{9/2} (-13 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a^2 f}-\frac{c (-13 B+5 i A) (c-i c \tan (e+f x))^{7/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{4 a^2 f (1+i \tan (e+f x))^2}",1,"(7*((5*I)*A - 13*B)*c^(9/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*f) - (7*((5*I)*A - 13*B)*c^4*Sqrt[c - I*c*Tan[e + f*x]])/(2*a^2*f) - (7*((5*I)*A - 13*B)*c^3*(c - I*c*Tan[e + f*x])^(3/2))/(12*a^2*f) - (7*((5*I)*A - 13*B)*c^2*(c - I*c*Tan[e + f*x])^(5/2))/(40*a^2*f) - (((5*I)*A - 13*B)*c*(c - I*c*Tan[e + f*x])^(7/2))/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(9/2))/(4*a^2*f*(1 + I*Tan[e + f*x])^2)","A",8,6,43,0.1395,1,"{3588, 78, 47, 50, 63, 208}"
772,1,238,0,0.2721661,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2))/(a + I*a*Tan[e + f*x])^2,x]","-\frac{5 c^3 (-11 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{4 a^2 f}-\frac{5 c^2 (-11 B+3 i A) (c-i c \tan (e+f x))^{3/2}}{24 a^2 f}+\frac{5 c^{7/2} (-11 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a^2 f}-\frac{c (-11 B+3 i A) (c-i c \tan (e+f x))^{5/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{4 a^2 f (1+i \tan (e+f x))^2}","-\frac{5 c^3 (-11 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{4 a^2 f}-\frac{5 c^2 (-11 B+3 i A) (c-i c \tan (e+f x))^{3/2}}{24 a^2 f}+\frac{5 c^{7/2} (-11 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a^2 f}-\frac{c (-11 B+3 i A) (c-i c \tan (e+f x))^{5/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{4 a^2 f (1+i \tan (e+f x))^2}",1,"(5*((3*I)*A - 11*B)*c^(7/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(2*Sqrt[2]*a^2*f) - (5*((3*I)*A - 11*B)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(4*a^2*f) - (5*((3*I)*A - 11*B)*c^2*(c - I*c*Tan[e + f*x])^(3/2))/(24*a^2*f) - (((3*I)*A - 11*B)*c*(c - I*c*Tan[e + f*x])^(5/2))/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(7/2))/(4*a^2*f*(1 + I*Tan[e + f*x])^2)","A",7,6,43,0.1395,1,"{3588, 78, 47, 50, 63, 208}"
773,1,199,0,0.2450097,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/(a + I*a*Tan[e + f*x])^2,x]","-\frac{3 c^2 (-9 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^2 f}+\frac{3 c^{5/2} (-9 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^2 f}-\frac{c (-9 B+i A) (c-i c \tan (e+f x))^{3/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{4 a^2 f (1+i \tan (e+f x))^2}","-\frac{3 c^2 (-9 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^2 f}+\frac{3 c^{5/2} (-9 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^2 f}-\frac{c (-9 B+i A) (c-i c \tan (e+f x))^{3/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{4 a^2 f (1+i \tan (e+f x))^2}",1,"(3*(I*A - 9*B)*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(4*Sqrt[2]*a^2*f) - (3*(I*A - 9*B)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(8*a^2*f) - ((I*A - 9*B)*c*(c - I*c*Tan[e + f*x])^(3/2))/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(4*a^2*f*(1 + I*Tan[e + f*x])^2)","A",6,6,43,0.1395,1,"{3588, 78, 47, 50, 63, 208}"
774,1,160,0,0.2260244,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/(a + I*a*Tan[e + f*x])^2,x]","-\frac{c^{3/2} (7 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^2 f}+\frac{c (7 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{4 a^2 f (1+i \tan (e+f x))^2}","-\frac{c^{3/2} (7 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^2 f}+\frac{c (7 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{4 a^2 f (1+i \tan (e+f x))^2}",1,"-((I*A + 7*B)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(8*Sqrt[2]*a^2*f) + ((I*A + 7*B)*c*Sqrt[c - I*c*Tan[e + f*x]])/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(4*a^2*f*(1 + I*Tan[e + f*x])^2)","A",5,5,43,0.1163,1,"{3588, 78, 47, 63, 208}"
775,1,159,0,0.2122863,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/(a + I*a*Tan[e + f*x])^2,x]","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (1+i \tan (e+f x))^2}+\frac{(5 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{16 a^2 f (1+i \tan (e+f x))}+\frac{\sqrt{c} (5 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^2 f}","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (1+i \tan (e+f x))^2}+\frac{(5 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{16 a^2 f (1+i \tan (e+f x))}+\frac{\sqrt{c} (5 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^2 f}",1,"(((3*I)*A + 5*B)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(16*Sqrt[2]*a^2*f) + ((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(4*a^2*f*(1 + I*Tan[e + f*x])^2) + (((3*I)*A + 5*B)*Sqrt[c - I*c*Tan[e + f*x]])/(16*a^2*f*(1 + I*Tan[e + f*x]))","A",5,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
776,1,195,0,0.2476759,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}-\frac{3 (3 B+5 i A)}{32 a^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{3 B+5 i A}{16 a^2 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{3 (3 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^2 \sqrt{c} f}","\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}-\frac{3 (3 B+5 i A)}{32 a^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{3 B+5 i A}{16 a^2 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{3 (3 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^2 \sqrt{c} f}",1,"(3*((5*I)*A + 3*B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(32*Sqrt[2]*a^2*Sqrt[c]*f) - (3*((5*I)*A + 3*B))/(32*a^2*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I*A - B)/(4*a^2*f*(1 + I*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]) + ((5*I)*A + 3*B)/(16*a^2*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",6,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
777,1,226,0,0.2903627,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{5 (B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{64 \sqrt{2} a^2 c^{3/2} f}+\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}-\frac{5 (B+7 i A)}{64 a^2 c f \sqrt{c-i c \tan (e+f x)}}-\frac{5 (B+7 i A)}{96 a^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{B+7 i A}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}","\frac{5 (B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{64 \sqrt{2} a^2 c^{3/2} f}+\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}-\frac{5 (B+7 i A)}{64 a^2 c f \sqrt{c-i c \tan (e+f x)}}-\frac{5 (B+7 i A)}{96 a^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{B+7 i A}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}",1,"(5*((7*I)*A + B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(64*Sqrt[2]*a^2*c^(3/2)*f) - (5*((7*I)*A + B))/(96*a^2*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I*A - B)/(4*a^2*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)) + ((7*I)*A + B)/(16*a^2*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - (5*((7*I)*A + B))/(64*a^2*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
778,1,273,0,0.3158556,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{7 (-B+9 i A)}{128 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{7 (-B+9 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{128 \sqrt{2} a^2 c^{5/2} f}+\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}-\frac{7 (-B+9 i A)}{192 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{7 (-B+9 i A)}{160 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+9 i A}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}","-\frac{7 (-B+9 i A)}{128 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{7 (-B+9 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{128 \sqrt{2} a^2 c^{5/2} f}+\frac{-B+i A}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}-\frac{7 (-B+9 i A)}{192 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{7 (-B+9 i A)}{160 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+9 i A}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}",1,"(7*((9*I)*A - B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(128*Sqrt[2]*a^2*c^(5/2)*f) - (7*((9*I)*A - B))/(160*a^2*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I*A - B)/(4*a^2*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)) + ((9*I)*A - B)/(16*a^2*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - (7*((9*I)*A - B))/(192*a^2*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (7*((9*I)*A - B))/(128*a^2*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",8,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
779,1,291,0,0.304555,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(9/2))/(a + I*a*Tan[e + f*x])^3,x]","\frac{35 c^4 (-5 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^3 f}+\frac{35 c^3 (-5 B+i A) (c-i c \tan (e+f x))^{3/2}}{48 a^3 f}+\frac{7 c^2 (-5 B+i A) (c-i c \tan (e+f x))^{5/2}}{16 a^3 f (1+i \tan (e+f x))}-\frac{35 c^{9/2} (-5 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^3 f}-\frac{c (-5 B+i A) (c-i c \tan (e+f x))^{7/2}}{8 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{6 a^3 f (1+i \tan (e+f x))^3}","\frac{35 c^4 (-5 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^3 f}+\frac{35 c^3 (-5 B+i A) (c-i c \tan (e+f x))^{3/2}}{48 a^3 f}+\frac{7 c^2 (-5 B+i A) (c-i c \tan (e+f x))^{5/2}}{16 a^3 f (1+i \tan (e+f x))}-\frac{35 c^{9/2} (-5 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^3 f}-\frac{c (-5 B+i A) (c-i c \tan (e+f x))^{7/2}}{8 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{6 a^3 f (1+i \tan (e+f x))^3}",1,"(-35*(I*A - 5*B)*c^(9/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(4*Sqrt[2]*a^3*f) + (35*(I*A - 5*B)*c^4*Sqrt[c - I*c*Tan[e + f*x]])/(8*a^3*f) + (35*(I*A - 5*B)*c^3*(c - I*c*Tan[e + f*x])^(3/2))/(48*a^3*f) + (7*(I*A - 5*B)*c^2*(c - I*c*Tan[e + f*x])^(5/2))/(16*a^3*f*(1 + I*Tan[e + f*x])) - ((I*A - 5*B)*c*(c - I*c*Tan[e + f*x])^(7/2))/(8*a^3*f*(1 + I*Tan[e + f*x])^2) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(9/2))/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",8,6,43,0.1395,1,"{3588, 78, 47, 50, 63, 208}"
780,1,252,0,0.2713017,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2))/(a + I*a*Tan[e + f*x])^3,x]","\frac{5 c^3 (-13 B+i A) \sqrt{c-i c \tan (e+f x)}}{16 a^3 f}+\frac{5 c^2 (-13 B+i A) (c-i c \tan (e+f x))^{3/2}}{48 a^3 f (1+i \tan (e+f x))}-\frac{5 c^{7/2} (-13 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^3 f}-\frac{c (-13 B+i A) (c-i c \tan (e+f x))^{5/2}}{24 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{6 a^3 f (1+i \tan (e+f x))^3}","\frac{5 c^3 (-13 B+i A) \sqrt{c-i c \tan (e+f x)}}{16 a^3 f}+\frac{5 c^2 (-13 B+i A) (c-i c \tan (e+f x))^{3/2}}{48 a^3 f (1+i \tan (e+f x))}-\frac{5 c^{7/2} (-13 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^3 f}-\frac{c (-13 B+i A) (c-i c \tan (e+f x))^{5/2}}{24 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{6 a^3 f (1+i \tan (e+f x))^3}",1,"(-5*(I*A - 13*B)*c^(7/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(8*Sqrt[2]*a^3*f) + (5*(I*A - 13*B)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(16*a^3*f) + (5*(I*A - 13*B)*c^2*(c - I*c*Tan[e + f*x])^(3/2))/(48*a^3*f*(1 + I*Tan[e + f*x])) - ((I*A - 13*B)*c*(c - I*c*Tan[e + f*x])^(5/2))/(24*a^3*f*(1 + I*Tan[e + f*x])^2) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(7/2))/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",7,6,43,0.1395,1,"{3588, 78, 47, 50, 63, 208}"
