1,1,102,0,0.1082473,"\int \tan ^5(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Tan[c + d*x]^5*(a + I*a*Tan[c + d*x]),x]","\frac{i a \tan ^5(c+d x)}{5 d}+\frac{a \tan ^4(c+d x)}{4 d}-\frac{i a \tan ^3(c+d x)}{3 d}-\frac{a \tan ^2(c+d x)}{2 d}+\frac{i a \tan (c+d x)}{d}-\frac{a \log (\cos (c+d x))}{d}-i a x","\frac{i a \tan ^5(c+d x)}{5 d}+\frac{a \tan ^4(c+d x)}{4 d}-\frac{i a \tan ^3(c+d x)}{3 d}-\frac{a \tan ^2(c+d x)}{2 d}+\frac{i a \tan (c+d x)}{d}-\frac{a \log (\cos (c+d x))}{d}-i a x",1,"(-I)*a*x - (a*Log[Cos[c + d*x]])/d + (I*a*Tan[c + d*x])/d - (a*Tan[c + d*x]^2)/(2*d) - ((I/3)*a*Tan[c + d*x]^3)/d + (a*Tan[c + d*x]^4)/(4*d) + ((I/5)*a*Tan[c + d*x]^5)/d","A",6,3,22,0.1364,1,"{3528, 3525, 3475}"
2,1,83,0,0.0825816,"\int \tan ^4(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Tan[c + d*x]^4*(a + I*a*Tan[c + d*x]),x]","\frac{i a \tan ^4(c+d x)}{4 d}+\frac{a \tan ^3(c+d x)}{3 d}-\frac{i a \tan ^2(c+d x)}{2 d}-\frac{a \tan (c+d x)}{d}-\frac{i a \log (\cos (c+d x))}{d}+a x","\frac{i a \tan ^4(c+d x)}{4 d}+\frac{a \tan ^3(c+d x)}{3 d}-\frac{i a \tan ^2(c+d x)}{2 d}-\frac{a \tan (c+d x)}{d}-\frac{i a \log (\cos (c+d x))}{d}+a x",1,"a*x - (I*a*Log[Cos[c + d*x]])/d - (a*Tan[c + d*x])/d - ((I/2)*a*Tan[c + d*x]^2)/d + (a*Tan[c + d*x]^3)/(3*d) + ((I/4)*a*Tan[c + d*x]^4)/d","A",5,3,22,0.1364,1,"{3528, 3525, 3475}"
3,1,67,0,0.0601947,"\int \tan ^3(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x]),x]","\frac{i a \tan ^3(c+d x)}{3 d}+\frac{a \tan ^2(c+d x)}{2 d}-\frac{i a \tan (c+d x)}{d}+\frac{a \log (\cos (c+d x))}{d}+i a x","\frac{i a \tan ^3(c+d x)}{3 d}+\frac{a \tan ^2(c+d x)}{2 d}-\frac{i a \tan (c+d x)}{d}+\frac{a \log (\cos (c+d x))}{d}+i a x",1,"I*a*x + (a*Log[Cos[c + d*x]])/d - (I*a*Tan[c + d*x])/d + (a*Tan[c + d*x]^2)/(2*d) + ((I/3)*a*Tan[c + d*x]^3)/d","A",4,3,22,0.1364,1,"{3528, 3525, 3475}"
4,1,49,0,0.0389246,"\int \tan ^2(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x]),x]","\frac{i a \tan ^2(c+d x)}{2 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \log (\cos (c+d x))}{d}-a x","\frac{i a \tan ^2(c+d x)}{2 d}+\frac{a \tan (c+d x)}{d}+\frac{i a \log (\cos (c+d x))}{d}-a x",1,"-(a*x) + (I*a*Log[Cos[c + d*x]])/d + (a*Tan[c + d*x])/d + ((I/2)*a*Tan[c + d*x]^2)/d","A",3,3,22,0.1364,1,"{3528, 3525, 3475}"
5,1,34,0,0.0175204,"\int \tan (c+d x) (a+i a \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x]),x]","\frac{i a \tan (c+d x)}{d}-\frac{a \log (\cos (c+d x))}{d}-i a x","\frac{i a \tan (c+d x)}{d}-\frac{a \log (\cos (c+d x))}{d}-i a x",1,"(-I)*a*x - (a*Log[Cos[c + d*x]])/d + (I*a*Tan[c + d*x])/d","A",2,2,20,0.1000,1,"{3525, 3475}"
6,1,19,0,0.0074158,"\int (a+i a \tan (c+d x)) \, dx","Int[a + I*a*Tan[c + d*x],x]","a x-\frac{i a \log (\cos (c+d x))}{d}","a x-\frac{i a \log (\cos (c+d x))}{d}",1,"a*x - (I*a*Log[Cos[c + d*x]])/d","A",2,1,13,0.07692,1,"{3475}"
7,1,19,0,0.0218355,"\int \cot (c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x]),x]","\frac{a \log (\sin (c+d x))}{d}+i a x","\frac{a \log (\sin (c+d x))}{d}+i a x",1,"I*a*x + (a*Log[Sin[c + d*x]])/d","A",2,2,20,0.1000,1,"{3531, 3475}"
8,1,32,0,0.0441037,"\int \cot ^2(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x]),x]","-\frac{a \cot (c+d x)}{d}+\frac{i a \log (\sin (c+d x))}{d}-a x","-\frac{a \cot (c+d x)}{d}+\frac{i a \log (\sin (c+d x))}{d}-a x",1,"-(a*x) - (a*Cot[c + d*x])/d + (I*a*Log[Sin[c + d*x]])/d","A",3,3,22,0.1364,1,"{3529, 3531, 3475}"
9,1,50,0,0.0670244,"\int \cot ^3(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x]),x]","-\frac{a \cot ^2(c+d x)}{2 d}-\frac{i a \cot (c+d x)}{d}-\frac{a \log (\sin (c+d x))}{d}-i a x","-\frac{a \cot ^2(c+d x)}{2 d}-\frac{i a \cot (c+d x)}{d}-\frac{a \log (\sin (c+d x))}{d}-i a x",1,"(-I)*a*x - (I*a*Cot[c + d*x])/d - (a*Cot[c + d*x]^2)/(2*d) - (a*Log[Sin[c + d*x]])/d","A",4,3,22,0.1364,1,"{3529, 3531, 3475}"
10,1,64,0,0.089368,"\int \cot ^4(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x]),x]","-\frac{a \cot ^3(c+d x)}{3 d}-\frac{i a \cot ^2(c+d x)}{2 d}+\frac{a \cot (c+d x)}{d}-\frac{i a \log (\sin (c+d x))}{d}+a x","-\frac{a \cot ^3(c+d x)}{3 d}-\frac{i a \cot ^2(c+d x)}{2 d}+\frac{a \cot (c+d x)}{d}-\frac{i a \log (\sin (c+d x))}{d}+a x",1,"a*x + (a*Cot[c + d*x])/d - ((I/2)*a*Cot[c + d*x]^2)/d - (a*Cot[c + d*x]^3)/(3*d) - (I*a*Log[Sin[c + d*x]])/d","A",5,3,22,0.1364,1,"{3529, 3531, 3475}"
11,1,83,0,0.1086502,"\int \cot ^5(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x]),x]","-\frac{a \cot ^4(c+d x)}{4 d}-\frac{i a \cot ^3(c+d x)}{3 d}+\frac{a \cot ^2(c+d x)}{2 d}+\frac{i a \cot (c+d x)}{d}+\frac{a \log (\sin (c+d x))}{d}+i a x","-\frac{a \cot ^4(c+d x)}{4 d}-\frac{i a \cot ^3(c+d x)}{3 d}+\frac{a \cot ^2(c+d x)}{2 d}+\frac{i a \cot (c+d x)}{d}+\frac{a \log (\sin (c+d x))}{d}+i a x",1,"I*a*x + (I*a*Cot[c + d*x])/d + (a*Cot[c + d*x]^2)/(2*d) - ((I/3)*a*Cot[c + d*x]^3)/d - (a*Cot[c + d*x]^4)/(4*d) + (a*Log[Sin[c + d*x]])/d","A",6,3,22,0.1364,1,"{3529, 3531, 3475}"
12,1,100,0,0.1318106,"\int \cot ^6(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x]),x]","-\frac{a \cot ^5(c+d x)}{5 d}-\frac{i a \cot ^4(c+d x)}{4 d}+\frac{a \cot ^3(c+d x)}{3 d}+\frac{i a \cot ^2(c+d x)}{2 d}-\frac{a \cot (c+d x)}{d}+\frac{i a \log (\sin (c+d x))}{d}-a x","-\frac{a \cot ^5(c+d x)}{5 d}-\frac{i a \cot ^4(c+d x)}{4 d}+\frac{a \cot ^3(c+d x)}{3 d}+\frac{i a \cot ^2(c+d x)}{2 d}-\frac{a \cot (c+d x)}{d}+\frac{i a \log (\sin (c+d x))}{d}-a x",1,"-(a*x) - (a*Cot[c + d*x])/d + ((I/2)*a*Cot[c + d*x]^2)/d + (a*Cot[c + d*x]^3)/(3*d) - ((I/4)*a*Cot[c + d*x]^4)/d - (a*Cot[c + d*x]^5)/(5*d) + (I*a*Log[Sin[c + d*x]])/d","A",7,3,22,0.1364,1,"{3529, 3531, 3475}"
13,1,112,0,0.1428581,"\int \tan ^4(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^4*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \tan ^5(c+d x)}{5 d}+\frac{i a^2 \tan ^4(c+d x)}{2 d}+\frac{2 a^2 \tan ^3(c+d x)}{3 d}-\frac{i a^2 \tan ^2(c+d x)}{d}-\frac{2 a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x","-\frac{a^2 \tan ^5(c+d x)}{5 d}+\frac{i a^2 \tan ^4(c+d x)}{2 d}+\frac{2 a^2 \tan ^3(c+d x)}{3 d}-\frac{i a^2 \tan ^2(c+d x)}{d}-\frac{2 a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x",1,"2*a^2*x - ((2*I)*a^2*Log[Cos[c + d*x]])/d - (2*a^2*Tan[c + d*x])/d - (I*a^2*Tan[c + d*x]^2)/d + (2*a^2*Tan[c + d*x]^3)/(3*d) + ((I/2)*a^2*Tan[c + d*x]^4)/d - (a^2*Tan[c + d*x]^5)/(5*d)","A",6,4,24,0.1667,1,"{3543, 3528, 3525, 3475}"
14,1,93,0,0.1142559,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \tan ^4(c+d x)}{4 d}+\frac{2 i a^2 \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan ^2(c+d x)}{d}-\frac{2 i a^2 \tan (c+d x)}{d}+\frac{2 a^2 \log (\cos (c+d x))}{d}+2 i a^2 x","-\frac{a^2 \tan ^4(c+d x)}{4 d}+\frac{2 i a^2 \tan ^3(c+d x)}{3 d}+\frac{a^2 \tan ^2(c+d x)}{d}-\frac{2 i a^2 \tan (c+d x)}{d}+\frac{2 a^2 \log (\cos (c+d x))}{d}+2 i a^2 x",1,"(2*I)*a^2*x + (2*a^2*Log[Cos[c + d*x]])/d - ((2*I)*a^2*Tan[c + d*x])/d + (a^2*Tan[c + d*x]^2)/d + (((2*I)/3)*a^2*Tan[c + d*x]^3)/d - (a^2*Tan[c + d*x]^4)/(4*d)","A",5,4,24,0.1667,1,"{3543, 3528, 3525, 3475}"
15,1,64,0,0.0546303,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^2,x]","\frac{a^2 \tan (c+d x)}{d}+\frac{2 i a^2 \log (\cos (c+d x))}{d}-2 a^2 x-\frac{i (a+i a \tan (c+d x))^3}{3 a d}","\frac{a^2 \tan (c+d x)}{d}+\frac{2 i a^2 \log (\cos (c+d x))}{d}-2 a^2 x-\frac{i (a+i a \tan (c+d x))^3}{3 a d}",1,"-2*a^2*x + ((2*I)*a^2*Log[Cos[c + d*x]])/d + (a^2*Tan[c + d*x])/d - ((I/3)*(a + I*a*Tan[c + d*x])^3)/(a*d)","A",3,3,24,0.1250,1,"{3543, 3477, 3475}"
16,1,62,0,0.0424361,"\int \tan (c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^2,x]","\frac{i a^2 \tan (c+d x)}{d}-\frac{2 a^2 \log (\cos (c+d x))}{d}-2 i a^2 x+\frac{(a+i a \tan (c+d x))^2}{2 d}","\frac{i a^2 \tan (c+d x)}{d}-\frac{2 a^2 \log (\cos (c+d x))}{d}-2 i a^2 x+\frac{(a+i a \tan (c+d x))^2}{2 d}",1,"(-2*I)*a^2*x - (2*a^2*Log[Cos[c + d*x]])/d + (I*a^2*Tan[c + d*x])/d + (a + I*a*Tan[c + d*x])^2/(2*d)","A",3,3,22,0.1364,1,"{3527, 3477, 3475}"
17,1,38,0,0.0182057,"\int (a+i a \tan (c+d x))^2 \, dx","Int[(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x","-\frac{a^2 \tan (c+d x)}{d}-\frac{2 i a^2 \log (\cos (c+d x))}{d}+2 a^2 x",1,"2*a^2*x - ((2*I)*a^2*Log[Cos[c + d*x]])/d - (a^2*Tan[c + d*x])/d","A",2,2,15,0.1333,1,"{3477, 3475}"
18,1,37,0,0.0390279,"\int \cot (c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^2,x]","\frac{a^2 \log (\sin (c+d x))}{d}+\frac{a^2 \log (\cos (c+d x))}{d}+2 i a^2 x","\frac{a^2 \log (\sin (c+d x))}{d}+\frac{a^2 \log (\cos (c+d x))}{d}+2 i a^2 x",1,"(2*I)*a^2*x + (a^2*Log[Cos[c + d*x]])/d + (a^2*Log[Sin[c + d*x]])/d","A",3,2,22,0.09091,1,"{3541, 3475}"
19,1,38,0,0.0618372,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \cot (c+d x)}{d}+\frac{2 i a^2 \log (\sin (c+d x))}{d}-2 a^2 x","-\frac{a^2 \cot (c+d x)}{d}+\frac{2 i a^2 \log (\sin (c+d x))}{d}-2 a^2 x",1,"-2*a^2*x - (a^2*Cot[c + d*x])/d + ((2*I)*a^2*Log[Sin[c + d*x]])/d","A",3,3,24,0.1250,1,"{3542, 3531, 3475}"
20,1,58,0,0.0926823,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \cot ^2(c+d x)}{2 d}-\frac{2 i a^2 \cot (c+d x)}{d}-\frac{2 a^2 \log (\sin (c+d x))}{d}-2 i a^2 x","-\frac{a^2 \cot ^2(c+d x)}{2 d}-\frac{2 i a^2 \cot (c+d x)}{d}-\frac{2 a^2 \log (\sin (c+d x))}{d}-2 i a^2 x",1,"(-2*I)*a^2*x - ((2*I)*a^2*Cot[c + d*x])/d - (a^2*Cot[c + d*x]^2)/(2*d) - (2*a^2*Log[Sin[c + d*x]])/d","A",4,4,24,0.1667,1,"{3542, 3529, 3531, 3475}"
21,1,74,0,0.1131938,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \cot ^3(c+d x)}{3 d}-\frac{i a^2 \cot ^2(c+d x)}{d}+\frac{2 a^2 \cot (c+d x)}{d}-\frac{2 i a^2 \log (\sin (c+d x))}{d}+2 a^2 x","-\frac{a^2 \cot ^3(c+d x)}{3 d}-\frac{i a^2 \cot ^2(c+d x)}{d}+\frac{2 a^2 \cot (c+d x)}{d}-\frac{2 i a^2 \log (\sin (c+d x))}{d}+2 a^2 x",1,"2*a^2*x + (2*a^2*Cot[c + d*x])/d - (I*a^2*Cot[c + d*x]^2)/d - (a^2*Cot[c + d*x]^3)/(3*d) - ((2*I)*a^2*Log[Sin[c + d*x]])/d","A",5,4,24,0.1667,1,"{3542, 3529, 3531, 3475}"
22,1,93,0,0.1399807,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \cot ^4(c+d x)}{4 d}-\frac{2 i a^2 \cot ^3(c+d x)}{3 d}+\frac{a^2 \cot ^2(c+d x)}{d}+\frac{2 i a^2 \cot (c+d x)}{d}+\frac{2 a^2 \log (\sin (c+d x))}{d}+2 i a^2 x","-\frac{a^2 \cot ^4(c+d x)}{4 d}-\frac{2 i a^2 \cot ^3(c+d x)}{3 d}+\frac{a^2 \cot ^2(c+d x)}{d}+\frac{2 i a^2 \cot (c+d x)}{d}+\frac{2 a^2 \log (\sin (c+d x))}{d}+2 i a^2 x",1,"(2*I)*a^2*x + ((2*I)*a^2*Cot[c + d*x])/d + (a^2*Cot[c + d*x]^2)/d - (((2*I)/3)*a^2*Cot[c + d*x]^3)/d - (a^2*Cot[c + d*x]^4)/(4*d) + (2*a^2*Log[Sin[c + d*x]])/d","A",6,4,24,0.1667,1,"{3542, 3529, 3531, 3475}"
23,1,112,0,0.1670118,"\int \cot ^6(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^2,x]","-\frac{a^2 \cot ^5(c+d x)}{5 d}-\frac{i a^2 \cot ^4(c+d x)}{2 d}+\frac{2 a^2 \cot ^3(c+d x)}{3 d}+\frac{i a^2 \cot ^2(c+d x)}{d}-\frac{2 a^2 \cot (c+d x)}{d}+\frac{2 i a^2 \log (\sin (c+d x))}{d}-2 a^2 x","-\frac{a^2 \cot ^5(c+d x)}{5 d}-\frac{i a^2 \cot ^4(c+d x)}{2 d}+\frac{2 a^2 \cot ^3(c+d x)}{3 d}+\frac{i a^2 \cot ^2(c+d x)}{d}-\frac{2 a^2 \cot (c+d x)}{d}+\frac{2 i a^2 \log (\sin (c+d x))}{d}-2 a^2 x",1,"-2*a^2*x - (2*a^2*Cot[c + d*x])/d + (I*a^2*Cot[c + d*x]^2)/d + (2*a^2*Cot[c + d*x]^3)/(3*d) - ((I/2)*a^2*Cot[c + d*x]^4)/d - (a^2*Cot[c + d*x]^5)/(5*d) + ((2*I)*a^2*Log[Sin[c + d*x]])/d","A",7,4,24,0.1667,1,"{3542, 3529, 3531, 3475}"
24,1,126,0,0.1714352,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^3,x]","-\frac{\tan ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{5 d}-\frac{11 a^3 \tan ^4(c+d x)}{20 d}+\frac{4 i a^3 \tan ^3(c+d x)}{3 d}+\frac{2 a^3 \tan ^2(c+d x)}{d}-\frac{4 i a^3 \tan (c+d x)}{d}+\frac{4 a^3 \log (\cos (c+d x))}{d}+4 i a^3 x","-\frac{\tan ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{5 d}-\frac{11 a^3 \tan ^4(c+d x)}{20 d}+\frac{4 i a^3 \tan ^3(c+d x)}{3 d}+\frac{2 a^3 \tan ^2(c+d x)}{d}-\frac{4 i a^3 \tan (c+d x)}{d}+\frac{4 a^3 \log (\cos (c+d x))}{d}+4 i a^3 x",1,"(4*I)*a^3*x + (4*a^3*Log[Cos[c + d*x]])/d - ((4*I)*a^3*Tan[c + d*x])/d + (2*a^3*Tan[c + d*x]^2)/d + (((4*I)/3)*a^3*Tan[c + d*x]^3)/d - (11*a^3*Tan[c + d*x]^4)/(20*d) - (Tan[c + d*x]^4*(a^3 + I*a^3*Tan[c + d*x]))/(5*d)","A",6,5,24,0.2083,1,"{3556, 3592, 3528, 3525, 3475}"
25,1,90,0,0.0698095,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^3,x]","\frac{2 a^3 \tan (c+d x)}{d}+\frac{4 i a^3 \log (\cos (c+d x))}{d}-4 a^3 x-\frac{i (a+i a \tan (c+d x))^4}{4 a d}-\frac{i a (a+i a \tan (c+d x))^2}{2 d}","\frac{2 a^3 \tan (c+d x)}{d}+\frac{4 i a^3 \log (\cos (c+d x))}{d}-4 a^3 x-\frac{i (a+i a \tan (c+d x))^4}{4 a d}-\frac{i a (a+i a \tan (c+d x))^2}{2 d}",1,"-4*a^3*x + ((4*I)*a^3*Log[Cos[c + d*x]])/d + (2*a^3*Tan[c + d*x])/d - ((I/2)*a*(a + I*a*Tan[c + d*x])^2)/d - ((I/4)*(a + I*a*Tan[c + d*x])^4)/(a*d)","A",4,4,24,0.1667,1,"{3543, 3478, 3477, 3475}"
26,1,85,0,0.0576672,"\int \tan (c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^3,x]","\frac{2 i a^3 \tan (c+d x)}{d}-\frac{4 a^3 \log (\cos (c+d x))}{d}-4 i a^3 x+\frac{a (a+i a \tan (c+d x))^2}{2 d}+\frac{(a+i a \tan (c+d x))^3}{3 d}","\frac{2 i a^3 \tan (c+d x)}{d}-\frac{4 a^3 \log (\cos (c+d x))}{d}-4 i a^3 x+\frac{a (a+i a \tan (c+d x))^2}{2 d}+\frac{(a+i a \tan (c+d x))^3}{3 d}",1,"(-4*I)*a^3*x - (4*a^3*Log[Cos[c + d*x]])/d + ((2*I)*a^3*Tan[c + d*x])/d + (a*(a + I*a*Tan[c + d*x])^2)/(2*d) + (a + I*a*Tan[c + d*x])^3/(3*d)","A",4,4,22,0.1818,1,"{3527, 3478, 3477, 3475}"
27,1,63,0,0.0323723,"\int (a+i a \tan (c+d x))^3 \, dx","Int[(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 a^3 \tan (c+d x)}{d}-\frac{4 i a^3 \log (\cos (c+d x))}{d}+4 a^3 x+\frac{i a (a+i a \tan (c+d x))^2}{2 d}","-\frac{2 a^3 \tan (c+d x)}{d}-\frac{4 i a^3 \log (\cos (c+d x))}{d}+4 a^3 x+\frac{i a (a+i a \tan (c+d x))^2}{2 d}",1,"4*a^3*x - ((4*I)*a^3*Log[Cos[c + d*x]])/d - (2*a^3*Tan[c + d*x])/d + ((I/2)*a*(a + I*a*Tan[c + d*x])^2)/d","A",3,3,15,0.2000,1,"{3478, 3477, 3475}"
28,1,60,0,0.1019053,"\int \cot (c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^3,x]","-\frac{a^3+i a^3 \tan (c+d x)}{d}+\frac{a^3 \log (\sin (c+d x))}{d}+\frac{3 a^3 \log (\cos (c+d x))}{d}+4 i a^3 x","-\frac{a^3+i a^3 \tan (c+d x)}{d}+\frac{a^3 \log (\sin (c+d x))}{d}+\frac{3 a^3 \log (\cos (c+d x))}{d}+4 i a^3 x",1,"(4*I)*a^3*x + (3*a^3*Log[Cos[c + d*x]])/d + (a^3*Log[Sin[c + d*x]])/d - (a^3 + I*a^3*Tan[c + d*x])/d","A",5,4,22,0.1818,1,"{3556, 3589, 3475, 3531}"
29,1,69,0,0.115582,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^3,x]","\frac{3 i a^3 \log (\sin (c+d x))}{d}+\frac{i a^3 \log (\cos (c+d x))}{d}-\frac{\cot (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{d}-4 a^3 x","\frac{3 i a^3 \log (\sin (c+d x))}{d}+\frac{i a^3 \log (\cos (c+d x))}{d}-\frac{\cot (c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{d}-4 a^3 x",1,"-4*a^3*x + (I*a^3*Log[Cos[c + d*x]])/d + ((3*I)*a^3*Log[Sin[c + d*x]])/d - (Cot[c + d*x]*(a^3 + I*a^3*Tan[c + d*x]))/d","A",5,4,24,0.1667,1,"{3553, 3589, 3475, 3531}"
30,1,71,0,0.1062495,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 i a^3 \cot (c+d x)}{d}-\frac{4 a^3 \log (\sin (c+d x))}{d}-4 i a^3 x-\frac{a \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}","-\frac{2 i a^3 \cot (c+d x)}{d}-\frac{4 a^3 \log (\sin (c+d x))}{d}-4 i a^3 x-\frac{a \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}",1,"(-4*I)*a^3*x - ((2*I)*a^3*Cot[c + d*x])/d - (4*a^3*Log[Sin[c + d*x]])/d - (a*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^2)/(2*d)","A",4,4,24,0.1667,1,"{3545, 3542, 3531, 3475}"
31,1,101,0,0.1516307,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^3,x]","\frac{2 a^3 \cot (c+d x)}{d}-\frac{4 i a^3 \log (\sin (c+d x))}{d}+4 a^3 x-\frac{i a \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}-\frac{\cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}","\frac{2 a^3 \cot (c+d x)}{d}-\frac{4 i a^3 \log (\sin (c+d x))}{d}+4 a^3 x-\frac{i a \cot ^2(c+d x) (a+i a \tan (c+d x))^2}{2 d}-\frac{\cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}",1,"4*a^3*x + (2*a^3*Cot[c + d*x])/d - ((4*I)*a^3*Log[Sin[c + d*x]])/d - ((I/2)*a*Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^2)/d - (Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/(3*d)","A",5,5,24,0.2083,1,"{3548, 3545, 3542, 3531, 3475}"
32,1,108,0,0.187054,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^3,x]","-\frac{3 i a^3 \cot ^3(c+d x)}{4 d}+\frac{2 a^3 \cot ^2(c+d x)}{d}+\frac{4 i a^3 \cot (c+d x)}{d}+\frac{4 a^3 \log (\sin (c+d x))}{d}-\frac{\cot ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{4 d}+4 i a^3 x","-\frac{3 i a^3 \cot ^3(c+d x)}{4 d}+\frac{2 a^3 \cot ^2(c+d x)}{d}+\frac{4 i a^3 \cot (c+d x)}{d}+\frac{4 a^3 \log (\sin (c+d x))}{d}-\frac{\cot ^4(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{4 d}+4 i a^3 x",1,"(4*I)*a^3*x + ((4*I)*a^3*Cot[c + d*x])/d + (2*a^3*Cot[c + d*x]^2)/d - (((3*I)/4)*a^3*Cot[c + d*x]^3)/d + (4*a^3*Log[Sin[c + d*x]])/d - (Cot[c + d*x]^4*(a^3 + I*a^3*Tan[c + d*x]))/(4*d)","A",6,5,24,0.2083,1,"{3553, 3591, 3529, 3531, 3475}"
33,1,126,0,0.210605,"\int \cot ^6(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^3,x]","-\frac{11 i a^3 \cot ^4(c+d x)}{20 d}+\frac{4 a^3 \cot ^3(c+d x)}{3 d}+\frac{2 i a^3 \cot ^2(c+d x)}{d}-\frac{4 a^3 \cot (c+d x)}{d}+\frac{4 i a^3 \log (\sin (c+d x))}{d}-\frac{\cot ^5(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{5 d}-4 a^3 x","-\frac{11 i a^3 \cot ^4(c+d x)}{20 d}+\frac{4 a^3 \cot ^3(c+d x)}{3 d}+\frac{2 i a^3 \cot ^2(c+d x)}{d}-\frac{4 a^3 \cot (c+d x)}{d}+\frac{4 i a^3 \log (\sin (c+d x))}{d}-\frac{\cot ^5(c+d x) \left(a^3+i a^3 \tan (c+d x)\right)}{5 d}-4 a^3 x",1,"-4*a^3*x - (4*a^3*Cot[c + d*x])/d + ((2*I)*a^3*Cot[c + d*x]^2)/d + (4*a^3*Cot[c + d*x]^3)/(3*d) - (((11*I)/20)*a^3*Cot[c + d*x]^4)/d + ((4*I)*a^3*Log[Sin[c + d*x]])/d - (Cot[c + d*x]^5*(a^3 + I*a^3*Tan[c + d*x]))/(5*d)","A",7,5,24,0.2083,1,"{3553, 3591, 3529, 3531, 3475}"
34,1,160,0,0.2713015,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^4,x]","-\frac{67 a^4 \tan ^4(c+d x)}{60 d}+\frac{8 i a^4 \tan ^3(c+d x)}{3 d}+\frac{4 a^4 \tan ^2(c+d x)}{d}-\frac{\tan ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{6 d}-\frac{7 \tan ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{15 d}-\frac{8 i a^4 \tan (c+d x)}{d}+\frac{8 a^4 \log (\cos (c+d x))}{d}+8 i a^4 x","-\frac{67 a^4 \tan ^4(c+d x)}{60 d}+\frac{8 i a^4 \tan ^3(c+d x)}{3 d}+\frac{4 a^4 \tan ^2(c+d x)}{d}-\frac{\tan ^4(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{6 d}-\frac{7 \tan ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{15 d}-\frac{8 i a^4 \tan (c+d x)}{d}+\frac{8 a^4 \log (\cos (c+d x))}{d}+8 i a^4 x",1,"(8*I)*a^4*x + (8*a^4*Log[Cos[c + d*x]])/d - ((8*I)*a^4*Tan[c + d*x])/d + (4*a^4*Tan[c + d*x]^2)/d + (((8*I)/3)*a^4*Tan[c + d*x]^3)/d - (67*a^4*Tan[c + d*x]^4)/(60*d) - (Tan[c + d*x]^4*(a^2 + I*a^2*Tan[c + d*x])^2)/(6*d) - (7*Tan[c + d*x]^4*(a^4 + I*a^4*Tan[c + d*x]))/(15*d)","A",7,6,24,0.2500,1,"{3556, 3594, 3592, 3528, 3525, 3475}"
35,1,116,0,0.091607,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^4,x]","-\frac{i \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+\frac{4 a^4 \tan (c+d x)}{d}+\frac{8 i a^4 \log (\cos (c+d x))}{d}-8 a^4 x-\frac{i (a+i a \tan (c+d x))^5}{5 a d}-\frac{i a (a+i a \tan (c+d x))^3}{3 d}","-\frac{i \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+\frac{4 a^4 \tan (c+d x)}{d}+\frac{8 i a^4 \log (\cos (c+d x))}{d}-8 a^4 x-\frac{i (a+i a \tan (c+d x))^5}{5 a d}-\frac{i a (a+i a \tan (c+d x))^3}{3 d}",1,"-8*a^4*x + ((8*I)*a^4*Log[Cos[c + d*x]])/d + (4*a^4*Tan[c + d*x])/d - ((I/3)*a*(a + I*a*Tan[c + d*x])^3)/d - ((I/5)*(a + I*a*Tan[c + d*x])^5)/(a*d) - (I*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",5,4,24,0.1667,1,"{3543, 3478, 3477, 3475}"
36,1,108,0,0.0799437,"\int \tan (c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^4,x]","\frac{4 i a^4 \tan (c+d x)}{d}+\frac{\left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 a^4 \log (\cos (c+d x))}{d}-8 i a^4 x+\frac{a (a+i a \tan (c+d x))^3}{3 d}+\frac{(a+i a \tan (c+d x))^4}{4 d}","\frac{4 i a^4 \tan (c+d x)}{d}+\frac{\left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 a^4 \log (\cos (c+d x))}{d}-8 i a^4 x+\frac{a (a+i a \tan (c+d x))^3}{3 d}+\frac{(a+i a \tan (c+d x))^4}{4 d}",1,"(-8*I)*a^4*x - (8*a^4*Log[Cos[c + d*x]])/d + ((4*I)*a^4*Tan[c + d*x])/d + (a*(a + I*a*Tan[c + d*x])^3)/(3*d) + (a + I*a*Tan[c + d*x])^4/(4*d) + (a^2 + I*a^2*Tan[c + d*x])^2/d","A",5,4,22,0.1818,1,"{3527, 3478, 3477, 3475}"
37,1,89,0,0.0514113,"\int (a+i a \tan (c+d x))^4 \, dx","Int[(a + I*a*Tan[c + d*x])^4,x]","-\frac{4 a^4 \tan (c+d x)}{d}+\frac{i \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 i a^4 \log (\cos (c+d x))}{d}+8 a^4 x+\frac{i a (a+i a \tan (c+d x))^3}{3 d}","-\frac{4 a^4 \tan (c+d x)}{d}+\frac{i \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-\frac{8 i a^4 \log (\cos (c+d x))}{d}+8 a^4 x+\frac{i a (a+i a \tan (c+d x))^3}{3 d}",1,"8*a^4*x - ((8*I)*a^4*Log[Cos[c + d*x]])/d - (4*a^4*Tan[c + d*x])/d + ((I/3)*a*(a + I*a*Tan[c + d*x])^3)/d + (I*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",4,3,15,0.2000,1,"{3478, 3477, 3475}"
38,1,86,0,0.1734305,"\int \cot (c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^4,x]","-\frac{\left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{3 \left(a^4+i a^4 \tan (c+d x)\right)}{d}+\frac{a^4 \log (\sin (c+d x))}{d}+\frac{7 a^4 \log (\cos (c+d x))}{d}+8 i a^4 x","-\frac{\left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{3 \left(a^4+i a^4 \tan (c+d x)\right)}{d}+\frac{a^4 \log (\sin (c+d x))}{d}+\frac{7 a^4 \log (\cos (c+d x))}{d}+8 i a^4 x",1,"(8*I)*a^4*x + (7*a^4*Log[Cos[c + d*x]])/d + (a^4*Log[Sin[c + d*x]])/d - (a^2 + I*a^2*Tan[c + d*x])^2/(2*d) - (3*(a^4 + I*a^4*Tan[c + d*x]))/d","A",6,5,22,0.2273,1,"{3556, 3594, 3589, 3475, 3531}"
39,1,71,0,0.0874361,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^4,x]","\frac{4 i a^4 \log (\sin (c+d x))}{d}+\frac{4 i a^4 \log (\cos (c+d x))}{d}-\frac{\cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-8 a^4 x","\frac{4 i a^4 \log (\sin (c+d x))}{d}+\frac{4 i a^4 \log (\cos (c+d x))}{d}-\frac{\cot (c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}-8 a^4 x",1,"-8*a^4*x + ((4*I)*a^4*Log[Cos[c + d*x]])/d + ((4*I)*a^4*Log[Sin[c + d*x]])/d - (Cot[c + d*x]*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",5,4,24,0.1667,1,"{3553, 12, 3541, 3475}"
40,1,103,0,0.2177093,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^4,x]","-\frac{7 a^4 \log (\sin (c+d x))}{d}-\frac{a^4 \log (\cos (c+d x))}{d}-\frac{\cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{3 i \cot (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}-8 i a^4 x","-\frac{7 a^4 \log (\sin (c+d x))}{d}-\frac{a^4 \log (\cos (c+d x))}{d}-\frac{\cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{2 d}-\frac{3 i \cot (c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{d}-8 i a^4 x",1,"(-8*I)*a^4*x - (a^4*Log[Cos[c + d*x]])/d - (7*a^4*Log[Sin[c + d*x]])/d - (Cot[c + d*x]^2*(a^2 + I*a^2*Tan[c + d*x])^2)/(2*d) - ((3*I)*Cot[c + d*x]*(a^4 + I*a^4*Tan[c + d*x]))/d","A",6,5,24,0.2083,1,"{3553, 3593, 3589, 3475, 3531}"
41,1,103,0,0.1567672,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^4,x]","\frac{4 a^4 \cot (c+d x)}{d}-\frac{8 i a^4 \log (\sin (c+d x))}{d}-\frac{i \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+8 a^4 x-\frac{a \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}","\frac{4 a^4 \cot (c+d x)}{d}-\frac{8 i a^4 \log (\sin (c+d x))}{d}-\frac{i \cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+8 a^4 x-\frac{a \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}",1,"8*a^4*x + (4*a^4*Cot[c + d*x])/d - ((8*I)*a^4*Log[Sin[c + d*x]])/d - (a*Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/(3*d) - (I*Cot[c + d*x]^2*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",5,4,24,0.1667,1,"{3545, 3542, 3531, 3475}"
42,1,134,0,0.2030497,"\int \cot ^5(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^5*(a + I*a*Tan[c + d*x])^4,x]","\frac{4 i a^4 \cot (c+d x)}{d}+\frac{8 a^4 \log (\sin (c+d x))}{d}+\frac{\cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+8 i a^4 x-\frac{i a \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}-\frac{\cot ^4(c+d x) (a+i a \tan (c+d x))^4}{4 d}","\frac{4 i a^4 \cot (c+d x)}{d}+\frac{8 a^4 \log (\sin (c+d x))}{d}+\frac{\cot ^2(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{d}+8 i a^4 x-\frac{i a \cot ^3(c+d x) (a+i a \tan (c+d x))^3}{3 d}-\frac{\cot ^4(c+d x) (a+i a \tan (c+d x))^4}{4 d}",1,"(8*I)*a^4*x + ((4*I)*a^4*Cot[c + d*x])/d + (8*a^4*Log[Sin[c + d*x]])/d - ((I/3)*a*Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^3)/d - (Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^4)/(4*d) + (Cot[c + d*x]^2*(a^2 + I*a^2*Tan[c + d*x])^2)/d","A",6,5,24,0.2083,1,"{3548, 3545, 3542, 3531, 3475}"
43,1,142,0,0.2914478,"\int \cot ^6(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^6*(a + I*a*Tan[c + d*x])^4,x]","\frac{23 a^4 \cot ^3(c+d x)}{15 d}+\frac{4 i a^4 \cot ^2(c+d x)}{d}-\frac{8 a^4 \cot (c+d x)}{d}+\frac{8 i a^4 \log (\sin (c+d x))}{d}-\frac{\cot ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{5 d}-\frac{3 i \cot ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{5 d}-8 a^4 x","\frac{23 a^4 \cot ^3(c+d x)}{15 d}+\frac{4 i a^4 \cot ^2(c+d x)}{d}-\frac{8 a^4 \cot (c+d x)}{d}+\frac{8 i a^4 \log (\sin (c+d x))}{d}-\frac{\cot ^5(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{5 d}-\frac{3 i \cot ^4(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{5 d}-8 a^4 x",1,"-8*a^4*x - (8*a^4*Cot[c + d*x])/d + ((4*I)*a^4*Cot[c + d*x]^2)/d + (23*a^4*Cot[c + d*x]^3)/(15*d) + ((8*I)*a^4*Log[Sin[c + d*x]])/d - (Cot[c + d*x]^5*(a^2 + I*a^2*Tan[c + d*x])^2)/(5*d) - (((3*I)/5)*Cot[c + d*x]^4*(a^4 + I*a^4*Tan[c + d*x]))/d","A",7,6,24,0.2500,1,"{3553, 3593, 3591, 3529, 3531, 3475}"
44,1,162,0,0.3341545,"\int \cot ^7(c+d x) (a+i a \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^7*(a + I*a*Tan[c + d*x])^4,x]","\frac{67 a^4 \cot ^4(c+d x)}{60 d}+\frac{8 i a^4 \cot ^3(c+d x)}{3 d}-\frac{4 a^4 \cot ^2(c+d x)}{d}-\frac{8 i a^4 \cot (c+d x)}{d}-\frac{8 a^4 \log (\sin (c+d x))}{d}-\frac{\cot ^6(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{6 d}-\frac{7 i \cot ^5(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{15 d}-8 i a^4 x","\frac{67 a^4 \cot ^4(c+d x)}{60 d}+\frac{8 i a^4 \cot ^3(c+d x)}{3 d}-\frac{4 a^4 \cot ^2(c+d x)}{d}-\frac{8 i a^4 \cot (c+d x)}{d}-\frac{8 a^4 \log (\sin (c+d x))}{d}-\frac{\cot ^6(c+d x) \left(a^2+i a^2 \tan (c+d x)\right)^2}{6 d}-\frac{7 i \cot ^5(c+d x) \left(a^4+i a^4 \tan (c+d x)\right)}{15 d}-8 i a^4 x",1,"(-8*I)*a^4*x - ((8*I)*a^4*Cot[c + d*x])/d - (4*a^4*Cot[c + d*x]^2)/d + (((8*I)/3)*a^4*Cot[c + d*x]^3)/d + (67*a^4*Cot[c + d*x]^4)/(60*d) - (8*a^4*Log[Sin[c + d*x]])/d - (Cot[c + d*x]^6*(a^2 + I*a^2*Tan[c + d*x])^2)/(6*d) - (((7*I)/15)*Cot[c + d*x]^5*(a^4 + I*a^4*Tan[c + d*x]))/d","A",8,6,24,0.2500,1,"{3553, 3593, 3591, 3529, 3531, 3475}"
45,1,130,0,0.1513993,"\int \frac{\tan ^6(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^6/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^5(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 i \tan ^4(c+d x)}{4 a d}+\frac{5 \tan ^3(c+d x)}{6 a d}+\frac{3 i \tan ^2(c+d x)}{2 a d}-\frac{5 \tan (c+d x)}{2 a d}+\frac{3 i \log (\cos (c+d x))}{a d}+\frac{5 x}{2 a}","-\frac{\tan ^5(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 i \tan ^4(c+d x)}{4 a d}+\frac{5 \tan ^3(c+d x)}{6 a d}+\frac{3 i \tan ^2(c+d x)}{2 a d}-\frac{5 \tan (c+d x)}{2 a d}+\frac{3 i \log (\cos (c+d x))}{a d}+\frac{5 x}{2 a}",1,"(5*x)/(2*a) + ((3*I)*Log[Cos[c + d*x]])/(a*d) - (5*Tan[c + d*x])/(2*a*d) + (((3*I)/2)*Tan[c + d*x]^2)/(a*d) + (5*Tan[c + d*x]^3)/(6*a*d) - (((3*I)/4)*Tan[c + d*x]^4)/(a*d) - Tan[c + d*x]^5/(2*d*(a + I*a*Tan[c + d*x]))","A",6,4,24,0.1667,1,"{3550, 3528, 3525, 3475}"
46,1,109,0,0.1238756,"\int \frac{\tan ^5(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^4(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{5 i \tan ^3(c+d x)}{6 a d}+\frac{\tan ^2(c+d x)}{a d}+\frac{5 i \tan (c+d x)}{2 a d}+\frac{2 \log (\cos (c+d x))}{a d}-\frac{5 i x}{2 a}","-\frac{\tan ^4(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{5 i \tan ^3(c+d x)}{6 a d}+\frac{\tan ^2(c+d x)}{a d}+\frac{5 i \tan (c+d x)}{2 a d}+\frac{2 \log (\cos (c+d x))}{a d}-\frac{5 i x}{2 a}",1,"(((-5*I)/2)*x)/a + (2*Log[Cos[c + d*x]])/(a*d) + (((5*I)/2)*Tan[c + d*x])/(a*d) + Tan[c + d*x]^2/(a*d) - (((5*I)/6)*Tan[c + d*x]^3)/(a*d) - Tan[c + d*x]^4/(2*d*(a + I*a*Tan[c + d*x]))","A",5,4,24,0.1667,1,"{3550, 3528, 3525, 3475}"
47,1,90,0,0.0942289,"\int \frac{\tan ^4(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^3(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{i \tan ^2(c+d x)}{a d}+\frac{3 \tan (c+d x)}{2 a d}-\frac{2 i \log (\cos (c+d x))}{a d}-\frac{3 x}{2 a}","-\frac{\tan ^3(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{i \tan ^2(c+d x)}{a d}+\frac{3 \tan (c+d x)}{2 a d}-\frac{2 i \log (\cos (c+d x))}{a d}-\frac{3 x}{2 a}",1,"(-3*x)/(2*a) - ((2*I)*Log[Cos[c + d*x]])/(a*d) + (3*Tan[c + d*x])/(2*a*d) - (I*Tan[c + d*x]^2)/(a*d) - Tan[c + d*x]^3/(2*d*(a + I*a*Tan[c + d*x]))","A",4,4,24,0.1667,1,"{3550, 3528, 3525, 3475}"
48,1,74,0,0.0679656,"\int \frac{\tan ^3(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 i \tan (c+d x)}{2 a d}-\frac{\log (\cos (c+d x))}{a d}+\frac{3 i x}{2 a}","-\frac{\tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 i \tan (c+d x)}{2 a d}-\frac{\log (\cos (c+d x))}{a d}+\frac{3 i x}{2 a}",1,"(((3*I)/2)*x)/a - Log[Cos[c + d*x]]/(a*d) - (((3*I)/2)*Tan[c + d*x])/(a*d) - Tan[c + d*x]^2/(2*d*(a + I*a*Tan[c + d*x]))","A",3,3,24,0.1250,1,"{3550, 3525, 3475}"
49,1,50,0,0.0552606,"\int \frac{\tan ^2(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x]),x]","-\frac{i}{2 d (a+i a \tan (c+d x))}+\frac{i \log (\cos (c+d x))}{a d}+\frac{x}{2 a}","-\frac{i}{2 d (a+i a \tan (c+d x))}+\frac{i \log (\cos (c+d x))}{a d}+\frac{x}{2 a}",1,"x/(2*a) + (I*Log[Cos[c + d*x]])/(a*d) - (I/2)/(d*(a + I*a*Tan[c + d*x]))","A",3,2,24,0.08333,1,"{3540, 3475}"
50,1,33,0,0.0263502,"\int \frac{\tan (c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x]),x]","-\frac{1}{2 d (a+i a \tan (c+d x))}-\frac{i x}{2 a}","-\frac{1}{2 d (a+i a \tan (c+d x))}-\frac{i x}{2 a}",1,"((-I/2)*x)/a - 1/(2*d*(a + I*a*Tan[c + d*x]))","A",2,2,22,0.09091,1,"{3526, 8}"
51,1,33,0,0.0159955,"\int \frac{1}{a+i a \tan (c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(-1),x]","\frac{x}{2 a}+\frac{i}{2 d (a+i a \tan (c+d x))}","\frac{x}{2 a}+\frac{i}{2 d (a+i a \tan (c+d x))}",1,"x/(2*a) + (I/2)/(d*(a + I*a*Tan[c + d*x]))","A",2,2,15,0.1333,1,"{3479, 8}"
52,1,47,0,0.056771,"\int \frac{\cot (c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x]),x]","\frac{1}{2 d (a+i a \tan (c+d x))}+\frac{\log (\sin (c+d x))}{a d}-\frac{i x}{2 a}","\frac{1}{2 d (a+i a \tan (c+d x))}+\frac{\log (\sin (c+d x))}{a d}-\frac{i x}{2 a}",1,"((-I/2)*x)/a + Log[Sin[c + d*x]]/(a*d) + 1/(2*d*(a + I*a*Tan[c + d*x]))","A",4,4,22,0.1818,1,"{3551, 3479, 8, 3475}"
53,1,70,0,0.098075,"\int \frac{\cot ^2(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x]),x]","-\frac{3 \cot (c+d x)}{2 a d}-\frac{i \log (\sin (c+d x))}{a d}+\frac{\cot (c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 x}{2 a}","-\frac{3 \cot (c+d x)}{2 a d}-\frac{i \log (\sin (c+d x))}{a d}+\frac{\cot (c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{3 x}{2 a}",1,"(-3*x)/(2*a) - (3*Cot[c + d*x])/(2*a*d) - (I*Log[Sin[c + d*x]])/(a*d) + Cot[c + d*x]/(2*d*(a + I*a*Tan[c + d*x]))","A",4,4,24,0.1667,1,"{3552, 3529, 3531, 3475}"
54,1,90,0,0.1211956,"\int \frac{\cot ^3(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^3/(a + I*a*Tan[c + d*x]),x]","-\frac{\cot ^2(c+d x)}{a d}+\frac{3 i \cot (c+d x)}{2 a d}-\frac{2 \log (\sin (c+d x))}{a d}+\frac{\cot ^2(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{3 i x}{2 a}","-\frac{\cot ^2(c+d x)}{a d}+\frac{3 i \cot (c+d x)}{2 a d}-\frac{2 \log (\sin (c+d x))}{a d}+\frac{\cot ^2(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{3 i x}{2 a}",1,"(((3*I)/2)*x)/a + (((3*I)/2)*Cot[c + d*x])/(a*d) - Cot[c + d*x]^2/(a*d) - (2*Log[Sin[c + d*x]])/(a*d) + Cot[c + d*x]^2/(2*d*(a + I*a*Tan[c + d*x]))","A",5,4,24,0.1667,1,"{3552, 3529, 3531, 3475}"
55,1,108,0,0.1451766,"\int \frac{\cot ^4(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^4/(a + I*a*Tan[c + d*x]),x]","-\frac{5 \cot ^3(c+d x)}{6 a d}+\frac{i \cot ^2(c+d x)}{a d}+\frac{5 \cot (c+d x)}{2 a d}+\frac{2 i \log (\sin (c+d x))}{a d}+\frac{\cot ^3(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{5 x}{2 a}","-\frac{5 \cot ^3(c+d x)}{6 a d}+\frac{i \cot ^2(c+d x)}{a d}+\frac{5 \cot (c+d x)}{2 a d}+\frac{2 i \log (\sin (c+d x))}{a d}+\frac{\cot ^3(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{5 x}{2 a}",1,"(5*x)/(2*a) + (5*Cot[c + d*x])/(2*a*d) + (I*Cot[c + d*x]^2)/(a*d) - (5*Cot[c + d*x]^3)/(6*a*d) + ((2*I)*Log[Sin[c + d*x]])/(a*d) + Cot[c + d*x]^3/(2*d*(a + I*a*Tan[c + d*x]))","A",6,4,24,0.1667,1,"{3552, 3529, 3531, 3475}"
56,1,142,0,0.2262741,"\int \frac{\tan ^6(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^6/(a + I*a*Tan[c + d*x])^2,x]","\frac{3 i \tan ^4(c+d x)}{2 a^2 d (1+i \tan (c+d x))}-\frac{25 \tan ^3(c+d x)}{12 a^2 d}-\frac{3 i \tan ^2(c+d x)}{a^2 d}+\frac{25 \tan (c+d x)}{4 a^2 d}-\frac{6 i \log (\cos (c+d x))}{a^2 d}-\frac{25 x}{4 a^2}-\frac{\tan ^5(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{3 i \tan ^4(c+d x)}{2 a^2 d (1+i \tan (c+d x))}-\frac{25 \tan ^3(c+d x)}{12 a^2 d}-\frac{3 i \tan ^2(c+d x)}{a^2 d}+\frac{25 \tan (c+d x)}{4 a^2 d}-\frac{6 i \log (\cos (c+d x))}{a^2 d}-\frac{25 x}{4 a^2}-\frac{\tan ^5(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-25*x)/(4*a^2) - ((6*I)*Log[Cos[c + d*x]])/(a^2*d) + (25*Tan[c + d*x])/(4*a^2*d) - ((3*I)*Tan[c + d*x]^2)/(a^2*d) - (25*Tan[c + d*x]^3)/(12*a^2*d) + (((3*I)/2)*Tan[c + d*x]^4)/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^5/(4*d*(a + I*a*Tan[c + d*x])^2)","A",6,5,24,0.2083,1,"{3558, 3595, 3528, 3525, 3475}"
57,1,124,0,0.1948787,"\int \frac{\tan ^5(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x])^2,x]","\frac{5 i \tan ^3(c+d x)}{4 a^2 d (1+i \tan (c+d x))}-\frac{2 \tan ^2(c+d x)}{a^2 d}-\frac{15 i \tan (c+d x)}{4 a^2 d}-\frac{4 \log (\cos (c+d x))}{a^2 d}+\frac{15 i x}{4 a^2}-\frac{\tan ^4(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{5 i \tan ^3(c+d x)}{4 a^2 d (1+i \tan (c+d x))}-\frac{2 \tan ^2(c+d x)}{a^2 d}-\frac{15 i \tan (c+d x)}{4 a^2 d}-\frac{4 \log (\cos (c+d x))}{a^2 d}+\frac{15 i x}{4 a^2}-\frac{\tan ^4(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((15*I)/4)*x)/a^2 - (4*Log[Cos[c + d*x]])/(a^2*d) - (((15*I)/4)*Tan[c + d*x])/(a^2*d) - (2*Tan[c + d*x]^2)/(a^2*d) + (((5*I)/4)*Tan[c + d*x]^3)/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^4/(4*d*(a + I*a*Tan[c + d*x])^2)","A",5,5,24,0.2083,1,"{3558, 3595, 3528, 3525, 3475}"
58,1,104,0,0.1648875,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^2,x]","\frac{i \tan ^2(c+d x)}{a^2 d (1+i \tan (c+d x))}-\frac{9 \tan (c+d x)}{4 a^2 d}+\frac{2 i \log (\cos (c+d x))}{a^2 d}+\frac{9 x}{4 a^2}-\frac{\tan ^3(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{i \tan ^2(c+d x)}{a^2 d (1+i \tan (c+d x))}-\frac{9 \tan (c+d x)}{4 a^2 d}+\frac{2 i \log (\cos (c+d x))}{a^2 d}+\frac{9 x}{4 a^2}-\frac{\tan ^3(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(9*x)/(4*a^2) + ((2*I)*Log[Cos[c + d*x]])/(a^2*d) - (9*Tan[c + d*x])/(4*a^2*d) + (I*Tan[c + d*x]^2)/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^3/(4*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,24,0.1667,1,"{3558, 3595, 3525, 3475}"
59,1,79,0,0.1400273,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^2,x]","-\frac{3}{4 a^2 d (1+i \tan (c+d x))}+\frac{\log (\cos (c+d x))}{a^2 d}-\frac{3 i x}{4 a^2}-\frac{\tan ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}","-\frac{3}{4 a^2 d (1+i \tan (c+d x))}+\frac{\log (\cos (c+d x))}{a^2 d}-\frac{3 i x}{4 a^2}-\frac{\tan ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((-3*I)/4)*x)/a^2 + Log[Cos[c + d*x]]/(a^2*d) - 3/(4*a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^2/(4*d*(a + I*a*Tan[c + d*x])^2)","A",6,6,24,0.2500,1,"{3558, 3589, 3475, 12, 3526, 8}"
60,1,59,0,0.0818277,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^2,x]","\frac{3 i}{4 a^2 d (1+i \tan (c+d x))}-\frac{x}{4 a^2}-\frac{i}{4 d (a+i a \tan (c+d x))^2}","\frac{3 i}{4 a^2 d (1+i \tan (c+d x))}-\frac{x}{4 a^2}-\frac{i}{4 d (a+i a \tan (c+d x))^2}",1,"-x/(4*a^2) + ((3*I)/4)/(a^2*d*(1 + I*Tan[c + d*x])) - (I/4)/(d*(a + I*a*Tan[c + d*x])^2)","A",3,3,24,0.1250,1,"{3540, 3526, 8}"
61,1,59,0,0.0428896,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^2,x]","\frac{1}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{i x}{4 a^2}-\frac{1}{4 d (a+i a \tan (c+d x))^2}","\frac{1}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}-\frac{i x}{4 a^2}-\frac{1}{4 d (a+i a \tan (c+d x))^2}",1,"((-I/4)*x)/a^2 - 1/(4*d*(a + I*a*Tan[c + d*x])^2) + 1/(4*d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,3,22,0.1364,1,"{3526, 3479, 8}"
62,1,61,0,0.0301909,"\int \frac{1}{(a+i a \tan (c+d x))^2} \, dx","Int[(a + I*a*Tan[c + d*x])^(-2),x]","\frac{i}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i}{4 d (a+i a \tan (c+d x))^2}","\frac{i}{4 d \left(a^2+i a^2 \tan (c+d x)\right)}+\frac{x}{4 a^2}+\frac{i}{4 d (a+i a \tan (c+d x))^2}",1,"x/(4*a^2) + (I/4)/(d*(a + I*a*Tan[c + d*x])^2) + (I/4)/(d*(a^2 + I*a^2*Tan[c + d*x]))","A",3,2,15,0.1333,1,"{3479, 8}"