781,1,213,0,0.2486026,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/(a + I*a*Tan[e + f*x])^3,x]","-\frac{c^2 (11 B+i A) \sqrt{c-i c \tan (e+f x)}}{16 a^3 f (1+i \tan (e+f x))}+\frac{c^{5/2} (11 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^3 f}+\frac{c (11 B+i A) (c-i c \tan (e+f x))^{3/2}}{24 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{6 a^3 f (1+i \tan (e+f x))^3}","-\frac{c^2 (11 B+i A) \sqrt{c-i c \tan (e+f x)}}{16 a^3 f (1+i \tan (e+f x))}+\frac{c^{5/2} (11 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^3 f}+\frac{c (11 B+i A) (c-i c \tan (e+f x))^{3/2}}{24 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{6 a^3 f (1+i \tan (e+f x))^3}",1,"((I*A + 11*B)*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(16*Sqrt[2]*a^3*f) - ((I*A + 11*B)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(16*a^3*f*(1 + I*Tan[e + f*x])) + ((I*A + 11*B)*c*(c - I*c*Tan[e + f*x])^(3/2))/(24*a^3*f*(1 + I*Tan[e + f*x])^2) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",6,5,43,0.1163,1,"{3588, 78, 47, 63, 208}"
782,1,211,0,0.2503078,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/(a + I*a*Tan[e + f*x])^3,x]","-\frac{c^{3/2} (3 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^3 f}-\frac{c (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{32 a^3 f (1+i \tan (e+f x))}+\frac{c (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{6 a^3 f (1+i \tan (e+f x))^3}","-\frac{c^{3/2} (3 B+i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^3 f}-\frac{c (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{32 a^3 f (1+i \tan (e+f x))}+\frac{c (3 B+i A) \sqrt{c-i c \tan (e+f x)}}{8 a^3 f (1+i \tan (e+f x))^2}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{6 a^3 f (1+i \tan (e+f x))^3}",1,"-((I*A + 3*B)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(32*Sqrt[2]*a^3*f) + ((I*A + 3*B)*c*Sqrt[c - I*c*Tan[e + f*x]])/(8*a^3*f*(1 + I*Tan[e + f*x])^2) - ((I*A + 3*B)*c*Sqrt[c - I*c*Tan[e + f*x]])/(32*a^3*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(6*a^3*f*(1 + I*Tan[e + f*x])^3)","A",6,6,43,0.1395,1,"{3588, 78, 47, 51, 63, 208}"
783,1,209,0,0.2395061,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^3} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/(a + I*a*Tan[e + f*x])^3,x]","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{6 a^3 f (1+i \tan (e+f x))^3}+\frac{(7 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{64 a^3 f (1+i \tan (e+f x))}+\frac{(7 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{48 a^3 f (1+i \tan (e+f x))^2}+\frac{\sqrt{c} (7 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{64 \sqrt{2} a^3 f}","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{6 a^3 f (1+i \tan (e+f x))^3}+\frac{(7 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{64 a^3 f (1+i \tan (e+f x))}+\frac{(7 B+5 i A) \sqrt{c-i c \tan (e+f x)}}{48 a^3 f (1+i \tan (e+f x))^2}+\frac{\sqrt{c} (7 B+5 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{64 \sqrt{2} a^3 f}",1,"(((5*I)*A + 7*B)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(64*Sqrt[2]*a^3*f) + ((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(6*a^3*f*(1 + I*Tan[e + f*x])^3) + (((5*I)*A + 7*B)*Sqrt[c - I*c*Tan[e + f*x]])/(48*a^3*f*(1 + I*Tan[e + f*x])^2) + (((5*I)*A + 7*B)*Sqrt[c - I*c*Tan[e + f*x]])/(64*a^3*f*(1 + I*Tan[e + f*x]))","A",6,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
784,1,245,0,0.2735468,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}}-\frac{5 (5 B+7 i A)}{128 a^3 f \sqrt{c-i c \tan (e+f x)}}+\frac{5 (5 B+7 i A)}{192 a^3 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{5 B+7 i A}{48 a^3 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{5 (5 B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{128 \sqrt{2} a^3 \sqrt{c} f}","\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}}-\frac{5 (5 B+7 i A)}{128 a^3 f \sqrt{c-i c \tan (e+f x)}}+\frac{5 (5 B+7 i A)}{192 a^3 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{5 B+7 i A}{48 a^3 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{5 (5 B+7 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{128 \sqrt{2} a^3 \sqrt{c} f}",1,"(5*((7*I)*A + 5*B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(128*Sqrt[2]*a^3*Sqrt[c]*f) - (5*((7*I)*A + 5*B))/(128*a^3*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I*A - B)/(6*a^3*f*(1 + I*Tan[e + f*x])^3*Sqrt[c - I*c*Tan[e + f*x]]) + ((7*I)*A + 5*B)/(48*a^3*f*(1 + I*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]) + (5*((7*I)*A + 5*B))/(192*a^3*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
785,1,274,0,0.309907,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{35 (B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{256 \sqrt{2} a^3 c^{3/2} f}+\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}}-\frac{35 (B+3 i A)}{256 a^3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 (B+3 i A)}{384 a^3 f (c-i c \tan (e+f x))^{3/2}}+\frac{7 (B+3 i A)}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{B+3 i A}{16 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}","\frac{35 (B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{256 \sqrt{2} a^3 c^{3/2} f}+\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}}-\frac{35 (B+3 i A)}{256 a^3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 (B+3 i A)}{384 a^3 f (c-i c \tan (e+f x))^{3/2}}+\frac{7 (B+3 i A)}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{B+3 i A}{16 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}",1,"(35*((3*I)*A + B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(256*Sqrt[2]*a^3*c^(3/2)*f) - (35*((3*I)*A + B))/(384*a^3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I*A - B)/(6*a^3*f*(1 + I*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(3/2)) + ((3*I)*A + B)/(16*a^3*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)) + (7*((3*I)*A + B))/(64*a^3*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - (35*((3*I)*A + B))/(256*a^3*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",8,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
786,1,311,0,0.3496972,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{21 (B+11 i A)}{512 a^3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{21 (B+11 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{512 \sqrt{2} a^3 c^{5/2} f}+\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}}-\frac{7 (B+11 i A)}{256 a^3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{21 (B+11 i A)}{640 a^3 f (c-i c \tan (e+f x))^{5/2}}+\frac{3 (B+11 i A)}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{B+11 i A}{48 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}","-\frac{21 (B+11 i A)}{512 a^3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{21 (B+11 i A) \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{512 \sqrt{2} a^3 c^{5/2} f}+\frac{-B+i A}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}}-\frac{7 (B+11 i A)}{256 a^3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{21 (B+11 i A)}{640 a^3 f (c-i c \tan (e+f x))^{5/2}}+\frac{3 (B+11 i A)}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{B+11 i A}{48 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}",1,"(21*((11*I)*A + B)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(512*Sqrt[2]*a^3*c^(5/2)*f) - (21*((11*I)*A + B))/(640*a^3*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I*A - B)/(6*a^3*f*(1 + I*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(5/2)) + ((11*I)*A + B)/(48*a^3*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)) + (3*((11*I)*A + B))/(64*a^3*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - (7*((11*I)*A + B))/(256*a^3*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (21*((11*I)*A + B))/(512*a^3*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",9,5,43,0.1163,1,"{3588, 78, 51, 63, 208}"
787,1,272,0,0.3290064,"\int \sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{5 \sqrt{a} c^{7/2} (-3 B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}-\frac{5 c^3 (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{5 c^2 (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{24 f}-\frac{c (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}{12 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{7/2}}{4 f}","-\frac{5 \sqrt{a} c^{7/2} (-3 B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}-\frac{5 c^3 (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{5 c^2 (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{24 f}-\frac{c (-3 B+4 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}{12 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{7/2}}{4 f}",1,"(-5*Sqrt[a]*((4*I)*A - 3*B)*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) - (5*((4*I)*A - 3*B)*c^3*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) - (5*((4*I)*A - 3*B)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(24*f) - (((4*I)*A - 3*B)*c*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2))/(12*f) + (B*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(7/2))/(4*f)","A",8,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
788,1,217,0,0.2956989,"\int \sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{\sqrt{a} c^{5/2} (-2 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}-\frac{c^2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{c (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}{3 f}","-\frac{\sqrt{a} c^{5/2} (-2 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}-\frac{c^2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{c (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}{3 f}",1,"-((Sqrt[a]*((3*I)*A - 2*B)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f) - (((3*I)*A - 2*B)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) - (((3*I)*A - 2*B)*c*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(6*f) + (B*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2))/(3*f)","A",7,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
789,1,164,0,0.2593421,"\int \sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{a} c^{3/2} (-B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}-\frac{c (-B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 f}","-\frac{\sqrt{a} c^{3/2} (-B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}-\frac{c (-B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 f}",1,"-((Sqrt[a]*((2*I)*A - B)*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f) - (((2*I)*A - B)*c*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) + (B*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(2*f)","A",6,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