63,1,71,0,0.1407429,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^2,x]","\frac{3}{4 a^2 d (1+i \tan (c+d x))}+\frac{\log (\sin (c+d x))}{a^2 d}-\frac{3 i x}{4 a^2}+\frac{1}{4 d (a+i a \tan (c+d x))^2}","\frac{3}{4 a^2 d (1+i \tan (c+d x))}+\frac{\log (\sin (c+d x))}{a^2 d}-\frac{3 i x}{4 a^2}+\frac{1}{4 d (a+i a \tan (c+d x))^2}",1,"(((-3*I)/4)*x)/a^2 + Log[Sin[c + d*x]]/(a^2*d) + 3/(4*a^2*d*(1 + I*Tan[c + d*x])) + 1/(4*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,22,0.1818,1,"{3559, 3596, 3531, 3475}"
64,1,97,0,0.2014858,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^2,x]","-\frac{9 \cot (c+d x)}{4 a^2 d}-\frac{2 i \log (\sin (c+d x))}{a^2 d}+\frac{\cot (c+d x)}{a^2 d (1+i \tan (c+d x))}-\frac{9 x}{4 a^2}+\frac{\cot (c+d x)}{4 d (a+i a \tan (c+d x))^2}","-\frac{9 \cot (c+d x)}{4 a^2 d}-\frac{2 i \log (\sin (c+d x))}{a^2 d}+\frac{\cot (c+d x)}{a^2 d (1+i \tan (c+d x))}-\frac{9 x}{4 a^2}+\frac{\cot (c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-9*x)/(4*a^2) - (9*Cot[c + d*x])/(4*a^2*d) - ((2*I)*Log[Sin[c + d*x]])/(a^2*d) + Cot[c + d*x]/(a^2*d*(1 + I*Tan[c + d*x])) + Cot[c + d*x]/(4*d*(a + I*a*Tan[c + d*x])^2)","A",5,5,24,0.2083,1,"{3559, 3596, 3529, 3531, 3475}"
65,1,122,0,0.2338788,"\int \frac{\cot ^3(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^3/(a + I*a*Tan[c + d*x])^2,x]","-\frac{2 \cot ^2(c+d x)}{a^2 d}+\frac{15 i \cot (c+d x)}{4 a^2 d}-\frac{4 \log (\sin (c+d x))}{a^2 d}+\frac{5 \cot ^2(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{15 i x}{4 a^2}+\frac{\cot ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}","-\frac{2 \cot ^2(c+d x)}{a^2 d}+\frac{15 i \cot (c+d x)}{4 a^2 d}-\frac{4 \log (\sin (c+d x))}{a^2 d}+\frac{5 \cot ^2(c+d x)}{4 a^2 d (1+i \tan (c+d x))}+\frac{15 i x}{4 a^2}+\frac{\cot ^2(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((15*I)/4)*x)/a^2 + (((15*I)/4)*Cot[c + d*x])/(a^2*d) - (2*Cot[c + d*x]^2)/(a^2*d) - (4*Log[Sin[c + d*x]])/(a^2*d) + (5*Cot[c + d*x]^2)/(4*a^2*d*(1 + I*Tan[c + d*x])) + Cot[c + d*x]^2/(4*d*(a + I*a*Tan[c + d*x])^2)","A",6,5,24,0.2083,1,"{3559, 3596, 3529, 3531, 3475}"
66,1,161,0,0.3184013,"\int \frac{\tan ^6(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^6/(a + I*a*Tan[c + d*x])^3,x]","\frac{55 \tan ^3(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{7 i \tan ^2(c+d x)}{2 a^3 d}-\frac{55 \tan (c+d x)}{8 a^3 d}+\frac{7 i \log (\cos (c+d x))}{a^3 d}+\frac{55 x}{8 a^3}-\frac{\tan ^5(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{13 i \tan ^4(c+d x)}{24 a d (a+i a \tan (c+d x))^2}","\frac{55 \tan ^3(c+d x)}{24 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{7 i \tan ^2(c+d x)}{2 a^3 d}-\frac{55 \tan (c+d x)}{8 a^3 d}+\frac{7 i \log (\cos (c+d x))}{a^3 d}+\frac{55 x}{8 a^3}-\frac{\tan ^5(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{13 i \tan ^4(c+d x)}{24 a d (a+i a \tan (c+d x))^2}",1,"(55*x)/(8*a^3) + ((7*I)*Log[Cos[c + d*x]])/(a^3*d) - (55*Tan[c + d*x])/(8*a^3*d) + (((7*I)/2)*Tan[c + d*x]^2)/(a^3*d) - Tan[c + d*x]^5/(6*d*(a + I*a*Tan[c + d*x])^3) + (((13*I)/24)*Tan[c + d*x]^4)/(a*d*(a + I*a*Tan[c + d*x])^2) + (55*Tan[c + d*x]^3)/(24*d*(a^3 + I*a^3*Tan[c + d*x]))","A",6,5,24,0.2083,1,"{3558, 3595, 3528, 3525, 3475}"
67,1,143,0,0.2870572,"\int \frac{\tan ^5(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x])^3,x]","\frac{3 \tan ^2(c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{25 i \tan (c+d x)}{8 a^3 d}+\frac{3 \log (\cos (c+d x))}{a^3 d}-\frac{25 i x}{8 a^3}-\frac{\tan ^4(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{11 i \tan ^3(c+d x)}{24 a d (a+i a \tan (c+d x))^2}","\frac{3 \tan ^2(c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{25 i \tan (c+d x)}{8 a^3 d}+\frac{3 \log (\cos (c+d x))}{a^3 d}-\frac{25 i x}{8 a^3}-\frac{\tan ^4(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{11 i \tan ^3(c+d x)}{24 a d (a+i a \tan (c+d x))^2}",1,"(((-25*I)/8)*x)/a^3 + (3*Log[Cos[c + d*x]])/(a^3*d) + (((25*I)/8)*Tan[c + d*x])/(a^3*d) - Tan[c + d*x]^4/(6*d*(a + I*a*Tan[c + d*x])^3) + (((11*I)/24)*Tan[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^2) + (3*Tan[c + d*x]^2)/(2*d*(a^3 + I*a^3*Tan[c + d*x]))","A",5,4,24,0.1667,1,"{3558, 3595, 3525, 3475}"
68,1,119,0,0.2414761,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^3,x]","\frac{7 i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i \log (\cos (c+d x))}{a^3 d}-\frac{7 x}{8 a^3}-\frac{\tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{3 i \tan ^2(c+d x)}{8 a d (a+i a \tan (c+d x))^2}","\frac{7 i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i \log (\cos (c+d x))}{a^3 d}-\frac{7 x}{8 a^3}-\frac{\tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}+\frac{3 i \tan ^2(c+d x)}{8 a d (a+i a \tan (c+d x))^2}",1,"(-7*x)/(8*a^3) - (I*Log[Cos[c + d*x]])/(a^3*d) - Tan[c + d*x]^3/(6*d*(a + I*a*Tan[c + d*x])^3) + (((3*I)/8)*Tan[c + d*x]^2)/(a*d*(a + I*a*Tan[c + d*x])^2) + ((7*I)/8)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",7,7,24,0.2917,1,"{3558, 3595, 3589, 3475, 12, 3526, 8}"
69,1,92,0,0.1297236,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^3,x]","\frac{3}{8 a^3 d (1+i \tan (c+d x))}+\frac{i x}{8 a^3}+\frac{i \tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}-\frac{1}{8 a d (a+i a \tan (c+d x))^2}","\frac{3}{8 a^3 d (1+i \tan (c+d x))}+\frac{i x}{8 a^3}+\frac{i \tan ^3(c+d x)}{6 d (a+i a \tan (c+d x))^3}-\frac{1}{8 a d (a+i a \tan (c+d x))^2}",1,"((I/8)*x)/a^3 + 3/(8*a^3*d*(1 + I*Tan[c + d*x])) + ((I/6)*Tan[c + d*x]^3)/(d*(a + I*a*Tan[c + d*x])^3) - 1/(8*a*d*(a + I*a*Tan[c + d*x])^2)","A",4,4,24,0.1667,1,"{3546, 3540, 3526, 8}"
70,1,88,0,0.0982562,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^3,x]","-\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x}{8 a^3}+\frac{3 i}{8 a d (a+i a \tan (c+d x))^2}-\frac{i}{6 d (a+i a \tan (c+d x))^3}","-\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{x}{8 a^3}+\frac{3 i}{8 a d (a+i a \tan (c+d x))^2}-\frac{i}{6 d (a+i a \tan (c+d x))^3}",1,"-x/(8*a^3) - (I/6)/(d*(a + I*a*Tan[c + d*x])^3) + ((3*I)/8)/(a*d*(a + I*a*Tan[c + d*x])^2) - (I/8)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,4,24,0.1667,1,"{3540, 3526, 3479, 8}"
71,1,84,0,0.0600328,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^3,x]","\frac{1}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i x}{8 a^3}+\frac{1}{8 a d (a+i a \tan (c+d x))^2}-\frac{1}{6 d (a+i a \tan (c+d x))^3}","\frac{1}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{i x}{8 a^3}+\frac{1}{8 a d (a+i a \tan (c+d x))^2}-\frac{1}{6 d (a+i a \tan (c+d x))^3}",1,"((-I/8)*x)/a^3 - 1/(6*d*(a + I*a*Tan[c + d*x])^3) + 1/(8*a*d*(a + I*a*Tan[c + d*x])^2) + 1/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,3,22,0.1364,1,"{3526, 3479, 8}"
72,1,88,0,0.0499407,"\int \frac{1}{(a+i a \tan (c+d x))^3} \, dx","Int[(a + I*a*Tan[c + d*x])^(-3),x]","\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x}{8 a^3}+\frac{i}{8 a d (a+i a \tan (c+d x))^2}+\frac{i}{6 d (a+i a \tan (c+d x))^3}","\frac{i}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{x}{8 a^3}+\frac{i}{8 a d (a+i a \tan (c+d x))^2}+\frac{i}{6 d (a+i a \tan (c+d x))^3}",1,"x/(8*a^3) + (I/6)/(d*(a + I*a*Tan[c + d*x])^3) + (I/8)/(a*d*(a + I*a*Tan[c + d*x])^2) + (I/8)/(d*(a^3 + I*a^3*Tan[c + d*x]))","A",4,2,15,0.1333,1,"{3479, 8}"
73,1,98,0,0.2301469,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^3,x]","\frac{7}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{\log (\sin (c+d x))}{a^3 d}-\frac{7 i x}{8 a^3}+\frac{3}{8 a d (a+i a \tan (c+d x))^2}+\frac{1}{6 d (a+i a \tan (c+d x))^3}","\frac{7}{8 d \left(a^3+i a^3 \tan (c+d x)\right)}+\frac{\log (\sin (c+d x))}{a^3 d}-\frac{7 i x}{8 a^3}+\frac{3}{8 a d (a+i a \tan (c+d x))^2}+\frac{1}{6 d (a+i a \tan (c+d x))^3}",1,"(((-7*I)/8)*x)/a^3 + Log[Sin[c + d*x]]/(a^3*d) + 1/(6*d*(a + I*a*Tan[c + d*x])^3) + 3/(8*a*d*(a + I*a*Tan[c + d*x])^2) + 7/(8*d*(a^3 + I*a^3*Tan[c + d*x]))","A",5,4,22,0.1818,1,"{3559, 3596, 3531, 3475}"
74,1,133,0,0.3209079,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^3,x]","-\frac{25 \cot (c+d x)}{8 a^3 d}-\frac{3 i \log (\sin (c+d x))}{a^3 d}+\frac{3 \cot (c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{25 x}{8 a^3}+\frac{11 \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{\cot (c+d x)}{6 d (a+i a \tan (c+d x))^3}","-\frac{25 \cot (c+d x)}{8 a^3 d}-\frac{3 i \log (\sin (c+d x))}{a^3 d}+\frac{3 \cot (c+d x)}{2 d \left(a^3+i a^3 \tan (c+d x)\right)}-\frac{25 x}{8 a^3}+\frac{11 \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^2}+\frac{\cot (c+d x)}{6 d (a+i a \tan (c+d x))^3}",1,"(-25*x)/(8*a^3) - (25*Cot[c + d*x])/(8*a^3*d) - ((3*I)*Log[Sin[c + d*x]])/(a^3*d) + Cot[c + d*x]/(6*d*(a + I*a*Tan[c + d*x])^3) + (11*Cot[c + d*x])/(24*a*d*(a + I*a*Tan[c + d*x])^2) + (3*Cot[c + d*x])/(2*d*(a^3 + I*a^3*Tan[c + d*x]))","A",6,5,24,0.2083,1,"{3559, 3596, 3529, 3531, 3475}"
75,1,171,0,0.3931831,"\int \frac{\tan ^6(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^6/(a + I*a*Tan[c + d*x])^4,x]","\frac{31 \tan ^3(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{2 i \tan ^2(c+d x)}{a^4 d (1+i \tan (c+d x))}+\frac{65 \tan (c+d x)}{16 a^4 d}-\frac{4 i \log (\cos (c+d x))}{a^4 d}-\frac{65 x}{16 a^4}-\frac{\tan ^5(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{7 i \tan ^4(c+d x)}{24 a d (a+i a \tan (c+d x))^3}","\frac{31 \tan ^3(c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{2 i \tan ^2(c+d x)}{a^4 d (1+i \tan (c+d x))}+\frac{65 \tan (c+d x)}{16 a^4 d}-\frac{4 i \log (\cos (c+d x))}{a^4 d}-\frac{65 x}{16 a^4}-\frac{\tan ^5(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{7 i \tan ^4(c+d x)}{24 a d (a+i a \tan (c+d x))^3}",1,"(-65*x)/(16*a^4) - ((4*I)*Log[Cos[c + d*x]])/(a^4*d) + (65*Tan[c + d*x])/(16*a^4*d) - ((2*I)*Tan[c + d*x]^2)/(a^4*d*(1 + I*Tan[c + d*x])) + (31*Tan[c + d*x]^3)/(48*a^4*d*(1 + I*Tan[c + d*x])^2) - Tan[c + d*x]^5/(8*d*(a + I*a*Tan[c + d*x])^4) + (((7*I)/24)*Tan[c + d*x]^4)/(a*d*(a + I*a*Tan[c + d*x])^3)","A",6,4,24,0.1667,1,"{3558, 3595, 3525, 3475}"
76,1,147,0,0.351491,"\int \frac{\tan ^5(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x])^4,x]","\frac{7 \tan ^2(c+d x)}{16 a^4 d (1+i \tan (c+d x))^2}+\frac{15}{16 a^4 d (1+i \tan (c+d x))}-\frac{\log (\cos (c+d x))}{a^4 d}+\frac{15 i x}{16 a^4}-\frac{\tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{i \tan ^3(c+d x)}{4 a d (a+i a \tan (c+d x))^3}","\frac{7 \tan ^2(c+d x)}{16 a^4 d (1+i \tan (c+d x))^2}+\frac{15}{16 a^4 d (1+i \tan (c+d x))}-\frac{\log (\cos (c+d x))}{a^4 d}+\frac{15 i x}{16 a^4}-\frac{\tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{i \tan ^3(c+d x)}{4 a d (a+i a \tan (c+d x))^3}",1,"(((15*I)/16)*x)/a^4 - Log[Cos[c + d*x]]/(a^4*d) + 15/(16*a^4*d*(1 + I*Tan[c + d*x])) + (7*Tan[c + d*x]^2)/(16*a^4*d*(1 + I*Tan[c + d*x])^2) - Tan[c + d*x]^4/(8*d*(a + I*a*Tan[c + d*x])^4) + ((I/4)*Tan[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^3)","A",8,7,24,0.2917,1,"{3558, 3595, 3589, 3475, 12, 3526, 8}"
77,1,128,0,0.1784457,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^4,x]","-\frac{3 i}{16 a^4 d (1+i \tan (c+d x))}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i \tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{\tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}","-\frac{3 i}{16 a^4 d (1+i \tan (c+d x))}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i \tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{\tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}",1,"x/(16*a^4) - ((3*I)/16)/(a^4*d*(1 + I*Tan[c + d*x])) + ((I/8)*Tan[c + d*x]^4)/(d*(a + I*a*Tan[c + d*x])^4) + Tan[c + d*x]^3/(12*a*d*(a + I*a*Tan[c + d*x])^3) + (I/16)/(d*(a^2 + I*a^2*Tan[c + d*x])^2)","A",5,4,24,0.1667,1,"{3546, 3540, 3526, 8}"
78,1,126,0,0.1782418,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^4,x]","\frac{3}{16 a^4 d (1+i \tan (c+d x))}-\frac{1}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{i x}{16 a^4}+\frac{\tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{i \tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}","\frac{3}{16 a^4 d (1+i \tan (c+d x))}-\frac{1}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{i x}{16 a^4}+\frac{\tan ^4(c+d x)}{8 d (a+i a \tan (c+d x))^4}+\frac{i \tan ^3(c+d x)}{12 a d (a+i a \tan (c+d x))^3}",1,"((I/16)*x)/a^4 + 3/(16*a^4*d*(1 + I*Tan[c + d*x])) + Tan[c + d*x]^4/(8*d*(a + I*a*Tan[c + d*x])^4) + ((I/12)*Tan[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^3) - 1/(16*d*(a^2 + I*a^2*Tan[c + d*x])^2)","A",5,5,24,0.2083,1,"{3547, 3546, 3540, 3526, 8}"
79,1,116,0,0.1190338,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^4,x]","-\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{x}{16 a^4}+\frac{i}{4 a d (a+i a \tan (c+d x))^3}-\frac{i}{8 d (a+i a \tan (c+d x))^4}","-\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}-\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{x}{16 a^4}+\frac{i}{4 a d (a+i a \tan (c+d x))^3}-\frac{i}{8 d (a+i a \tan (c+d x))^4}",1,"-x/(16*a^4) - (I/8)/(d*(a + I*a*Tan[c + d*x])^4) + (I/4)/(a*d*(a + I*a*Tan[c + d*x])^3) - (I/16)/(d*(a^2 + I*a^2*Tan[c + d*x])^2) - (I/16)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,4,24,0.1667,1,"{3540, 3526, 3479, 8}"
80,1,110,0,0.0807473,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^4,x]","\frac{1}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{1}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{i x}{16 a^4}+\frac{1}{12 a d (a+i a \tan (c+d x))^3}-\frac{1}{8 d (a+i a \tan (c+d x))^4}","\frac{1}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{1}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}-\frac{i x}{16 a^4}+\frac{1}{12 a d (a+i a \tan (c+d x))^3}-\frac{1}{8 d (a+i a \tan (c+d x))^4}",1,"((-I/16)*x)/a^4 - 1/(8*d*(a + I*a*Tan[c + d*x])^4) + 1/(12*a*d*(a + I*a*Tan[c + d*x])^3) + 1/(16*d*(a^2 + I*a^2*Tan[c + d*x])^2) + 1/(16*d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,3,22,0.1364,1,"{3526, 3479, 8}"
81,1,116,0,0.0690521,"\int \frac{1}{(a+i a \tan (c+d x))^4} \, dx","Int[(a + I*a*Tan[c + d*x])^(-4),x]","\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i}{12 a d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^4}","\frac{i}{16 d \left(a^4+i a^4 \tan (c+d x)\right)}+\frac{i}{16 d \left(a^2+i a^2 \tan (c+d x)\right)^2}+\frac{x}{16 a^4}+\frac{i}{12 a d (a+i a \tan (c+d x))^3}+\frac{i}{8 d (a+i a \tan (c+d x))^4}",1,"x/(16*a^4) + (I/8)/(d*(a + I*a*Tan[c + d*x])^4) + (I/12)/(a*d*(a + I*a*Tan[c + d*x])^3) + (I/16)/(d*(a^2 + I*a^2*Tan[c + d*x])^2) + (I/16)/(d*(a^4 + I*a^4*Tan[c + d*x]))","A",5,2,15,0.1333,1,"{3479, 8}"
82,1,120,0,0.3204239,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^4,x]","\frac{15}{16 a^4 d (1+i \tan (c+d x))}+\frac{7}{16 a^4 d (1+i \tan (c+d x))^2}+\frac{\log (\sin (c+d x))}{a^4 d}-\frac{15 i x}{16 a^4}+\frac{1}{4 a d (a+i a \tan (c+d x))^3}+\frac{1}{8 d (a+i a \tan (c+d x))^4}","\frac{15}{16 a^4 d (1+i \tan (c+d x))}+\frac{7}{16 a^4 d (1+i \tan (c+d x))^2}+\frac{\log (\sin (c+d x))}{a^4 d}-\frac{15 i x}{16 a^4}+\frac{1}{4 a d (a+i a \tan (c+d x))^3}+\frac{1}{8 d (a+i a \tan (c+d x))^4}",1,"(((-15*I)/16)*x)/a^4 + Log[Sin[c + d*x]]/(a^4*d) + 7/(16*a^4*d*(1 + I*Tan[c + d*x])^2) + 15/(16*a^4*d*(1 + I*Tan[c + d*x])) + 1/(8*d*(a + I*a*Tan[c + d*x])^4) + 1/(4*a*d*(a + I*a*Tan[c + d*x])^3)","A",6,4,22,0.1818,1,"{3559, 3596, 3531, 3475}"
83,1,159,0,0.4370611,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^4} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^4,x]","-\frac{65 \cot (c+d x)}{16 a^4 d}-\frac{4 i \log (\sin (c+d x))}{a^4 d}+\frac{2 \cot (c+d x)}{a^4 d (1+i \tan (c+d x))}+\frac{31 \cot (c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{65 x}{16 a^4}+\frac{7 \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{\cot (c+d x)}{8 d (a+i a \tan (c+d x))^4}","-\frac{65 \cot (c+d x)}{16 a^4 d}-\frac{4 i \log (\sin (c+d x))}{a^4 d}+\frac{2 \cot (c+d x)}{a^4 d (1+i \tan (c+d x))}+\frac{31 \cot (c+d x)}{48 a^4 d (1+i \tan (c+d x))^2}-\frac{65 x}{16 a^4}+\frac{7 \cot (c+d x)}{24 a d (a+i a \tan (c+d x))^3}+\frac{\cot (c+d x)}{8 d (a+i a \tan (c+d x))^4}",1,"(-65*x)/(16*a^4) - (65*Cot[c + d*x])/(16*a^4*d) - ((4*I)*Log[Sin[c + d*x]])/(a^4*d) + (31*Cot[c + d*x])/(48*a^4*d*(1 + I*Tan[c + d*x])^2) + (2*Cot[c + d*x])/(a^4*d*(1 + I*Tan[c + d*x])) + Cot[c + d*x]/(8*d*(a + I*a*Tan[c + d*x])^4) + (7*Cot[c + d*x])/(24*a*d*(a + I*a*Tan[c + d*x])^3)","A",7,5,24,0.2083,1,"{3559, 3596, 3529, 3531, 3475}"
84,1,168,0,0.3472522,"\int \tan ^4(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^4*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}-\frac{2 i \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{62 i (a+i a \tan (c+d x))^{3/2}}{105 a d}+\frac{8 i \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","\frac{2 \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}-\frac{2 i \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}+\frac{62 i (a+i a \tan (c+d x))^{3/2}}{105 a d}+\frac{8 i \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (((8*I)/35)*Sqrt[a + I*a*Tan[c + d*x]])/d - (((2*I)/35)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(7*d) + (((62*I)/105)*(a + I*a*Tan[c + d*x])^(3/2))/(a*d)","A",6,6,26,0.2308,1,"{3560, 3597, 3592, 3527, 3480, 206}"
85,1,127,0,0.2121387,"\int \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{2 (a+i a \tan (c+d x))^{3/2}}{15 a d}-\frac{8 \sqrt{a+i a \tan (c+d x)}}{5 d}+\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","\frac{2 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{2 (a+i a \tan (c+d x))^{3/2}}{15 a d}-\frac{8 \sqrt{a+i a \tan (c+d x)}}{5 d}+\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"(Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (8*Sqrt[a + I*a*Tan[c + d*x]])/(5*d) + (2*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(5*d) - (2*(a + I*a*Tan[c + d*x])^(3/2))/(15*a*d)","A",5,5,26,0.1923,1,"{3560, 3592, 3527, 3480, 206}"
86,1,76,0,0.079921,"\int \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a d}","\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{3/2}}{3 a d}",1,"(I*Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (((2*I)/3)*(a + I*a*Tan[c + d*x])^(3/2))/(a*d)","A",3,3,26,0.1154,1,"{3543, 3480, 206}"
87,1,67,0,0.0584919,"\int \tan (c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","\frac{2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"-((Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d) + (2*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,3,24,0.1250,1,"{3527, 3480, 206}"
88,1,46,0,0.0224428,"\int \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d","A",2,2,17,0.1176,1,"{3480, 206}"
89,1,78,0,0.1738336,"\int \cot (c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}","\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d","A",6,6,24,0.2500,1,"{3562, 3480, 206, 3599, 63, 208}"
90,1,111,0,0.2516434,"\int \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{\cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{i \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{\cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"((-I)*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (I*Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",8,8,26,0.3077,1,"{3561, 21, 3554, 3480, 206, 3599, 63, 208}"
91,1,145,0,0.4376214,"\int \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{7 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{\cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}-\frac{i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}","\frac{7 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{\sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{\cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}-\frac{i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}",1,"(7*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (Sqrt[2]*Sqrt[a]*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((I/4)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",8,8,26,0.3077,1,"{3561, 3598, 3600, 3480, 206, 3599, 63, 208}"
92,1,199,0,0.5102788,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \tan ^4(c+d x)}{7 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i a^2 \tan ^3(c+d x)}{7 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{16 a \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{76 (a+i a \tan (c+d x))^{3/2}}{105 d}-\frac{64 a \sqrt{a+i a \tan (c+d x)}}{35 d}","-\frac{2 a^2 \tan ^4(c+d x)}{7 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 i a^2 \tan ^3(c+d x)}{7 d \sqrt{a+i a \tan (c+d x)}}+\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{16 a \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 d}-\frac{76 (a+i a \tan (c+d x))^{3/2}}{105 d}-\frac{64 a \sqrt{a+i a \tan (c+d x)}}{35 d}",1,"(2*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (((2*I)/7)*a^2*Tan[c + d*x]^3)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (2*a^2*Tan[c + d*x]^4)/(7*d*Sqrt[a + I*a*Tan[c + d*x]]) - (64*a*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) + (16*a*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(35*d) - (76*(a + I*a*Tan[c + d*x])^(3/2))/(105*d)","A",7,7,26,0.2692,1,"{3556, 3595, 3597, 3592, 3527, 3480, 206}"
93,1,101,0,0.1057233,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a d}-\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d}","\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{5/2}}{5 a d}-\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d}",1,"((2*I)*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((2*I)*a*Sqrt[a + I*a*Tan[c + d*x]])/d - (((2*I)/5)*(a + I*a*Tan[c + d*x])^(5/2))/(a*d)","A",4,4,26,0.1538,1,"{3543, 3478, 3480, 206}"
94,1,92,0,0.0838814,"\int \tan (c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 \sqrt{2} a^{3/2} \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 (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{2 \sqrt{2} a^{3/2} \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 (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"(-2*Sqrt[2]*a^(3/2)*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*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",4,4,24,0.1667,1,"{3527, 3478, 3480, 206}"
95,1,72,0,0.041887,"\int (a+i a \tan (c+d x))^{3/2} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"((-2*I)*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + ((2*I)*a*Sqrt[a + I*a*Tan[c + d*x]])/d","A",3,3,17,0.1765,1,"{3478, 3480, 206}"
96,1,79,0,0.1760794,"\int \cot (c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}","\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}",1,"(-2*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (2*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d","A",6,6,24,0.2500,1,"{3554, 3480, 206, 3599, 63, 208}"
97,1,141,0,0.4085629,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{i a^2}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}","-\frac{i a^2}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}",1,"((-3*I)*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + ((2*I)*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (I*a^2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (a^2*Cot[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,8,26,0.3077,1,"{3553, 3596, 3600, 3480, 206, 3599, 63, 208}"
98,1,184,0,0.6058918,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{11 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^2(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i a^2 \cot (c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}","\frac{11 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{2 \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^2(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i a^2 \cot (c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{5 i a \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}",1,"(11*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (2*Sqrt[2]*a^(3/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((I/2)*a^2*Cot[c + d*x])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (a^2*Cot[c + d*x]^2)/(2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((5*I)/4)*a*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",9,9,26,0.3462,1,"{3553, 3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
99,1,204,0,0.4957932,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \tan ^4(c+d x) \sqrt{a+i a \tan (c+d x)}}{9 d}+\frac{38 i a^2 \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{63 d}+\frac{92 a^2 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{368 a^2 \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{472 a (a+i a \tan (c+d x))^{3/2}}{315 d}","-\frac{2 a^2 \tan ^4(c+d x) \sqrt{a+i a \tan (c+d x)}}{9 d}+\frac{38 i a^2 \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{63 d}+\frac{92 a^2 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{105 d}-\frac{368 a^2 \sqrt{a+i a \tan (c+d x)}}{105 d}+\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{472 a (a+i a \tan (c+d x))^{3/2}}{315 d}",1,"(4*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (368*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) + (92*a^2*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(105*d) + (((38*I)/63)*a^2*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*a^2*Tan[c + d*x]^4*Sqrt[a + I*a*Tan[c + d*x]])/(9*d) - (472*a*(a + I*a*Tan[c + d*x])^(3/2))/(315*d)","A",7,6,26,0.2308,1,"{3556, 3597, 3592, 3527, 3480, 206}"
100,1,130,0,0.1249604,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a d}-\frac{2 i a (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{2 i (a+i a \tan (c+d x))^{7/2}}{7 a d}-\frac{2 i a (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"((4*I)*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - ((4*I)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/d - (((2*I)/3)*a*(a + I*a*Tan[c + d*x])^(3/2))/d - (((2*I)/7)*(a + I*a*Tan[c + d*x])^(7/2))/(a*d)","A",5,4,26,0.1538,1,"{3543, 3478, 3480, 206}"
101,1,119,0,0.1018398,"\int \tan (c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{4 a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 (a+i a \tan (c+d x))^{5/2}}{5 d}","\frac{4 a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 a (a+i a \tan (c+d x))^{3/2}}{3 d}+\frac{2 (a+i a \tan (c+d x))^{5/2}}{5 d}",1,"(-4*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (4*a^2*Sqrt[a + I*a*Tan[c + d*x]])/d + (2*a*(a + I*a*Tan[c + d*x])^(3/2))/(3*d) + (2*(a + I*a*Tan[c + d*x])^(5/2))/(5*d)","A",5,4,24,0.1667,1,"{3527, 3478, 3480, 206}"
102,1,101,0,0.0613302,"\int (a+i a \tan (c+d x))^{5/2} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 i a (a+i a \tan (c+d x))^{3/2}}{3 d}","\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 i a (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"((-4*I)*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + ((4*I)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/d + (((2*I)/3)*a*(a + I*a*Tan[c + d*x])^(3/2))/d","A",4,3,17,0.1765,1,"{3478, 3480, 206}"
103,1,104,0,0.2865888,"\int \cot (c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}","-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{d}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}",1,"(-2*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + (4*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (2*a^2*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,7,24,0.2917,1,"{3556, 3600, 3480, 206, 3599, 63, 208}"
104,1,114,0,0.2929548,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{5 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{5 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{d}",1,"((-5*I)*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d + ((4*I)*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (a^2*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",7,7,26,0.2692,1,"{3553, 3600, 3480, 206, 3599, 63, 208}"
105,1,151,0,0.442497,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{23 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}-\frac{9 i a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}","\frac{23 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{4 \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}-\frac{9 i a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}",1,"(23*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*d) - (4*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d - (((9*I)/4)*a^2*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/d - (a^2*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",8,8,26,0.3077,1,"{3553, 3598, 3600, 3480, 206, 3599, 63, 208}"
106,1,190,0,0.5899922,"\int \cot ^4(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^4*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{45 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{13 i a^2 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{19 a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}","\frac{45 i a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{8 d}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}-\frac{a^2 \cot ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{13 i a^2 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{19 a^2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{8 d}",1,"(((45*I)/8)*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/d - ((4*I)*Sqrt[2]*a^(5/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + (19*a^2*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) - (((13*I)/12)*a^2*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/d - (a^2*Cot[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",9,8,26,0.3077,1,"{3553, 3598, 3600, 3480, 206, 3599, 63, 208}"
107,1,130,0,0.0815251,"\int (a+i a \tan (c+d x))^{7/2} \, dx","Int[(a + I*a*Tan[c + d*x])^(7/2),x]","\frac{8 i a^3 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 i a^2 (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{8 i \sqrt{2} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 i a (a+i a \tan (c+d x))^{5/2}}{5 d}","\frac{8 i a^3 \sqrt{a+i a \tan (c+d x)}}{d}+\frac{4 i a^2 (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{8 i \sqrt{2} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{d}+\frac{2 i a (a+i a \tan (c+d x))^{5/2}}{5 d}",1,"((-8*I)*Sqrt[2]*a^(7/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/d + ((8*I)*a^3*Sqrt[a + I*a*Tan[c + d*x]])/d + (((4*I)/3)*a^2*(a + I*a*Tan[c + d*x])^(3/2))/d + (((2*I)/5)*a*(a + I*a*Tan[c + d*x])^(5/2))/d","A",5,3,17,0.1765,1,"{3478, 3480, 206}"
108,1,201,0,0.4884133,"\int \frac{\tan ^5(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^5/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{223 (a+i a \tan (c+d x))^{3/2}}{105 a^2 d}-\frac{\tan ^4(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{9 i \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 a d}+\frac{47 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 a d}-\frac{188 \sqrt{a+i a \tan (c+d x)}}{35 a d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","\frac{223 (a+i a \tan (c+d x))^{3/2}}{105 a^2 d}-\frac{\tan ^4(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{9 i \tan ^3(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 a d}+\frac{47 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{35 a d}-\frac{188 \sqrt{a+i a \tan (c+d x)}}{35 a d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"-(ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(Sqrt[2]*Sqrt[a]*d)) - Tan[c + d*x]^4/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (188*Sqrt[a + I*a*Tan[c + d*x]])/(35*a*d) + (47*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(35*a*d) - (((9*I)/7)*Tan[c + d*x]^3*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) + (223*(a + I*a*Tan[c + d*x])^(3/2))/(105*a^2*d)","A",7,6,26,0.2308,1,"{3558, 3597, 3592, 3527, 3480, 206}"
109,1,172,0,0.3385326,"\int \frac{\tan ^4(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^4/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{23 i (a+i a \tan (c+d x))^{3/2}}{15 a^2 d}-\frac{\tan ^3(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{7 i \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{28 i \sqrt{a+i a \tan (c+d x)}}{5 a d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","-\frac{23 i (a+i a \tan (c+d x))^{3/2}}{15 a^2 d}-\frac{\tan ^3(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{7 i \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 a d}+\frac{28 i \sqrt{a+i a \tan (c+d x)}}{5 a d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"((-I)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) - Tan[c + d*x]^3/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((28*I)/5)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (((7*I)/5)*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (((23*I)/15)*(a + I*a*Tan[c + d*x])^(3/2))/(a^2*d)","A",6,6,26,0.2308,1,"{3558, 3597, 3592, 3527, 3480, 206}"
110,1,126,0,0.2010038,"\int \frac{\tan ^3(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^3/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{5 (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}-\frac{\tan ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{4 \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","-\frac{5 (a+i a \tan (c+d x))^{3/2}}{3 a^2 d}-\frac{\tan ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{4 \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(Sqrt[2]*Sqrt[a]*d) - Tan[c + d*x]^2/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (4*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (5*(a + I*a*Tan[c + d*x])^(3/2))/(3*a^2*d)","A",5,5,26,0.1923,1,"{3558, 3592, 3527, 3480, 206}"
111,1,98,0,0.0957389,"\int \frac{\tan ^2(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^2/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{a d}-\frac{i}{d \sqrt{a+i a \tan (c+d x)}}+\frac{i \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 \sqrt{a+i a \tan (c+d x)}}{a d}-\frac{i}{d \sqrt{a+i a \tan (c+d x)}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"(I*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) - I/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((2*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",4,4,26,0.1538,1,"{3543, 3479, 3480, 206}"
112,1,67,0,0.0562232,"\int \frac{\tan (c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{1}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","-\frac{1}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"-(ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(Sqrt[2]*Sqrt[a]*d)) - 1/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,3,24,0.1250,1,"{3526, 3480, 206}"
113,1,71,0,0.0380318,"\int \frac{1}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i}{d \sqrt{a+i a \tan (c+d x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","\frac{i}{d \sqrt{a+i a \tan (c+d x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"((-I)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + I/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,3,17,0.1765,1,"{3479, 3480, 206}"
114,1,99,0,0.2654059,"\int \frac{\cot (c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{1}{d \sqrt{a+i a \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}","\frac{1}{d \sqrt{a+i a \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}",1,"(-2*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(Sqrt[2]*Sqrt[a]*d) + 1/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",7,7,24,0.2917,1,"{3559, 3600, 3480, 206, 3599, 63, 208}"
115,1,141,0,0.4258267,"\int \frac{\cot ^2(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^2/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{2 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\cot (c+d x)}{d \sqrt{a+i a \tan (c+d x)}}",1,"(I*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + (I*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*Sqrt[a]*d) + Cot[c + d*x]/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (2*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",8,8,26,0.3077,1,"{3559, 3598, 3600, 3480, 206, 3599, 63, 208}"
116,1,180,0,0.5686494,"\int \frac{\cot ^3(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^3/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{11 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{3 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{\cot ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}","\frac{11 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{\sqrt{2} \sqrt{a} d}-\frac{3 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{\cot ^2(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a d}",1,"(11*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*Sqrt[a]*d) - ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(Sqrt[2]*Sqrt[a]*d) + Cot[c + d*x]^2/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((7*I)/4)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (3*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(2*a*d)","A",9,8,26,0.3077,1,"{3559, 3598, 3600, 3480, 206, 3599, 63, 208}"