790,1,104,0,0.2084209,"\int \sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{B \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i \sqrt{a} A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}","\frac{B \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i \sqrt{a} A \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}",1,"((-2*I)*Sqrt[a]*A*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (B*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/f","A",5,5,45,0.1111,1,"{3588, 80, 63, 217, 203}"
791,1,109,0,0.2197207,"\int \frac{\sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 \sqrt{a} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{2 \sqrt{a} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}",1,"(2*Sqrt[a]*B*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((I*A + B)*Sqrt[a + I*a*Tan[e + f*x]])/(f*Sqrt[c - I*c*Tan[e + f*x]])","A",5,5,45,0.1111,1,"{3588, 78, 63, 217, 203}"
792,1,102,0,0.2183652,"\int \frac{\sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{(-2 B+i A) \sqrt{a+i a \tan (e+f x)}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{(-2 B+i A) \sqrt{a+i a \tan (e+f x)}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"-((I*A + B)*Sqrt[a + I*a*Tan[e + f*x]])/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((I*A - 2*B)*Sqrt[a + I*a*Tan[e + f*x]])/(3*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,3,45,0.06667,1,"{3588, 78, 37}"
793,1,155,0,0.2465015,"\int \frac{\sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{(-3 B+2 i A) \sqrt{a+i a \tan (e+f x)}}{15 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{(-3 B+2 i A) \sqrt{a+i a \tan (e+f x)}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{(-3 B+2 i A) \sqrt{a+i a \tan (e+f x)}}{15 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{(-3 B+2 i A) \sqrt{a+i a \tan (e+f x)}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"-((I*A + B)*Sqrt[a + I*a*Tan[e + f*x]])/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) - (((2*I)*A - 3*B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)*A - 3*B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
794,1,208,0,0.276411,"\int \frac{\sqrt{a+i a \tan (e+f x)} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[(Sqrt[a + I*a*Tan[e + f*x]]*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{2 (-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{105 c^3 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{105 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{7 f (c-i c \tan (e+f x))^{7/2}}","-\frac{2 (-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{105 c^3 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{105 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(-4 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) \sqrt{a+i a \tan (e+f x)}}{7 f (c-i c \tan (e+f x))^{7/2}}",1,"-((I*A + B)*Sqrt[a + I*a*Tan[e + f*x]])/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) - (((3*I)*A - 4*B)*Sqrt[a + I*a*Tan[e + f*x]])/(35*c*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*((3*I)*A - 4*B)*Sqrt[a + I*a*Tan[e + f*x]])/(105*c^2*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*((3*I)*A - 4*B)*Sqrt[a + I*a*Tan[e + f*x]])/(105*c^3*f*Sqrt[c - I*c*Tan[e + f*x]])","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
795,1,279,0,0.3365482,"\int (a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{a^{3/2} c^{7/2} (-2 B+5 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a c^3 (5 A+2 i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{c^2 (-2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}-\frac{c (-2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}{20 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{7/2}}{5 f}","-\frac{a^{3/2} c^{7/2} (-2 B+5 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a c^3 (5 A+2 i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{c^2 (-2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}-\frac{c (-2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}{20 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{7/2}}{5 f}",1,"-(a^(3/2)*((5*I)*A - 2*B)*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) + (a*(5*A + (2*I)*B)*c^3*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) - (((5*I)*A - 2*B)*c^2*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(12*f) - (((5*I)*A - 2*B)*c*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2))/(20*f) + (B*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(7/2))/(5*f)","A",8,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
796,1,226,0,0.3063042,"\int (a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{a^{3/2} c^{5/2} (-B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a c^2 (4 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{c (-B+4 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}{4 f}","-\frac{a^{3/2} c^{5/2} (-B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a c^2 (4 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}-\frac{c (-B+4 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}{4 f}",1,"-(a^(3/2)*((4*I)*A - B)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) + (a*(4*A + I*B)*c^2*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) - (((4*I)*A - B)*c*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(12*f) + (B*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2))/(4*f)","A",7,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
797,1,157,0,0.2571734,"\int (a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{i a^{3/2} A c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a A c \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{3 f}","-\frac{i a^{3/2} A c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a A c \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{3 f}",1,"((-I)*a^(3/2)*A*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (a*A*c*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) + (B*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(3*f)","A",6,6,45,0.1333,1,"{3588, 80, 38, 63, 217, 203}"
798,1,160,0,0.2610307,"\int (a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{a^{3/2} \sqrt{c} (B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a (B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 f}","-\frac{a^{3/2} \sqrt{c} (B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a (B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{B (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 f}",1,"-((a^(3/2)*((2*I)*A + B)*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f) + (a*((2*I)*A + B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) + (B*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(2*f)","A",6,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
799,1,169,0,0.269004,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 a^{3/2} (2 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{a (2 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{2 a^{3/2} (2 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{a (2 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{f \sqrt{c-i c \tan (e+f x)}}",1,"(2*a^(3/2)*(I*A + 2*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (a*(I*A + 2*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c*f)","A",6,6,45,0.1333,1,"{3588, 78, 50, 63, 217, 203}"
800,1,155,0,0.2645572,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 a^{3/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}+\frac{2 a B \sqrt{a+i a \tan (e+f x)}}{c f \sqrt{c-i c \tan (e+f x)}}","-\frac{2 a^{3/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}+\frac{2 a B \sqrt{a+i a \tan (e+f x)}}{c f \sqrt{c-i c \tan (e+f x)}}",1,"(-2*a^(3/2)*B*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(3/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a*B*Sqrt[a + I*a*Tan[e + f*x]])/(c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",6,6,45,0.1333,1,"{3588, 78, 47, 63, 217, 203}"
801,1,102,0,0.2337172,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{(-4 B+i A) (a+i a \tan (e+f x))^{3/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{(-4 B+i A) (a+i a \tan (e+f x))^{3/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) - ((I*A - 4*B)*(a + I*a*Tan[e + f*x])^(3/2))/(15*c*f*(c - I*c*Tan[e + f*x])^(3/2))","A",3,3,45,0.06667,1,"{3588, 78, 37}"
802,1,155,0,0.2628018,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{(-5 B+2 i A) (a+i a \tan (e+f x))^{3/2}}{105 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(-5 B+2 i A) (a+i a \tan (e+f x))^{3/2}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{7 f (c-i c \tan (e+f x))^{7/2}}","-\frac{(-5 B+2 i A) (a+i a \tan (e+f x))^{3/2}}{105 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(-5 B+2 i A) (a+i a \tan (e+f x))^{3/2}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{7 f (c-i c \tan (e+f x))^{7/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) - (((2*I)*A - 5*B)*(a + I*a*Tan[e + f*x])^(3/2))/(35*c*f*(c - I*c*Tan[e + f*x])^(5/2)) - (((2*I)*A - 5*B)*(a + I*a*Tan[e + f*x])^(3/2))/(105*c^2*f*(c - I*c*Tan[e + f*x])^(3/2))","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
803,1,208,0,0.2822409,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(9/2),x]","-\frac{2 (-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{315 c^3 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 (-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{105 c^2 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{21 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{9 f (c-i c \tan (e+f x))^{9/2}}","-\frac{2 (-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{315 c^3 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 (-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{105 c^2 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-2 B+i A) (a+i a \tan (e+f x))^{3/2}}{21 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{9 f (c-i c \tan (e+f x))^{9/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(9*f*(c - I*c*Tan[e + f*x])^(9/2)) - ((I*A - 2*B)*(a + I*a*Tan[e + f*x])^(3/2))/(21*c*f*(c - I*c*Tan[e + f*x])^(7/2)) - (2*(I*A - 2*B)*(a + I*a*Tan[e + f*x])^(3/2))/(105*c^2*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*(I*A - 2*B)*(a + I*a*Tan[e + f*x])^(3/2))/(315*c^3*f*(c - I*c*Tan[e + f*x])^(3/2))","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
804,1,261,0,0.3207269,"\int \frac{(a+i a \tan (e+f x))^{3/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(3/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(11/2),x]","-\frac{2 (-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{3465 c^4 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 (-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{1155 c^3 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{231 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{11 f (c-i c \tan (e+f x))^{11/2}}","-\frac{2 (-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{3465 c^4 f (c-i c \tan (e+f x))^{3/2}}-\frac{2 (-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{1155 c^3 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{231 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-7 B+4 i A) (a+i a \tan (e+f x))^{3/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{3/2}}{11 f (c-i c \tan (e+f x))^{11/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(3/2))/(11*f*(c - I*c*Tan[e + f*x])^(11/2)) - (((4*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(3/2))/(99*c*f*(c - I*c*Tan[e + f*x])^(9/2)) - (((4*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(3/2))/(231*c^2*f*(c - I*c*Tan[e + f*x])^(7/2)) - (2*((4*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(3/2))/(1155*c^3*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*((4*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(3/2))/(3465*c^4*f*(c - I*c*Tan[e + f*x])^(3/2))","A",6,4,45,0.08889,1,"{3588, 78, 45, 37}"
805,1,288,0,0.3297127,"\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{a^{5/2} c^{7/2} (-B+6 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{a^2 c^3 (6 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{a c^2 (6 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}-\frac{c (-B+6 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{30 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{7/2}}{6 f}","-\frac{a^{5/2} c^{7/2} (-B+6 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{a^2 c^3 (6 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{a c^2 (6 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}-\frac{c (-B+6 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{30 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{7/2}}{6 f}",1,"-(a^(5/2)*((6*I)*A - B)*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(8*f) + (a^2*(6*A + I*B)*c^3*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(16*f) + (a*(6*A + I*B)*c^2*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(24*f) - (((6*I)*A - B)*c*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2))/(30*f) + (B*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(7/2))/(6*f)","A",8,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
806,1,213,0,0.2745124,"\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{3 i a^{5/2} A c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{3 a^2 A c^2 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a A c \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{4 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{5 f}","-\frac{3 i a^{5/2} A c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{3 a^2 A c^2 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a A c \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{4 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{5 f}",1,"(((-3*I)/4)*a^(5/2)*A*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (3*a^2*A*c^2*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) + (a*A*c*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(4*f) + (B*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2))/(5*f)","A",7,6,45,0.1333,1,"{3588, 80, 38, 63, 217, 203}"
807,1,222,0,0.304214,"\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{a^{5/2} c^{3/2} (B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a^2 c (4 A-i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a (B+4 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}{4 f}","-\frac{a^{5/2} c^{3/2} (B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a^2 c (4 A-i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a (B+4 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{B (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}{4 f}",1,"-(a^(5/2)*((4*I)*A + B)*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) + (a^2*(4*A - I*B)*c*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) + (a*((4*I)*A + B)*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(12*f) + (B*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2))/(4*f)","A",7,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
808,1,217,0,0.2900314,"\int (a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{a^{5/2} \sqrt{c} (2 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a^2 (2 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{a (2 B+3 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 f}+\frac{B (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{3 f}","-\frac{a^{5/2} \sqrt{c} (2 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{f}+\frac{a^2 (2 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{a (2 B+3 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 f}+\frac{B (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{3 f}",1,"-((a^(5/2)*((3*I)*A + 2*B)*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f) + (a^2*((3*I)*A + 2*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) + (a*((3*I)*A + 2*B)*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(6*f) + (B*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]])/(3*f)","A",7,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
809,1,227,0,0.304716,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{3 a^{5/2} (3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{3 a^2 (3 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{a (3 B+2 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{3 a^{5/2} (3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{3 a^2 (3 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{a (3 B+2 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{f \sqrt{c-i c \tan (e+f x)}}",1,"(3*a^(5/2)*((2*I)*A + 3*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (3*a^2*((2*I)*A + 3*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*c*f) - (a*((2*I)*A + 3*B)*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(2*c*f)","A",7,6,45,0.1333,1,"{3588, 78, 50, 63, 217, 203}"
810,1,226,0,0.3148899,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 a^{5/2} (4 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}+\frac{a^2 (4 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{2 a (4 B+i A) (a+i a \tan (e+f x))^{3/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{2 a^{5/2} (4 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}+\frac{a^2 (4 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{2 a (4 B+i A) (a+i a \tan (e+f x))^{3/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(-2*a^(5/2)*(I*A + 4*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(3/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a*(I*A + 4*B)*(a + I*a*Tan[e + f*x])^(3/2))/(3*c*f*Sqrt[c - I*c*Tan[e + f*x]]) + (a^2*(I*A + 4*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f)","A",7,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
811,1,203,0,0.2894273,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a^{5/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{5/2} f}-\frac{2 a^2 B \sqrt{a+i a \tan (e+f x)}}{c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}+\frac{2 a B (a+i a \tan (e+f x))^{3/2}}{3 c f (c-i c \tan (e+f x))^{3/2}}","\frac{2 a^{5/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{5/2} f}-\frac{2 a^2 B \sqrt{a+i a \tan (e+f x)}}{c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}+\frac{2 a B (a+i a \tan (e+f x))^{3/2}}{3 c f (c-i c \tan (e+f x))^{3/2}}",1,"(2*a^(5/2)*B*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(5/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) + (2*a*B*(a + I*a*Tan[e + f*x])^(3/2))/(3*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*a^2*B*Sqrt[a + I*a*Tan[e + f*x]])/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",7,6,45,0.1333,1,"{3588, 78, 47, 63, 217, 203}"
812,1,102,0,0.2307416,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{(-6 B+i A) (a+i a \tan (e+f x))^{5/2}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{7 f (c-i c \tan (e+f x))^{7/2}}","-\frac{(-6 B+i A) (a+i a \tan (e+f x))^{5/2}}{35 c f (c-i c \tan (e+f x))^{5/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{7 f (c-i c \tan (e+f x))^{7/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) - ((I*A - 6*B)*(a + I*a*Tan[e + f*x])^(5/2))/(35*c*f*(c - I*c*Tan[e + f*x])^(5/2))","A",3,3,45,0.06667,1,"{3588, 78, 37}"
813,1,155,0,0.2593786,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(9/2),x]","-\frac{(-7 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{315 c^2 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-7 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{63 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{9 f (c-i c \tan (e+f x))^{9/2}}","-\frac{(-7 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{315 c^2 f (c-i c \tan (e+f x))^{5/2}}-\frac{(-7 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{63 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{9 f (c-i c \tan (e+f x))^{9/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(9*f*(c - I*c*Tan[e + f*x])^(9/2)) - (((2*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(5/2))/(63*c*f*(c - I*c*Tan[e + f*x])^(7/2)) - (((2*I)*A - 7*B)*(a + I*a*Tan[e + f*x])^(5/2))/(315*c^2*f*(c - I*c*Tan[e + f*x])^(5/2))","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
814,1,208,0,0.2910193,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(11/2),x]","-\frac{2 (-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{3465 c^3 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 (-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{693 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{11 f (c-i c \tan (e+f x))^{11/2}}","-\frac{2 (-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{3465 c^3 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 (-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{693 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-8 B+3 i A) (a+i a \tan (e+f x))^{5/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{11 f (c-i c \tan (e+f x))^{11/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(11*f*(c - I*c*Tan[e + f*x])^(11/2)) - (((3*I)*A - 8*B)*(a + I*a*Tan[e + f*x])^(5/2))/(99*c*f*(c - I*c*Tan[e + f*x])^(9/2)) - (2*((3*I)*A - 8*B)*(a + I*a*Tan[e + f*x])^(5/2))/(693*c^2*f*(c - I*c*Tan[e + f*x])^(7/2)) - (2*((3*I)*A - 8*B)*(a + I*a*Tan[e + f*x])^(5/2))/(3465*c^3*f*(c - I*c*Tan[e + f*x])^(5/2))","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