117,1,205,0,0.4918534,"\int \frac{\tan ^5(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{39 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{10 a^2 d}-\frac{151 (a+i a \tan (c+d x))^{3/2}}{30 a^3 d}+\frac{78 \sqrt{a+i a \tan (c+d x)}}{5 a^2 d}-\frac{\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{\tan ^4(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{19 i \tan ^3(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{39 \tan ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{10 a^2 d}-\frac{151 (a+i a \tan (c+d x))^{3/2}}{30 a^3 d}+\frac{78 \sqrt{a+i a \tan (c+d x)}}{5 a^2 d}-\frac{\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{\tan ^4(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{19 i \tan ^3(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"-ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(2*Sqrt[2]*a^(3/2)*d) - Tan[c + d*x]^4/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((19*I)/6)*Tan[c + d*x]^3)/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) + (78*Sqrt[a + I*a*Tan[c + d*x]])/(5*a^2*d) - (39*Tan[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(10*a^2*d) - (151*(a + I*a*Tan[c + d*x])^(3/2))/(30*a^3*d)","A",7,7,26,0.2692,1,"{3558, 3595, 3597, 3592, 3527, 3480, 206}"
118,1,174,0,0.3534255,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{7 i (a+i a \tan (c+d x))^{3/2}}{2 a^3 d}-\frac{10 i \sqrt{a+i a \tan (c+d x)}}{a^2 d}-\frac{i \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{\tan ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i \tan ^2(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}","\frac{7 i (a+i a \tan (c+d x))^{3/2}}{2 a^3 d}-\frac{10 i \sqrt{a+i a \tan (c+d x)}}{a^2 d}-\frac{i \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{\tan ^3(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{5 i \tan ^2(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"((-I/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) - Tan[c + d*x]^3/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((5*I)/2)*Tan[c + d*x]^2)/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) - ((10*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) + (((7*I)/2)*(a + I*a*Tan[c + d*x])^(3/2))/(a^3*d)","A",6,6,26,0.2308,1,"{3558, 3595, 3592, 3527, 3480, 206}"
119,1,133,0,0.2141507,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{7 \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{\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{\tan ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}-\frac{11}{6 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{7 \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{\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{\tan ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}-\frac{11}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(2*Sqrt[2]*a^(3/2)*d) - Tan[c + d*x]^2/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) - 11/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Sqrt[a + I*a*Tan[c + d*x]])/(3*a^2*d)","A",5,5,26,0.1923,1,"{3558, 3592, 3526, 3480, 206}"
120,1,104,0,0.1393956,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{i \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{3 i}{2 a d \sqrt{a+i a \tan (c+d x)}}-\frac{i}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{i \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{3 i}{2 a d \sqrt{a+i a \tan (c+d x)}}-\frac{i}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((I/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) - (I/3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + ((3*I)/2)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,26,0.1538,1,"{3540, 3526, 3480, 206}"
121,1,98,0,0.0816194,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{\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{1}{2 a d \sqrt{a+i a \tan (c+d x)}}-\frac{1}{3 d (a+i a \tan (c+d x))^{3/2}}","-\frac{\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{1}{2 a d \sqrt{a+i a \tan (c+d x)}}-\frac{1}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"-ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(2*Sqrt[2]*a^(3/2)*d) - 1/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + 1/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,24,0.1667,1,"{3526, 3479, 3480, 206}"
122,1,104,0,0.0608089,"\int \frac{1}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-3/2),x]","-\frac{i \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{i}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i}{3 d (a+i a \tan (c+d x))^{3/2}}","-\frac{i \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{i}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{i}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((-I/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) + (I/3)/(d*(a + I*a*Tan[c + d*x])^(3/2)) + (I/2)/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,3,17,0.1765,1,"{3479, 3480, 206}"
123,1,132,0,0.3911728,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{\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{3}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d (a+i a \tan (c+d x))^{3/2}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{\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{3}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"(-2*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(2*Sqrt[2]*a^(3/2)*d) + 1/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + 3/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,8,24,0.3333,1,"{3559, 3596, 3600, 3480, 206, 3599, 63, 208}"
124,1,181,0,0.5841962,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{i \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 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{13 \cot (c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot (c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{i \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 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{13 \cot (c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot (c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((3*I)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ((I/2)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(3/2)*d) + Cot[c + d*x]/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (13*Cot[c + d*x])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d)","A",9,9,26,0.3462,1,"{3559, 3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
125,1,220,0,0.7390875,"\int \frac{\cot ^3(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^3/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{23 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{\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{11 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{21 i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^2 d}+\frac{17 \cot ^2(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{23 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d}-\frac{\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{11 \cot ^2(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a^2 d}+\frac{21 i \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^2 d}+\frac{17 \cot ^2(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot ^2(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"(23*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(4*a^(3/2)*d) - ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(2*Sqrt[2]*a^(3/2)*d) + Cot[c + d*x]^2/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (17*Cot[c + d*x]^2)/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((21*I)/4)*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) - (11*Cot[c + d*x]^2*Sqrt[a + I*a*Tan[c + d*x]])/(3*a^2*d)","A",10,9,26,0.3462,1,"{3559, 3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
126,1,205,0,0.5177828,"\int \frac{\tan ^5(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^5/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{89 \tan ^2(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{361 (a+i a \tan (c+d x))^{3/2}}{60 a^4 d}-\frac{89 \sqrt{a+i a \tan (c+d x)}}{5 a^3 d}-\frac{\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{\tan ^4(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{7 i \tan ^3(c+d x)}{10 a d (a+i a \tan (c+d x))^{3/2}}","\frac{89 \tan ^2(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{361 (a+i a \tan (c+d x))^{3/2}}{60 a^4 d}-\frac{89 \sqrt{a+i a \tan (c+d x)}}{5 a^3 d}-\frac{\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{\tan ^4(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{7 i \tan ^3(c+d x)}{10 a d (a+i a \tan (c+d x))^{3/2}}",1,"-ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(4*Sqrt[2]*a^(5/2)*d) - Tan[c + d*x]^4/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((7*I)/10)*Tan[c + d*x]^3)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (89*Tan[c + d*x]^2)/(20*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (89*Sqrt[a + I*a*Tan[c + d*x]])/(5*a^3*d) + (361*(a + I*a*Tan[c + d*x])^(3/2))/(60*a^4*d)","A",7,6,26,0.2308,1,"{3558, 3595, 3592, 3527, 3480, 206}"
127,1,176,0,0.3709262,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{83 i \sqrt{a+i a \tan (c+d x)}}{30 a^3 d}+\frac{151 i}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i \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{\tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{17 i \tan ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{83 i \sqrt{a+i a \tan (c+d x)}}{30 a^3 d}+\frac{151 i}{60 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i \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{\tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{17 i \tan ^2(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"((-I/4)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) - Tan[c + d*x]^3/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((17*I)/30)*Tan[c + d*x]^2)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((151*I)/60)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((83*I)/30)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",6,6,26,0.2308,1,"{3558, 3595, 3592, 3526, 3480, 206}"
128,1,133,0,0.236378,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{31}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\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{\tan ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}-\frac{13}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{31}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{\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{\tan ^2(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}-\frac{13}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(4*Sqrt[2]*a^(5/2)*d) - Tan[c + d*x]^2/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) - 13/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + 31/(20*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,26,0.1923,1,"{3558, 3590, 3526, 3480, 206}"
129,1,133,0,0.1620839,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{i \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{i}{2 a d (a+i a \tan (c+d x))^{3/2}}-\frac{i}{5 d (a+i a \tan (c+d x))^{5/2}}","-\frac{i}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{i \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{i}{2 a d (a+i a \tan (c+d x))^{3/2}}-\frac{i}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((I/4)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) - (I/5)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (I/2)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) - (I/4)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,26,0.1923,1,"{3540, 3526, 3479, 3480, 206}"
130,1,125,0,0.101062,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{1}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\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{1}{6 a d (a+i a \tan (c+d x))^{3/2}}-\frac{1}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{1}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\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{1}{6 a d (a+i a \tan (c+d x))^{3/2}}-\frac{1}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"-ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(4*Sqrt[2]*a^(5/2)*d) - 1/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + 1/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + 1/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,24,0.1667,1,"{3526, 3479, 3480, 206}"
131,1,133,0,0.0771873,"\int \frac{1}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-5/2),x]","\frac{i}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i \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{i}{6 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{i}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{i \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{i}{6 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((-I/4)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) + (I/5)/(d*(a + I*a*Tan[c + d*x])^(5/2)) + (I/6)/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (I/4)/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,3,17,0.1765,1,"{3479, 3480, 206}"
132,1,159,0,0.5310389,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{7}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{\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{1}{2 a d (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{7}{4 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{\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{1}{2 a d (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"(-2*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])]/(4*Sqrt[2]*a^(5/2)*d) + 1/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + 1/(2*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + 7/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,8,24,0.3333,1,"{3559, 3596, 3600, 3480, 206, 3599, 63, 208}"
133,1,214,0,0.7570115,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{i \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{21 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{41 \cot (c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{19 \cot (c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\cot (c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{5 i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{i \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{21 \cot (c+d x) \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}+\frac{41 \cot (c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{19 \cot (c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\cot (c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((5*I)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ((I/4)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(5/2)*d) + Cot[c + d*x]/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (19*Cot[c + d*x])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (41*Cot[c + d*x])/(12*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (21*Cot[c + d*x]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a^3*d)","A",10,9,26,0.3462,1,"{3559, 3596, 3598, 3600, 3480, 206, 3599, 63, 208}"
134,1,162,0,0.1078344,"\int \frac{1}{(a+i a \tan (c+d x))^{7/2}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-7/2),x]","\frac{i}{8 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{i}{12 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} a^{7/2} d}+\frac{i}{10 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i}{7 d (a+i a \tan (c+d x))^{7/2}}","\frac{i}{8 a^3 d \sqrt{a+i a \tan (c+d x)}}+\frac{i}{12 a^2 d (a+i a \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{2} \sqrt{a}}\right)}{8 \sqrt{2} a^{7/2} d}+\frac{i}{10 a d (a+i a \tan (c+d x))^{5/2}}+\frac{i}{7 d (a+i a \tan (c+d x))^{7/2}}",1,"((-I/8)*ArcTanh[Sqrt[a + I*a*Tan[c + d*x]]/(Sqrt[2]*Sqrt[a])])/(Sqrt[2]*a^(7/2)*d) + (I/7)/(d*(a + I*a*Tan[c + d*x])^(7/2)) + (I/10)/(a*d*(a + I*a*Tan[c + d*x])^(5/2)) + (I/12)/(a^2*d*(a + I*a*Tan[c + d*x])^(3/2)) + (I/8)/(a^3*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,3,17,0.1765,1,"{3479, 3480, 206}"
135,1,107,0,0.1602667,"\int (d \tan (e+f x))^{5/2} (a+i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + I*a*Tan[e + f*x]),x]","-\frac{2 (-1)^{3/4} a d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 i a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}+\frac{2 i a (d \tan (e+f x))^{5/2}}{5 f}","-\frac{2 (-1)^{3/4} a d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 i a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}+\frac{2 i a (d \tan (e+f x))^{5/2}}{5 f}",1,"(-2*(-1)^(3/4)*a*d^(5/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - ((2*I)*a*d^2*Sqrt[d*Tan[e + f*x]])/f + (2*a*d*(d*Tan[e + f*x])^(3/2))/(3*f) + (((2*I)/5)*a*(d*Tan[e + f*x])^(5/2))/f","A",5,3,26,0.1154,1,"{3528, 3533, 205}"
136,1,82,0,0.116535,"\int (d \tan (e+f x))^{3/2} (a+i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x]),x]","\frac{2 \sqrt[4]{-1} a d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}+\frac{2 i a (d \tan (e+f x))^{3/2}}{3 f}","\frac{2 \sqrt[4]{-1} a d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}+\frac{2 i a (d \tan (e+f x))^{3/2}}{3 f}",1,"(2*(-1)^(1/4)*a*d^(3/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + (2*a*d*Sqrt[d*Tan[e + f*x]])/f + (((2*I)/3)*a*(d*Tan[e + f*x])^(3/2))/f","A",4,3,26,0.1154,1,"{3528, 3533, 205}"
137,1,61,0,0.0727427,"\int \sqrt{d \tan (e+f x)} (a+i a \tan (e+f x)) \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x]),x]","\frac{2 (-1)^{3/4} a \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 i a \sqrt{d \tan (e+f x)}}{f}","\frac{2 (-1)^{3/4} a \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 i a \sqrt{d \tan (e+f x)}}{f}",1,"(2*(-1)^(3/4)*a*Sqrt[d]*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + ((2*I)*a*Sqrt[d*Tan[e + f*x]])/f","A",3,3,26,0.1154,1,"{3528, 3533, 205}"
138,1,40,0,0.0415236,"\int \frac{a+i a \tan (e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])/Sqrt[d*Tan[e + f*x]],x]","-\frac{2 \sqrt[4]{-1} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}","-\frac{2 \sqrt[4]{-1} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}",1,"(-2*(-1)^(1/4)*a*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f)","A",2,2,26,0.07692,1,"{3533, 205}"
139,1,62,0,0.0833165,"\int \frac{a+i a \tan (e+f x)}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(3/2),x]","-\frac{2 (-1)^{3/4} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}","-\frac{2 (-1)^{3/4} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}",1,"(-2*(-1)^(3/4)*a*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f) - (2*a)/(d*f*Sqrt[d*Tan[e + f*x]])","A",3,3,26,0.1154,1,"{3529, 3533, 205}"
140,1,87,0,0.123151,"\int \frac{a+i a \tan (e+f x)}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(5/2),x]","\frac{2 \sqrt[4]{-1} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{2 i a}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}","\frac{2 \sqrt[4]{-1} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{2 i a}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}",1,"(2*(-1)^(1/4)*a*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (2*a)/(3*d*f*(d*Tan[e + f*x])^(3/2)) - ((2*I)*a)/(d^2*f*Sqrt[d*Tan[e + f*x]])","A",4,3,26,0.1154,1,"{3529, 3533, 205}"
141,1,110,0,0.170372,"\int \frac{a+i a \tan (e+f x)}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(7/2),x]","\frac{2 (-1)^{3/4} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{2 i a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}","\frac{2 (-1)^{3/4} a \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{2 i a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}",1,"(2*(-1)^(3/4)*a*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(7/2)*f) - (2*a)/(5*d*f*(d*Tan[e + f*x])^(5/2)) - (((2*I)/3)*a)/(d^2*f*(d*Tan[e + f*x])^(3/2)) + (2*a)/(d^3*f*Sqrt[d*Tan[e + f*x]])","A",5,3,26,0.1154,1,"{3529, 3533, 205}"
142,1,107,0,0.1470936,"\int (d \tan (e+f x))^{5/2} (a-i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a - I*a*Tan[e + f*x]),x]","\frac{2 i a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 (-1)^{3/4} a d^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a (d \tan (e+f x))^{5/2}}{5 f}","\frac{2 i a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 (-1)^{3/4} a d^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a (d \tan (e+f x))^{5/2}}{5 f}",1,"(2*(-1)^(3/4)*a*d^(5/2)*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + ((2*I)*a*d^2*Sqrt[d*Tan[e + f*x]])/f + (2*a*d*(d*Tan[e + f*x])^(3/2))/(3*f) - (((2*I)/5)*a*(d*Tan[e + f*x])^(5/2))/f","A",5,3,26,0.1154,1,"{3528, 3533, 208}"
143,1,82,0,0.1063019,"\int (d \tan (e+f x))^{3/2} (a-i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a - I*a*Tan[e + f*x]),x]","\frac{2 \sqrt[4]{-1} a d^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}-\frac{2 i a (d \tan (e+f x))^{3/2}}{3 f}","\frac{2 \sqrt[4]{-1} a d^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}-\frac{2 i a (d \tan (e+f x))^{3/2}}{3 f}",1,"(2*(-1)^(1/4)*a*d^(3/2)*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + (2*a*d*Sqrt[d*Tan[e + f*x]])/f - (((2*I)/3)*a*(d*Tan[e + f*x])^(3/2))/f","A",4,3,26,0.1154,1,"{3528, 3533, 208}"
144,1,61,0,0.0681346,"\int \sqrt{d \tan (e+f x)} (a-i a \tan (e+f x)) \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a - I*a*Tan[e + f*x]),x]","-\frac{2 (-1)^{3/4} a \sqrt{d} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 i a \sqrt{d \tan (e+f x)}}{f}","-\frac{2 (-1)^{3/4} a \sqrt{d} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 i a \sqrt{d \tan (e+f x)}}{f}",1,"(-2*(-1)^(3/4)*a*Sqrt[d]*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - ((2*I)*a*Sqrt[d*Tan[e + f*x]])/f","A",3,3,26,0.1154,1,"{3528, 3533, 208}"
145,1,40,0,0.0391566,"\int \frac{a-i a \tan (e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a - I*a*Tan[e + f*x])/Sqrt[d*Tan[e + f*x]],x]","-\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}","-\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}",1,"(-2*(-1)^(1/4)*a*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f)","A",2,2,26,0.07692,1,"{3533, 208}"
146,1,62,0,0.0777917,"\int \frac{a-i a \tan (e+f x)}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a - I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(3/2),x]","\frac{2 (-1)^{3/4} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}","\frac{2 (-1)^{3/4} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}",1,"(2*(-1)^(3/4)*a*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f) - (2*a)/(d*f*Sqrt[d*Tan[e + f*x]])","A",3,3,26,0.1154,1,"{3529, 3533, 208}"
147,1,87,0,0.1251834,"\int \frac{a-i a \tan (e+f x)}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a - I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(5/2),x]","\frac{2 i a}{d^2 f \sqrt{d \tan (e+f x)}}+\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}","\frac{2 i a}{d^2 f \sqrt{d \tan (e+f x)}}+\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}",1,"(2*(-1)^(1/4)*a*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (2*a)/(3*d*f*(d*Tan[e + f*x])^(3/2)) + ((2*I)*a)/(d^2*f*Sqrt[d*Tan[e + f*x]])","A",4,3,26,0.1154,1,"{3529, 3533, 208}"
148,1,110,0,0.1704496,"\int \frac{a-i a \tan (e+f x)}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a - I*a*Tan[e + f*x])/(d*Tan[e + f*x])^(7/2),x]","\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}+\frac{2 i a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}","\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}+\frac{2 i a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}",1,"(-2*(-1)^(3/4)*a*ArcTanh[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(7/2)*f) - (2*a)/(5*d*f*(d*Tan[e + f*x])^(5/2)) + (((2*I)/3)*a)/(d^2*f*(d*Tan[e + f*x])^(3/2)) + (2*a)/(d^3*f*Sqrt[d*Tan[e + f*x]])","A",5,3,26,0.1154,1,"{3529, 3533, 208}"
149,1,140,0,0.2175043,"\int (d \tan (e+f x))^{5/2} (a+i a \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + I*a*Tan[e + f*x])^2,x]","-\frac{4 (-1)^{3/4} a^2 d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{4 i a^2 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{2 a^2 (d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 i a^2 (d \tan (e+f x))^{5/2}}{5 f}+\frac{4 a^2 d (d \tan (e+f x))^{3/2}}{3 f}","-\frac{4 (-1)^{3/4} a^2 d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{4 i a^2 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{2 a^2 (d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 i a^2 (d \tan (e+f x))^{5/2}}{5 f}+\frac{4 a^2 d (d \tan (e+f x))^{3/2}}{3 f}",1,"(-4*(-1)^(3/4)*a^2*d^(5/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - ((4*I)*a^2*d^2*Sqrt[d*Tan[e + f*x]])/f + (4*a^2*d*(d*Tan[e + f*x])^(3/2))/(3*f) + (((4*I)/5)*a^2*(d*Tan[e + f*x])^(5/2))/f - (2*a^2*(d*Tan[e + f*x])^(7/2))/(7*d*f)","A",6,4,28,0.1429,1,"{3543, 3528, 3533, 205}"
150,1,113,0,0.1731029,"\int (d \tan (e+f x))^{3/2} (a+i a \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])^2,x]","\frac{4 \sqrt[4]{-1} a^2 d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 a^2 (d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 i a^2 (d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^2 d \sqrt{d \tan (e+f x)}}{f}","\frac{4 \sqrt[4]{-1} a^2 d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 a^2 (d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 i a^2 (d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^2 d \sqrt{d \tan (e+f x)}}{f}",1,"(4*(-1)^(1/4)*a^2*d^(3/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + (4*a^2*d*Sqrt[d*Tan[e + f*x]])/f + (((4*I)/3)*a^2*(d*Tan[e + f*x])^(3/2))/f - (2*a^2*(d*Tan[e + f*x])^(5/2))/(5*d*f)","A",5,4,28,0.1429,1,"{3543, 3528, 3533, 205}"
151,1,90,0,0.1323678,"\int \sqrt{d \tan (e+f x)} (a+i a \tan (e+f x))^2 \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^2,x]","\frac{4 (-1)^{3/4} a^2 \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 a^2 (d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 i a^2 \sqrt{d \tan (e+f x)}}{f}","\frac{4 (-1)^{3/4} a^2 \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{2 a^2 (d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 i a^2 \sqrt{d \tan (e+f x)}}{f}",1,"(4*(-1)^(3/4)*a^2*Sqrt[d]*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + ((4*I)*a^2*Sqrt[d*Tan[e + f*x]])/f - (2*a^2*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",4,4,28,0.1429,1,"{3543, 3528, 3533, 205}"
152,1,66,0,0.0982788,"\int \frac{(a+i a \tan (e+f x))^2}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/Sqrt[d*Tan[e + f*x]],x]","-\frac{4 \sqrt[4]{-1} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}-\frac{2 a^2 \sqrt{d \tan (e+f x)}}{d f}","-\frac{4 \sqrt[4]{-1} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}-\frac{2 a^2 \sqrt{d \tan (e+f x)}}{d f}",1,"(-4*(-1)^(1/4)*a^2*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f) - (2*a^2*Sqrt[d*Tan[e + f*x]])/(d*f)","A",3,3,28,0.1071,1,"{3543, 3533, 205}"
153,1,66,0,0.1101973,"\int \frac{(a+i a \tan (e+f x))^2}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(d*Tan[e + f*x])^(3/2),x]","-\frac{4 (-1)^{3/4} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a^2}{d f \sqrt{d \tan (e+f x)}}","-\frac{4 (-1)^{3/4} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 a^2}{d f \sqrt{d \tan (e+f x)}}",1,"(-4*(-1)^(3/4)*a^2*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f) - (2*a^2)/(d*f*Sqrt[d*Tan[e + f*x]])","A",3,3,28,0.1071,1,"{3542, 3533, 205}"
154,1,93,0,0.1547502,"\int \frac{(a+i a \tan (e+f x))^2}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(d*Tan[e + f*x])^(5/2),x]","\frac{4 \sqrt[4]{-1} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{4 i a^2}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a^2}{3 d f (d \tan (e+f x))^{3/2}}","\frac{4 \sqrt[4]{-1} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{4 i a^2}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a^2}{3 d f (d \tan (e+f x))^{3/2}}",1,"(4*(-1)^(1/4)*a^2*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (2*a^2)/(3*d*f*(d*Tan[e + f*x])^(3/2)) - ((4*I)*a^2)/(d^2*f*Sqrt[d*Tan[e + f*x]])","A",4,4,28,0.1429,1,"{3542, 3529, 3533, 205}"
155,1,118,0,0.2032345,"\int \frac{(a+i a \tan (e+f x))^2}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(d*Tan[e + f*x])^(7/2),x]","\frac{4 (-1)^{3/4} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{4 a^2}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{4 i a^2}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 a^2}{5 d f (d \tan (e+f x))^{5/2}}","\frac{4 (-1)^{3/4} a^2 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{4 a^2}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{4 i a^2}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 a^2}{5 d f (d \tan (e+f x))^{5/2}}",1,"(4*(-1)^(3/4)*a^2*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(7/2)*f) - (2*a^2)/(5*d*f*(d*Tan[e + f*x])^(5/2)) - (((4*I)/3)*a^2)/(d^2*f*(d*Tan[e + f*x])^(3/2)) + (4*a^2)/(d^3*f*Sqrt[d*Tan[e + f*x]])","A",5,4,28,0.1429,1,"{3542, 3529, 3533, 205}"
156,1,179,0,0.3188027,"\int (d \tan (e+f x))^{5/2} (a+i a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + I*a*Tan[e + f*x])^3,x]","-\frac{8 (-1)^{3/4} a^3 d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{8 i a^3 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{7/2}}{9 d f}-\frac{40 a^3 (d \tan (e+f x))^{7/2}}{63 d f}+\frac{8 i a^3 (d \tan (e+f x))^{5/2}}{5 f}+\frac{8 a^3 d (d \tan (e+f x))^{3/2}}{3 f}","-\frac{8 (-1)^{3/4} a^3 d^{5/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{8 i a^3 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{7/2}}{9 d f}-\frac{40 a^3 (d \tan (e+f x))^{7/2}}{63 d f}+\frac{8 i a^3 (d \tan (e+f x))^{5/2}}{5 f}+\frac{8 a^3 d (d \tan (e+f x))^{3/2}}{3 f}",1,"(-8*(-1)^(3/4)*a^3*d^(5/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - ((8*I)*a^3*d^2*Sqrt[d*Tan[e + f*x]])/f + (8*a^3*d*(d*Tan[e + f*x])^(3/2))/(3*f) + (((8*I)/5)*a^3*(d*Tan[e + f*x])^(5/2))/f - (40*a^3*(d*Tan[e + f*x])^(7/2))/(63*d*f) - (2*(d*Tan[e + f*x])^(7/2)*(a^3 + I*a^3*Tan[e + f*x]))/(9*d*f)","A",7,5,28,0.1786,1,"{3556, 3592, 3528, 3533, 205}"
157,1,152,0,0.2663879,"\int (d \tan (e+f x))^{3/2} (a+i a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])^3,x]","\frac{8 \sqrt[4]{-1} a^3 d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{32 a^3 (d \tan (e+f x))^{5/2}}{35 d f}+\frac{8 i a^3 (d \tan (e+f x))^{3/2}}{3 f}+\frac{8 a^3 d \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{5/2}}{7 d f}","\frac{8 \sqrt[4]{-1} a^3 d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{32 a^3 (d \tan (e+f x))^{5/2}}{35 d f}+\frac{8 i a^3 (d \tan (e+f x))^{3/2}}{3 f}+\frac{8 a^3 d \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{5/2}}{7 d f}",1,"(8*(-1)^(1/4)*a^3*d^(3/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + (8*a^3*d*Sqrt[d*Tan[e + f*x]])/f + (((8*I)/3)*a^3*(d*Tan[e + f*x])^(3/2))/f - (32*a^3*(d*Tan[e + f*x])^(5/2))/(35*d*f) - (2*(d*Tan[e + f*x])^(5/2)*(a^3 + I*a^3*Tan[e + f*x]))/(7*d*f)","A",6,5,28,0.1786,1,"{3556, 3592, 3528, 3533, 205}"
158,1,129,0,0.2186866,"\int \sqrt{d \tan (e+f x)} (a+i a \tan (e+f x))^3 \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^3,x]","\frac{8 (-1)^{3/4} a^3 \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{8 a^3 (d \tan (e+f x))^{3/2}}{5 d f}+\frac{8 i a^3 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{3/2}}{5 d f}","\frac{8 (-1)^{3/4} a^3 \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{8 a^3 (d \tan (e+f x))^{3/2}}{5 d f}+\frac{8 i a^3 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{3/2}}{5 d f}",1,"(8*(-1)^(3/4)*a^3*Sqrt[d]*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + ((8*I)*a^3*Sqrt[d*Tan[e + f*x]])/f - (8*a^3*(d*Tan[e + f*x])^(3/2))/(5*d*f) - (2*(d*Tan[e + f*x])^(3/2)*(a^3 + I*a^3*Tan[e + f*x]))/(5*d*f)","A",5,5,28,0.1786,1,"{3556, 3592, 3528, 3533, 205}"
159,1,107,0,0.1819892,"\int \frac{(a+i a \tan (e+f x))^3}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/Sqrt[d*Tan[e + f*x]],x]","-\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}-\frac{16 a^3 \sqrt{d \tan (e+f x)}}{3 d f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{d \tan (e+f x)}}{3 d f}","-\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}-\frac{16 a^3 \sqrt{d \tan (e+f x)}}{3 d f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{d \tan (e+f x)}}{3 d f}",1,"(-8*(-1)^(1/4)*a^3*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f) - (16*a^3*Sqrt[d*Tan[e + f*x]])/(3*d*f) - (2*Sqrt[d*Tan[e + f*x]]*(a^3 + I*a^3*Tan[e + f*x]))/(3*d*f)","A",4,4,28,0.1429,1,"{3556, 3592, 3533, 205}"
160,1,80,0,0.1115145,"\int \frac{(a+i a \tan (e+f x))^3}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(3/2),x]","-\frac{8 (-1)^{3/4} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{d f \sqrt{d \tan (e+f x)}}","-\frac{8 (-1)^{3/4} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{d f \sqrt{d \tan (e+f x)}}",1,"(-8*(-1)^(3/4)*a^3*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f) - (2*(a^3 + I*a^3*Tan[e + f*x]))/(d*f*Sqrt[d*Tan[e + f*x]])","A",4,4,28,0.1429,1,"{3553, 12, 3533, 205}"
161,1,109,0,0.2037898,"\int \frac{(a+i a \tan (e+f x))^3}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(5/2),x]","\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{16 i a^3}{3 d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{3 d f (d \tan (e+f x))^{3/2}}","\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{16 i a^3}{3 d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{3 d f (d \tan (e+f x))^{3/2}}",1,"(8*(-1)^(1/4)*a^3*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (((16*I)/3)*a^3)/(d^2*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + I*a^3*Tan[e + f*x]))/(3*d*f*(d*Tan[e + f*x])^(3/2))","A",4,4,28,0.1429,1,"{3553, 3591, 3533, 205}"
162,1,132,0,0.2613558,"\int \frac{(a+i a \tan (e+f x))^3}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(7/2),x]","\frac{8 (-1)^{3/4} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{8 a^3}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{8 i a^3}{5 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{5 d f (d \tan (e+f x))^{5/2}}","\frac{8 (-1)^{3/4} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{7/2} f}+\frac{8 a^3}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{8 i a^3}{5 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{5 d f (d \tan (e+f x))^{5/2}}",1,"(8*(-1)^(3/4)*a^3*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(7/2)*f) - (((8*I)/5)*a^3)/(d^2*f*(d*Tan[e + f*x])^(3/2)) + (8*a^3)/(d^3*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + I*a^3*Tan[e + f*x]))/(5*d*f*(d*Tan[e + f*x])^(5/2))","A",5,5,28,0.1786,1,"{3553, 3591, 3529, 3533, 205}"
163,1,159,0,0.3146875,"\int \frac{(a+i a \tan (e+f x))^3}{(d \tan (e+f x))^{9/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(9/2),x]","-\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{9/2} f}+\frac{8 i a^3}{d^4 f \sqrt{d \tan (e+f x)}}+\frac{8 a^3}{3 d^3 f (d \tan (e+f x))^{3/2}}-\frac{32 i a^3}{35 d^2 f (d \tan (e+f x))^{5/2}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{7 d f (d \tan (e+f x))^{7/2}}","-\frac{8 \sqrt[4]{-1} a^3 \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{9/2} f}+\frac{8 i a^3}{d^4 f \sqrt{d \tan (e+f x)}}+\frac{8 a^3}{3 d^3 f (d \tan (e+f x))^{3/2}}-\frac{32 i a^3}{35 d^2 f (d \tan (e+f x))^{5/2}}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right)}{7 d f (d \tan (e+f x))^{7/2}}",1,"(-8*(-1)^(1/4)*a^3*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(9/2)*f) - (((32*I)/35)*a^3)/(d^2*f*(d*Tan[e + f*x])^(5/2)) + (8*a^3)/(3*d^3*f*(d*Tan[e + f*x])^(3/2)) + ((8*I)*a^3)/(d^4*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + I*a^3*Tan[e + f*x]))/(7*d*f*(d*Tan[e + f*x])^(7/2))","A",6,5,28,0.1786,1,"{3553, 3591, 3529, 3533, 205}"
164,1,312,0,0.3440643,"\int \frac{(d \tan (e+f x))^{7/2}}{a+i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^(7/2)/(a + I*a*Tan[e + f*x]),x]","\frac{\left(\frac{5}{4}-\frac{7 i}{4}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}-\frac{\left(\frac{5}{4}-\frac{7 i}{4}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}+\frac{5 d^3 \sqrt{d \tan (e+f x)}}{2 a f}-\frac{7 i d^2 (d \tan (e+f x))^{3/2}}{6 a f}+\frac{\left(\frac{5}{8}+\frac{7 i}{8}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{\left(\frac{5}{8}+\frac{7 i}{8}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d (d \tan (e+f x))^{5/2}}{2 f (a+i a \tan (e+f x))}","\frac{\left(\frac{5}{4}-\frac{7 i}{4}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}-\frac{\left(\frac{5}{4}-\frac{7 i}{4}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}+\frac{5 d^3 \sqrt{d \tan (e+f x)}}{2 a f}-\frac{7 i d^2 (d \tan (e+f x))^{3/2}}{6 a f}+\frac{\left(\frac{5}{8}+\frac{7 i}{8}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{\left(\frac{5}{8}+\frac{7 i}{8}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d (d \tan (e+f x))^{5/2}}{2 f (a+i a \tan (e+f x))}",1,"((5/4 - (7*I)/4)*d^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) - ((5/4 - (7*I)/4)*d^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) + ((5/8 + (7*I)/8)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) - ((5/8 + (7*I)/8)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) + (5*d^3*Sqrt[d*Tan[e + f*x]])/(2*a*f) - (((7*I)/6)*d^2*(d*Tan[e + f*x])^(3/2))/(a*f) - (d*(d*Tan[e + f*x])^(5/2))/(2*f*(a + I*a*Tan[e + f*x]))","A",13,9,28,0.3214,1,"{3550, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
165,1,287,0,0.2789342,"\int \frac{(d \tan (e+f x))^{5/2}}{a+i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x]),x]","-\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}+\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}-\frac{5 i d^2 \sqrt{d \tan (e+f x)}}{2 a f}+\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d (d \tan (e+f x))^{3/2}}{2 f (a+i a \tan (e+f x))}","-\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}+\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}-\frac{5 i d^2 \sqrt{d \tan (e+f x)}}{2 a f}+\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d (d \tan (e+f x))^{3/2}}{2 f (a+i a \tan (e+f x))}",1,"((-3/4 - (5*I)/4)*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) + ((3/4 + (5*I)/4)*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) + ((3/8 - (5*I)/8)*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) - ((3/8 - (5*I)/8)*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) - (((5*I)/2)*d^2*Sqrt[d*Tan[e + f*x]])/(a*f) - (d*(d*Tan[e + f*x])^(3/2))/(2*f*(a + I*a*Tan[e + f*x]))","A",12,9,28,0.3214,1,"{3550, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
166,1,260,0,0.2404035,"\int \frac{(d \tan (e+f x))^{3/2}}{a+i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x]),x]","-\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}+\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}-\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}+\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d \sqrt{d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}","-\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a f}+\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a f}-\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}+\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a f}-\frac{d \sqrt{d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}",1,"((-1/4 + (3*I)/4)*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) + ((1/4 - (3*I)/4)*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*f) - ((1/8 + (3*I)/8)*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) + ((1/8 + (3*I)/8)*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*f) - (d*Sqrt[d*Tan[e + f*x]])/(2*f*(a + I*a*Tan[e + f*x]))","A",11,8,28,0.2857,1,"{3550, 3534, 1168, 1162, 617, 204, 1165, 628}"
167,1,81,0,0.1187798,"\int \frac{\sqrt{d \tan (e+f x)}}{a+i a \tan (e+f x)} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x]),x]","\frac{(-1)^{3/4} \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a f}+\frac{i \sqrt{d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}","\frac{(-1)^{3/4} \sqrt{d} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a f}+\frac{i \sqrt{d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}",1,"((-1)^(3/4)*Sqrt[d]*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*a*f) + ((I/2)*Sqrt[d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x]))","A",3,3,28,0.1071,1,"{3549, 3533, 205}"
168,1,262,0,0.2377003,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+i a \tan (e+f x))} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])),x]","-\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{2 d f (a+i a \tan (e+f x))}-\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a \sqrt{d} f}","-\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{2 d f (a+i a \tan (e+f x))}-\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a \sqrt{d} f}+\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a \sqrt{d} f}",1,"((-3/4 + I/4)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*Sqrt[d]*f) + ((3/4 - I/4)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*Sqrt[d]*f) - ((3/8 + I/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*Sqrt[d]*f) + ((3/8 + I/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*Sqrt[d]*f) + Sqrt[d*Tan[e + f*x]]/(2*d*f*(a + I*a*Tan[e + f*x]))","A",11,8,28,0.2857,1,"{3552, 3534, 1168, 1162, 617, 204, 1165, 628}"
169,1,287,0,0.3092434,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+i a \tan (e+f x))} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])),x]","\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a d^{3/2} f}-\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a d^{3/2} f}-\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{3/2} f}+\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{3/2} f}-\frac{5}{2 a d f \sqrt{d \tan (e+f x)}}+\frac{1}{2 d f (a+i a \tan (e+f x)) \sqrt{d \tan (e+f x)}}","\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a d^{3/2} f}-\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a d^{3/2} f}-\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{3/2} f}+\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{3/2} f}-\frac{5}{2 a d f \sqrt{d \tan (e+f x)}}+\frac{1}{2 d f (a+i a \tan (e+f x)) \sqrt{d \tan (e+f x)}}",1,"((5/4 + (3*I)/4)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*d^(3/2)*f) - ((5/4 + (3*I)/4)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*d^(3/2)*f) - ((5/8 - (3*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*d^(3/2)*f) + ((5/8 - (3*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*d^(3/2)*f) - 5/(2*a*d*f*Sqrt[d*Tan[e + f*x]]) + 1/(2*d*f*Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x]))","A",12,9,28,0.3214,1,"{3552, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
170,1,314,0,0.391818,"\int \frac{1}{(d \tan (e+f x))^{5/2} (a+i a \tan (e+f x))} \, dx","Int[1/((d*Tan[e + f*x])^(5/2)*(a + I*a*Tan[e + f*x])),x]","\frac{\left(\frac{7}{4}-\frac{5 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a d^{5/2} f}-\frac{\left(\frac{7}{4}-\frac{5 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a d^{5/2} f}+\frac{5 i}{2 a d^2 f \sqrt{d \tan (e+f x)}}+\frac{\left(\frac{7}{8}+\frac{5 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{5/2} f}-\frac{\left(\frac{7}{8}+\frac{5 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{5/2} f}+\frac{1}{2 d f (a+i a \tan (e+f x)) (d \tan (e+f x))^{3/2}}-\frac{7}{6 a d f (d \tan (e+f x))^{3/2}}","\frac{\left(\frac{7}{4}-\frac{5 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a d^{5/2} f}-\frac{\left(\frac{7}{4}-\frac{5 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a d^{5/2} f}+\frac{5 i}{2 a d^2 f \sqrt{d \tan (e+f x)}}+\frac{\left(\frac{7}{8}+\frac{5 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{5/2} f}-\frac{\left(\frac{7}{8}+\frac{5 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a d^{5/2} f}+\frac{1}{2 d f (a+i a \tan (e+f x)) (d \tan (e+f x))^{3/2}}-\frac{7}{6 a d f (d \tan (e+f x))^{3/2}}",1,"((7/4 - (5*I)/4)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*d^(5/2)*f) - ((7/4 - (5*I)/4)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a*d^(5/2)*f) + ((7/8 + (5*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*d^(5/2)*f) - ((7/8 + (5*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a*d^(5/2)*f) - 7/(6*a*d*f*(d*Tan[e + f*x])^(3/2)) + ((5*I)/2)/(a*d^2*f*Sqrt[d*Tan[e + f*x]]) + 1/(2*d*f*(d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x]))","A",13,9,28,0.3214,1,"{3552, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
171,1,353,0,0.5356321,"\int \frac{(d \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(9/2)/(a + I*a*Tan[e + f*x])^2,x]","-\frac{\left(\frac{49}{16}+\frac{45 i}{16}\right) d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{49}{16}+\frac{45 i}{16}\right) d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}-\frac{45 i d^4 \sqrt{d \tan (e+f x)}}{8 a^2 f}-\frac{49 d^3 (d \tan (e+f x))^{3/2}}{24 a^2 f}+\frac{9 i d^2 (d \tan (e+f x))^{5/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{\left(\frac{49}{32}-\frac{45 i}{32}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{49}{32}-\frac{45 i}{32}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{7/2}}{4 f (a+i a \tan (e+f x))^2}","-\frac{\left(\frac{49}{16}+\frac{45 i}{16}\right) d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{49}{16}+\frac{45 i}{16}\right) d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}-\frac{45 i d^4 \sqrt{d \tan (e+f x)}}{8 a^2 f}-\frac{49 d^3 (d \tan (e+f x))^{3/2}}{24 a^2 f}+\frac{9 i d^2 (d \tan (e+f x))^{5/2}}{8 a^2 f (1+i \tan (e+f x))}+\frac{\left(\frac{49}{32}-\frac{45 i}{32}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{49}{32}-\frac{45 i}{32}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{7/2}}{4 f (a+i a \tan (e+f x))^2}",1,"((-49/16 - (45*I)/16)*d^(9/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((49/16 + (45*I)/16)*d^(9/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((49/32 - (45*I)/32)*d^(9/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) - ((49/32 - (45*I)/32)*d^(9/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) - (((45*I)/8)*d^4*Sqrt[d*Tan[e + f*x]])/(a^2*f) - (49*d^3*(d*Tan[e + f*x])^(3/2))/(24*a^2*f) + (((9*I)/8)*d^2*(d*Tan[e + f*x])^(5/2))/(a^2*f*(1 + I*Tan[e + f*x])) - (d*(d*Tan[e + f*x])^(7/2))/(4*f*(a + I*a*Tan[e + f*x])^2)","A",14,10,28,0.3571,1,"{3558, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
172,1,326,0,0.4838628,"\int \frac{(d \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(7/2)/(a + I*a*Tan[e + f*x])^2,x]","-\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}-\frac{25 d^3 \sqrt{d \tan (e+f x)}}{8 a^2 f}+\frac{7 i d^2 (d \tan (e+f x))^{3/2}}{8 a^2 f (1+i \tan (e+f x))}-\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{5/2}}{4 f (a+i a \tan (e+f x))^2}","-\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}-\frac{25 d^3 \sqrt{d \tan (e+f x)}}{8 a^2 f}+\frac{7 i d^2 (d \tan (e+f x))^{3/2}}{8 a^2 f (1+i \tan (e+f x))}-\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{5/2}}{4 f (a+i a \tan (e+f x))^2}",1,"((-25/16 + (21*I)/16)*d^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((25/16 - (21*I)/16)*d^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) - ((25/32 + (21*I)/32)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) + ((25/32 + (21*I)/32)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) - (25*d^3*Sqrt[d*Tan[e + f*x]])/(8*a^2*f) + (((7*I)/8)*d^2*(d*Tan[e + f*x])^(3/2))/(a^2*f*(1 + I*Tan[e + f*x])) - (d*(d*Tan[e + f*x])^(5/2))/(4*f*(a + I*a*Tan[e + f*x])^2)","A",13,10,28,0.3571,1,"{3558, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
173,1,301,0,0.4273648,"\int \frac{(d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{5 i d^2 \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{3/2}}{4 f (a+i a \tan (e+f x))^2}","\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{5 i d^2 \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{d (d \tan (e+f x))^{3/2}}{4 f (a+i a \tan (e+f x))^2}",1,"((9/16 + (5*I)/16)*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) - ((9/16 + (5*I)/16)*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) - ((9/32 - (5*I)/32)*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) + ((9/32 - (5*I)/32)*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) + (((5*I)/8)*d^2*Sqrt[d*Tan[e + f*x]])/(a^2*f*(1 + I*Tan[e + f*x])) - (d*(d*Tan[e + f*x])^(3/2))/(4*f*(a + I*a*Tan[e + f*x])^2)","A",12,9,28,0.3214,1,"{3558, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
174,1,297,0,0.4260347,"\int \frac{(d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{3 d \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{d \sqrt{d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}","\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{3 d \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{d \sqrt{d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}",1,"((1/16 + (3*I)/16)*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) - ((1/16 + (3*I)/16)*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((1/32 - (3*I)/32)*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) - ((1/32 - (3*I)/32)*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) + (3*d*Sqrt[d*Tan[e + f*x]])/(8*a^2*f*(1 + I*Tan[e + f*x])) - (d*Sqrt[d*Tan[e + f*x]])/(4*f*(a + I*a*Tan[e + f*x])^2)","A",12,9,28,0.3214,1,"{3558, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
175,1,299,0,0.3849108,"\int \frac{\sqrt{d \tan (e+f x)}}{(a+i a \tan (e+f x))^2} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^2,x]","-\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{i \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}+\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{i \sqrt{d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}","-\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 f}+\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 f}+\frac{i \sqrt{d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}+\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}-\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 f}+\frac{i \sqrt{d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}",1,"((-1/16 + (3*I)/16)*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((1/16 - (3*I)/16)*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*f) + ((1/32 + (3*I)/32)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) - ((1/32 + (3*I)/32)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*f) + ((I/8)*Sqrt[d*Tan[e + f*x]])/(a^2*f*(1 + I*Tan[e + f*x])) + ((I/4)*Sqrt[d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^2)","A",12,9,28,0.3214,1,"{3557, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
176,1,301,0,0.405107,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+i a \tan (e+f x))^2} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^2),x]","-\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{5 \sqrt{d \tan (e+f x)}}{8 a^2 d f (1+i \tan (e+f x))}-\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{4 d f (a+i a \tan (e+f x))^2}","-\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{5 \sqrt{d \tan (e+f x)}}{8 a^2 d f (1+i \tan (e+f x))}-\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{4 d f (a+i a \tan (e+f x))^2}",1,"((-9/16 + (5*I)/16)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*Sqrt[d]*f) + ((9/16 - (5*I)/16)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*Sqrt[d]*f) - ((9/32 + (5*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*Sqrt[d]*f) + ((9/32 + (5*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*Sqrt[d]*f) + (5*Sqrt[d*Tan[e + f*x]])/(8*a^2*d*f*(1 + I*Tan[e + f*x])) + Sqrt[d*Tan[e + f*x]]/(4*d*f*(a + I*a*Tan[e + f*x])^2)","A",12,9,28,0.3214,1,"{3559, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
177,1,326,0,0.5207254,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+i a \tan (e+f x))^2} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])^2),x]","\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{3/2} f}+\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{25}{8 a^2 d f \sqrt{d \tan (e+f x)}}+\frac{7}{8 a^2 d f (1+i \tan (e+f x)) \sqrt{d \tan (e+f x)}}+\frac{1}{4 d f (a+i a \tan (e+f x))^2 \sqrt{d \tan (e+f x)}}","\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{3/2} f}+\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{3/2} f}-\frac{25}{8 a^2 d f \sqrt{d \tan (e+f x)}}+\frac{7}{8 a^2 d f (1+i \tan (e+f x)) \sqrt{d \tan (e+f x)}}+\frac{1}{4 d f (a+i a \tan (e+f x))^2 \sqrt{d \tan (e+f x)}}",1,"((25/16 + (21*I)/16)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*d^(3/2)*f) - ((25/16 + (21*I)/16)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*d^(3/2)*f) - ((25/32 - (21*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*d^(3/2)*f) + ((25/32 - (21*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*d^(3/2)*f) - 25/(8*a^2*d*f*Sqrt[d*Tan[e + f*x]]) + 7/(8*a^2*d*f*(1 + I*Tan[e + f*x])*Sqrt[d*Tan[e + f*x]]) + 1/(4*d*f*Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^2)","A",13,10,28,0.3571,1,"{3559, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
178,1,353,0,0.5913203,"\int \frac{1}{(d \tan (e+f x))^{5/2} (a+i a \tan (e+f x))^2} \, dx","Int[1/((d*Tan[e + f*x])^(5/2)*(a + I*a*Tan[e + f*x])^2),x]","\frac{\left(\frac{49}{16}-\frac{45 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{\left(\frac{49}{16}-\frac{45 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 d^{5/2} f}+\frac{45 i}{8 a^2 d^2 f \sqrt{d \tan (e+f x)}}+\frac{\left(\frac{49}{32}+\frac{45 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{\left(\frac{49}{32}+\frac{45 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{49}{24 a^2 d f (d \tan (e+f x))^{3/2}}+\frac{9}{8 a^2 d f (1+i \tan (e+f x)) (d \tan (e+f x))^{3/2}}+\frac{1}{4 d f (a+i a \tan (e+f x))^2 (d \tan (e+f x))^{3/2}}","\frac{\left(\frac{49}{16}-\frac{45 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{\left(\frac{49}{16}-\frac{45 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^2 d^{5/2} f}+\frac{45 i}{8 a^2 d^2 f \sqrt{d \tan (e+f x)}}+\frac{\left(\frac{49}{32}+\frac{45 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{\left(\frac{49}{32}+\frac{45 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^2 d^{5/2} f}-\frac{49}{24 a^2 d f (d \tan (e+f x))^{3/2}}+\frac{9}{8 a^2 d f (1+i \tan (e+f x)) (d \tan (e+f x))^{3/2}}+\frac{1}{4 d f (a+i a \tan (e+f x))^2 (d \tan (e+f x))^{3/2}}",1,"((49/16 - (45*I)/16)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*d^(5/2)*f) - ((49/16 - (45*I)/16)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^2*d^(5/2)*f) + ((49/32 + (45*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*d^(5/2)*f) - ((49/32 + (45*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^2*d^(5/2)*f) - 49/(24*a^2*d*f*(d*Tan[e + f*x])^(3/2)) + 9/(8*a^2*d*f*(1 + I*Tan[e + f*x])*(d*Tan[e + f*x])^(3/2)) + ((45*I)/8)/(a^2*d^2*f*Sqrt[d*Tan[e + f*x]]) + 1/(4*d*f*(d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])^2)","A",14,10,28,0.3571,1,"{3559, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
179,1,370,0,0.6745076,"\int \frac{(d \tan (e+f x))^{9/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(9/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{\left(\frac{7}{4}+\frac{15 i}{8}\right) d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{7}{4}+\frac{15 i}{8}\right) d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 f}+\frac{15 i d^4 \sqrt{d \tan (e+f x)}}{4 a^3 f}+\frac{7 d^3 (d \tan (e+f x))^{3/2}}{6 f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{\left(\frac{7}{8}-\frac{15 i}{16}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{\left(\frac{7}{8}-\frac{15 i}{16}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{5 i d^2 (d \tan (e+f x))^{5/2}}{12 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{7/2}}{6 f (a+i a \tan (e+f x))^3}","\frac{\left(\frac{7}{4}+\frac{15 i}{8}\right) d^{9/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{7}{4}+\frac{15 i}{8}\right) d^{9/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 f}+\frac{15 i d^4 \sqrt{d \tan (e+f x)}}{4 a^3 f}+\frac{7 d^3 (d \tan (e+f x))^{3/2}}{6 f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{\left(\frac{7}{8}-\frac{15 i}{16}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{\left(\frac{7}{8}-\frac{15 i}{16}\right) d^{9/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{5 i d^2 (d \tan (e+f x))^{5/2}}{12 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{7/2}}{6 f (a+i a \tan (e+f x))^3}",1,"((7/4 + (15*I)/8)*d^(9/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) - ((7/4 + (15*I)/8)*d^(9/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) - ((7/8 - (15*I)/16)*d^(9/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) + ((7/8 - (15*I)/16)*d^(9/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) + (((15*I)/4)*d^4*Sqrt[d*Tan[e + f*x]])/(a^3*f) - (d*(d*Tan[e + f*x])^(7/2))/(6*f*(a + I*a*Tan[e + f*x])^3) + (((5*I)/12)*d^2*(d*Tan[e + f*x])^(5/2))/(a*f*(a + I*a*Tan[e + f*x])^2) + (7*d^3*(d*Tan[e + f*x])^(3/2))/(6*f*(a^3 + I*a^3*Tan[e + f*x]))","A",14,10,28,0.3571,1,"{3558, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
180,1,343,0,0.6107542,"\int \frac{(d \tan (e+f x))^{7/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(7/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 f}+\frac{5 d^3 \sqrt{d \tan (e+f x)}}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{i d^2 (d \tan (e+f x))^{3/2}}{3 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{5/2}}{6 f (a+i a \tan (e+f x))^3}","\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) d^{7/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) d^{7/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 f}+\frac{5 d^3 \sqrt{d \tan (e+f x)}}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}-\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) d^{7/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 f}+\frac{i d^2 (d \tan (e+f x))^{3/2}}{3 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{5/2}}{6 f (a+i a \tan (e+f x))^3}",1,"((5/16 - (7*I)/16)*d^(7/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) - ((5/16 - (7*I)/16)*d^(7/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) + ((5/32 + (7*I)/32)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) - ((5/32 + (7*I)/32)*d^(7/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) - (d*(d*Tan[e + f*x])^(5/2))/(6*f*(a + I*a*Tan[e + f*x])^3) + ((I/3)*d^2*(d*Tan[e + f*x])^(3/2))/(a*f*(a + I*a*Tan[e + f*x])^2) + (5*d^3*Sqrt[d*Tan[e + f*x]])/(8*f*(a^3 + I*a^3*Tan[e + f*x]))","A",13,9,28,0.3214,1,"{3558, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
181,1,329,0,0.5999286,"\int \frac{(d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 \sqrt{2} a^3 f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{8 \sqrt{2} a^3 f}-\frac{i d^2 \sqrt{d \tan (e+f x)}}{4 f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{i d^2 \sqrt{d \tan (e+f x)}}{4 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{3/2}}{6 f (a+i a \tan (e+f x))^3}","\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 \sqrt{2} a^3 f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{8 \sqrt{2} a^3 f}-\frac{i d^2 \sqrt{d \tan (e+f x)}}{4 f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{i d^2 \sqrt{d \tan (e+f x)}}{4 a f (a+i a \tan (e+f x))^2}-\frac{d (d \tan (e+f x))^{3/2}}{6 f (a+i a \tan (e+f x))^3}",1,"(d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(8*Sqrt[2]*a^3*f) - (d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(8*Sqrt[2]*a^3*f) - (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(16*Sqrt[2]*a^3*f) + (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(16*Sqrt[2]*a^3*f) - (d*(d*Tan[e + f*x])^(3/2))/(6*f*(a + I*a*Tan[e + f*x])^3) + ((I/4)*d^2*Sqrt[d*Tan[e + f*x]])/(a*f*(a + I*a*Tan[e + f*x])^2) - ((I/4)*d^2*Sqrt[d*Tan[e + f*x]])/(f*(a^3 + I*a^3*Tan[e + f*x]))","A",16,13,28,0.4643,1,"{3558, 3595, 3596, 12, 16, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
182,1,157,0,0.3721505,"\int \frac{(d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{\sqrt[4]{-1} d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{d \sqrt{d \tan (e+f x)}}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{d \sqrt{d \tan (e+f x)}}{6 a f (a+i a \tan (e+f x))^2}-\frac{d \sqrt{d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}","\frac{\sqrt[4]{-1} d^{3/2} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{d \sqrt{d \tan (e+f x)}}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{d \sqrt{d \tan (e+f x)}}{6 a f (a+i a \tan (e+f x))^2}-\frac{d \sqrt{d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}",1,"((-1)^(1/4)*d^(3/2)*ArcTan[((-1)^(3/4)*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(8*a^3*f) - (d*Sqrt[d*Tan[e + f*x]])/(6*f*(a + I*a*Tan[e + f*x])^3) + (d*Sqrt[d*Tan[e + f*x]])/(6*a*f*(a + I*a*Tan[e + f*x])^2) + (d*Sqrt[d*Tan[e + f*x]])/(8*f*(a^3 + I*a^3*Tan[e + f*x]))","A",7,7,28,0.2500,1,"{3558, 3596, 12, 16, 3549, 3533, 205}"
183,1,292,0,0.3717632,"\int \frac{\sqrt{d \tan (e+f x)}}{(a+i a \tan (e+f x))^3} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^3,x]","\frac{i \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 \sqrt{2} a^3 f}-\frac{i \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{8 \sqrt{2} a^3 f}+\frac{i \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}-\frac{i \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{i \sqrt{d \tan (e+f x)}}{12 a f (a+i a \tan (e+f x))^2}+\frac{i \sqrt{d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}","\frac{i \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 \sqrt{2} a^3 f}-\frac{i \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{8 \sqrt{2} a^3 f}+\frac{i \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}-\frac{i \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{16 \sqrt{2} a^3 f}+\frac{i \sqrt{d \tan (e+f x)}}{12 a f (a+i a \tan (e+f x))^2}+\frac{i \sqrt{d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}",1,"((I/8)*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) - ((I/8)*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*f) + ((I/16)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) - ((I/16)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*f) + ((I/6)*Sqrt[d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^3) + ((I/12)*Sqrt[d*Tan[e + f*x]])/(a*f*(a + I*a*Tan[e + f*x])^2)","A",14,11,28,0.3929,1,"{3557, 3596, 21, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
184,1,343,0,0.5896378,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+i a \tan (e+f x))^3} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^3),x]","-\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{5 \sqrt{d \tan (e+f x)}}{8 d f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{3 a d f (a+i a \tan (e+f x))^2}+\frac{\sqrt{d \tan (e+f x)}}{6 d f (a+i a \tan (e+f x))^3}","-\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{5 \sqrt{d \tan (e+f x)}}{8 d f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{3 a d f (a+i a \tan (e+f x))^2}+\frac{\sqrt{d \tan (e+f x)}}{6 d f (a+i a \tan (e+f x))^3}",1,"((-7/16 + (5*I)/16)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*Sqrt[d]*f) + ((7/16 - (5*I)/16)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*Sqrt[d]*f) - ((7/32 + (5*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*Sqrt[d]*f) + ((7/32 + (5*I)/32)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*Sqrt[d]*f) + Sqrt[d*Tan[e + f*x]]/(6*d*f*(a + I*a*Tan[e + f*x])^3) + Sqrt[d*Tan[e + f*x]]/(3*a*d*f*(a + I*a*Tan[e + f*x])^2) + (5*Sqrt[d*Tan[e + f*x]])/(8*d*f*(a^3 + I*a^3*Tan[e + f*x]))","A",13,9,28,0.3214,1,"{3559, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
185,1,368,0,0.6918284,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+i a \tan (e+f x))^3} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + I*a*Tan[e + f*x])^3),x]","\frac{\left(\frac{15}{8}+\frac{7 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{\left(\frac{15}{8}+\frac{7 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{\left(\frac{15}{16}-\frac{7 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 d^{3/2} f}+\frac{\left(\frac{15}{16}-\frac{7 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{15}{4 a^3 d f \sqrt{d \tan (e+f x)}}+\frac{7}{6 d f \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{d \tan (e+f x)}}+\frac{5}{12 a d f (a+i a \tan (e+f x))^2 \sqrt{d \tan (e+f x)}}+\frac{1}{6 d f (a+i a \tan (e+f x))^3 \sqrt{d \tan (e+f x)}}","\frac{\left(\frac{15}{8}+\frac{7 i}{4}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{\left(\frac{15}{8}+\frac{7 i}{4}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{\left(\frac{15}{16}-\frac{7 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 d^{3/2} f}+\frac{\left(\frac{15}{16}-\frac{7 i}{8}\right) \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} a^3 d^{3/2} f}-\frac{15}{4 a^3 d f \sqrt{d \tan (e+f x)}}+\frac{7}{6 d f \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{d \tan (e+f x)}}+\frac{5}{12 a d f (a+i a \tan (e+f x))^2 \sqrt{d \tan (e+f x)}}+\frac{1}{6 d f (a+i a \tan (e+f x))^3 \sqrt{d \tan (e+f x)}}",1,"((15/8 + (7*I)/4)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*d^(3/2)*f) - ((15/8 + (7*I)/4)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[2]*a^3*d^(3/2)*f) - ((15/16 - (7*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*d^(3/2)*f) + ((15/16 - (7*I)/8)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*a^3*d^(3/2)*f) - 15/(4*a^3*d*f*Sqrt[d*Tan[e + f*x]]) + 1/(6*d*f*Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^3) + 5/(12*a*d*f*Sqrt[d*Tan[e + f*x]]*(a + I*a*Tan[e + f*x])^2) + 7/(6*d*f*Sqrt[d*Tan[e + f*x]]*(a^3 + I*a^3*Tan[e + f*x]))","A",14,10,28,0.3571,1,"{3559, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
186,1,176,0,0.5744896,"\int \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}+\frac{7 (-1)^{3/4} \sqrt{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{i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(1+i) \sqrt{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{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}+\frac{7 (-1)^{3/4} \sqrt{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{i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{(1+i) \sqrt{a} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(7*(-1)^(3/4)*Sqrt[a]*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]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - ((I/4)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + (Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",9,9,28,0.3214,1,"{3560, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
187,1,135,0,0.3690638,"\int \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{\sqrt[4]{-1} \sqrt{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{\sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(1-i) \sqrt{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{\sqrt[4]{-1} \sqrt{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{\sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(1-i) \sqrt{a} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"-(((-1)^(1/4)*Sqrt[a]*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d) - ((1 - I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",9,9,28,0.3214,1,"{3560, 21, 3555, 3544, 205, 3599, 63, 217, 203}"
188,1,104,0,0.2696644,"\int \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 (-1)^{3/4} \sqrt{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{(1+i) \sqrt{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} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-2*(-1)^(3/4)*Sqrt[a]*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - ((1 + I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d","A",7,7,28,0.2500,1,"{3563, 3544, 205, 3599, 63, 217, 203}"
189,1,49,0,0.0667326,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{\tan (c+d x)}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[Tan[c + d*x]],x]","\frac{(1-i) \sqrt{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{(1-i) \sqrt{a} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"((1 - I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d","A",2,2,28,0.07143,1,"{3544, 205}"
190,1,82,0,0.1316547,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(3/2),x]","\frac{(1+i) \sqrt{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 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","\frac{(1+i) \sqrt{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 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"((1 + I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",3,3,28,0.1071,1,"{3548, 3544, 205}"
191,1,120,0,0.2710808,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(5/2),x]","-\frac{2 \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{(1-i) \sqrt{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 \sqrt{a+i a \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{(1-i) \sqrt{a} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"((-1 + I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*Sqrt[a + I*a*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (((2*I)/3)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",5,5,28,0.1786,1,"{3561, 3598, 12, 3544, 205}"
192,1,154,0,0.4135819,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(7/2),x]","-\frac{2 i \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{26 \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(1+i) \sqrt{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 i \sqrt{a+i a \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{26 \sqrt{a+i a \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{(1+i) \sqrt{a} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"((-1 - I)*Sqrt[a]*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*Sqrt[a + I*a*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (((2*I)/15)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(3/2)) + (26*Sqrt[a + I*a*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]])","A",6,5,28,0.1786,1,"{3561, 3598, 12, 3544, 205}"
193,1,254,0,0.8464244,"\int \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{a^2 \tan ^{\frac{7}{2}}(c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a^2 \tan ^{\frac{5}{2}}(c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{23 (-1)^{3/4} a^{3/2} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{7 a \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}-\frac{9 i a \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}","-\frac{a^2 \tan ^{\frac{7}{2}}(c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a^2 \tan ^{\frac{5}{2}}(c+d x)}{3 d \sqrt{a+i a \tan (c+d x)}}+\frac{23 (-1)^{3/4} a^{3/2} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{7 a \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}-\frac{9 i a \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}",1,"(23*(-1)^(3/4)*a^(3/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((I/3)*a^2*Tan[c + d*x]^(5/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (a^2*Tan[c + d*x]^(7/2))/(3*d*Sqrt[a + I*a*Tan[c + d*x]]) - (((9*I)/8)*a*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + (7*a*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(12*d)","A",11,10,28,0.3571,1,"{3556, 3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
194,1,217,0,0.7142393,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{a^2 \tan ^{\frac{5}{2}}(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a^2 \tan ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{11 \sqrt[4]{-1} a^{3/2} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{5 a \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}","-\frac{a^2 \tan ^{\frac{5}{2}}(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}+\frac{i a^2 \tan ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{a+i a \tan (c+d x)}}-\frac{11 \sqrt[4]{-1} a^{3/2} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{5 a \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}",1,"(-11*(-1)^(1/4)*a^(3/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + ((I/2)*a^2*Tan[c + d*x]^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (a^2*Tan[c + d*x]^(5/2))/(2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (5*a*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(4*d)","A",10,10,28,0.3571,1,"{3556, 3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
195,1,176,0,0.5734326,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{a^2 \tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 (-1)^{3/4} a^{3/2} \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{i a^2 \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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^2 \tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 (-1)^{3/4} a^{3/2} \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{i a^2 \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-3*(-1)^(3/4)*a^(3/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (I*a^2*Sqrt[Tan[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (a^2*Tan[c + d*x]^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,9,28,0.3214,1,"{3556, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
196,1,104,0,0.2830379,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Sqrt[Tan[c + d*x]],x]","\frac{2 \sqrt[4]{-1} a^{3/2} \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} \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} \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} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(2*(-1)^(1/4)*a^(3/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d","A",7,7,28,0.2500,1,"{3555, 3544, 205, 3599, 63, 217, 203}"
197,1,83,0,0.1459575,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(3/2),x]","\frac{(2+2 i) a^{3/2} \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{(2+2 i) a^{3/2} \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,"((2 + 2*I)*a^(3/2)*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",3,3,28,0.1071,1,"{3545, 3544, 205}"
198,1,119,0,0.2244343,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(5/2),x]","-\frac{(2-2 i) a^{3/2} \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+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}","-\frac{(2-2 i) a^{3/2} \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+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 i a \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}",1,"((-2 + 2*I)*a^(3/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - ((2*I)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (2*(a + I*a*Tan[c + d*x])^(3/2))/(3*d*Tan[c + d*x]^(3/2))","A",4,4,28,0.1429,1,"{3548, 3545, 3544, 205}"