815,1,261,0,0.3213131,"\int \frac{(a+i a \tan (e+f x))^{5/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{13/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(5/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(13/2),x]","-\frac{2 (-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{15015 c^4 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 (-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{3003 c^3 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{429 c^2 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{143 c f (c-i c \tan (e+f x))^{11/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{13 f (c-i c \tan (e+f x))^{13/2}}","-\frac{2 (-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{15015 c^4 f (c-i c \tan (e+f x))^{5/2}}-\frac{2 (-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{3003 c^3 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{429 c^2 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-9 B+4 i A) (a+i a \tan (e+f x))^{5/2}}{143 c f (c-i c \tan (e+f x))^{11/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{5/2}}{13 f (c-i c \tan (e+f x))^{13/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(5/2))/(13*f*(c - I*c*Tan[e + f*x])^(13/2)) - (((4*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(5/2))/(143*c*f*(c - I*c*Tan[e + f*x])^(11/2)) - (((4*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(5/2))/(429*c^2*f*(c - I*c*Tan[e + f*x])^(9/2)) - (2*((4*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(5/2))/(3003*c^3*f*(c - I*c*Tan[e + f*x])^(7/2)) - (2*((4*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(5/2))/(15015*c^4*f*(c - I*c*Tan[e + f*x])^(5/2))","A",6,4,45,0.08889,1,"{3588, 78, 45, 37}"
816,1,350,0,0.3691213,"\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(9/2),x]","-\frac{5 a^{7/2} c^{9/2} (-B+8 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{64 f}+\frac{5 a^3 c^4 (8 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{128 f}+\frac{5 a^2 c^3 (8 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{192 f}+\frac{a c^2 (8 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{48 f}-\frac{c (-B+8 i A) (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{7/2}}{56 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{9/2}}{8 f}","-\frac{5 a^{7/2} c^{9/2} (-B+8 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{64 f}+\frac{5 a^3 c^4 (8 A+i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{128 f}+\frac{5 a^2 c^3 (8 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{192 f}+\frac{a c^2 (8 A+i B) \tan (e+f x) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{48 f}-\frac{c (-B+8 i A) (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{7/2}}{56 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{9/2}}{8 f}",1,"(-5*a^(7/2)*((8*I)*A - B)*c^(9/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(64*f) + (5*a^3*(8*A + I*B)*c^4*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(128*f) + (5*a^2*(8*A + I*B)*c^3*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(192*f) + (a*(8*A + I*B)*c^2*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2))/(48*f) - (((8*I)*A - B)*c*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(7/2))/(56*f) + (B*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(9/2))/(8*f)","A",9,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
817,1,267,0,0.297291,"\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{5 i a^{7/2} A c^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{5 a^3 A c^3 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{5 a^2 A c^2 \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}+\frac{a A c \tan (e+f x) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{6 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{7/2}}{7 f}","-\frac{5 i a^{7/2} A c^{7/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{5 a^3 A c^3 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{5 a^2 A c^2 \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}+\frac{a A c \tan (e+f x) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{6 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{7/2}}{7 f}",1,"(((-5*I)/8)*a^(7/2)*A*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (5*a^3*A*c^3*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(16*f) + (5*a^2*A*c^2*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(24*f) + (a*A*c*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2))/(6*f) + (B*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(7/2))/(7*f)","A",8,6,45,0.1333,1,"{3588, 80, 38, 63, 217, 203}"
818,1,284,0,0.3265344,"\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{a^{7/2} c^{5/2} (B+6 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{a^3 c^2 (6 A-i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{a^2 c (6 A-i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}+\frac{a (B+6 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{30 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{5/2}}{6 f}","-\frac{a^{7/2} c^{5/2} (B+6 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{8 f}+\frac{a^3 c^2 (6 A-i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{16 f}+\frac{a^2 c (6 A-i B) \tan (e+f x) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{24 f}+\frac{a (B+6 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}{30 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{5/2}}{6 f}",1,"-(a^(7/2)*((6*I)*A + B)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(8*f) + (a^3*(6*A - I*B)*c^2*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(16*f) + (a^2*(6*A - I*B)*c*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(24*f) + (a*((6*I)*A + B)*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2))/(30*f) + (B*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(5/2))/(6*f)","A",8,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
819,1,279,0,0.3286467,"\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{a^{7/2} c^{3/2} (2 B+5 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a^3 c (5 A-2 i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a^2 (2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{a (2 B+5 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}{20 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{3/2}}{5 f}","-\frac{a^{7/2} c^{3/2} (2 B+5 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{a^3 c (5 A-2 i B) \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{a^2 (2 B+5 i A) (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{12 f}+\frac{a (2 B+5 i A) (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}{20 f}+\frac{B (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{3/2}}{5 f}",1,"-(a^(7/2)*((5*I)*A + 2*B)*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) + (a^3*(5*A - (2*I)*B)*c*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) + (a^2*((5*I)*A + 2*B)*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/(12*f) + (a*((5*I)*A + 2*B)*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2))/(20*f) + (B*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(3/2))/(5*f)","A",8,7,45,0.1556,1,"{3588, 80, 49, 38, 63, 217, 203}"
820,1,272,0,0.3200355,"\int (a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{5 a^{7/2} \sqrt{c} (3 B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{5 a^3 (3 B+4 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{5 a^2 (3 B+4 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{24 f}+\frac{a (3 B+4 i A) (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{12 f}+\frac{B (a+i a \tan (e+f x))^{7/2} \sqrt{c-i c \tan (e+f x)}}{4 f}","-\frac{5 a^{7/2} \sqrt{c} (3 B+4 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{4 f}+\frac{5 a^3 (3 B+4 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{8 f}+\frac{5 a^2 (3 B+4 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{24 f}+\frac{a (3 B+4 i A) (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{12 f}+\frac{B (a+i a \tan (e+f x))^{7/2} \sqrt{c-i c \tan (e+f x)}}{4 f}",1,"(-5*a^(7/2)*((4*I)*A + 3*B)*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(4*f) + (5*a^3*((4*I)*A + 3*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(8*f) + (5*a^2*((4*I)*A + 3*B)*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(24*f) + (a*((4*I)*A + 3*B)*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]])/(12*f) + (B*(a + I*a*Tan[e + f*x])^(7/2)*Sqrt[c - I*c*Tan[e + f*x]])/(4*f)","A",8,6,45,0.1333,1,"{3588, 80, 50, 63, 217, 203}"
821,1,283,0,0.3359868,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{5 a^{7/2} (4 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{5 a^3 (4 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{5 a^2 (4 B+3 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c f}-\frac{a (4 B+3 i A) (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{3 c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{5 a^{7/2} (4 B+3 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{c} f}-\frac{5 a^3 (4 B+3 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{5 a^2 (4 B+3 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c f}-\frac{a (4 B+3 i A) (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}{3 c f}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{f \sqrt{c-i c \tan (e+f x)}}",1,"(5*a^(7/2)*((3*I)*A + 4*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (5*a^3*((3*I)*A + 4*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*c*f) - (5*a^2*((3*I)*A + 4*B)*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(6*c*f) - (a*((3*I)*A + 4*B)*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]])/(3*c*f)","A",8,6,45,0.1333,1,"{3588, 78, 50, 63, 217, 203}"
822,1,285,0,0.3443299,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{5 a^{7/2} (5 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}+\frac{5 a^3 (5 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^2 f}+\frac{5 a^2 (5 B+2 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c^2 f}+\frac{2 a (5 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{5 a^{7/2} (5 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{3/2} f}+\frac{5 a^3 (5 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^2 f}+\frac{5 a^2 (5 B+2 i A) (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c^2 f}+\frac{2 a (5 B+2 i A) (a+i a \tan (e+f x))^{5/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(-5*a^(7/2)*((2*I)*A + 5*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(3/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a*((2*I)*A + 5*B)*(a + I*a*Tan[e + f*x])^(5/2))/(3*c*f*Sqrt[c - I*c*Tan[e + f*x]]) + (5*a^3*((2*I)*A + 5*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*c^2*f) + (5*a^2*((2*I)*A + 5*B)*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(6*c^2*f)","A",8,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