199,1,198,0,0.5968708,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(7/2),x]","-\frac{2 i a^2}{5 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{2 a^2}{5 d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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 i a \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{12 a \sqrt{a+i a \tan (c+d x)}}{5 d \sqrt{\tan (c+d x)}}","-\frac{2 i a^2}{5 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{2 a^2}{5 d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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 i a \sqrt{a+i a \tan (c+d x)}}{5 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{12 a \sqrt{a+i a \tan (c+d x)}}{5 d \sqrt{\tan (c+d x)}}",1,"((-2 - 2*I)*a^(3/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2)/(5*d*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/5)*a^2)/(d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((4*I)/5)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(3/2)) + (12*a*Sqrt[a + I*a*Tan[c + d*x]])/(5*d*Sqrt[Tan[c + d*x]])","A",7,6,28,0.2143,1,"{3553, 3596, 3598, 12, 3544, 205}"
200,1,235,0,0.7441447,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(9/2),x]","-\frac{2 i a^2}{7 d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{2 a^2}{7 d \tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(2-2 i) a^{3/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{76 a \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{16 i a \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{268 i a \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}","-\frac{2 i a^2}{7 d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{2 a^2}{7 d \tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{(2-2 i) a^{3/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}+\frac{76 a \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{16 i a \sqrt{a+i a \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{268 i a \sqrt{a+i a \tan (c+d x)}}{105 d \sqrt{\tan (c+d x)}}",1,"((2 - 2*I)*a^(3/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2)/(7*d*Tan[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((2*I)/7)*a^2)/(d*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (((16*I)/35)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(5/2)) + (76*a*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(3/2)) + (((268*I)/105)*a*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",8,6,28,0.2143,1,"{3553, 3596, 3598, 12, 3544, 205}"
201,1,258,0,0.841514,"\int \tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{a^2 \tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{17 i a^2 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{107 a^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{363 (-1)^{3/4} a^{5/2} \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{149 i a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{(4+4 i) a^{5/2} \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^2 \tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{4 d}+\frac{17 i a^2 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{24 d}+\frac{107 a^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{96 d}+\frac{363 (-1)^{3/4} a^{5/2} \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{149 i a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{64 d}+\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(363*(-1)^(3/4)*a^(5/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (((149*I)/64)*a^2*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + (107*a^2*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(96*d) + (((17*I)/24)*a^2*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (a^2*Tan[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d)","A",11,9,28,0.3214,1,"{3556, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
202,1,219,0,0.7028641,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{45 \sqrt[4]{-1} a^{5/2} \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 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{13 i a^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{19 a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","-\frac{45 \sqrt[4]{-1} a^{5/2} \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 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}+\frac{13 i a^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{12 d}+\frac{19 a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{8 d}-\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-45*(-1)^(1/4)*a^(5/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (19*a^2*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(8*d) + (((13*I)/12)*a^2*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (a^2*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",10,9,28,0.3214,1,"{3556, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
203,1,182,0,0.5491874,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{23 (-1)^{3/4} a^{5/2} \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 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}+\frac{9 i a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","-\frac{23 (-1)^{3/4} a^{5/2} \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 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 d}+\frac{9 i a^2 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 d}-\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(-23*(-1)^(3/4)*a^(5/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (((9*I)/4)*a^2*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (a^2*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(2*d)","A",9,9,28,0.3214,1,"{3556, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
204,1,139,0,0.4067666,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Sqrt[Tan[c + d*x]],x]","\frac{5 \sqrt[4]{-1} a^{5/2} \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 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","\frac{5 \sqrt[4]{-1} a^{5/2} \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 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(5*(-1)^(1/4)*a^(5/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (a^2*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",8,8,28,0.2857,1,"{3556, 3601, 3544, 205, 3599, 63, 217, 203}"
205,1,139,0,0.4160931,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(3/2),x]","\frac{2 (-1)^{3/4} a^{5/2} \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^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} \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} \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^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"(2*(-1)^(3/4)*a^(5/2)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",8,8,28,0.2857,1,"{3553, 3601, 3544, 205, 3599, 63, 217, 203}"
206,1,122,0,0.20735,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(5/2),x]","-\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(4-4 i) a^{5/2} \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+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{4 i a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(4-4 i) a^{5/2} \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+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"((-4 + 4*I)*a^(5/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - ((4*I)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (2*a*(a + I*a*Tan[c + d*x])^(3/2))/(3*d*Tan[c + d*x]^(3/2))","A",4,3,28,0.1071,1,"{3545, 3544, 205}"
207,1,156,0,0.2819749,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(7/2),x]","\frac{4 a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(4+4 i) a^{5/2} \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 i a (a+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (a+i a \tan (c+d x))^{5/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{4 a^2 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{(4+4 i) a^{5/2} \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 i a (a+i a \tan (c+d x))^{3/2}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 (a+i a \tan (c+d x))^{5/2}}{5 d \tan ^{\frac{5}{2}}(c+d x)}",1,"((-4 - 4*I)*a^(5/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d + (4*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]]) - (((2*I)/3)*a*(a + I*a*Tan[c + d*x])^(3/2))/(d*Tan[c + d*x]^(3/2)) - (2*(a + I*a*Tan[c + d*x])^(5/2))/(5*d*Tan[c + d*x]^(5/2))","A",5,4,28,0.1429,1,"{3548, 3545, 3544, 205}"
208,1,202,0,0.5706109,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(9/2),x]","\frac{32 a^2 \sqrt{a+i a \tan (c+d x)}}{21 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{6 i a^2 \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}+\frac{104 i a^2 \sqrt{a+i a \tan (c+d x)}}{21 d \sqrt{\tan (c+d x)}}+\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","\frac{32 a^2 \sqrt{a+i a \tan (c+d x)}}{21 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{6 i a^2 \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}+\frac{104 i a^2 \sqrt{a+i a \tan (c+d x)}}{21 d \sqrt{\tan (c+d x)}}+\frac{(4-4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"((4 - 4*I)*a^(5/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (((6*I)/7)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(5/2)) + (32*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(21*d*Tan[c + d*x]^(3/2)) + (((104*I)/21)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",7,5,28,0.1786,1,"{3553, 3598, 12, 3544, 205}"
209,1,239,0,0.7402304,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(11/2),x]","\frac{472 i a^2 \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{92 a^2 \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{38 i a^2 \sqrt{a+i a \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{1576 a^2 \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}","\frac{472 i a^2 \sqrt{a+i a \tan (c+d x)}}{315 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{92 a^2 \sqrt{a+i a \tan (c+d x)}}{105 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{38 i a^2 \sqrt{a+i a \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{2 a^2 \sqrt{a+i a \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{1576 a^2 \sqrt{a+i a \tan (c+d x)}}{315 d \sqrt{\tan (c+d x)}}+\frac{(4+4 i) a^{5/2} \tanh ^{-1}\left(\frac{(1+i) \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{d}",1,"((4 + 4*I)*a^(5/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(9*d*Tan[c + d*x]^(9/2)) - (((38*I)/63)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(7/2)) + (92*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(5/2)) + (((472*I)/315)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Tan[c + d*x]^(3/2)) - (1576*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(315*d*Sqrt[Tan[c + d*x]])","A",8,5,28,0.1786,1,"{3553, 3598, 12, 3544, 205}"
210,1,218,0,0.6893397,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(7/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{\tan ^{\frac{5}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{11 \sqrt[4]{-1} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{a} d}+\frac{7 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 a d}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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{\tan ^{\frac{5}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{3 i \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a d}+\frac{11 \sqrt[4]{-1} \tan ^{-1}\left(\frac{(-1)^{3/4} \sqrt{a} \sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}}\right)}{4 \sqrt{a} d}+\frac{7 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 a d}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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,"(11*(-1)^(1/4)*ArcTan[((-1)^(3/4)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(4*Sqrt[a]*d) + ((1/2 - I/2)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) - Tan[c + d*x]^(5/2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (7*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(4*a*d) - (((3*I)/2)*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",10,9,28,0.3214,1,"{3558, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
211,1,177,0,0.5449766,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(5/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{\tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(-1)^{3/4} \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{2 i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{\tan ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}-\frac{(-1)^{3/4} \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{2 i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) - Tan[c + d*x]^(3/2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) - ((2*I)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",9,9,28,0.3214,1,"{3558, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
212,1,140,0,0.4018351,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(3/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 \sqrt[4]{-1} \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{\sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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} \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{\sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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,"(-2*(-1)^(1/4)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) - Sqrt[Tan[c + d*x]]/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",8,8,28,0.2857,1,"{3558, 3601, 3544, 205, 3599, 63, 217, 203}"
213,1,88,0,0.1339051,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{i \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{i \sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + (I*Sqrt[Tan[c + d*x]])/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",3,3,28,0.1071,1,"{3546, 3544, 205}"
214,1,85,0,0.2001983,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{\sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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{\sqrt{\tan (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + Sqrt[Tan[c + d*x]]/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3548, 3546, 3544, 205}"
215,1,120,0,0.2689127,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{3 \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{1}{d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{3 \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{1}{d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + 1/(d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (3*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",5,5,28,0.1786,1,"{3559, 3598, 12, 3544, 205}"
216,1,161,0,0.4091431,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{5 \sqrt{a+i a \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{1}{d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \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) \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 \sqrt{a+i a \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{1}{d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \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) \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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + 1/(d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (5*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d*Tan[c + d*x]^(3/2)) + (((7*I)/3)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",6,5,28,0.1786,1,"{3559, 3598, 12, 3544, 205}"
217,1,198,0,0.5590271,"\int \frac{1}{\tan ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{23 i \sqrt{a+i a \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{7 \sqrt{a+i a \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{1}{d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{61 \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) \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{23 i \sqrt{a+i a \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{7 \sqrt{a+i a \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}+\frac{1}{d \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{61 \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) \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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(Sqrt[a]*d) + 1/(d*Tan[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Sqrt[a + I*a*Tan[c + d*x]])/(5*a*d*Tan[c + d*x]^(5/2)) + (((23*I)/15)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Tan[c + d*x]^(3/2)) + (61*Sqrt[a + I*a*Tan[c + d*x]])/(15*a*d*Sqrt[Tan[c + d*x]])","A",7,5,28,0.1786,1,"{3559, 3598, 12, 3544, 205}"
218,1,218,0,0.6907291,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(7/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{3 \sqrt[4]{-1} \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{7 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{\tan ^{\frac{5}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{13 i \tan ^{\frac{3}{2}}(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}","-\frac{3 \sqrt[4]{-1} \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{7 \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{\tan ^{\frac{5}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{13 i \tan ^{\frac{3}{2}}(c+d x)}{6 a d \sqrt{a+i a \tan (c+d x)}}",1,"(-3*(-1)^(1/4)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) - Tan[c + d*x]^(5/2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((13*I)/6)*Tan[c + d*x]^(3/2))/(a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d)","A",10,10,28,0.3571,1,"{3558, 3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
219,1,181,0,0.5450881,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(5/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 (-1)^{3/4} \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{\left(\frac{1}{4}+\frac{i}{4}\right) \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{\tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{3 i \sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}","\frac{2 (-1)^{3/4} \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{\left(\frac{1}{4}+\frac{i}{4}\right) \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{\tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{3 i \sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"(2*(-1)^(3/4)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) - Tan[c + d*x]^(3/2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (((3*I)/2)*Sqrt[Tan[c + d*x]])/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",9,9,28,0.3214,1,"{3558, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
220,1,127,0,0.2060644,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{i \tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{\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) \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{i \tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{\sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 + I/4)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + ((I/3)*Tan[c + d*x]^(3/2))/(d*(a + I*a*Tan[c + d*x])^(3/2)) + Sqrt[Tan[c + d*x]]/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,3,28,0.1071,1,"{3546, 3544, 205}"
221,1,127,0,0.2044835,"\int \frac{\sqrt{\tan (c+d x)}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \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{\tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{i \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) \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{\tan ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}+\frac{i \sqrt{\tan (c+d x)}}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 - I/4)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + Tan[c + d*x]^(3/2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + ((I/2)*Sqrt[Tan[c + d*x]])/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3547, 3546, 3544, 205}"
222,1,125,0,0.2767483,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{7 \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{7 \sqrt{\tan (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\sqrt{\tan (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((1/4 - I/4)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + Sqrt[Tan[c + d*x]]/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (7*Sqrt[Tan[c + d*x]])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,28,0.1786,1,"{3559, 3596, 12, 3544, 205}"
223,1,162,0,0.4188333,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{25 \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) \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{11}{6 a d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}","-\frac{25 \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) \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{11}{6 a d \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}",1,"((1/4 + I/4)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + 1/(3*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + 11/(6*a*d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (25*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d*Sqrt[Tan[c + d*x]])","A",6,6,28,0.2143,1,"{3559, 3596, 3598, 12, 3544, 205}"
224,1,201,0,0.5765897,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{7 \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{13 i \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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}{2 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}","-\frac{7 \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{13 i \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \sqrt{\tan (c+d x)}}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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}{2 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}",1,"((-1/4 + I/4)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(3/2)*d) + 1/(3*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + 5/(2*a*d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d*Tan[c + d*x]^(3/2)) + (((13*I)/2)*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d*Sqrt[Tan[c + d*x]])","A",7,6,28,0.2143,1,"{3559, 3596, 3598, 12, 3544, 205}"
225,1,257,0,0.8620194,"\int \frac{\tan ^{\frac{9}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(9/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{41 \tan ^{\frac{3}{2}}(c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{5 (-1)^{3/4} \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{21 i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \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{\tan ^{\frac{7}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{19 i \tan ^{\frac{5}{2}}(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}","\frac{41 \tan ^{\frac{3}{2}}(c+d x)}{12 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{5 (-1)^{3/4} \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{21 i \sqrt{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}{4 a^3 d}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \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{\tan ^{\frac{7}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{19 i \tan ^{\frac{5}{2}}(c+d x)}{30 a d (a+i a \tan (c+d x))^{3/2}}",1,"(5*(-1)^(3/4)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) - Tan[c + d*x]^(7/2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (((19*I)/30)*Tan[c + d*x]^(5/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (41*Tan[c + d*x]^(3/2))/(12*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((21*I)/4)*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d)","A",11,10,28,0.3571,1,"{3558, 3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
226,1,218,0,0.7142377,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(7/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 \sqrt[4]{-1} \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{7 \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) \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{\tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{i \tan ^{\frac{3}{2}}(c+d x)}{2 a d (a+i a \tan (c+d x))^{3/2}}","\frac{2 \sqrt[4]{-1} \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{7 \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) \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{\tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{i \tan ^{\frac{3}{2}}(c+d x)}{2 a d (a+i a \tan (c+d x))^{3/2}}",1,"(2*(-1)^(1/4)*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)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) - Tan[c + d*x]^(5/2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((I/2)*Tan[c + d*x]^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (7*Sqrt[Tan[c + d*x]])/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",10,9,28,0.3214,1,"{3558, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
227,1,166,0,0.287158,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(5/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i \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) \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{i \tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{\tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}","-\frac{i \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) \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{i \tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{\tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}",1,"((1/8 + I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((I/5)*Tan[c + d*x]^(5/2))/(d*(a + I*a*Tan[c + d*x])^(5/2)) + Tan[c + d*x]^(3/2)/(6*a*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I/4)*Sqrt[Tan[c + d*x]])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,3,28,0.1071,1,"{3546, 3544, 205}"
228,1,164,0,0.2821228,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{\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) \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{\tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{i \tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}","\frac{\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) \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{\tan ^{\frac{5}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}+\frac{i \tan ^{\frac{3}{2}}(c+d x)}{6 a d (a+i a \tan (c+d x))^{3/2}}",1,"((-1/8 + I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + Tan[c + d*x]^(5/2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + ((I/6)*Tan[c + d*x]^(3/2))/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) + Sqrt[Tan[c + d*x]]/(4*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,28,0.1429,1,"{3547, 3546, 3544, 205}"
229,1,168,0,0.4243739,"\int \frac{\sqrt{\tan (c+d x)}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{i \sqrt{\tan (c+d x)}}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \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{i \sqrt{\tan (c+d x)}}{10 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}","-\frac{i \sqrt{\tan (c+d x)}}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \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{i \sqrt{\tan (c+d x)}}{10 a d (a+i a \tan (c+d x))^{3/2}}+\frac{i \sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 - I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + ((I/5)*Sqrt[Tan[c + d*x]])/(d*(a + I*a*Tan[c + d*x])^(5/2)) + ((I/10)*Sqrt[Tan[c + d*x]])/(a*d*(a + I*a*Tan[c + d*x])^(3/2)) - ((I/20)*Sqrt[Tan[c + d*x]])/(a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,28,0.1786,1,"{3557, 3596, 12, 3544, 205}"
230,1,162,0,0.4392592,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{67 \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) \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{13 \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}","\frac{67 \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) \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{13 \sqrt{\tan (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\sqrt{\tan (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 - I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + Sqrt[Tan[c + d*x]]/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (13*Sqrt[Tan[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (67*Sqrt[Tan[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,28,0.1786,1,"{3559, 3596, 12, 3544, 205}"
231,1,199,0,0.5968928,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{317 \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{151}{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) \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{17}{30 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}}","-\frac{317 \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \sqrt{\tan (c+d x)}}+\frac{151}{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) \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{17}{30 a d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 + I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + 1/(5*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + 17/(30*a*d*Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + 151/(60*a^2*d*Sqrt[Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]) - (317*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*Sqrt[Tan[c + d*x]])","A",7,6,28,0.2143,1,"{3559, 3596, 3598, 12, 3544, 205}"
232,1,238,0,0.7548817,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{361 \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{89}{20 a^2 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{707 i \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) \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}{10 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","-\frac{361 \sqrt{a+i a \tan (c+d x)}}{60 a^3 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{89}{20 a^2 d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}+\frac{707 i \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) \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}{10 a d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 + I/8)*ArcTanh[((1 + I)*Sqrt[a]*Sqrt[Tan[c + d*x]])/Sqrt[a + I*a*Tan[c + d*x]]])/(a^(5/2)*d) + 1/(5*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)) + 7/(10*a*d*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + 89/(20*a^2*d*Tan[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (361*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d*Tan[c + d*x]^(3/2)) + (((707*I)/60)*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d*Sqrt[Tan[c + d*x]])","A",8,6,28,0.2143,1,"{3559, 3596, 3598, 12, 3544, 205}"
233,1,343,0,0.4578123,"\int \frac{\tan ^{\frac{10}{3}}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(10/3)/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^{\frac{7}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{5 i \tan ^{\frac{4}{3}}(c+d x)}{4 a d}+\frac{7 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{7 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{5 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}-\frac{7 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{7 \sqrt[3]{\tan (c+d x)}}{2 a d}-\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{7 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{7 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{5 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}","-\frac{\tan ^{\frac{7}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{5 i \tan ^{\frac{4}{3}}(c+d x)}{4 a d}+\frac{7 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{7 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{5 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}-\frac{7 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{7 \sqrt[3]{\tan (c+d x)}}{2 a d}-\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{7 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{7 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{5 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}",1,"(7*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(12*a*d) - (7*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(12*a*d) - (((5*I)/2)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a*d) - (7*ArcTan[Tan[c + d*x]^(1/3)])/(6*a*d) - (((5*I)/6)*Log[1 + Tan[c + d*x]^(2/3)])/(a*d) + (7*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(8*Sqrt[3]*a*d) - (7*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(8*Sqrt[3]*a*d) + (((5*I)/12)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a*d) + (7*Tan[c + d*x]^(1/3))/(2*a*d) - (((5*I)/4)*Tan[c + d*x]^(4/3))/(a*d) - Tan[c + d*x]^(7/3)/(2*d*(a + I*a*Tan[c + d*x]))","A",25,14,26,0.5385,1,"{3550, 3528, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
234,1,319,0,0.4955872,"\int \frac{\tan ^{\frac{8}{3}}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(8/3)/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^{\frac{5}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{2 i \tan ^{\frac{2}{3}}(c+d x)}{a d}-\frac{5 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{5 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{2 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}+\frac{5 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{2 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}+\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}","-\frac{\tan ^{\frac{5}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{2 i \tan ^{\frac{2}{3}}(c+d x)}{a d}-\frac{5 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{5 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{2 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}+\frac{5 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{2 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}+\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}",1,"(-5*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(12*a*d) + (5*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(12*a*d) - ((2*I)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a*d) + (5*ArcTan[Tan[c + d*x]^(1/3)])/(6*a*d) + (((2*I)/3)*Log[1 + Tan[c + d*x]^(2/3)])/(a*d) + (5*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(8*Sqrt[3]*a*d) - (5*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(8*Sqrt[3]*a*d) - ((I/3)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a*d) - ((2*I)*Tan[c + d*x]^(2/3))/(a*d) - Tan[c + d*x]^(5/3)/(2*d*(a + I*a*Tan[c + d*x]))","A",24,14,26,0.5385,1,"{3550, 3528, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
235,1,299,0,0.3936562,"\int \frac{\tan ^{\frac{4}{3}}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(4/3)/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}-\frac{\sqrt[3]{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}","-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}-\frac{\sqrt[3]{\tan (c+d x)}}{2 d (a+i a \tan (c+d x))}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}",1,"-ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)]/(12*a*d) + ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)]/(12*a*d) + (I*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a*d) + ArcTan[Tan[c + d*x]^(1/3)]/(6*a*d) + ((I/3)*Log[1 + Tan[c + d*x]^(2/3)])/(a*d) - Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(8*Sqrt[3]*a*d) + Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(8*Sqrt[3]*a*d) - ((I/6)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a*d) - Tan[c + d*x]^(1/3)/(2*d*(a + I*a*Tan[c + d*x]))","A",23,13,26,0.5000,1,"{3550, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
236,1,303,0,0.4595185,"\int \frac{\tan ^{\frac{2}{3}}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(2/3)/(a + I*a*Tan[c + d*x]),x]","-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{i \tan ^{\frac{2}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}","-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{i \tan ^{\frac{2}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}",1,"-ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)]/(12*a*d) + ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)]/(12*a*d) + ((I/2)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a*d) + ArcTan[Tan[c + d*x]^(1/3)]/(6*a*d) - ((I/6)*Log[1 + Tan[c + d*x]^(2/3)])/(a*d) + Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(8*Sqrt[3]*a*d) - Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(8*Sqrt[3]*a*d) + ((I/12)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a*d) + ((I/2)*Tan[c + d*x]^(2/3))/(d*(a + I*a*Tan[c + d*x]))","A",23,13,26,0.5000,1,"{3549, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
237,1,303,0,0.4674264,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} (a+i a \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(1/3)*(a + I*a*Tan[c + d*x])),x]","\frac{i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{\tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}-\frac{i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{\tan ^{\frac{2}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}","\frac{i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}-\frac{\tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}-\frac{i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{\tan ^{\frac{2}{3}}(c+d x)}{2 d (a+i a \tan (c+d x))}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}",1,"((I/12)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a*d) - ((I/12)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a*d) - ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]]/(Sqrt[3]*a*d) - ((I/6)*ArcTan[Tan[c + d*x]^(1/3)])/(a*d) + Log[1 + Tan[c + d*x]^(2/3)]/(3*a*d) - ((I/8)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) + ((I/8)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) - Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)]/(6*a*d) + Tan[c + d*x]^(2/3)/(2*d*(a + I*a*Tan[c + d*x]))","A",23,13,26,0.5000,1,"{3552, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
238,1,321,0,0.4171091,"\int \frac{1}{\tan ^{\frac{5}{3}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(5/3)*(a + I*a*Tan[c + d*x])),x]","\frac{5 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{5 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{2 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}-\frac{5 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}-\frac{2}{a d \tan ^{\frac{2}{3}}(c+d x)}+\frac{1}{2 d \tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))}+\frac{2 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}+\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}","\frac{5 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}-\frac{5 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{2 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{\sqrt{3} a d}-\frac{5 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}-\frac{2}{a d \tan ^{\frac{2}{3}}(c+d x)}+\frac{1}{2 d \tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))}+\frac{2 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}+\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{3 a d}",1,"(((5*I)/12)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a*d) - (((5*I)/12)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a*d) + (2*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a*d) - (((5*I)/6)*ArcTan[Tan[c + d*x]^(1/3)])/(a*d) + (2*Log[1 + Tan[c + d*x]^(2/3)])/(3*a*d) + (((5*I)/8)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) - (((5*I)/8)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) - Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)]/(3*a*d) - 2/(a*d*Tan[c + d*x]^(2/3)) + 1/(2*d*Tan[c + d*x]^(2/3)*(a + I*a*Tan[c + d*x]))","A",24,14,26,0.5385,1,"{3552, 3529, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
239,1,347,0,0.5309173,"\int \frac{1}{\tan ^{\frac{7}{3}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(7/3)*(a + I*a*Tan[c + d*x])),x]","-\frac{7 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{7 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{5 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}+\frac{7 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{1}{2 d \tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))}-\frac{5}{4 a d \tan ^{\frac{4}{3}}(c+d x)}+\frac{7 i}{2 a d \sqrt[3]{\tan (c+d x)}}-\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{5 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}","-\frac{7 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{12 a d}+\frac{7 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{12 a d}+\frac{5 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 \sqrt{3} a d}+\frac{7 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{6 a d}+\frac{1}{2 d \tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))}-\frac{5}{4 a d \tan ^{\frac{4}{3}}(c+d x)}+\frac{7 i}{2 a d \sqrt[3]{\tan (c+d x)}}-\frac{5 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{6 a d}+\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}-\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{8 \sqrt{3} a d}+\frac{5 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{12 a d}",1,"(((-7*I)/12)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a*d) + (((7*I)/12)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a*d) + (5*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(2*Sqrt[3]*a*d) + (((7*I)/6)*ArcTan[Tan[c + d*x]^(1/3)])/(a*d) - (5*Log[1 + Tan[c + d*x]^(2/3)])/(6*a*d) + (((7*I)/8)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) - (((7*I)/8)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a*d) + (5*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(12*a*d) - 5/(4*a*d*Tan[c + d*x]^(4/3)) + ((7*I)/2)/(a*d*Tan[c + d*x]^(1/3)) + 1/(2*d*Tan[c + d*x]^(4/3)*(a + I*a*Tan[c + d*x]))","A",25,14,26,0.5385,1,"{3552, 3529, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
240,1,379,0,0.6638252,"\int \frac{\tan ^{\frac{14}{3}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(14/3)/(a + I*a*Tan[c + d*x])^2,x]","\frac{7 i \tan ^{\frac{8}{3}}(c+d x)}{6 a^2 d (1+i \tan (c+d x))}-\frac{121 \tan ^{\frac{5}{3}}(c+d x)}{60 a^2 d}-\frac{14 i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d}-\frac{121 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{121 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}-\frac{14 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{121 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{14 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{121 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{121 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{7 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{\tan ^{\frac{11}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{7 i \tan ^{\frac{8}{3}}(c+d x)}{6 a^2 d (1+i \tan (c+d x))}-\frac{121 \tan ^{\frac{5}{3}}(c+d x)}{60 a^2 d}-\frac{14 i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d}-\frac{121 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{121 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}-\frac{14 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{121 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{14 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{121 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{121 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{7 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{\tan ^{\frac{11}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-121*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) + (121*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) - (((14*I)/3)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a^2*d) + (121*ArcTan[Tan[c + d*x]^(1/3)])/(36*a^2*d) + (((14*I)/9)*Log[1 + Tan[c + d*x]^(2/3)])/(a^2*d) + (121*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) - (121*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) - (((7*I)/9)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a^2*d) - (((14*I)/3)*Tan[c + d*x]^(2/3))/(a^2*d) - (121*Tan[c + d*x]^(5/3))/(60*a^2*d) + (((7*I)/6)*Tan[c + d*x]^(8/3))/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^(11/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",26,15,26,0.5769,1,"{3558, 3595, 3528, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
241,1,357,0,0.5622699,"\int \frac{\tan ^{\frac{10}{3}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(10/3)/(a + I*a*Tan[c + d*x])^2,x]","\frac{5 i \tan ^{\frac{4}{3}}(c+d x)}{6 a^2 d (1+i \tan (c+d x))}-\frac{49 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{49 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{5 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{49 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{49 \sqrt[3]{\tan (c+d x)}}{12 a^2 d}+\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{49 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{49 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{5 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}-\frac{\tan ^{\frac{7}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{5 i \tan ^{\frac{4}{3}}(c+d x)}{6 a^2 d (1+i \tan (c+d x))}-\frac{49 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{49 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{5 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{49 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{49 \sqrt[3]{\tan (c+d x)}}{12 a^2 d}+\frac{5 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{49 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{49 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{5 i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}-\frac{\tan ^{\frac{7}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(-49*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) + (49*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) + (((5*I)/3)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a^2*d) + (49*ArcTan[Tan[c + d*x]^(1/3)])/(36*a^2*d) + (((5*I)/9)*Log[1 + Tan[c + d*x]^(2/3)])/(a^2*d) - (49*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) + (49*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) - (((5*I)/18)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a^2*d) - (49*Tan[c + d*x]^(1/3))/(12*a^2*d) + (((5*I)/6)*Tan[c + d*x]^(4/3))/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^(7/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",25,15,26,0.5769,1,"{3558, 3595, 3528, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
242,1,337,0,0.5872984,"\int \frac{\tan ^{\frac{8}{3}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(8/3)/(a + I*a*Tan[c + d*x])^2,x]","\frac{2 i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d (1+i \tan (c+d x))}+\frac{25 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{25 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{2 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{25 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{2 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{\tan ^{\frac{5}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{2 i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d (1+i \tan (c+d x))}+\frac{25 \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{25 \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{2 i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{25 \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{2 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{\tan ^{\frac{5}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(25*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) - (25*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(72*a^2*d) + (((2*I)/3)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a^2*d) - (25*ArcTan[Tan[c + d*x]^(1/3)])/(36*a^2*d) - (((2*I)/9)*Log[1 + Tan[c + d*x]^(2/3)])/(a^2*d) - (25*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) + (25*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(48*Sqrt[3]*a^2*d) + ((I/9)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a^2*d) + (((2*I)/3)*Tan[c + d*x]^(2/3))/(a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^(5/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",24,14,26,0.5385,1,"{3558, 3595, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
243,1,335,0,0.5267974,"\int \frac{\tan ^{\frac{4}{3}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(4/3)/(a + I*a*Tan[c + d*x])^2,x]","\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{\sqrt[3]{\tan (c+d x)}}{3 a^2 d (1+i \tan (c+d x))}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}-\frac{\sqrt[3]{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}","\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{\sqrt[3]{\tan (c+d x)}}{3 a^2 d (1+i \tan (c+d x))}+\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}-\frac{\sqrt[3]{\tan (c+d x)}}{4 d (a+i a \tan (c+d x))^2}",1,"ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)]/(72*a^2*d) - ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)]/(72*a^2*d) + ((I/3)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a^2*d) - ArcTan[Tan[c + d*x]^(1/3)]/(36*a^2*d) + ((I/9)*Log[1 + Tan[c + d*x]^(2/3)])/(a^2*d) + Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(48*Sqrt[3]*a^2*d) - Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(48*Sqrt[3]*a^2*d) - ((I/18)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a^2*d) + Tan[c + d*x]^(1/3)/(3*a^2*d*(1 + I*Tan[c + d*x])) - Tan[c + d*x]^(1/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",24,14,26,0.5385,1,"{3558, 3596, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
244,1,337,0,0.5884463,"\int \frac{\tan ^{\frac{2}{3}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(2/3)/(a + I*a*Tan[c + d*x])^2,x]","\frac{i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d (1+i \tan (c+d x))}-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}+\frac{\tan ^{\frac{5}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{i \tan ^{\frac{2}{3}}(c+d x)}{3 a^2 d (1+i \tan (c+d x))}-\frac{\tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{\tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{i \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}+\frac{\tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{i \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{i \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}+\frac{\tan ^{\frac{5}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"-ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)]/(72*a^2*d) + ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)]/(72*a^2*d) + ((I/3)*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(Sqrt[3]*a^2*d) + ArcTan[Tan[c + d*x]^(1/3)]/(36*a^2*d) - ((I/9)*Log[1 + Tan[c + d*x]^(2/3)])/(a^2*d) + Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(48*Sqrt[3]*a^2*d) - Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)]/(48*Sqrt[3]*a^2*d) + ((I/18)*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(a^2*d) + ((I/3)*Tan[c + d*x]^(2/3))/(a^2*d*(1 + I*Tan[c + d*x])) + Tan[c + d*x]^(5/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",24,14,26,0.5385,1,"{3559, 3595, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
245,1,339,0,0.5892713,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[1/(Tan[c + d*x]^(1/3)*(a + I*a*Tan[c + d*x])^2),x]","\frac{7 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{7 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}-\frac{2 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{7 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{7 \tan ^{\frac{2}{3}}(c+d x)}{12 a^2 d (1+i \tan (c+d x))}+\frac{2 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\tan ^{\frac{2}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}","\frac{7 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{7 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}-\frac{2 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{7 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}+\frac{7 \tan ^{\frac{2}{3}}(c+d x)}{12 a^2 d (1+i \tan (c+d x))}+\frac{2 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}-\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{7 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{\log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{\tan ^{\frac{2}{3}}(c+d x)}{4 d (a+i a \tan (c+d x))^2}",1,"(((7*I)/72)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a^2*d) - (((7*I)/72)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a^2*d) - (2*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(3*Sqrt[3]*a^2*d) - (((7*I)/36)*ArcTan[Tan[c + d*x]^(1/3)])/(a^2*d) + (2*Log[1 + Tan[c + d*x]^(2/3)])/(9*a^2*d) - (((7*I)/48)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) + (((7*I)/48)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) - Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)]/(9*a^2*d) + (7*Tan[c + d*x]^(2/3))/(12*a^2*d*(1 + I*Tan[c + d*x])) + Tan[c + d*x]^(2/3)/(4*d*(a + I*a*Tan[c + d*x])^2)","A",24,14,26,0.5385,1,"{3559, 3596, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
246,1,359,0,0.5642058,"\int \frac{1}{\tan ^{\frac{5}{3}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[1/(Tan[c + d*x]^(5/3)*(a + I*a*Tan[c + d*x])^2),x]","\frac{55 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{55 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{8 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{55 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{8}{3 a^2 d \tan ^{\frac{2}{3}}(c+d x)}+\frac{11}{12 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{2}{3}}(c+d x)}+\frac{8 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{55 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{55 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{4 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{1}{4 d \tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))^2}","\frac{55 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}-\frac{55 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{8 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{3 \sqrt{3} a^2 d}-\frac{55 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{8}{3 a^2 d \tan ^{\frac{2}{3}}(c+d x)}+\frac{11}{12 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{2}{3}}(c+d x)}+\frac{8 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{55 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{55 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{4 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{9 a^2 d}+\frac{1}{4 d \tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))^2}",1,"(((55*I)/72)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a^2*d) - (((55*I)/72)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a^2*d) + (8*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(3*Sqrt[3]*a^2*d) - (((55*I)/36)*ArcTan[Tan[c + d*x]^(1/3)])/(a^2*d) + (8*Log[1 + Tan[c + d*x]^(2/3)])/(9*a^2*d) + (((55*I)/48)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) - (((55*I)/48)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) - (4*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(9*a^2*d) - 8/(3*a^2*d*Tan[c + d*x]^(2/3)) + 11/(12*a^2*d*(1 + I*Tan[c + d*x])*Tan[c + d*x]^(2/3)) + 1/(4*d*Tan[c + d*x]^(2/3)*(a + I*a*Tan[c + d*x])^2)","A",25,15,26,0.5769,1,"{3559, 3596, 3529, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31}"
247,1,381,0,0.6663981,"\int \frac{1}{\tan ^{\frac{7}{3}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[1/(Tan[c + d*x]^(7/3)*(a + I*a*Tan[c + d*x])^2),x]","-\frac{91 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{91 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{25 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{6 \sqrt{3} a^2 d}+\frac{91 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{25}{12 a^2 d \tan ^{\frac{4}{3}}(c+d x)}+\frac{13}{12 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{4}{3}}(c+d x)}+\frac{91 i}{12 a^2 d \sqrt[3]{\tan (c+d x)}}-\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}+\frac{91 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{91 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{25 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{36 a^2 d}+\frac{1}{4 d \tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))^2}","-\frac{91 i \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{72 a^2 d}+\frac{91 i \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{72 a^2 d}+\frac{25 \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{6 \sqrt{3} a^2 d}+\frac{91 i \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{36 a^2 d}-\frac{25}{12 a^2 d \tan ^{\frac{4}{3}}(c+d x)}+\frac{13}{12 a^2 d (1+i \tan (c+d x)) \tan ^{\frac{4}{3}}(c+d x)}+\frac{91 i}{12 a^2 d \sqrt[3]{\tan (c+d x)}}-\frac{25 \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{18 a^2 d}+\frac{91 i \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}-\frac{91 i \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{48 \sqrt{3} a^2 d}+\frac{25 \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{36 a^2 d}+\frac{1}{4 d \tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))^2}",1,"(((-91*I)/72)*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(a^2*d) + (((91*I)/72)*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(a^2*d) + (25*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(6*Sqrt[3]*a^2*d) + (((91*I)/36)*ArcTan[Tan[c + d*x]^(1/3)])/(a^2*d) - (25*Log[1 + Tan[c + d*x]^(2/3)])/(18*a^2*d) + (((91*I)/48)*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) - (((91*I)/48)*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(Sqrt[3]*a^2*d) + (25*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(36*a^2*d) - 25/(12*a^2*d*Tan[c + d*x]^(4/3)) + 13/(12*a^2*d*(1 + I*Tan[c + d*x])*Tan[c + d*x]^(4/3)) + ((91*I)/12)/(a^2*d*Tan[c + d*x]^(1/3)) + 1/(4*d*Tan[c + d*x]^(4/3)*(a + I*a*Tan[c + d*x])^2)","A",26,15,26,0.5769,1,"{3559, 3596, 3529, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203}"
248,1,82,0,0.146212,"\int \tan ^{\frac{4}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(4/3)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{1}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{1}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*a*AppellF1[7/3, 1/2, 1, 10/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(7/3))/(7*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
249,1,82,0,0.1488238,"\int \tan ^{\frac{2}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(2/3)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{1}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{1}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*a*AppellF1[5/3, 1/2, 1, 8/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(5/3))/(5*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
250,1,82,0,0.1433934,"\int \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{1}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{1}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*a*AppellF1[4/3, 1/2, 1, 7/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(4/3))/(4*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
251,1,82,0,0.1272346,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt[3]{\tan (c+d x)}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(1/3),x]","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 a \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*a*AppellF1[2/3, 1/2, 1, 5/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(2/3))/(2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
252,1,80,0,0.1165873,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\tan ^{\frac{2}{3}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(2/3),x]","\frac{3 a \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{1}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{3 a \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{1}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{a+i a \tan (c+d x)}}",1,"(3*a*AppellF1[1/3, 1/2, 1, 4/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1/3))/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 430, 429}"
253,1,80,0,0.1437114,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\tan ^{\frac{4}{3}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Tan[c + d*x]^(4/3),x]","-\frac{3 a \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{1}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{3 a \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{1}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"(-3*a*AppellF1[-1/3, 1/2, 1, 2/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]])/(d*Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
254,1,82,0,0.1582016,"\int \tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(4/3)*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 a \tan ^{\frac{7}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{7}{3};-\frac{1}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{1+i \tan (c+d x)}}","\frac{3 a \tan ^{\frac{7}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{7}{3};-\frac{1}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{1+i \tan (c+d x)}}",1,"(3*a*AppellF1[7/3, -1/2, 1, 10/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(7/3)*Sqrt[a + I*a*Tan[c + d*x]])/(7*d*Sqrt[1 + I*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
255,1,82,0,0.1467633,"\int \tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(2/3)*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 a \tan ^{\frac{5}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{5}{3};-\frac{1}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{1+i \tan (c+d x)}}","\frac{3 a \tan ^{\frac{5}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{5}{3};-\frac{1}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{1+i \tan (c+d x)}}",1,"(3*a*AppellF1[5/3, -1/2, 1, 8/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(5/3)*Sqrt[a + I*a*Tan[c + d*x]])/(5*d*Sqrt[1 + I*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
256,1,82,0,0.1440522,"\int \sqrt[3]{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(1/3)*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 a \tan ^{\frac{4}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{4}{3};-\frac{1}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{1+i \tan (c+d x)}}","\frac{3 a \tan ^{\frac{4}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{4}{3};-\frac{1}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{1+i \tan (c+d x)}}",1,"(3*a*AppellF1[4/3, -1/2, 1, 7/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(4/3)*Sqrt[a + I*a*Tan[c + d*x]])/(4*d*Sqrt[1 + I*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
257,1,82,0,0.1310335,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\sqrt[3]{\tan (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(1/3),x]","\frac{3 a \tan ^{\frac{2}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{2}{3};-\frac{1}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{1+i \tan (c+d x)}}","\frac{3 a \tan ^{\frac{2}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{2}{3};-\frac{1}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{1+i \tan (c+d x)}}",1,"(3*a*AppellF1[2/3, -1/2, 1, 5/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(2/3)*Sqrt[a + I*a*Tan[c + d*x]])/(2*d*Sqrt[1 + I*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
258,1,80,0,0.1223101,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{2}{3}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(2/3),x]","\frac{3 a \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{1}{3};-\frac{1}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{1+i \tan (c+d x)}}","\frac{3 a \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)} F_1\left(\frac{1}{3};-\frac{1}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{1+i \tan (c+d x)}}",1,"(3*a*AppellF1[1/3, -1/2, 1, 4/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[1 + I*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 430, 429}"
259,1,80,0,0.1471513,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\tan ^{\frac{4}{3}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(4/3),x]","-\frac{3 a \sqrt{a+i a \tan (c+d x)} F_1\left(-\frac{1}{3};-\frac{1}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)}}","-\frac{3 a \sqrt{a+i a \tan (c+d x)} F_1\left(-\frac{1}{3};-\frac{1}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)}}",1,"(-3*a*AppellF1[-1/3, -1/2, 1, 2/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1/3))","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
260,1,81,0,0.1405594,"\int \frac{\tan ^{\frac{4}{3}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(4/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{3}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{3}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[7/3, 3/2, 1, 10/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(7/3))/(7*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
261,1,81,0,0.1420851,"\int \frac{\tan ^{\frac{2}{3}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(2/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{3}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{3}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[5/3, 3/2, 1, 8/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(5/3))/(5*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
262,1,81,0,0.1406635,"\int \frac{\sqrt[3]{\tan (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(1/3)/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{3}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{3}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[4/3, 3/2, 1, 7/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(4/3))/(4*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
263,1,81,0,0.1290135,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{3}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{3}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[2/3, 3/2, 1, 5/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(2/3))/(2*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
264,1,79,0,0.1236389,"\int \frac{1}{\tan ^{\frac{2}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(2/3)*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{3}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{3}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[1/3, 3/2, 1, 4/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1/3))/(d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 430, 429}"
265,1,79,0,0.1481313,"\int \frac{1}{\tan ^{\frac{4}{3}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(4/3)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{3 \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{3}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{3 \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{3}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"(-3*AppellF1[-1/3, 3/2, 1, 2/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]])/(d*Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
266,1,84,0,0.1480704,"\int \frac{\tan ^{\frac{4}{3}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(4/3)/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{5}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 a d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{7}{3}}(c+d x) F_1\left(\frac{7}{3};\frac{5}{2},1;\frac{10}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{7 a d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[7/3, 5/2, 1, 10/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(7/3))/(7*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
267,1,84,0,0.1490177,"\int \frac{\tan ^{\frac{2}{3}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(2/3)/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{5}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 a d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{5}{3}}(c+d x) F_1\left(\frac{5}{3};\frac{5}{2},1;\frac{8}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{5 a d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[5/3, 5/2, 1, 8/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(5/3))/(5*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
268,1,84,0,0.1463519,"\int \frac{\sqrt[3]{\tan (c+d x)}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(1/3)/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{5}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 a d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{4}{3}}(c+d x) F_1\left(\frac{4}{3};\frac{5}{2},1;\frac{7}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{4 a d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[4/3, 5/2, 1, 7/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(4/3))/(4*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
269,1,84,0,0.1325786,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(1/3)*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{5}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 a d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \tan ^{\frac{2}{3}}(c+d x) F_1\left(\frac{2}{3};\frac{5}{2},1;\frac{5}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{2 a d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[2/3, 5/2, 1, 5/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(2/3))/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
270,1,82,0,0.1219718,"\int \frac{1}{\tan ^{\frac{2}{3}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(2/3)*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{3 \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{5}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{a d \sqrt{a+i a \tan (c+d x)}}","\frac{3 \sqrt{1+i \tan (c+d x)} \sqrt[3]{\tan (c+d x)} F_1\left(\frac{1}{3};\frac{5}{2},1;\frac{4}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{a d \sqrt{a+i a \tan (c+d x)}}",1,"(3*AppellF1[1/3, 5/2, 1, 4/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]]*Tan[c + d*x]^(1/3))/(a*d*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 430, 429}"
271,1,82,0,0.1467339,"\int \frac{1}{\tan ^{\frac{4}{3}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(4/3)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{3 \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{5}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{a d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}","-\frac{3 \sqrt{1+i \tan (c+d x)} F_1\left(-\frac{1}{3};\frac{5}{2},1;\frac{2}{3};-i \tan (c+d x),i \tan (c+d x)\right)}{a d \sqrt[3]{\tan (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"(-3*AppellF1[-1/3, 5/2, 1, 2/3, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[1 + I*Tan[c + d*x]])/(a*d*Tan[c + d*x]^(1/3)*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
272,1,234,0,0.292819,"\int \tan ^3(c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{3 \tan ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{7 d}+\frac{\sqrt{3} \sqrt[3]{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 (a+i a \tan (c+d x))^{4/3}}{28 a d}-\frac{18 \sqrt[3]{a+i a \tan (c+d x)}}{7 d}-\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}","\frac{3 \tan ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{7 d}+\frac{\sqrt{3} \sqrt[3]{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 (a+i a \tan (c+d x))^{4/3}}{28 a d}-\frac{18 \sqrt[3]{a+i a \tan (c+d x)}}{7 d}-\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}",1,"((-I/2)*a^(1/3)*x)/2^(2/3) + (Sqrt[3]*a^(1/3)*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)*Log[Cos[c + d*x]])/(2*2^(2/3)*d) - (3*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(2/3)*d) - (18*(a + I*a*Tan[c + d*x])^(1/3))/(7*d) + (3*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(1/3))/(7*d) - (3*(a + I*a*Tan[c + d*x])^(4/3))/(28*a*d)","A",8,8,26,0.3077,1,"{3560, 3592, 3527, 3481, 57, 617, 204, 31}"
273,1,185,0,0.126797,"\int \tan ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{i \sqrt{3} \sqrt[3]{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 i (a+i a \tan (c+d x))^{4/3}}{4 a d}-\frac{3 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}+\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}","\frac{i \sqrt{3} \sqrt[3]{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 i (a+i a \tan (c+d x))^{4/3}}{4 a d}-\frac{3 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}+\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}",1,"(a^(1/3)*x)/(2*2^(2/3)) + (I*Sqrt[3]*a^(1/3)*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) - ((I/2)*a^(1/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - (((3*I)/2)*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) - (((3*I)/4)*(a + I*a*Tan[c + d*x])^(4/3))/(a*d)","A",6,6,26,0.2308,1,"{3543, 3481, 57, 617, 204, 31}"
274,1,174,0,0.1180276,"\int \tan (c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{\sqrt{3} \sqrt[3]{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+i a \tan (c+d x)}}{d}+\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}+\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}","-\frac{\sqrt{3} \sqrt[3]{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+i a \tan (c+d x)}}{d}+\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}+\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}",1,"((I/2)*a^(1/3)*x)/2^(2/3) - (Sqrt[3]*a^(1/3)*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)*Log[Cos[c + d*x]])/(2*2^(2/3)*d) + (3*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(2/3)*d) + (3*(a + I*a*Tan[c + d*x])^(1/3))/d","A",6,6,24,0.2500,1,"{3527, 3481, 57, 617, 204, 31}"
275,1,156,0,0.0740147,"\int \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{i \sqrt{3} \sqrt[3]{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 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}","-\frac{i \sqrt{3} \sqrt[3]{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 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}",1,"-(a^(1/3)*x)/(2*2^(2/3)) - (I*Sqrt[3]*a^(1/3)*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) + ((I/2)*a^(1/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) + (((3*I)/2)*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d)","A",5,5,17,0.2941,1,"{3481, 57, 617, 204, 31}"
276,1,260,0,0.2845769,"\int \cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{\sqrt{3} \sqrt[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{\sqrt{3} \sqrt[3]{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{\sqrt[3]{a} \log (\tan (c+d x))}{2 d}+\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}","-\frac{\sqrt{3} \sqrt[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{\sqrt{3} \sqrt[3]{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{\sqrt[3]{a} \log (\tan (c+d x))}{2 d}+\frac{3 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}",1,"((-I/2)*a^(1/3)*x)/2^(2/3) - (Sqrt[3]*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (Sqrt[3]*a^(1/3)*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)*Log[Cos[c + d*x]])/(2*2^(2/3)*d) - (a^(1/3)*Log[Tan[c + d*x]])/(2*d) + (3*a^(1/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*d) - (3*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(2/3)*d)","A",11,7,24,0.2917,1,"{3562, 3481, 57, 617, 204, 31, 3599}"