823,1,283,0,0.3476814,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 a^{7/2} (6 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{5/2} f}-\frac{a^3 (6 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^3 f}-\frac{2 a^2 (6 B+i A) (a+i a \tan (e+f x))^{3/2}}{3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{2 a (6 B+i A) (a+i a \tan (e+f x))^{5/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{2 a^{7/2} (6 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{5/2} f}-\frac{a^3 (6 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^3 f}-\frac{2 a^2 (6 B+i A) (a+i a \tan (e+f x))^{3/2}}{3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{2 a (6 B+i A) (a+i a \tan (e+f x))^{5/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"(2*a^(7/2)*(I*A + 6*B)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(5/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(5*f*(c - I*c*Tan[e + f*x])^(5/2)) + (2*a*(I*A + 6*B)*(a + I*a*Tan[e + f*x])^(5/2))/(15*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*a^2*(I*A + 6*B)*(a + I*a*Tan[e + f*x])^(3/2))/(3*c^2*f*Sqrt[c - I*c*Tan[e + f*x]]) - (a^3*(I*A + 6*B)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^3*f)","A",8,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
824,1,251,0,0.3152529,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{7/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(7/2),x]","-\frac{2 a^{7/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{7/2} f}+\frac{2 a^3 B \sqrt{a+i a \tan (e+f x)}}{c^3 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a^2 B (a+i a \tan (e+f x))^{3/2}}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{7 f (c-i c \tan (e+f x))^{7/2}}+\frac{2 a B (a+i a \tan (e+f x))^{5/2}}{5 c f (c-i c \tan (e+f x))^{5/2}}","-\frac{2 a^{7/2} B \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{c^{7/2} f}+\frac{2 a^3 B \sqrt{a+i a \tan (e+f x)}}{c^3 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 a^2 B (a+i a \tan (e+f x))^{3/2}}{3 c^2 f (c-i c \tan (e+f x))^{3/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{7 f (c-i c \tan (e+f x))^{7/2}}+\frac{2 a B (a+i a \tan (e+f x))^{5/2}}{5 c f (c-i c \tan (e+f x))^{5/2}}",1,"(-2*a^(7/2)*B*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(c^(7/2)*f) - ((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(7*f*(c - I*c*Tan[e + f*x])^(7/2)) + (2*a*B*(a + I*a*Tan[e + f*x])^(5/2))/(5*c*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*a^2*B*(a + I*a*Tan[e + f*x])^(3/2))/(3*c^2*f*(c - I*c*Tan[e + f*x])^(3/2)) + (2*a^3*B*Sqrt[a + I*a*Tan[e + f*x]])/(c^3*f*Sqrt[c - I*c*Tan[e + f*x]])","A",8,6,45,0.1333,1,"{3588, 78, 47, 63, 217, 203}"
825,1,102,0,0.2282824,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{9/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(9/2),x]","-\frac{(-8 B+i A) (a+i a \tan (e+f x))^{7/2}}{63 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{9 f (c-i c \tan (e+f x))^{9/2}}","-\frac{(-8 B+i A) (a+i a \tan (e+f x))^{7/2}}{63 c f (c-i c \tan (e+f x))^{7/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{9 f (c-i c \tan (e+f x))^{9/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(9*f*(c - I*c*Tan[e + f*x])^(9/2)) - ((I*A - 8*B)*(a + I*a*Tan[e + f*x])^(7/2))/(63*c*f*(c - I*c*Tan[e + f*x])^(7/2))","A",3,3,45,0.06667,1,"{3588, 78, 37}"
826,1,155,0,0.2637887,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{11/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(11/2),x]","-\frac{(-9 B+2 i A) (a+i a \tan (e+f x))^{7/2}}{693 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-9 B+2 i A) (a+i a \tan (e+f x))^{7/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{11 f (c-i c \tan (e+f x))^{11/2}}","-\frac{(-9 B+2 i A) (a+i a \tan (e+f x))^{7/2}}{693 c^2 f (c-i c \tan (e+f x))^{7/2}}-\frac{(-9 B+2 i A) (a+i a \tan (e+f x))^{7/2}}{99 c f (c-i c \tan (e+f x))^{9/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{11 f (c-i c \tan (e+f x))^{11/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(11*f*(c - I*c*Tan[e + f*x])^(11/2)) - (((2*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(7/2))/(99*c*f*(c - I*c*Tan[e + f*x])^(9/2)) - (((2*I)*A - 9*B)*(a + I*a*Tan[e + f*x])^(7/2))/(693*c^2*f*(c - I*c*Tan[e + f*x])^(7/2))","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
827,1,208,0,0.2858632,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{13/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(13/2),x]","-\frac{2 (-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{9009 c^3 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 (-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{1287 c^2 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{143 c f (c-i c \tan (e+f x))^{11/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{13 f (c-i c \tan (e+f x))^{13/2}}","-\frac{2 (-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{9009 c^3 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 (-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{1287 c^2 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-10 B+3 i A) (a+i a \tan (e+f x))^{7/2}}{143 c f (c-i c \tan (e+f x))^{11/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{13 f (c-i c \tan (e+f x))^{13/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(13*f*(c - I*c*Tan[e + f*x])^(13/2)) - (((3*I)*A - 10*B)*(a + I*a*Tan[e + f*x])^(7/2))/(143*c*f*(c - I*c*Tan[e + f*x])^(11/2)) - (2*((3*I)*A - 10*B)*(a + I*a*Tan[e + f*x])^(7/2))/(1287*c^2*f*(c - I*c*Tan[e + f*x])^(9/2)) - (2*((3*I)*A - 10*B)*(a + I*a*Tan[e + f*x])^(7/2))/(9009*c^3*f*(c - I*c*Tan[e + f*x])^(7/2))","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
828,1,261,0,0.3155091,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{15/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(15/2),x]","-\frac{2 (-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{45045 c^4 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 (-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{6435 c^3 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{715 c^2 f (c-i c \tan (e+f x))^{11/2}}-\frac{(-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{195 c f (c-i c \tan (e+f x))^{13/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{15 f (c-i c \tan (e+f x))^{15/2}}","-\frac{2 (-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{45045 c^4 f (c-i c \tan (e+f x))^{7/2}}-\frac{2 (-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{6435 c^3 f (c-i c \tan (e+f x))^{9/2}}-\frac{(-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{715 c^2 f (c-i c \tan (e+f x))^{11/2}}-\frac{(-11 B+4 i A) (a+i a \tan (e+f x))^{7/2}}{195 c f (c-i c \tan (e+f x))^{13/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{15 f (c-i c \tan (e+f x))^{15/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(15*f*(c - I*c*Tan[e + f*x])^(15/2)) - (((4*I)*A - 11*B)*(a + I*a*Tan[e + f*x])^(7/2))/(195*c*f*(c - I*c*Tan[e + f*x])^(13/2)) - (((4*I)*A - 11*B)*(a + I*a*Tan[e + f*x])^(7/2))/(715*c^2*f*(c - I*c*Tan[e + f*x])^(11/2)) - (2*((4*I)*A - 11*B)*(a + I*a*Tan[e + f*x])^(7/2))/(6435*c^3*f*(c - I*c*Tan[e + f*x])^(9/2)) - (2*((4*I)*A - 11*B)*(a + I*a*Tan[e + f*x])^(7/2))/(45045*c^4*f*(c - I*c*Tan[e + f*x])^(7/2))","A",6,4,45,0.08889,1,"{3588, 78, 45, 37}"
829,1,314,0,0.3538857,"\int \frac{(a+i a \tan (e+f x))^{7/2} (A+B \tan (e+f x))}{(c-i c \tan (e+f x))^{17/2}} \, dx","Int[((a + I*a*Tan[e + f*x])^(7/2)*(A + B*Tan[e + f*x]))/(c - I*c*Tan[e + f*x])^(17/2),x]","-\frac{8 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{765765 c^5 f (c-i c \tan (e+f x))^{7/2}}-\frac{8 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{109395 c^4 f (c-i c \tan (e+f x))^{9/2}}-\frac{4 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{12155 c^3 f (c-i c \tan (e+f x))^{11/2}}-\frac{4 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{3315 c^2 f (c-i c \tan (e+f x))^{13/2}}-\frac{(-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{255 c f (c-i c \tan (e+f x))^{15/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{17 f (c-i c \tan (e+f x))^{17/2}}","-\frac{8 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{765765 c^5 f (c-i c \tan (e+f x))^{7/2}}-\frac{8 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{109395 c^4 f (c-i c \tan (e+f x))^{9/2}}-\frac{4 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{12155 c^3 f (c-i c \tan (e+f x))^{11/2}}-\frac{4 (-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{3315 c^2 f (c-i c \tan (e+f x))^{13/2}}-\frac{(-12 B+5 i A) (a+i a \tan (e+f x))^{7/2}}{255 c f (c-i c \tan (e+f x))^{15/2}}-\frac{(B+i A) (a+i a \tan (e+f x))^{7/2}}{17 f (c-i c \tan (e+f x))^{17/2}}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(7/2))/(17*f*(c - I*c*Tan[e + f*x])^(17/2)) - (((5*I)*A - 12*B)*(a + I*a*Tan[e + f*x])^(7/2))/(255*c*f*(c - I*c*Tan[e + f*x])^(15/2)) - (4*((5*I)*A - 12*B)*(a + I*a*Tan[e + f*x])^(7/2))/(3315*c^2*f*(c - I*c*Tan[e + f*x])^(13/2)) - (4*((5*I)*A - 12*B)*(a + I*a*Tan[e + f*x])^(7/2))/(12155*c^3*f*(c - I*c*Tan[e + f*x])^(11/2)) - (8*((5*I)*A - 12*B)*(a + I*a*Tan[e + f*x])^(7/2))/(109395*c^4*f*(c - I*c*Tan[e + f*x])^(9/2)) - (8*((5*I)*A - 12*B)*(a + I*a*Tan[e + f*x])^(7/2))/(765765*c^5*f*(c - I*c*Tan[e + f*x])^(7/2))","A",7,4,45,0.08889,1,"{3588, 78, 45, 37}"
830,1,228,0,0.2965978,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{3 c^{5/2} (-3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{3 c^2 (-3 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a f}+\frac{c (-3 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{f \sqrt{a+i a \tan (e+f x)}}","\frac{3 c^{5/2} (-3 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{3 c^2 (-3 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a f}+\frac{c (-3 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{f \sqrt{a+i a \tan (e+f x)}}",1,"(3*((2*I)*A - 3*B)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[a]*f) + (3*((2*I)*A - 3*B)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*a*f) + (((2*I)*A - 3*B)*c*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(2*a*f) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",7,6,45,0.1333,1,"{3588, 78, 50, 63, 217, 203}"
831,1,169,0,0.2639503,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{2 c^{3/2} (-2 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{c (-2 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}","\frac{2 c^{3/2} (-2 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{c (-2 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}",1,"(2*(I*A - 2*B)*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[a]*f) + ((I*A - 2*B)*c*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(a*f) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",6,6,45,0.1333,1,"{3588, 78, 50, 63, 217, 203}"
832,1,110,0,0.2190407,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{2 B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{2 B \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{\sqrt{a} f}",1,"(-2*B*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[a]*f) + ((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",5,5,45,0.1111,1,"{3588, 78, 63, 217, 203}"