277,1,299,0,0.4244093,"\int \cot ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{i \sqrt[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)}{\sqrt{3} d}+\frac{i \sqrt{3} \sqrt[3]{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{i \sqrt[3]{a} \log (\tan (c+d x))}{6 d}+\frac{i \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{d}+\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}","-\frac{i \sqrt[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)}{\sqrt{3} d}+\frac{i \sqrt{3} \sqrt[3]{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{i \sqrt[3]{a} \log (\tan (c+d x))}{6 d}+\frac{i \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 i \sqrt[3]{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{i \sqrt[3]{a} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{d}+\frac{\sqrt[3]{a} x}{2\ 2^{2/3}}",1,"(a^(1/3)*x)/(2*2^(2/3)) - (I*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*d) + (I*Sqrt[3]*a^(1/3)*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) - ((I/2)*a^(1/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - ((I/6)*a^(1/3)*Log[Tan[c + d*x]])/d + ((I/2)*a^(1/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/d - (((3*I)/2)*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) - (Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(1/3))/d","A",12,8,26,0.3077,1,"{3561, 3600, 3481, 57, 617, 204, 31, 3599}"
278,1,327,0,0.5657072,"\int \cot ^3(c+d x) \sqrt[3]{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{8 \sqrt[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)}{3 \sqrt{3} d}-\frac{\sqrt{3} \sqrt[3]{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{4 \sqrt[3]{a} \log (\tan (c+d x))}{9 d}-\frac{4 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{3 d}+\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\cot ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{2 d}-\frac{i \cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{6 d}+\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}","\frac{8 \sqrt[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)}{3 \sqrt{3} d}-\frac{\sqrt{3} \sqrt[3]{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{4 \sqrt[3]{a} \log (\tan (c+d x))}{9 d}-\frac{4 \sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{3 d}+\frac{3 \sqrt[3]{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} \log (\cos (c+d x))}{2\ 2^{2/3} d}-\frac{\cot ^2(c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{2 d}-\frac{i \cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{6 d}+\frac{i \sqrt[3]{a} x}{2\ 2^{2/3}}",1,"((I/2)*a^(1/3)*x)/2^(2/3) + (8*a^(1/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*d) - (Sqrt[3]*a^(1/3)*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)*Log[Cos[c + d*x]])/(2*2^(2/3)*d) + (4*a^(1/3)*Log[Tan[c + d*x]])/(9*d) - (4*a^(1/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(3*d) + (3*a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*2^(2/3)*d) - ((I/6)*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(1/3))/d - (Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(1/3))/(2*d)","A",13,9,26,0.3462,1,"{3561, 3598, 3600, 3481, 57, 617, 204, 31, 3599}"
279,1,156,0,0.081721,"\int (a+i a \tan (c+d x))^{2/3} \, dx","Int[(a + I*a*Tan[c + d*x])^(2/3),x]","\frac{i \sqrt{3} a^{2/3} \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 i a^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{i a^{2/3} \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x}{2 \sqrt[3]{2}}","\frac{i \sqrt{3} a^{2/3} \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 i a^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{2} d}+\frac{i a^{2/3} \log (\cos (c+d x))}{2 \sqrt[3]{2} d}-\frac{a^{2/3} x}{2 \sqrt[3]{2}}",1,"-(a^(2/3)*x)/(2*2^(1/3)) + (I*Sqrt[3]*a^(2/3)*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) + ((I/2)*a^(2/3)*Log[Cos[c + d*x]])/(2^(1/3)*d) + (((3*I)/2)*a^(2/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*d)","A",5,5,17,0.2941,1,"{3481, 55, 617, 204, 31}"
280,1,251,0,0.3418498,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{i a^{4/3} x}{2^{2/3}}+\frac{3 \tan ^2(c+d x) (a+i a \tan (c+d x))^{4/3}}{10 d}-\frac{6 (a+i a \tan (c+d x))^{7/3}}{35 a d}-\frac{9 (a+i a \tan (c+d x))^{4/3}}{20 d}-\frac{3 a \sqrt[3]{a+i a \tan (c+d x)}}{d}","\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{i a^{4/3} x}{2^{2/3}}+\frac{3 \tan ^2(c+d x) (a+i a \tan (c+d x))^{4/3}}{10 d}-\frac{6 (a+i a \tan (c+d x))^{7/3}}{35 a d}-\frac{9 (a+i a \tan (c+d x))^{4/3}}{20 d}-\frac{3 a \sqrt[3]{a+i a \tan (c+d x)}}{d}",1,"((-I)*a^(4/3)*x)/2^(2/3) + (2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d - (a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - (3*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) - (3*a*(a + I*a*Tan[c + d*x])^(1/3))/d - (9*(a + I*a*Tan[c + d*x])^(4/3))/(20*d) + (3*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(4/3))/(10*d) - (6*(a + I*a*Tan[c + d*x])^(7/3))/(35*a*d)","A",9,9,26,0.3462,1,"{3560, 3592, 3527, 3478, 3481, 57, 617, 204, 31}"
281,1,203,0,0.1565061,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{a^{4/3} x}{2^{2/3}}-\frac{3 i (a+i a \tan (c+d x))^{7/3}}{7 a d}-\frac{3 i a \sqrt[3]{a+i a \tan (c+d x)}}{d}","\frac{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{a^{4/3} x}{2^{2/3}}-\frac{3 i (a+i a \tan (c+d x))^{7/3}}{7 a d}-\frac{3 i a \sqrt[3]{a+i a \tan (c+d x)}}{d}",1,"(a^(4/3)*x)/2^(2/3) + (I*2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d - (I*a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - ((3*I)*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) - ((3*I)*a*(a + I*a*Tan[c + d*x])^(1/3))/d - (((3*I)/7)*(a + I*a*Tan[c + d*x])^(7/3))/(a*d)","A",7,7,26,0.2692,1,"{3543, 3478, 3481, 57, 617, 204, 31}"
282,1,192,0,0.1476367,"\int \tan (c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{i a^{4/3} x}{2^{2/3}}+\frac{3 a \sqrt[3]{a+i a \tan (c+d x)}}{d}+\frac{3 (a+i a \tan (c+d x))^{4/3}}{4 d}","-\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{i a^{4/3} x}{2^{2/3}}+\frac{3 a \sqrt[3]{a+i a \tan (c+d x)}}{d}+\frac{3 (a+i a \tan (c+d x))^{4/3}}{4 d}",1,"(I*a^(4/3)*x)/2^(2/3) - (2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) + (3*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) + (3*a*(a + I*a*Tan[c + d*x])^(1/3))/d + (3*(a + I*a*Tan[c + d*x])^(4/3))/(4*d)","A",7,7,24,0.2917,1,"{3527, 3478, 3481, 57, 617, 204, 31}"
283,1,175,0,0.0937833,"\int (a+i a \tan (c+d x))^{4/3} \, dx","Int[(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{a^{4/3} x}{2^{2/3}}+\frac{3 i a \sqrt[3]{a+i a \tan (c+d x)}}{d}","-\frac{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{a^{4/3} x}{2^{2/3}}+\frac{3 i a \sqrt[3]{a+i a \tan (c+d x)}}{d}",1,"-((a^(4/3)*x)/2^(2/3)) - (I*2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (I*a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) + ((3*I)*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) + ((3*I)*a*(a + I*a*Tan[c + d*x])^(1/3))/d","A",6,6,17,0.3529,1,"{3478, 3481, 57, 617, 204, 31}"
284,1,254,0,0.4159978,"\int \cot (c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{\sqrt{3} a^{4/3} \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{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{a^{4/3} \log (\tan (c+d x))}{2 d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{i a^{4/3} x}{2^{2/3}}","-\frac{\sqrt{3} a^{4/3} \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{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{a^{4/3} \log (\tan (c+d x))}{2 d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 d}-\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}-\frac{i a^{4/3} x}{2^{2/3}}",1,"((-I)*a^(4/3)*x)/2^(2/3) - (Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d - (a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - (a^(4/3)*Log[Tan[c + d*x]])/(2*d) + (3*a^(4/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*d) - (3*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d)","A",13,9,24,0.3750,1,"{3562, 3478, 3481, 57, 617, 204, 31, 3594, 3599}"
285,1,315,0,0.5294679,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{4 i a^{4/3} \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{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{2 i a^{4/3} \log (\tan (c+d x))}{3 d}+\frac{2 i a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{d}-\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{a^{4/3} x}{2^{2/3}}+\frac{i a \sqrt[3]{a+i a \tan (c+d x)}}{d}-\frac{\cot (c+d x) (a+i a \tan (c+d x))^{4/3}}{d}","-\frac{4 i a^{4/3} \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{i \sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}-\frac{2 i a^{4/3} \log (\tan (c+d x))}{3 d}+\frac{2 i a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{d}-\frac{3 i a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}-\frac{i a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{a^{4/3} x}{2^{2/3}}+\frac{i a \sqrt[3]{a+i a \tan (c+d x)}}{d}-\frac{\cot (c+d x) (a+i a \tan (c+d x))^{4/3}}{d}",1,"(a^(4/3)*x)/2^(2/3) - ((4*I)*a^(4/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*d) + (I*2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d - (I*a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) - (((2*I)/3)*a^(4/3)*Log[Tan[c + d*x]])/d + ((2*I)*a^(4/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/d - ((3*I)*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) + (I*a*(a + I*a*Tan[c + d*x])^(1/3))/d - (Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(4/3))/d","A",13,9,26,0.3462,1,"{3561, 3594, 3600, 3481, 57, 617, 204, 31, 3599}"
286,1,321,0,0.5411023,"\int \cot ^3(c+d x) (a+i a \tan (c+d x))^{4/3} \, dx","Int[Cot[c + d*x]^3*(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{11 a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} d}-\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{11 a^{4/3} \log (\tan (c+d x))}{18 d}-\frac{11 a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{6 d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{i a^{4/3} x}{2^{2/3}}-\frac{\cot ^2(c+d x) (a+i a \tan (c+d x))^{4/3}}{2 d}-\frac{2 i a \cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{3 d}","\frac{11 a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} d}-\frac{\sqrt[3]{2} \sqrt{3} a^{4/3} \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)}{d}+\frac{11 a^{4/3} \log (\tan (c+d x))}{18 d}-\frac{11 a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{6 d}+\frac{3 a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2^{2/3} d}+\frac{a^{4/3} \log (\cos (c+d x))}{2^{2/3} d}+\frac{i a^{4/3} x}{2^{2/3}}-\frac{\cot ^2(c+d x) (a+i a \tan (c+d x))^{4/3}}{2 d}-\frac{2 i a \cot (c+d x) \sqrt[3]{a+i a \tan (c+d x)}}{3 d}",1,"(I*a^(4/3)*x)/2^(2/3) + (11*a^(4/3)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*d) - (2^(1/3)*Sqrt[3]*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (a^(4/3)*Log[Cos[c + d*x]])/(2^(2/3)*d) + (11*a^(4/3)*Log[Tan[c + d*x]])/(18*d) - (11*a^(4/3)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(6*d) + (3*a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*d) - (((2*I)/3)*a*Cot[c + d*x]*(a + I*a*Tan[c + d*x])^(1/3))/d - (Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^(4/3))/(2*d)","A",13,9,26,0.3462,1,"{3561, 3593, 3600, 3481, 57, 617, 204, 31, 3599}"
287,1,177,0,0.1002168,"\int (a+i a \tan (c+d x))^{5/3} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/3),x]","\frac{i 2^{2/3} \sqrt{3} a^{5/3} \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)}{d}+\frac{3 i a^{5/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{\sqrt[3]{2} d}+\frac{i a^{5/3} \log (\cos (c+d x))}{\sqrt[3]{2} d}-\frac{a^{5/3} x}{\sqrt[3]{2}}+\frac{3 i a (a+i a \tan (c+d x))^{2/3}}{2 d}","\frac{i 2^{2/3} \sqrt{3} a^{5/3} \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)}{d}+\frac{3 i a^{5/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{\sqrt[3]{2} d}+\frac{i a^{5/3} \log (\cos (c+d x))}{\sqrt[3]{2} d}-\frac{a^{5/3} x}{\sqrt[3]{2}}+\frac{3 i a (a+i a \tan (c+d x))^{2/3}}{2 d}",1,"-((a^(5/3)*x)/2^(1/3)) + (I*2^(2/3)*Sqrt[3]*a^(5/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/d + (I*a^(5/3)*Log[Cos[c + d*x]])/(2^(1/3)*d) + ((3*I)*a^(5/3)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*d) + (((3*I)/2)*a*(a + I*a*Tan[c + d*x])^(2/3))/d","A",6,6,17,0.3529,1,"{3478, 3481, 55, 617, 204, 31}"
288,1,83,0,0.1038061,"\int \frac{\tan ^m(c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^m/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{\sqrt[3]{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{4}{3},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt[3]{a+i a \tan (c+d x)}}","\frac{\sqrt[3]{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{4}{3},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{d (m+1) \sqrt[3]{a+i a \tan (c+d x)}}",1,"(AppellF1[1 + m, 4/3, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(1 + I*Tan[c + d*x])^(1/3)*Tan[c + d*x]^(1 + m))/(d*(1 + m)*(a + I*a*Tan[c + d*x])^(1/3))","A",3,3,26,0.1154,1,"{3564, 135, 133}"
289,1,81,0,0.1403701,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{2 \sqrt[3]{1+i \tan (c+d x)} \tan ^{\frac{3}{2}}(c+d x) F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d \sqrt[3]{a+i a \tan (c+d x)}}","\frac{2 \sqrt[3]{1+i \tan (c+d x)} \tan ^{\frac{3}{2}}(c+d x) F_1\left(\frac{3}{2};\frac{4}{3},1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d \sqrt[3]{a+i a \tan (c+d x)}}",1,"(2*AppellF1[3/2, 4/3, 1, 5/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(1 + I*Tan[c + d*x])^(1/3)*Tan[c + d*x]^(3/2))/(3*d*(a + I*a*Tan[c + d*x])^(1/3))","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
290,1,282,0,0.4424923,"\int \frac{\tan ^4(c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{39 i (a+i a \tan (c+d x))^{5/3}}{20 a^2 d}+\frac{3 \tan ^3(c+d x)}{8 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{15 i \tan ^2(c+d x)}{8 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{i \sqrt{3} \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{45 i (a+i a \tan (c+d x))^{2/3}}{8 a d}+\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}","-\frac{39 i (a+i a \tan (c+d x))^{5/3}}{20 a^2 d}+\frac{3 \tan ^3(c+d x)}{8 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{15 i \tan ^2(c+d x)}{8 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{i \sqrt{3} \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{45 i (a+i a \tan (c+d x))^{2/3}}{8 a d}+\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"-x/(4*2^(1/3)*a^(1/3)) + ((I/2)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(1/3)*d) + ((I/4)*Log[Cos[c + d*x]])/(2^(1/3)*a^(1/3)*d) + (((3*I)/4)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(1/3)*d) - (((15*I)/8)*Tan[c + d*x]^2)/(d*(a + I*a*Tan[c + d*x])^(1/3)) + (3*Tan[c + d*x]^3)/(8*d*(a + I*a*Tan[c + d*x])^(1/3)) + (((45*I)/8)*(a + I*a*Tan[c + d*x])^(2/3))/(a*d) - (((39*I)/20)*(a + I*a*Tan[c + d*x])^(5/3))/(a^2*d)","A",9,9,26,0.3462,1,"{3560, 3595, 3592, 3527, 3481, 55, 617, 204, 31}"
291,1,237,0,0.2749392,"\int \frac{\tan ^3(c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{3 \tan ^2(c+d x)}{5 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{\sqrt{3} \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 (a+i a \tan (c+d x))^{2/3}}{10 a d}+\frac{21}{10 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}","\frac{3 \tan ^2(c+d x)}{5 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{\sqrt{3} \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 (a+i a \tan (c+d x))^{2/3}}{10 a d}+\frac{21}{10 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"((-I/4)*x)/(2^(1/3)*a^(1/3)) - (Sqrt[3]*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) - Log[Cos[c + d*x]]/(4*2^(1/3)*a^(1/3)*d) - (3*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(4*2^(1/3)*a^(1/3)*d) + 21/(10*d*(a + I*a*Tan[c + d*x])^(1/3)) + (3*Tan[c + d*x]^2)/(5*d*(a + I*a*Tan[c + d*x])^(1/3)) + (3*(a + I*a*Tan[c + d*x])^(2/3))/(10*a*d)","A",8,8,26,0.3077,1,"{3560, 3592, 3526, 3481, 55, 617, 204, 31}"
292,1,213,0,0.1556328,"\int \frac{\tan ^2(c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{i \sqrt{3} \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 i (a+i a \tan (c+d x))^{2/3}}{2 a d}-\frac{3 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}","-\frac{i \sqrt{3} \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 i (a+i a \tan (c+d x))^{2/3}}{2 a d}-\frac{3 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"x/(4*2^(1/3)*a^(1/3)) - ((I/2)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(1/3)*d) - ((I/4)*Log[Cos[c + d*x]])/(2^(1/3)*a^(1/3)*d) - (((3*I)/4)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(1/3)*d) - ((3*I)/2)/(d*(a + I*a*Tan[c + d*x])^(1/3)) - (((3*I)/2)*(a + I*a*Tan[c + d*x])^(2/3))/(a*d)","A",7,7,26,0.2692,1,"{3543, 3479, 3481, 55, 617, 204, 31}"
293,1,178,0,0.1180311,"\int \frac{\tan (c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{\sqrt{3} \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}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}","\frac{\sqrt{3} \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}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"((I/4)*x)/(2^(1/3)*a^(1/3)) + (Sqrt[3]*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) + Log[Cos[c + d*x]]/(4*2^(1/3)*a^(1/3)*d) + (3*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/(2*d*(a + I*a*Tan[c + d*x])^(1/3))","A",6,6,24,0.2500,1,"{3526, 3481, 55, 617, 204, 31}"
294,1,184,0,0.0982843,"\int \frac{1}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-1/3),x]","\frac{i \sqrt{3} \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 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}","\frac{i \sqrt{3} \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 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"-x/(4*2^(1/3)*a^(1/3)) + ((I/2)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(1/3)*d) + ((I/4)*Log[Cos[c + d*x]])/(2^(1/3)*a^(1/3)*d) + (((3*I)/4)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(1/3)*d) + ((3*I)/2)/(d*(a + I*a*Tan[c + d*x])^(1/3))","A",6,6,17,0.3529,1,"{3479, 3481, 55, 617, 204, 31}"
295,1,286,0,0.4282901,"\int \frac{\cot (c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^(1/3),x]","\frac{\sqrt{3} \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]{a} d}-\frac{\sqrt{3} \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}{2 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{\log (\tan (c+d x))}{2 \sqrt[3]{a} d}+\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{a} d}-\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}","\frac{\sqrt{3} \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]{a} d}-\frac{\sqrt{3} \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}{2 d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{\log (\tan (c+d x))}{2 \sqrt[3]{a} d}+\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{a} d}-\frac{3 \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{\log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{i x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"((-I/4)*x)/(2^(1/3)*a^(1/3)) + (Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(1/3)*d) - (Sqrt[3]*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) - Log[Cos[c + d*x]]/(4*2^(1/3)*a^(1/3)*d) - Log[Tan[c + d*x]]/(2*a^(1/3)*d) + (3*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*a^(1/3)*d) - (3*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/(2*d*(a + I*a*Tan[c + d*x])^(1/3))","A",13,9,24,0.3750,1,"{3562, 3479, 3481, 55, 617, 204, 31, 3596, 3599}"
296,1,327,0,0.5779219,"\int \frac{\cot ^2(c+d x)}{\sqrt[3]{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^(1/3),x]","-\frac{i \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} \sqrt[3]{a} d}-\frac{i \sqrt{3} \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{5 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{i \log (\tan (c+d x))}{6 \sqrt[3]{a} d}-\frac{i \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{a} d}-\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{\cot (c+d x)}{d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}","-\frac{i \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} \sqrt[3]{a} d}-\frac{i \sqrt{3} \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{5 i}{2 d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{i \log (\tan (c+d x))}{6 \sqrt[3]{a} d}-\frac{i \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 \sqrt[3]{a} d}-\frac{3 i \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{i \log (\cos (c+d x))}{4 \sqrt[3]{2} \sqrt[3]{a} d}-\frac{\cot (c+d x)}{d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{x}{4 \sqrt[3]{2} \sqrt[3]{a}}",1,"x/(4*2^(1/3)*a^(1/3)) - (I*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*d) - ((I/2)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(1/3)*d) - ((I/4)*Log[Cos[c + d*x]])/(2^(1/3)*a^(1/3)*d) + ((I/6)*Log[Tan[c + d*x]])/(a^(1/3)*d) - ((I/2)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(a^(1/3)*d) - (((3*I)/4)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(1/3)*d) - ((5*I)/2)/(d*(a + I*a*Tan[c + d*x])^(1/3)) - Cot[c + d*x]/(d*(a + I*a*Tan[c + d*x])^(1/3))","A",13,9,26,0.3462,1,"{3561, 3596, 3600, 3481, 55, 617, 204, 31, 3599}"
297,1,184,0,0.1098777,"\int \frac{1}{(a+i a \tan (c+d x))^{2/3}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-2/3),x]","-\frac{i \sqrt{3} \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 i \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{i \log (\cos (c+d x))}{4\ 2^{2/3} a^{2/3} d}-\frac{x}{4\ 2^{2/3} a^{2/3}}+\frac{3 i}{4 d (a+i a \tan (c+d x))^{2/3}}","-\frac{i \sqrt{3} \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 i \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{i \log (\cos (c+d x))}{4\ 2^{2/3} a^{2/3} d}-\frac{x}{4\ 2^{2/3} a^{2/3}}+\frac{3 i}{4 d (a+i a \tan (c+d x))^{2/3}}",1,"-x/(4*2^(2/3)*a^(2/3)) - ((I/2)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(2/3)*a^(2/3)*d) + ((I/4)*Log[Cos[c + d*x]])/(2^(2/3)*a^(2/3)*d) + (((3*I)/4)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*a^(2/3)*d) + ((3*I)/4)/(d*(a + I*a*Tan[c + d*x])^(2/3))","A",6,6,17,0.3529,1,"{3479, 3481, 57, 617, 204, 31}"
298,1,86,0,0.1149508,"\int \frac{\tan ^m(c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Tan[c + d*x]^m/(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{\sqrt[3]{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{7}{3},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{a d (m+1) \sqrt[3]{a+i a \tan (c+d x)}}","\frac{\sqrt[3]{1+i \tan (c+d x)} \tan ^{m+1}(c+d x) F_1\left(m+1;\frac{7}{3},1;m+2;-i \tan (c+d x),i \tan (c+d x)\right)}{a d (m+1) \sqrt[3]{a+i a \tan (c+d x)}}",1,"(AppellF1[1 + m, 7/3, 1, 2 + m, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(1 + I*Tan[c + d*x])^(1/3)*Tan[c + d*x]^(1 + m))/(a*d*(1 + m)*(a + I*a*Tan[c + d*x])^(1/3))","A",3,3,26,0.1154,1,"{3564, 135, 133}"
299,1,84,0,0.1669781,"\int \frac{\sqrt{\tan (c+d x)}}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{2 \sqrt[3]{1+i \tan (c+d x)} \tan ^{\frac{3}{2}}(c+d x) F_1\left(\frac{3}{2};\frac{7}{3},1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 a d \sqrt[3]{a+i a \tan (c+d x)}}","\frac{2 \sqrt[3]{1+i \tan (c+d x)} \tan ^{\frac{3}{2}}(c+d x) F_1\left(\frac{3}{2};\frac{7}{3},1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 a d \sqrt[3]{a+i a \tan (c+d x)}}",1,"(2*AppellF1[3/2, 7/3, 1, 5/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(1 + I*Tan[c + d*x])^(1/3)*Tan[c + d*x]^(3/2))/(3*a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",4,4,28,0.1429,1,"{3564, 130, 511, 510}"
300,1,282,0,0.4533736,"\int \frac{\tan ^4(c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Tan[c + d*x]^4/(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{87 i (a+i a \tan (c+d x))^{2/3}}{40 a^2 d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 \tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{4/3}}-\frac{39 i \tan ^2(c+d x)}{40 d (a+i a \tan (c+d x))^{4/3}}-\frac{51 i}{10 a d \sqrt[3]{a+i a \tan (c+d x)}}","\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{87 i (a+i a \tan (c+d x))^{2/3}}{40 a^2 d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 \tan ^3(c+d x)}{5 d (a+i a \tan (c+d x))^{4/3}}-\frac{39 i \tan ^2(c+d x)}{40 d (a+i a \tan (c+d x))^{4/3}}-\frac{51 i}{10 a d \sqrt[3]{a+i a \tan (c+d x)}}",1,"-x/(8*2^(1/3)*a^(4/3)) + ((I/4)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(4/3)*d) + ((I/8)*Log[Cos[c + d*x]])/(2^(1/3)*a^(4/3)*d) + (((3*I)/8)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(4/3)*d) - (((39*I)/40)*Tan[c + d*x]^2)/(d*(a + I*a*Tan[c + d*x])^(4/3)) + (3*Tan[c + d*x]^3)/(5*d*(a + I*a*Tan[c + d*x])^(4/3)) - ((51*I)/10)/(a*d*(a + I*a*Tan[c + d*x])^(1/3)) - (((87*I)/40)*(a + I*a*Tan[c + d*x])^(2/3))/(a^2*d)","A",9,9,26,0.3462,1,"{3560, 3595, 3592, 3526, 3481, 55, 617, 204, 31}"
301,1,237,0,0.3073542,"\int \frac{\tan ^3(c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Tan[c + d*x]^3/(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 \tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))^{4/3}}-\frac{27}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{15}{8 d (a+i a \tan (c+d x))^{4/3}}","-\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 \tan ^2(c+d x)}{2 d (a+i a \tan (c+d x))^{4/3}}-\frac{27}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{15}{8 d (a+i a \tan (c+d x))^{4/3}}",1,"((-I/8)*x)/(2^(1/3)*a^(4/3)) - (Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(4*2^(1/3)*a^(4/3)*d) - Log[Cos[c + d*x]]/(8*2^(1/3)*a^(4/3)*d) - (3*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(8*2^(1/3)*a^(4/3)*d) + 15/(8*d*(a + I*a*Tan[c + d*x])^(4/3)) + (3*Tan[c + d*x]^2)/(2*d*(a + I*a*Tan[c + d*x])^(4/3)) - 27/(4*a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",8,8,26,0.3077,1,"{3560, 3590, 3526, 3481, 55, 617, 204, 31}"
302,1,213,0,0.2021644,"\int \frac{\tan ^2(c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Tan[c + d*x]^2/(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{9 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 i}{8 d (a+i a \tan (c+d x))^{4/3}}","-\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{9 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3 i}{8 d (a+i a \tan (c+d x))^{4/3}}",1,"x/(8*2^(1/3)*a^(4/3)) - ((I/4)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(4/3)*d) - ((I/8)*Log[Cos[c + d*x]])/(2^(1/3)*a^(4/3)*d) - (((3*I)/8)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(4/3)*d) - ((3*I)/8)/(d*(a + I*a*Tan[c + d*x])^(4/3)) + ((9*I)/4)/(a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",7,7,26,0.2692,1,"{3540, 3526, 3481, 55, 617, 204, 31}"
303,1,205,0,0.1542347,"\int \frac{\tan (c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Tan[c + d*x]/(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3}{8 d (a+i a \tan (c+d x))^{4/3}}","\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{3}{8 d (a+i a \tan (c+d x))^{4/3}}",1,"((I/8)*x)/(2^(1/3)*a^(4/3)) + (Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(4*2^(1/3)*a^(4/3)*d) + Log[Cos[c + d*x]]/(8*2^(1/3)*a^(4/3)*d) + (3*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(8*2^(1/3)*a^(4/3)*d) - 3/(8*d*(a + I*a*Tan[c + d*x])^(4/3)) + 3/(4*a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",7,7,24,0.2917,1,"{3526, 3479, 3481, 55, 617, 204, 31}"
304,1,213,0,0.1283108,"\int \frac{1}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-4/3),x]","\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 i}{8 d (a+i a \tan (c+d x))^{4/3}}","\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}+\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{x}{8 \sqrt[3]{2} a^{4/3}}+\frac{3 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3 i}{8 d (a+i a \tan (c+d x))^{4/3}}",1,"-x/(8*2^(1/3)*a^(4/3)) + ((I/4)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(4/3)*d) + ((I/8)*Log[Cos[c + d*x]])/(2^(1/3)*a^(4/3)*d) + (((3*I)/8)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(4/3)*d) + ((3*I)/8)/(d*(a + I*a*Tan[c + d*x])^(4/3)) + ((3*I)/4)/(a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",7,6,17,0.3529,1,"{3479, 3481, 55, 617, 204, 31}"
305,1,313,0,0.596277,"\int \frac{\cot (c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Cot[c + d*x]/(a + I*a*Tan[c + d*x])^(4/3),x]","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3} d}-\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\tan (c+d x))}{2 a^{4/3} d}+\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 a^{4/3} d}-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{9}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3}{8 d (a+i a \tan (c+d x))^{4/3}}","\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{a}+2 \sqrt[3]{a+i a \tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{4/3} d}-\frac{\sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\tan (c+d x))}{2 a^{4/3} d}+\frac{3 \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{2 a^{4/3} d}-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{\log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i x}{8 \sqrt[3]{2} a^{4/3}}+\frac{9}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}+\frac{3}{8 d (a+i a \tan (c+d x))^{4/3}}",1,"((-I/8)*x)/(2^(1/3)*a^(4/3)) + (Sqrt[3]*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(4/3)*d) - (Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(4*2^(1/3)*a^(4/3)*d) - Log[Cos[c + d*x]]/(8*2^(1/3)*a^(4/3)*d) - Log[Tan[c + d*x]]/(2*a^(4/3)*d) + (3*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2*a^(4/3)*d) - (3*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(8*2^(1/3)*a^(4/3)*d) + 3/(8*d*(a + I*a*Tan[c + d*x])^(4/3)) + 9/(4*a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",15,9,24,0.3750,1,"{3562, 3479, 3481, 55, 617, 204, 31, 3596, 3599}"
306,1,354,0,0.7105542,"\int \frac{\cot ^2(c+d x)}{(a+i a \tan (c+d x))^{4/3}} \, dx","Int[Cot[c + d*x]^2/(a + I*a*Tan[c + d*x])^(4/3),x]","-\frac{4 i \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} a^{4/3} d}-\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{2 i \log (\tan (c+d x))}{3 a^{4/3} d}-\frac{2 i \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{a^{4/3} d}-\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{x}{8 \sqrt[3]{2} a^{4/3}}-\frac{19 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{11 i}{8 d (a+i a \tan (c+d x))^{4/3}}-\frac{\cot (c+d x)}{d (a+i a \tan (c+d x))^{4/3}}","-\frac{4 i \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} a^{4/3} d}-\frac{i \sqrt{3} \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)}{4 \sqrt[3]{2} a^{4/3} d}+\frac{2 i \log (\tan (c+d x))}{3 a^{4/3} d}-\frac{2 i \log \left(\sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{a^{4/3} d}-\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8 \sqrt[3]{2} a^{4/3} d}-\frac{i \log (\cos (c+d x))}{8 \sqrt[3]{2} a^{4/3} d}+\frac{x}{8 \sqrt[3]{2} a^{4/3}}-\frac{19 i}{4 a d \sqrt[3]{a+i a \tan (c+d x)}}-\frac{11 i}{8 d (a+i a \tan (c+d x))^{4/3}}-\frac{\cot (c+d x)}{d (a+i a \tan (c+d x))^{4/3}}",1,"x/(8*2^(1/3)*a^(4/3)) - ((4*I)*ArcTan[(a^(1/3) + 2*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d) - ((I/4)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(1/3)*a^(4/3)*d) - ((I/8)*Log[Cos[c + d*x]])/(2^(1/3)*a^(4/3)*d) + (((2*I)/3)*Log[Tan[c + d*x]])/(a^(4/3)*d) - ((2*I)*Log[a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(a^(4/3)*d) - (((3*I)/8)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(1/3)*a^(4/3)*d) - ((11*I)/8)/(d*(a + I*a*Tan[c + d*x])^(4/3)) - Cot[c + d*x]/(d*(a + I*a*Tan[c + d*x])^(4/3)) - ((19*I)/4)/(a*d*(a + I*a*Tan[c + d*x])^(1/3))","A",14,9,26,0.3462,1,"{3561, 3596, 3600, 3481, 55, 617, 204, 31, 3599}"
307,1,213,0,0.1323816,"\int \frac{1}{(a+i a \tan (c+d x))^{5/3}} \, dx","Int[(a + I*a*Tan[c + d*x])^(-5/3),x]","-\frac{i \sqrt{3} \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)}{4\ 2^{2/3} a^{5/3} d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8\ 2^{2/3} a^{5/3} d}+\frac{i \log (\cos (c+d x))}{8\ 2^{2/3} a^{5/3} d}-\frac{x}{8\ 2^{2/3} a^{5/3}}+\frac{3 i}{8 a d (a+i a \tan (c+d x))^{2/3}}+\frac{3 i}{10 d (a+i a \tan (c+d x))^{5/3}}","-\frac{i \sqrt{3} \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)}{4\ 2^{2/3} a^{5/3} d}+\frac{3 i \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+i a \tan (c+d x)}\right)}{8\ 2^{2/3} a^{5/3} d}+\frac{i \log (\cos (c+d x))}{8\ 2^{2/3} a^{5/3} d}-\frac{x}{8\ 2^{2/3} a^{5/3}}+\frac{3 i}{8 a d (a+i a \tan (c+d x))^{2/3}}+\frac{3 i}{10 d (a+i a \tan (c+d x))^{5/3}}",1,"-x/(8*2^(2/3)*a^(5/3)) - ((I/4)*Sqrt[3]*ArcTan[(a^(1/3) + 2^(2/3)*(a + I*a*Tan[c + d*x])^(1/3))/(Sqrt[3]*a^(1/3))])/(2^(2/3)*a^(5/3)*d) + ((I/8)*Log[Cos[c + d*x]])/(2^(2/3)*a^(5/3)*d) + (((3*I)/8)*Log[2^(1/3)*a^(1/3) - (a + I*a*Tan[c + d*x])^(1/3)])/(2^(2/3)*a^(5/3)*d) + ((3*I)/10)/(d*(a + I*a*Tan[c + d*x])^(5/3)) + ((3*I)/8)/(a*d*(a + I*a*Tan[c + d*x])^(2/3))","A",7,6,17,0.3529,1,"{3479, 3481, 57, 617, 204, 31}"
308,1,43,0,0.0462262,"\int (e \tan (c+d x))^m (a+i a \tan (c+d x)) \, dx","Int[(e*Tan[c + d*x])^m*(a + I*a*Tan[c + d*x]),x]","\frac{a (e \tan (c+d x))^{m+1} \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d e (m+1)}","\frac{a (e \tan (c+d x))^{m+1} \, _2F_1(1,m+1;m+2;i \tan (c+d x))}{d e (m+1)}",1,"(a*Hypergeometric2F1[1, 1 + m, 2 + m, I*Tan[c + d*x]]*(e*Tan[c + d*x])^(1 + m))/(d*e*(1 + m))","A",2,2,24,0.08333,1,"{3537, 64}"
309,1,43,0,0.041055,"\int (e \tan (c+d x))^m (a-i a \tan (c+d x)) \, dx","Int[(e*Tan[c + d*x])^m*(a - I*a*Tan[c + d*x]),x]","\frac{a (e \tan (c+d x))^{m+1} \, _2F_1(1,m+1;m+2;-i \tan (c+d x))}{d e (m+1)}","\frac{a (e \tan (c+d x))^{m+1} \, _2F_1(1,m+1;m+2;-i \tan (c+d x))}{d e (m+1)}",1,"(a*Hypergeometric2F1[1, 1 + m, 2 + m, (-I)*Tan[c + d*x]]*(e*Tan[c + d*x])^(1 + m))/(d*e*(1 + m))","A",2,2,24,0.08333,1,"{3537, 64}"
310,1,189,0,0.530527,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x))^4 \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x])^4,x]","\frac{8 a^4 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}-\frac{2 a^4 \left(2 n^2+11 n+16\right) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2) (n+3)}-\frac{\left(a^2+i a^2 \tan (e+f x)\right)^2 (d \tan (e+f x))^{n+1}}{d f (n+3)}-\frac{2 (n+4) \left(a^4+i a^4 \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+2) (n+3)}","\frac{8 a^4 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}-\frac{2 a^4 \left(2 n^2+11 n+16\right) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2) (n+3)}-\frac{\left(a^2+i a^2 \tan (e+f x)\right)^2 (d \tan (e+f x))^{n+1}}{d f (n+3)}-\frac{2 (n+4) \left(a^4+i a^4 \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+2) (n+3)}",1,"(-2*a^4*(16 + 11*n + 2*n^2)*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n)*(3 + n)) + (8*a^4*Hypergeometric2F1[1, 1 + n, 2 + n, I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) - ((d*Tan[e + f*x])^(1 + n)*(a^2 + I*a^2*Tan[e + f*x])^2)/(d*f*(3 + n)) - (2*(4 + n)*(d*Tan[e + f*x])^(1 + n)*(a^4 + I*a^4*Tan[e + f*x]))/(d*f*(2 + n)*(3 + n))","A",6,6,26,0.2308,1,"{3556, 3594, 3592, 3537, 12, 64}"
311,1,127,0,0.2590307,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x])^3,x]","\frac{4 a^3 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}-\frac{a^3 (2 n+5) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2)}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+2)}","\frac{4 a^3 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}-\frac{a^3 (2 n+5) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2)}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+2)}",1,"-((a^3*(5 + 2*n)*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n))) + (4*a^3*Hypergeometric2F1[1, 1 + n, 2 + n, I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) - ((d*Tan[e + f*x])^(1 + n)*(a^3 + I*a^3*Tan[e + f*x]))/(d*f*(2 + n))","A",5,5,26,0.1923,1,"{3556, 3592, 3537, 12, 64}"
312,1,75,0,0.1149569,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x])^2,x]","-\frac{a^2 (d \tan (e+f x))^{n+1}}{d f (n+1)}+\frac{2 a^2 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}","-\frac{a^2 (d \tan (e+f x))^{n+1}}{d f (n+1)}+\frac{2 a^2 (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}",1,"-((a^2*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n))) + (2*a^2*Hypergeometric2F1[1, 1 + n, 2 + n, I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n))","A",4,4,26,0.1538,1,"{3543, 3537, 12, 64}"
313,1,43,0,0.0457455,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x]),x]","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;i \tan (e+f x))}{d f (n+1)}",1,"(a*Hypergeometric2F1[1, 1 + n, 2 + n, I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n))","A",2,2,24,0.08333,1,"{3537, 64}"
314,1,158,0,0.1806113,"\int \frac{(d \tan (e+f x))^n}{a+i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x]),x]","\frac{i n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(1-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{2 a d f (n+1)}+\frac{(d \tan (e+f x))^{n+1}}{2 d f (a+i a \tan (e+f x))}","\frac{i n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(1-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{2 a d f (n+1)}+\frac{(d \tan (e+f x))^{n+1}}{2 d f (a+i a \tan (e+f x))}",1,"((1 - n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(2*a*d*f*(1 + n)) + ((I/2)*n*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(a*d^2*f*(2 + n)) + (d*Tan[e + f*x])^(1 + n)/(2*d*f*(a + I*a*Tan[e + f*x]))","A",6,4,26,0.1538,1,"{3552, 3538, 3476, 364}"