833,1,92,0,0.1997288,"\int \frac{A+B \tan (e+f x)}{\sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/(Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{i A \sqrt{c-i c \tan (e+f x)}}{c f \sqrt{a+i a \tan (e+f x)}}-\frac{B+i A}{f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}","\frac{i A \sqrt{c-i c \tan (e+f x)}}{c f \sqrt{a+i a \tan (e+f x)}}-\frac{B+i A}{f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}",1,"-((I*A + B)/(f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])) + (I*A*Sqrt[c - I*c*Tan[e + f*x]])/(c*f*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,45,0.06667,1,"{3588, 78, 37}"
834,1,157,0,0.2512876,"\int \frac{A+B \tan (e+f x)}{\sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/(Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{-B+i A}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}-\frac{(-B+2 i A) \sqrt{a+i a \tan (e+f x)}}{3 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{(-B+2 i A) \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i c \tan (e+f x))^{3/2}}","\frac{-B+i A}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}-\frac{(-B+2 i A) \sqrt{a+i a \tan (e+f x)}}{3 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{(-B+2 i A) \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i c \tan (e+f x))^{3/2}}",1,"(I*A - B)/(f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)*A - B)*Sqrt[a + I*a*Tan[e + f*x]])/(3*a*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)*A - B)*Sqrt[a + I*a*Tan[e + f*x]])/(3*a*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
835,1,213,0,0.2750415,"\int \frac{A+B \tan (e+f x)}{\sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/(Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{15 a c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{15 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{(-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{5 a f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}","-\frac{2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{15 a c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{15 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{(-2 B+3 i A) \sqrt{a+i a \tan (e+f x)}}{5 a f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}",1,"(I*A - B)/(f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)) - (((3*I)*A - 2*B)*Sqrt[a + I*a*Tan[e + f*x]])/(5*a*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*((3*I)*A - 2*B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*a*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*((3*I)*A - 2*B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*a*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
836,1,287,0,0.3426764,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2))/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{5 c^{7/2} (-5 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{5 c^3 (-5 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a^2 f}-\frac{5 c^2 (-5 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 a^2 f}-\frac{2 c (-5 B+2 i A) (c-i c \tan (e+f x))^{5/2}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{3 f (a+i a \tan (e+f x))^{3/2}}","-\frac{5 c^{7/2} (-5 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{5 c^3 (-5 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a^2 f}-\frac{5 c^2 (-5 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 a^2 f}-\frac{2 c (-5 B+2 i A) (c-i c \tan (e+f x))^{5/2}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{3 f (a+i a \tan (e+f x))^{3/2}}",1,"(-5*((2*I)*A - 5*B)*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(3/2)*f) - (5*((2*I)*A - 5*B)*c^3*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*a^2*f) - (5*((2*I)*A - 5*B)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(6*a^2*f) - (2*((2*I)*A - 5*B)*c*(c - I*c*Tan[e + f*x])^(5/2))/(3*a*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(7/2))/(3*f*(a + I*a*Tan[e + f*x])^(3/2))","A",8,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
837,1,229,0,0.307727,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{2 c^{5/2} (-4 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{c^2 (-4 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a^2 f}-\frac{2 c (-4 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{3 f (a+i a \tan (e+f x))^{3/2}}","-\frac{2 c^{5/2} (-4 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{c^2 (-4 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a^2 f}-\frac{2 c (-4 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{3 f (a+i a \tan (e+f x))^{3/2}}",1,"(-2*(I*A - 4*B)*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(3/2)*f) - ((I*A - 4*B)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f) - (2*(I*A - 4*B)*c*(c - I*c*Tan[e + f*x])^(3/2))/(3*a*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(3*f*(a + I*a*Tan[e + f*x])^(3/2))","A",7,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
838,1,157,0,0.2652708,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{2 B c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 B c \sqrt{c-i c \tan (e+f x)}}{a f \sqrt{a+i a \tan (e+f x)}}","\frac{2 B c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{3/2} f}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 B c \sqrt{c-i c \tan (e+f x)}}{a f \sqrt{a+i a \tan (e+f x)}}",1,"(2*B*c^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(3/2)*f) + (2*B*c*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(3*f*(a + I*a*Tan[e + f*x])^(3/2))","A",6,6,45,0.1333,1,"{3588, 78, 47, 63, 217, 203}"
839,1,104,0,0.2149546,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(2 B+i A) \sqrt{c-i c \tan (e+f x)}}{3 a f \sqrt{a+i a \tan (e+f x)}}","\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(2 B+i A) \sqrt{c-i c \tan (e+f x)}}{3 a f \sqrt{a+i a \tan (e+f x)}}",1,"((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(3*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I*A + 2*B)*Sqrt[c - I*c*Tan[e + f*x]])/(3*a*f*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,45,0.06667,1,"{3588, 78, 37}"
840,1,152,0,0.2460766,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]),x]","-\frac{B+i A}{f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{(B+2 i A) \sqrt{c-i c \tan (e+f x)}}{3 a c f \sqrt{a+i a \tan (e+f x)}}+\frac{(B+2 i A) \sqrt{c-i c \tan (e+f x)}}{3 c f (a+i a \tan (e+f x))^{3/2}}","-\frac{B+i A}{f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{(B+2 i A) \sqrt{c-i c \tan (e+f x)}}{3 a c f \sqrt{a+i a \tan (e+f x)}}+\frac{(B+2 i A) \sqrt{c-i c \tan (e+f x)}}{3 c f (a+i a \tan (e+f x))^{3/2}}",1,"-((I*A + B)/(f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])) + (((2*I)*A + B)*Sqrt[c - I*c*Tan[e + f*x]])/(3*c*f*(a + I*a*Tan[e + f*x])^(3/2)) + (((2*I)*A + B)*Sqrt[c - I*c*Tan[e + f*x]])/(3*a*c*f*Sqrt[a + I*a*Tan[e + f*x]])","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
841,1,150,0,0.2453983,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)),x]","-\frac{B+i A}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{2 A \tan (e+f x)}{3 a c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i A}{3 c f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}","-\frac{B+i A}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{2 A \tan (e+f x)}{3 a c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i A}{3 c f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}",1,"-(I*A + B)/(3*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + ((I/3)*A)/(c*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (2*A*Tan[e + f*x])/(3*a*c*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",4,4,45,0.08889,1,"{3588, 78, 45, 39}"
842,1,269,0,0.3174563,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{2 (-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{15 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{15 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{5 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}+\frac{-B+4 i A}{3 a f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}","-\frac{2 (-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{15 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 (-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{15 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{(-B+4 i A) \sqrt{a+i a \tan (e+f x)}}{5 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{-B+i A}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}+\frac{-B+4 i A}{3 a f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}",1,"(I*A - B)/(3*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2)) + ((4*I)*A - B)/(3*a*f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)) - (((4*I)*A - B)*Sqrt[a + I*a*Tan[e + f*x]])/(5*a^2*f*(c - I*c*Tan[e + f*x])^(5/2)) - (2*((4*I)*A - B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*a^2*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (2*((4*I)*A - B)*Sqrt[a + I*a*Tan[e + f*x]])/(15*a^2*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",6,4,45,0.08889,1,"{3588, 78, 45, 37}"
843,1,343,0,0.3809885,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(9/2))/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{7 c^{9/2} (-7 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}+\frac{7 c^4 (-7 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a^3 f}+\frac{7 c^3 (-7 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 a^3 f}+\frac{14 c^2 (-7 B+2 i A) (c-i c \tan (e+f x))^{5/2}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{2 c (-7 B+2 i A) (c-i c \tan (e+f x))^{7/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{7 c^{9/2} (-7 B+2 i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}+\frac{7 c^4 (-7 B+2 i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 a^3 f}+\frac{7 c^3 (-7 B+2 i A) \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{6 a^3 f}+\frac{14 c^2 (-7 B+2 i A) (c-i c \tan (e+f x))^{5/2}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{2 c (-7 B+2 i A) (c-i c \tan (e+f x))^{7/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{9/2}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"(7*((2*I)*A - 7*B)*c^(9/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(5/2)*f) + (7*((2*I)*A - 7*B)*c^4*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*a^3*f) + (7*((2*I)*A - 7*B)*c^3*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/(6*a^3*f) + (14*((2*I)*A - 7*B)*c^2*(c - I*c*Tan[e + f*x])^(5/2))/(15*a^2*f*Sqrt[a + I*a*Tan[e + f*x]]) - (2*((2*I)*A - 7*B)*c*(c - I*c*Tan[e + f*x])^(7/2))/(15*a*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(9/2))/(5*f*(a + I*a*Tan[e + f*x])^(5/2))","A",9,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
844,1,284,0,0.3428937,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(7/2))/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{2 c^{7/2} (-6 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}+\frac{c^3 (-6 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a^3 f}+\frac{2 c^2 (-6 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{2 c (-6 B+i A) (c-i c \tan (e+f x))^{5/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{2 c^{7/2} (-6 B+i A) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}+\frac{c^3 (-6 B+i A) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a^3 f}+\frac{2 c^2 (-6 B+i A) (c-i c \tan (e+f x))^{3/2}}{3 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{2 c (-6 B+i A) (c-i c \tan (e+f x))^{5/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{7/2}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"(2*(I*A - 6*B)*c^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(5/2)*f) + ((I*A - 6*B)*c^3*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f) + (2*(I*A - 6*B)*c^2*(c - I*c*Tan[e + f*x])^(3/2))/(3*a^2*f*Sqrt[a + I*a*Tan[e + f*x]]) - (2*(I*A - 6*B)*c*(c - I*c*Tan[e + f*x])^(5/2))/(15*a*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(7/2))/(5*f*(a + I*a*Tan[e + f*x])^(5/2))","A",8,7,45,0.1556,1,"{3588, 78, 47, 50, 63, 217, 203}"
845,1,205,0,0.2894918,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2))/(a + I*a*Tan[e + f*x])^(5/2),x]","-\frac{2 B c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}-\frac{2 B c^2 \sqrt{c-i c \tan (e+f x)}}{a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 B c (c-i c \tan (e+f x))^{3/2}}{3 a f (a+i a \tan (e+f x))^{3/2}}","-\frac{2 B c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c-i c \tan (e+f x)}}\right)}{a^{5/2} f}-\frac{2 B c^2 \sqrt{c-i c \tan (e+f x)}}{a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 B c (c-i c \tan (e+f x))^{3/2}}{3 a f (a+i a \tan (e+f x))^{3/2}}",1,"(-2*B*c^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(a^(5/2)*f) - (2*B*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*Sqrt[a + I*a*Tan[e + f*x]]) + (2*B*c*(c - I*c*Tan[e + f*x])^(3/2))/(3*a*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I*A - B)*(c - I*c*Tan[e + f*x])^(5/2))/(5*f*(a + I*a*Tan[e + f*x])^(5/2))","A",7,6,45,0.1333,1,"{3588, 78, 47, 63, 217, 203}"
846,1,104,0,0.2285211,"\int \frac{(A+B \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2))/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{(4 B+i A) (c-i c \tan (e+f x))^{3/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{(4 B+i A) (c-i c \tan (e+f x))^{3/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{(-B+i A) (c-i c \tan (e+f x))^{3/2}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"((I*A - B)*(c - I*c*Tan[e + f*x])^(3/2))/(5*f*(a + I*a*Tan[e + f*x])^(5/2)) + ((I*A + 4*B)*(c - I*c*Tan[e + f*x])^(3/2))/(15*a*f*(a + I*a*Tan[e + f*x])^(3/2))","A",3,3,45,0.06667,1,"{3588, 78, 37}"
847,1,157,0,0.2440081,"\int \frac{(A+B \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[((A + B*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{(3 B+2 i A) \sqrt{c-i c \tan (e+f x)}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{(3 B+2 i A) \sqrt{c-i c \tan (e+f x)}}{15 a f (a+i a \tan (e+f x))^{3/2}}","\frac{(3 B+2 i A) \sqrt{c-i c \tan (e+f x)}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{(-B+i A) \sqrt{c-i c \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{(3 B+2 i A) \sqrt{c-i c \tan (e+f x)}}{15 a f (a+i a \tan (e+f x))^{3/2}}",1,"((I*A - B)*Sqrt[c - I*c*Tan[e + f*x]])/(5*f*(a + I*a*Tan[e + f*x])^(5/2)) + (((2*I)*A + 3*B)*Sqrt[c - I*c*Tan[e + f*x]])/(15*a*f*(a + I*a*Tan[e + f*x])^(3/2)) + (((2*I)*A + 3*B)*Sqrt[c - I*c*Tan[e + f*x]])/(15*a^2*f*Sqrt[a + I*a*Tan[e + f*x]])","A",4,4,45,0.08889,1,"{3588, 78, 45, 37}"
848,1,212,0,0.2784139,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{2 (2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{15 a^2 c f \sqrt{a+i a \tan (e+f x)}}-\frac{B+i A}{f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}+\frac{2 (2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{15 a c f (a+i a \tan (e+f x))^{3/2}}+\frac{(2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{5 c f (a+i a \tan (e+f x))^{5/2}}","\frac{2 (2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{15 a^2 c f \sqrt{a+i a \tan (e+f x)}}-\frac{B+i A}{f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}+\frac{2 (2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{15 a c f (a+i a \tan (e+f x))^{3/2}}+\frac{(2 B+3 i A) \sqrt{c-i c \tan (e+f x)}}{5 c f (a+i a \tan (e+f x))^{5/2}}",1,"-((I*A + B)/(f*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]])) + (((3*I)*A + 2*B)*Sqrt[c - I*c*Tan[e + f*x]])/(5*c*f*(a + I*a*Tan[e + f*x])^(5/2)) + (2*((3*I)*A + 2*B)*Sqrt[c - I*c*Tan[e + f*x]])/(15*a*c*f*(a + I*a*Tan[e + f*x])^(3/2)) + (2*((3*I)*A + 2*B)*Sqrt[c - I*c*Tan[e + f*x]])/(15*a^2*c*f*Sqrt[a + I*a*Tan[e + f*x]])","A",5,4,45,0.08889,1,"{3588, 78, 45, 37}"
849,1,216,0,0.2936488,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{2 (4 A-i B) \tan (e+f x)}{15 a^2 c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}-\frac{B+i A}{3 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}+\frac{B+4 i A}{15 a c f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{B+4 i A}{15 c f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}","\frac{2 (4 A-i B) \tan (e+f x)}{15 a^2 c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}-\frac{B+i A}{3 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}+\frac{B+4 i A}{15 a c f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{B+4 i A}{15 c f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}",1,"-(I*A + B)/(3*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)) + ((4*I)*A + B)/(15*c*f*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]]) + ((4*I)*A + B)/(15*a*c*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (2*(4*A - I*B)*Tan[e + f*x])/(15*a^2*c*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",5,4,45,0.08889,1,"{3588, 78, 45, 39}"
850,1,204,0,0.2751425,"\int \frac{A+B \tan (e+f x)}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[(A + B*Tan[e + f*x])/((a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2)),x]","\frac{8 A \tan (e+f x)}{15 a^2 c^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}-\frac{B+i A}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}+\frac{4 A \tan (e+f x)}{15 a c f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i A}{5 c f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}","\frac{8 A \tan (e+f x)}{15 a^2 c^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}-\frac{B+i A}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}+\frac{4 A \tan (e+f x)}{15 a c f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i A}{5 c f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}",1,"-(I*A + B)/(5*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2)) + ((I/5)*A)/(c*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (4*A*Tan[e + f*x])/(15*a*c*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (8*A*Tan[e + f*x])/(15*a^2*c^2*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",5,5,45,0.1111,1,"{3588, 78, 45, 40, 39}"
851,1,150,0,0.2272029,"\int (a+i a \tan (e+f x))^m (A+B \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^m*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n,x]","\frac{(B+i A) (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n}{2 f n}-\frac{2^{n-1} (B (m-n)+i A (m+n)) (1-i \tan (e+f x))^{-n} (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n \, _2F_1\left(m,-n;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{f m n}","\frac{(B+i A) (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n}{2 f n}-\frac{2^{n-1} (B (m-n)+i A (m+n)) (1-i \tan (e+f x))^{-n} (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n \, _2F_1\left(m,-n;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{f m n}",1,"((I*A + B)*(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^n)/(2*f*n) - (2^(-1 + n)*(B*(m - n) + I*A*(m + n))*Hypergeometric2F1[m, -n, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^n)/(f*m*n*(1 - I*Tan[e + f*x])^n)","A",4,4,41,0.09756,1,"{3588, 79, 70, 69}"
852,1,147,0,0.2248908,"\int (a+i a \tan (e+f x))^{1+m} (A+B \tan (e+f x)) (c-i c \tan (e+f x))^{-1-m} \, dx","Int[(a + I*a*Tan[e + f*x])^(1 + m)*(A + B*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(-1 - m),x]","\frac{a B 2^m (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^{-m} \, _2F_1\left(-m,-m;1-m;\frac{1}{2} (1-i \tan (e+f x))\right)}{c f m}-\frac{(B+i A) (a+i a \tan (e+f x))^{m+1} (c-i c \tan (e+f x))^{-m-1}}{2 f (m+1)}","\frac{a B 2^m (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^{-m} \, _2F_1\left(-m,-m;1-m;\frac{1}{2} (1-i \tan (e+f x))\right)}{c f m}-\frac{(B+i A) (a+i a \tan (e+f x))^{m+1} (c-i c \tan (e+f x))^{-m-1}}{2 f (m+1)}",1,"-((I*A + B)*(a + I*a*Tan[e + f*x])^(1 + m)*(c - I*c*Tan[e + f*x])^(-1 - m))/(2*f*(1 + m)) + (2^m*a*B*Hypergeometric2F1[-m, -m, 1 - m, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(c*f*m*(1 + I*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^m)","A",4,4,47,0.08511,1,"{3588, 79, 70, 69}"
853,1,33,0,0.1058142,"\int \frac{(c-i c \tan (e+f x))^n (-i (2+n)+(-2+n) \tan (e+f x))}{(-i+\tan (e+f x))^2} \, dx","Int[((c - I*c*Tan[e + f*x])^n*((-I)*(2 + n) + (-2 + n)*Tan[e + f*x]))/(-I + Tan[e + f*x])^2,x]","\frac{(c-i c \tan (e+f x))^n}{f (-\tan (e+f x)+i)^2}","\frac{(c-i c \tan (e+f x))^n}{f (-\tan (e+f x)+i)^2}",1,"(c - I*c*Tan[e + f*x])^n/(f*(I - Tan[e + f*x])^2)","A",2,2,46,0.04348,1,"{3588, 74}"
854,1,104,0,0.2382474,"\int \frac{(A+B \tan (e+f x)) (c+d \tan (e+f x))}{(a+i a \tan (e+f x))^2} \, dx","Int[((A + B*Tan[e + f*x])*(c + d*Tan[e + f*x]))/(a + I*a*Tan[e + f*x])^2,x]","\frac{A (d+i c)+B (c+3 i d)}{4 a^2 f (1+i \tan (e+f x))}+\frac{x (A-i B) (c-i d)}{4 a^2}+\frac{(-B+i A) (c+i d)}{4 f (a+i a \tan (e+f x))^2}","\frac{A (d+i c)+B (c+3 i d)}{4 a^2 f (1+i \tan (e+f x))}+\frac{x (A-i B) (c-i d)}{4 a^2}+\frac{(-B+i A) (c+i d)}{4 f (a+i a \tan (e+f x))^2}",1,"((A - I*B)*(c - I*d)*x)/(4*a^2) + (B*(c + (3*I)*d) + A*(I*c + d))/(4*a^2*f*(1 + I*Tan[e + f*x])) + ((I*A - B)*(c + I*d))/(4*f*(a + I*a*Tan[e + f*x])^2)","A",3,3,36,0.08333,1,"{3590, 3526, 8}"
855,1,147,0,0.2954786,"\int \frac{(A+B \tan (e+f x)) (c+d \tan (e+f x))}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[((A + B*Tan[e + f*x])*(c + d*Tan[e + f*x]))/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{(B+i A) (c-i d) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (e+f x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{(-B+i A) (c+i d)}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{A (d+i c)+B (c+3 i d)}{2 a f \sqrt{a+i a \tan (e+f x)}}","-\frac{(B+i A) (c-i d) \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (e+f x)}}{\sqrt{2} \sqrt{a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{(-B+i A) (c+i d)}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{A (d+i c)+B (c+3 i d)}{2 a f \sqrt{a+i a \tan (e+f x)}}",1,"-((I*A + B)*(c - I*d)*ArcTanh[Sqrt[a + I*a*Tan[e + f*x]]/(Sqrt[2]*Sqrt[a])])/(2*Sqrt[2]*a^(3/2)*f) + ((I*A - B)*(c + I*d))/(3*f*(a + I*a*Tan[e + f*x])^(3/2)) + (B*(c + (3*I)*d) + A*(I*c + d))/(2*a*f*Sqrt[a + I*a*Tan[e + f*x]])","A",4,4,38,0.1053,1,"{3590, 3526, 3480, 206}"