315,1,209,0,0.3616717,"\int \frac{(d \tan (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^2,x]","\frac{i (2-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{4 a^2 d^2 f (n+2)}+\frac{(1-n)^2 (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{4 a^2 d f (n+1)}+\frac{(2-n) (d \tan (e+f x))^{n+1}}{4 a^2 d f (1+i \tan (e+f x))}+\frac{(d \tan (e+f x))^{n+1}}{4 d f (a+i a \tan (e+f x))^2}","\frac{i (2-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{4 a^2 d^2 f (n+2)}+\frac{(1-n)^2 (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{4 a^2 d f (n+1)}+\frac{(2-n) (d \tan (e+f x))^{n+1}}{4 a^2 d f (1+i \tan (e+f x))}+\frac{(d \tan (e+f x))^{n+1}}{4 d f (a+i a \tan (e+f x))^2}",1,"((1 - n)^2*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(4*a^2*d*f*(1 + n)) + ((2 - n)*(d*Tan[e + f*x])^(1 + n))/(4*a^2*d*f*(1 + I*Tan[e + f*x])) + ((I/4)*(2 - n)*n*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(a^2*d^2*f*(2 + n)) + (d*Tan[e + f*x])^(1 + n)/(4*d*f*(a + I*a*Tan[e + f*x])^2)","A",7,5,26,0.1923,1,"{3559, 3596, 3538, 3476, 364}"
316,1,274,0,0.6686505,"\int \frac{(d \tan (e+f x))^n}{(a+i a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^3,x]","\frac{i (5-2 n) (2-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{24 a^3 d^2 f (n+2)}+\frac{(1-2 n) (1-n) (3-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{24 a^3 d f (n+1)}+\frac{(5-2 n) (2-n) (d \tan (e+f x))^{n+1}}{24 d f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{(7-2 n) (d \tan (e+f x))^{n+1}}{24 a d f (a+i a \tan (e+f x))^2}+\frac{(d \tan (e+f x))^{n+1}}{6 d f (a+i a \tan (e+f x))^3}","\frac{i (5-2 n) (2-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{24 a^3 d^2 f (n+2)}+\frac{(1-2 n) (1-n) (3-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{24 a^3 d f (n+1)}+\frac{(5-2 n) (2-n) (d \tan (e+f x))^{n+1}}{24 d f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{(7-2 n) (d \tan (e+f x))^{n+1}}{24 a d f (a+i a \tan (e+f x))^2}+\frac{(d \tan (e+f x))^{n+1}}{6 d f (a+i a \tan (e+f x))^3}",1,"((1 - 2*n)*(1 - n)*(3 - n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(24*a^3*d*f*(1 + n)) + ((I/24)*(5 - 2*n)*(2 - n)*n*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(a^3*d^2*f*(2 + n)) + (d*Tan[e + f*x])^(1 + n)/(6*d*f*(a + I*a*Tan[e + f*x])^3) + ((7 - 2*n)*(d*Tan[e + f*x])^(1 + n))/(24*a*d*f*(a + I*a*Tan[e + f*x])^2) + ((5 - 2*n)*(2 - n)*(d*Tan[e + f*x])^(1 + n))/(24*d*f*(a^3 + I*a^3*Tan[e + f*x]))","A",8,5,26,0.1923,1,"{3559, 3596, 3538, 3476, 364}"
317,1,326,0,0.9730917,"\int \frac{(d \tan (e+f x))^n}{(a+i a \tan (e+f x))^4} \, dx","Int[(d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^4,x]","\frac{i (2-n)^2 (4-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{48 a^4 d^2 f (n+2)}+\frac{(1-n) (3-n) \left(n^2-4 n+1\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{48 a^4 d f (n+1)}+\frac{\left(n^2-7 n+13\right) (d \tan (e+f x))^{n+1}}{48 a^4 d f (1+i \tan (e+f x))^2}+\frac{(2-n)^2 (4-n) (d \tan (e+f x))^{n+1}}{48 a^4 d f (1+i \tan (e+f x))}+\frac{(5-n) (d \tan (e+f x))^{n+1}}{24 a d f (a+i a \tan (e+f x))^3}+\frac{(d \tan (e+f x))^{n+1}}{8 d f (a+i a \tan (e+f x))^4}","\frac{i (2-n)^2 (4-n) n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{48 a^4 d^2 f (n+2)}+\frac{(1-n) (3-n) \left(n^2-4 n+1\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{48 a^4 d f (n+1)}+\frac{\left(n^2-7 n+13\right) (d \tan (e+f x))^{n+1}}{48 a^4 d f (1+i \tan (e+f x))^2}+\frac{(2-n)^2 (4-n) (d \tan (e+f x))^{n+1}}{48 a^4 d f (1+i \tan (e+f x))}+\frac{(5-n) (d \tan (e+f x))^{n+1}}{24 a d f (a+i a \tan (e+f x))^3}+\frac{(d \tan (e+f x))^{n+1}}{8 d f (a+i a \tan (e+f x))^4}",1,"((1 - n)*(3 - n)*(1 - 4*n + n^2)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(48*a^4*d*f*(1 + n)) + ((13 - 7*n + n^2)*(d*Tan[e + f*x])^(1 + n))/(48*a^4*d*f*(1 + I*Tan[e + f*x])^2) + ((2 - n)^2*(4 - n)*(d*Tan[e + f*x])^(1 + n))/(48*a^4*d*f*(1 + I*Tan[e + f*x])) + ((I/48)*(2 - n)^2*(4 - n)*n*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(a^4*d^2*f*(2 + n)) + (d*Tan[e + f*x])^(1 + n)/(8*d*f*(a + I*a*Tan[e + f*x])^4) + ((5 - n)*(d*Tan[e + f*x])^(1 + n))/(24*a*d*f*(a + I*a*Tan[e + f*x])^3)","A",9,5,26,0.1923,1,"{3559, 3596, 3538, 3476, 364}"
318,1,43,0,0.0488593,"\int (d \tan (e+f x))^n (a-i a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^n*(a - I*a*Tan[e + f*x]),x]","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;-i \tan (e+f x))}{d f (n+1)}","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1(1,n+1;n+2;-i \tan (e+f x))}{d f (n+1)}",1,"(a*Hypergeometric2F1[1, 1 + n, 2 + n, (-I)*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n))","A",2,2,24,0.08333,1,"{3537, 64}"
319,1,158,0,0.1737779,"\int \frac{(d \tan (e+f x))^n}{a-i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^n/(a - I*a*Tan[e + f*x]),x]","-\frac{i n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(1-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{2 a d f (n+1)}+\frac{(d \tan (e+f x))^{n+1}}{2 d f (a-i a \tan (e+f x))}","-\frac{i n (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(1-n) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{2 a d f (n+1)}+\frac{(d \tan (e+f x))^{n+1}}{2 d f (a-i a \tan (e+f x))}",1,"((1 - n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(2*a*d*f*(1 + n)) - ((I/2)*n*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(a*d^2*f*(2 + n)) + (d*Tan[e + f*x])^(1 + n)/(2*d*f*(a - I*a*Tan[e + f*x]))","A",6,4,26,0.1538,1,"{3552, 3538, 3476, 364}"
320,1,89,0,0.1384211,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x))^{3/2} \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{a \sqrt{a+i a \tan (e+f x)} F_1\left(n+1;-\frac{1}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{1+i \tan (e+f x)}}","\frac{a \sqrt{a+i a \tan (e+f x)} F_1\left(n+1;-\frac{1}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{1+i \tan (e+f x)}}",1,"(a*AppellF1[1 + n, -1/2, 1, 2 + n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*Sqrt[a + I*a*Tan[e + f*x]])/(d*f*(1 + n)*Sqrt[1 + I*Tan[e + f*x]])","A",3,3,28,0.1071,1,"{3564, 135, 133}"
321,1,89,0,0.120176,"\int (d \tan (e+f x))^n \sqrt{a+i a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^n*Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{a \sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{1}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{a+i a \tan (e+f x)}}","\frac{a \sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{1}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{a+i a \tan (e+f x)}}",1,"(a*AppellF1[1 + n, 1/2, 1, 2 + n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*Sqrt[1 + I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,28,0.1071,1,"{3564, 135, 133}"
322,1,88,0,0.1243403,"\int \frac{(d \tan (e+f x))^n}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[(d*Tan[e + f*x])^n/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{\sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{3}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{a+i a \tan (e+f x)}}","\frac{\sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{3}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) \sqrt{a+i a \tan (e+f x)}}",1,"(AppellF1[1 + n, 3/2, 1, 2 + n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*Sqrt[1 + I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,28,0.1071,1,"{3564, 135, 133}"
323,1,91,0,0.1291668,"\int \frac{(d \tan (e+f x))^n}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[(d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{\sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{5}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{a d f (n+1) \sqrt{a+i a \tan (e+f x)}}","\frac{\sqrt{1+i \tan (e+f x)} F_1\left(n+1;\frac{5}{2},1;n+2;-i \tan (e+f x),i \tan (e+f x)\right) (d \tan (e+f x))^{n+1}}{a d f (n+1) \sqrt{a+i a \tan (e+f x)}}",1,"(AppellF1[1 + n, 5/2, 1, 2 + n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*Sqrt[1 + I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n))/(a*d*f*(1 + n)*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,28,0.1071,1,"{3564, 135, 133}"
324,1,88,0,0.0970577,"\int (d \tan (e+f x))^n (a+i a \tan (e+f x))^m \, dx","Int[(d*Tan[e + f*x])^n*(a + I*a*Tan[e + f*x])^m,x]","\frac{(1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (d \tan (e+f x))^{n+1} F_1(n+1;1-m,1;n+2;-i \tan (e+f x),i \tan (e+f x))}{d f (n+1)}","\frac{(1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (d \tan (e+f x))^{n+1} F_1(n+1;1-m,1;n+2;-i \tan (e+f x),i \tan (e+f x))}{d f (n+1)}",1,"(AppellF1[1 + n, 1 - m, 1, 2 + n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*(a + I*a*Tan[e + f*x])^m)/(d*f*(1 + n)*(1 + I*Tan[e + f*x])^m)","A",3,3,26,0.1154,1,"{3564, 135, 133}"
325,1,205,0,0.3586612,"\int \tan ^4(c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Tan[c + d*x]^4*(a + I*a*Tan[c + d*x])^m,x]","-\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i m \tan ^2(c+d x) (a+i a \tan (c+d x))^m}{d \left(m^2+5 m+6\right)}+\frac{2 i (a+i a \tan (c+d x))^m}{d \left(m^2+5 m+6\right)}+\frac{i \left(m^2+3 m+6\right) (a+i a \tan (c+d x))^{m+1}}{a d (m+1) (m+2) (m+3)}+\frac{\tan ^3(c+d x) (a+i a \tan (c+d x))^m}{d (m+3)}","-\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i m \tan ^2(c+d x) (a+i a \tan (c+d x))^m}{d \left(m^2+5 m+6\right)}+\frac{2 i (a+i a \tan (c+d x))^m}{d \left(m^2+5 m+6\right)}+\frac{i \left(m^2+3 m+6\right) (a+i a \tan (c+d x))^{m+1}}{a d (m+1) (m+2) (m+3)}+\frac{\tan ^3(c+d x) (a+i a \tan (c+d x))^m}{d (m+3)}",1,"((2*I)*(a + I*a*Tan[c + d*x])^m)/(d*(6 + 5*m + m^2)) - ((I/2)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(d*m) - (I*m*Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^m)/(d*(6 + 5*m + m^2)) + (Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^m)/(d*(3 + m)) + (I*(6 + 3*m + m^2)*(a + I*a*Tan[c + d*x])^(1 + m))/(a*d*(1 + m)*(2 + m)*(3 + m))","A",6,6,24,0.2500,1,"{3560, 3597, 3592, 3527, 3481, 68}"
326,1,144,0,0.1919031,"\int \tan ^3(c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Tan[c + d*x]^3*(a + I*a*Tan[c + d*x])^m,x]","\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{m (a+i a \tan (c+d x))^{m+1}}{a d \left(m^2+3 m+2\right)}+\frac{\tan ^2(c+d x) (a+i a \tan (c+d x))^m}{d (m+2)}-\frac{2 (a+i a \tan (c+d x))^m}{d m (m+2)}","\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{m (a+i a \tan (c+d x))^{m+1}}{a d \left(m^2+3 m+2\right)}+\frac{\tan ^2(c+d x) (a+i a \tan (c+d x))^m}{d (m+2)}-\frac{2 (a+i a \tan (c+d x))^m}{d m (m+2)}",1,"(-2*(a + I*a*Tan[c + d*x])^m)/(d*m*(2 + m)) + (Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(2*d*m) + (Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^m)/(d*(2 + m)) - (m*(a + I*a*Tan[c + d*x])^(1 + m))/(a*d*(2 + 3*m + m^2))","A",5,5,24,0.2083,1,"{3560, 3592, 3527, 3481, 68}"
327,1,82,0,0.0696865,"\int \tan ^2(c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Tan[c + d*x]^2*(a + I*a*Tan[c + d*x])^m,x]","\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i (a+i a \tan (c+d x))^{m+1}}{a d (m+1)}","\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i (a+i a \tan (c+d x))^{m+1}}{a d (m+1)}",1,"((I/2)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(d*m) - (I*(a + I*a*Tan[c + d*x])^(1 + m))/(a*d*(1 + m))","A",3,3,24,0.1250,1,"{3543, 3481, 68}"
328,1,70,0,0.0536973,"\int \tan (c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Tan[c + d*x]*(a + I*a*Tan[c + d*x])^m,x]","\frac{(a+i a \tan (c+d x))^m}{d m}-\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}","\frac{(a+i a \tan (c+d x))^m}{d m}-\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}",1,"(a + I*a*Tan[c + d*x])^m/(d*m) - (Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(2*d*m)","A",3,3,22,0.1364,1,"{3527, 3481, 68}"
329,1,49,0,0.0250745,"\int (a+i a \tan (c+d x))^m \, dx","Int[(a + I*a*Tan[c + d*x])^m,x]","-\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}","-\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}",1,"((-I/2)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(d*m)","A",2,2,15,0.1333,1,"{3481, 68}"
330,1,89,0,0.1402383,"\int \cot (c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Cot[c + d*x]*(a + I*a*Tan[c + d*x])^m,x]","\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{(a+i a \tan (c+d x))^m \, _2F_1(1,m;m+1;i \tan (c+d x)+1)}{d m}","\frac{(a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{(a+i a \tan (c+d x))^m \, _2F_1(1,m;m+1;i \tan (c+d x)+1)}{d m}",1,"(Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(2*d*m) - (Hypergeometric2F1[1, m, 1 + m, 1 + I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^m)/(d*m)","A",5,5,22,0.2273,1,"{3562, 3481, 68, 3599, 65}"
331,1,116,0,0.2585739,"\int \cot ^2(c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Cot[c + d*x]^2*(a + I*a*Tan[c + d*x])^m,x]","\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i (a+i a \tan (c+d x))^m \, _2F_1(1,m;m+1;i \tan (c+d x)+1)}{d}-\frac{\cot (c+d x) (a+i a \tan (c+d x))^m}{d}","\frac{i (a+i a \tan (c+d x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (c+d x)+1)\right)}{2 d m}-\frac{i (a+i a \tan (c+d x))^m \, _2F_1(1,m;m+1;i \tan (c+d x)+1)}{d}-\frac{\cot (c+d x) (a+i a \tan (c+d x))^m}{d}",1,"-((Cot[c + d*x]*(a + I*a*Tan[c + d*x])^m)/d) + ((I/2)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[c + d*x])/2]*(a + I*a*Tan[c + d*x])^m)/(d*m) - (I*Hypergeometric2F1[1, m, 1 + m, 1 + I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^m)/d","A",6,6,24,0.2500,1,"{3561, 3600, 3481, 68, 3599, 65}"
332,1,81,0,0.1251079,"\int \tan ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^m \, dx","Int[Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^m,x]","\frac{2 \tan ^{\frac{5}{2}}(c+d x) (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{5}{2};1-m,1;\frac{7}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d}","\frac{2 \tan ^{\frac{5}{2}}(c+d x) (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{5}{2};1-m,1;\frac{7}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d}",1,"(2*AppellF1[5/2, 1 - m, 1, 7/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^m)/(5*d*(1 + I*Tan[c + d*x])^m)","A",4,4,26,0.1538,1,"{3564, 130, 511, 510}"
333,1,81,0,0.1174133,"\int \sqrt{\tan (c+d x)} (a+i a \tan (c+d x))^m \, dx","Int[Sqrt[Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^m,x]","\frac{2 \tan ^{\frac{3}{2}}(c+d x) (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{3}{2};1-m,1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d}","\frac{2 \tan ^{\frac{3}{2}}(c+d x) (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{3}{2};1-m,1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d}",1,"(2*AppellF1[3/2, 1 - m, 1, 5/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Tan[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^m)/(3*d*(1 + I*Tan[c + d*x])^m)","A",4,4,26,0.1538,1,"{3564, 130, 511, 510}"
334,1,79,0,0.0994344,"\int \frac{(a+i a \tan (c+d x))^m}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^m/Sqrt[Tan[c + d*x]],x]","\frac{2 \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{1}{2};1-m,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}","\frac{2 \sqrt{\tan (c+d x)} (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(\frac{1}{2};1-m,1;\frac{3}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}",1,"(2*AppellF1[1/2, 1 - m, 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])^m)/(d*(1 + I*Tan[c + d*x])^m)","A",4,4,26,0.1538,1,"{3564, 130, 430, 429}"
335,1,79,0,0.1190748,"\int \frac{(a+i a \tan (c+d x))^m}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^m/Tan[c + d*x]^(3/2),x]","-\frac{2 (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(-\frac{1}{2};1-m,1;\frac{1}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\tan (c+d x)}}","-\frac{2 (1+i \tan (c+d x))^{-m} (a+i a \tan (c+d x))^m F_1\left(-\frac{1}{2};1-m,1;\frac{1}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d \sqrt{\tan (c+d x)}}",1,"(-2*AppellF1[-1/2, 1 - m, 1, 1/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^m)/(d*(1 + I*Tan[c + d*x])^m*Sqrt[Tan[c + d*x]])","A",4,4,26,0.1538,1,"{3564, 130, 511, 510}"
336,1,115,0,0.1488183,"\int (d \tan (e+f x))^{5/2} (a+a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x]),x]","-\frac{2 a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{\sqrt{2} a d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}+\frac{2 a (d \tan (e+f x))^{5/2}}{5 f}","-\frac{2 a d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{\sqrt{2} a d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 a d (d \tan (e+f x))^{3/2}}{3 f}+\frac{2 a (d \tan (e+f x))^{5/2}}{5 f}",1,"(Sqrt[2]*a*d^(5/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f - (2*a*d^2*Sqrt[d*Tan[e + f*x]])/f + (2*a*d*(d*Tan[e + f*x])^(3/2))/(3*f) + (2*a*(d*Tan[e + f*x])^(5/2))/(5*f)","A",5,3,23,0.1304,1,"{3528, 3532, 208}"
337,1,93,0,0.1085723,"\int (d \tan (e+f x))^{3/2} (a+a \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x]),x]","\frac{\sqrt{2} a d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}+\frac{2 a (d \tan (e+f x))^{3/2}}{3 f}","\frac{\sqrt{2} a d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 a d \sqrt{d \tan (e+f x)}}{f}+\frac{2 a (d \tan (e+f x))^{3/2}}{3 f}",1,"(Sqrt[2]*a*d^(3/2)*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f + (2*a*d*Sqrt[d*Tan[e + f*x]])/f + (2*a*(d*Tan[e + f*x])^(3/2))/(3*f)","A",4,3,23,0.1304,1,"{3528, 3532, 205}"
338,1,72,0,0.0730247,"\int \sqrt{d \tan (e+f x)} (a+a \tan (e+f x)) \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x]),x]","\frac{2 a \sqrt{d \tan (e+f x)}}{f}-\frac{\sqrt{2} a \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}","\frac{2 a \sqrt{d \tan (e+f x)}}{f}-\frac{\sqrt{2} a \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}",1,"-((Sqrt[2]*a*Sqrt[d]*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f) + (2*a*Sqrt[d*Tan[e + f*x]])/f","A",3,3,23,0.1304,1,"{3528, 3532, 208}"
339,1,50,0,0.0410533,"\int \frac{a+a \tan (e+f x)}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + a*Tan[e + f*x])/Sqrt[d*Tan[e + f*x]],x]","-\frac{\sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{d} (1-\tan (e+f x))}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{d} f}","-\frac{\sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{d} (1-\tan (e+f x))}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{d} f}",1,"-((Sqrt[2]*a*ArcTan[(Sqrt[d]*(1 - Tan[e + f*x]))/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(Sqrt[d]*f))","A",2,2,23,0.08696,1,"{3532, 205}"
340,1,74,0,0.0792321,"\int \frac{a+a \tan (e+f x)}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + a*Tan[e + f*x])/(d*Tan[e + f*x])^(3/2),x]","\frac{\sqrt{2} a \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}","\frac{\sqrt{2} a \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{2 a}{d f \sqrt{d \tan (e+f x)}}",1,"(Sqrt[2]*a*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(3/2)*f) - (2*a)/(d*f*Sqrt[d*Tan[e + f*x]])","A",3,3,23,0.1304,1,"{3529, 3532, 208}"
341,1,98,0,0.1224554,"\int \frac{a+a \tan (e+f x)}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + a*Tan[e + f*x])/(d*Tan[e + f*x])^(5/2),x]","\frac{\sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 a}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}","\frac{\sqrt{2} a \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 a}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d f (d \tan (e+f x))^{3/2}}",1,"(Sqrt[2]*a*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(5/2)*f) - (2*a)/(3*d*f*(d*Tan[e + f*x])^(3/2)) - (2*a)/(d^2*f*Sqrt[d*Tan[e + f*x]])","A",4,3,23,0.1304,1,"{3529, 3532, 205}"
342,1,121,0,0.1655017,"\int \frac{a+a \tan (e+f x)}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a + a*Tan[e + f*x])/(d*Tan[e + f*x])^(7/2),x]","\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{\sqrt{2} a \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}","\frac{2 a}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{2 a}{3 d^2 f (d \tan (e+f x))^{3/2}}-\frac{\sqrt{2} a \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{2 a}{5 d f (d \tan (e+f x))^{5/2}}",1,"-((Sqrt[2]*a*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(7/2)*f)) - (2*a)/(5*d*f*(d*Tan[e + f*x])^(5/2)) - (2*a)/(3*d^2*f*(d*Tan[e + f*x])^(3/2)) + (2*a)/(d^3*f*Sqrt[d*Tan[e + f*x]])","A",5,3,23,0.1304,1,"{3529, 3532, 208}"
343,1,269,0,0.2582402,"\int (d \tan (e+f x))^{5/2} (a+a \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x])^2,x]","-\frac{\sqrt{2} a^2 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{\sqrt{2} a^2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}-\frac{4 a^2 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{a^2 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{a^2 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{2 a^2 (d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 a^2 (d \tan (e+f x))^{5/2}}{5 f}","-\frac{\sqrt{2} a^2 d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}+\frac{\sqrt{2} a^2 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}-\frac{4 a^2 d^2 \sqrt{d \tan (e+f x)}}{f}-\frac{a^2 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{a^2 d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{2 a^2 (d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 a^2 (d \tan (e+f x))^{5/2}}{5 f}",1,"-((Sqrt[2]*a^2*d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f) + (Sqrt[2]*a^2*d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - (a^2*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) + (a^2*d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) - (4*a^2*d^2*Sqrt[d*Tan[e + f*x]])/f + (4*a^2*(d*Tan[e + f*x])^(5/2))/(5*f) + (2*a^2*(d*Tan[e + f*x])^(7/2))/(7*d*f)","A",16,12,25,0.4800,1,"{3543, 12, 16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
344,1,246,0,0.2276387,"\int (d \tan (e+f x))^{3/2} (a+a \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])^2,x]","\frac{\sqrt{2} a^2 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{\sqrt{2} a^2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}-\frac{a^2 d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{a^2 d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{2 a^2 (d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 a^2 (d \tan (e+f x))^{3/2}}{3 f}","\frac{\sqrt{2} a^2 d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{\sqrt{2} a^2 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}-\frac{a^2 d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{a^2 d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}+\frac{2 a^2 (d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 a^2 (d \tan (e+f x))^{3/2}}{3 f}",1,"(Sqrt[2]*a^2*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - (Sqrt[2]*a^2*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - (a^2*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) + (a^2*d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) + (4*a^2*(d*Tan[e + f*x])^(3/2))/(3*f) + (2*a^2*(d*Tan[e + f*x])^(5/2))/(5*d*f)","A",15,12,25,0.4800,1,"{3543, 12, 16, 3473, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
345,1,244,0,0.2190884,"\int \sqrt{d \tan (e+f x)} (a+a \tan (e+f x))^2 \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])^2,x]","\frac{\sqrt{2} a^2 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{\sqrt{2} a^2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}+\frac{2 a^2 (d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 a^2 \sqrt{d \tan (e+f x)}}{f}+\frac{a^2 \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}-\frac{a^2 \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}","\frac{\sqrt{2} a^2 \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{f}-\frac{\sqrt{2} a^2 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{f}+\frac{2 a^2 (d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 a^2 \sqrt{d \tan (e+f x)}}{f}+\frac{a^2 \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}-\frac{a^2 \sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} f}",1,"(Sqrt[2]*a^2*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f - (Sqrt[2]*a^2*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/f + (a^2*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) - (a^2*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*f) + (4*a^2*Sqrt[d*Tan[e + f*x]])/f + (2*a^2*(d*Tan[e + f*x])^(3/2))/(3*d*f)","A",15,12,25,0.4800,1,"{3543, 12, 16, 3473, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
346,1,222,0,0.1944391,"\int \frac{(a+a \tan (e+f x))^2}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + a*Tan[e + f*x])^2/Sqrt[d*Tan[e + f*x]],x]","-\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}+\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{d} f}+\frac{2 a^2 \sqrt{d \tan (e+f x)}}{d f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} \sqrt{d} f}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} \sqrt{d} f}","-\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{\sqrt{d} f}+\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{\sqrt{d} f}+\frac{2 a^2 \sqrt{d \tan (e+f x)}}{d f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} \sqrt{d} f}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} \sqrt{d} f}",1,"-((Sqrt[2]*a^2*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f)) + (Sqrt[2]*a^2*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(Sqrt[d]*f) + (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*Sqrt[d]*f) - (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*Sqrt[d]*f) + (2*a^2*Sqrt[d*Tan[e + f*x]])/(d*f)","A",14,11,25,0.4400,1,"{3543, 12, 16, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
347,1,222,0,0.1993647,"\int \frac{(a+a \tan (e+f x))^2}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + a*Tan[e + f*x])^2/(d*Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}+\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{d^{3/2} f}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{3/2} f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{3/2} f}-\frac{2 a^2}{d f \sqrt{d \tan (e+f x)}}","-\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{3/2} f}+\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{d^{3/2} f}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{3/2} f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{3/2} f}-\frac{2 a^2}{d f \sqrt{d \tan (e+f x)}}",1,"-((Sqrt[2]*a^2*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f)) + (Sqrt[2]*a^2*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(3/2)*f) - (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*d^(3/2)*f) + (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*d^(3/2)*f) - (2*a^2)/(d*f*Sqrt[d*Tan[e + f*x]])","A",13,10,25,0.4000,1,"{3542, 12, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
348,1,247,0,0.235596,"\int \frac{(a+a \tan (e+f x))^2}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + a*Tan[e + f*x])^2/(d*Tan[e + f*x])^(5/2),x]","\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{d^{5/2} f}-\frac{4 a^2}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{5/2} f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{5/2} f}-\frac{2 a^2}{3 d f (d \tan (e+f x))^{3/2}}","\frac{\sqrt{2} a^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{d^{5/2} f}-\frac{\sqrt{2} a^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{d^{5/2} f}-\frac{4 a^2}{d^2 f \sqrt{d \tan (e+f x)}}-\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{5/2} f}+\frac{a^2 \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{\sqrt{2} d^{5/2} f}-\frac{2 a^2}{3 d f (d \tan (e+f x))^{3/2}}",1,"(Sqrt[2]*a^2*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (Sqrt[2]*a^2*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(d^(5/2)*f) - (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*d^(5/2)*f) + (a^2*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(Sqrt[2]*d^(5/2)*f) - (2*a^2)/(3*d*f*(d*Tan[e + f*x])^(3/2)) - (4*a^2)/(d^2*f*Sqrt[d*Tan[e + f*x]])","A",14,11,25,0.4400,1,"{3542, 12, 3474, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
349,1,210,0,0.3237813,"\int (d \tan (e+f x))^{7/2} (a+a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^(7/2)*(a + a*Tan[e + f*x])^3,x]","-\frac{4 a^3 d^2 (d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^3 d^3 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \sqrt{2} a^3 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{9/2}}{11 d f}+\frac{16 a^3 (d \tan (e+f x))^{9/2}}{33 d f}+\frac{4 a^3 (d \tan (e+f x))^{7/2}}{7 f}-\frac{4 a^3 d (d \tan (e+f x))^{5/2}}{5 f}","-\frac{4 a^3 d^2 (d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^3 d^3 \sqrt{d \tan (e+f x)}}{f}-\frac{2 \sqrt{2} a^3 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{9/2}}{11 d f}+\frac{16 a^3 (d \tan (e+f x))^{9/2}}{33 d f}+\frac{4 a^3 (d \tan (e+f x))^{7/2}}{7 f}-\frac{4 a^3 d (d \tan (e+f x))^{5/2}}{5 f}",1,"(-2*Sqrt[2]*a^3*d^(7/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f + (4*a^3*d^3*Sqrt[d*Tan[e + f*x]])/f - (4*a^3*d^2*(d*Tan[e + f*x])^(3/2))/(3*f) - (4*a^3*d*(d*Tan[e + f*x])^(5/2))/(5*f) + (4*a^3*(d*Tan[e + f*x])^(7/2))/(7*f) + (16*a^3*(d*Tan[e + f*x])^(9/2))/(33*d*f) + (2*(d*Tan[e + f*x])^(9/2)*(a^3 + a^3*Tan[e + f*x]))/(11*d*f)","A",8,5,25,0.2000,1,"{3566, 3630, 3528, 3532, 208}"
350,1,186,0,0.2789756,"\int (d \tan (e+f x))^{5/2} (a+a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x])^3,x]","-\frac{2 \sqrt{2} a^3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}-\frac{4 a^3 d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{7/2}}{9 d f}+\frac{40 a^3 (d \tan (e+f x))^{7/2}}{63 d f}+\frac{4 a^3 (d \tan (e+f x))^{5/2}}{5 f}-\frac{4 a^3 d (d \tan (e+f x))^{3/2}}{3 f}","-\frac{2 \sqrt{2} a^3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}-\frac{4 a^3 d^2 \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{7/2}}{9 d f}+\frac{40 a^3 (d \tan (e+f x))^{7/2}}{63 d f}+\frac{4 a^3 (d \tan (e+f x))^{5/2}}{5 f}-\frac{4 a^3 d (d \tan (e+f x))^{3/2}}{3 f}",1,"(-2*Sqrt[2]*a^3*d^(5/2)*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f - (4*a^3*d^2*Sqrt[d*Tan[e + f*x]])/f - (4*a^3*d*(d*Tan[e + f*x])^(3/2))/(3*f) + (4*a^3*(d*Tan[e + f*x])^(5/2))/(5*f) + (40*a^3*(d*Tan[e + f*x])^(7/2))/(63*d*f) + (2*(d*Tan[e + f*x])^(7/2)*(a^3 + a^3*Tan[e + f*x]))/(9*d*f)","A",7,5,25,0.2000,1,"{3566, 3630, 3528, 3532, 205}"
351,1,160,0,0.2365464,"\int (d \tan (e+f x))^{3/2} (a+a \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])^3,x]","\frac{2 \sqrt{2} a^3 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{32 a^3 (d \tan (e+f x))^{5/2}}{35 d f}+\frac{4 a^3 (d \tan (e+f x))^{3/2}}{3 f}-\frac{4 a^3 d \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{5/2}}{7 d f}","\frac{2 \sqrt{2} a^3 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{32 a^3 (d \tan (e+f x))^{5/2}}{35 d f}+\frac{4 a^3 (d \tan (e+f x))^{3/2}}{3 f}-\frac{4 a^3 d \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{5/2}}{7 d f}",1,"(2*Sqrt[2]*a^3*d^(3/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f - (4*a^3*d*Sqrt[d*Tan[e + f*x]])/f + (4*a^3*(d*Tan[e + f*x])^(3/2))/(3*f) + (32*a^3*(d*Tan[e + f*x])^(5/2))/(35*d*f) + (2*(d*Tan[e + f*x])^(5/2)*(a^3 + a^3*Tan[e + f*x]))/(7*d*f)","A",6,5,25,0.2000,1,"{3566, 3630, 3528, 3532, 208}"
352,1,138,0,0.1834297,"\int \sqrt{d \tan (e+f x)} (a+a \tan (e+f x))^3 \, dx","Int[Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])^3,x]","\frac{2 \sqrt{2} a^3 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{8 a^3 (d \tan (e+f x))^{3/2}}{5 d f}+\frac{4 a^3 \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{3/2}}{5 d f}","\frac{2 \sqrt{2} a^3 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{f}+\frac{8 a^3 (d \tan (e+f x))^{3/2}}{5 d f}+\frac{4 a^3 \sqrt{d \tan (e+f x)}}{f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) (d \tan (e+f x))^{3/2}}{5 d f}",1,"(2*Sqrt[2]*a^3*Sqrt[d]*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/f + (4*a^3*Sqrt[d*Tan[e + f*x]])/f + (8*a^3*(d*Tan[e + f*x])^(3/2))/(5*d*f) + (2*(d*Tan[e + f*x])^(3/2)*(a^3 + a^3*Tan[e + f*x]))/(5*d*f)","A",5,5,25,0.2000,1,"{3566, 3630, 3528, 3532, 205}"
353,1,117,0,0.1548862,"\int \frac{(a+a \tan (e+f x))^3}{\sqrt{d \tan (e+f x)}} \, dx","Int[(a + a*Tan[e + f*x])^3/Sqrt[d*Tan[e + f*x]],x]","\frac{16 a^3 \sqrt{d \tan (e+f x)}}{3 d f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) \sqrt{d \tan (e+f x)}}{3 d f}-\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{d} f}","\frac{16 a^3 \sqrt{d \tan (e+f x)}}{3 d f}+\frac{2 \left(a^3 \tan (e+f x)+a^3\right) \sqrt{d \tan (e+f x)}}{3 d f}-\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{d} f}",1,"(-2*Sqrt[2]*a^3*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(Sqrt[d]*f) + (16*a^3*Sqrt[d*Tan[e + f*x]])/(3*d*f) + (2*Sqrt[d*Tan[e + f*x]]*(a^3 + a^3*Tan[e + f*x]))/(3*d*f)","A",4,4,25,0.1600,1,"{3566, 3630, 3532, 208}"
354,1,114,0,0.1544261,"\int \frac{(a+a \tan (e+f x))^3}{(d \tan (e+f x))^{3/2}} \, dx","Int[(a + a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(3/2),x]","-\frac{2 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{4 a^3 \sqrt{d \tan (e+f x)}}{d^2 f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{d f \sqrt{d \tan (e+f x)}}","-\frac{2 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{4 a^3 \sqrt{d \tan (e+f x)}}{d^2 f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{d f \sqrt{d \tan (e+f x)}}",1,"(-2*Sqrt[2]*a^3*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(3/2)*f) + (4*a^3*Sqrt[d*Tan[e + f*x]])/(d^2*f) - (2*(a^3 + a^3*Tan[e + f*x]))/(d*f*Sqrt[d*Tan[e + f*x]])","A",4,4,25,0.1600,1,"{3565, 3630, 3532, 205}"
355,1,117,0,0.1755194,"\int \frac{(a+a \tan (e+f x))^3}{(d \tan (e+f x))^{5/2}} \, dx","Int[(a + a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(5/2),x]","-\frac{16 a^3}{3 d^2 f \sqrt{d \tan (e+f x)}}+\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{3 d f (d \tan (e+f x))^{3/2}}","-\frac{16 a^3}{3 d^2 f \sqrt{d \tan (e+f x)}}+\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{3 d f (d \tan (e+f x))^{3/2}}",1,"(2*Sqrt[2]*a^3*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(5/2)*f) - (16*a^3)/(3*d^2*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + a^3*Tan[e + f*x]))/(3*d*f*(d*Tan[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{3565, 3628, 3532, 208}"
356,1,141,0,0.2219371,"\int \frac{(a+a \tan (e+f x))^3}{(d \tan (e+f x))^{7/2}} \, dx","Int[(a + a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(7/2),x]","\frac{2 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{4 a^3}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{8 a^3}{5 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{5 d f (d \tan (e+f x))^{5/2}}","\frac{2 \sqrt{2} a^3 \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{4 a^3}{d^3 f \sqrt{d \tan (e+f x)}}-\frac{8 a^3}{5 d^2 f (d \tan (e+f x))^{3/2}}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{5 d f (d \tan (e+f x))^{5/2}}",1,"(2*Sqrt[2]*a^3*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(7/2)*f) - (8*a^3)/(5*d^2*f*(d*Tan[e + f*x])^(3/2)) - (4*a^3)/(d^3*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + a^3*Tan[e + f*x]))/(5*d*f*(d*Tan[e + f*x])^(5/2))","A",5,5,25,0.2000,1,"{3565, 3628, 3529, 3532, 205}"
357,1,165,0,0.2704712,"\int \frac{(a+a \tan (e+f x))^3}{(d \tan (e+f x))^{9/2}} \, dx","Int[(a + a*Tan[e + f*x])^3/(d*Tan[e + f*x])^(9/2),x]","\frac{4 a^3}{d^4 f \sqrt{d \tan (e+f x)}}-\frac{4 a^3}{3 d^3 f (d \tan (e+f x))^{3/2}}-\frac{32 a^3}{35 d^2 f (d \tan (e+f x))^{5/2}}-\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{9/2} f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{7 d f (d \tan (e+f x))^{7/2}}","\frac{4 a^3}{d^4 f \sqrt{d \tan (e+f x)}}-\frac{4 a^3}{3 d^3 f (d \tan (e+f x))^{3/2}}-\frac{32 a^3}{35 d^2 f (d \tan (e+f x))^{5/2}}-\frac{2 \sqrt{2} a^3 \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{d^{9/2} f}-\frac{2 \left(a^3 \tan (e+f x)+a^3\right)}{7 d f (d \tan (e+f x))^{7/2}}",1,"(-2*Sqrt[2]*a^3*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(d^(9/2)*f) - (32*a^3)/(35*d^2*f*(d*Tan[e + f*x])^(5/2)) - (4*a^3)/(3*d^3*f*(d*Tan[e + f*x])^(3/2)) + (4*a^3)/(d^4*f*Sqrt[d*Tan[e + f*x]]) - (2*(a^3 + a^3*Tan[e + f*x]))/(7*d*f*(d*Tan[e + f*x])^(7/2))","A",6,5,25,0.2000,1,"{3565, 3628, 3529, 3532, 208}"
358,1,111,0,0.406006,"\int \frac{(d \tan (e+f x))^{5/2}}{a+a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + a*Tan[e + f*x]),x]","-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}+\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}+\frac{2 d^2 \sqrt{d \tan (e+f x)}}{a f}","-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}+\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}+\frac{2 d^2 \sqrt{d \tan (e+f x)}}{a f}",1,"-((d^(5/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(a*f)) + (d^(5/2)*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(Sqrt[2]*a*f) + (2*d^2*Sqrt[d*Tan[e + f*x]])/(a*f)","A",7,6,25,0.2400,1,"{3566, 3653, 3532, 205, 3634, 63}"
359,1,87,0,0.2230153,"\int \frac{(d \tan (e+f x))^{3/2}}{a+a \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + a*Tan[e + f*x]),x]","\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}","\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}",1,"(d^(3/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(a*f) - (d^(3/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(Sqrt[2]*a*f)","A",6,6,25,0.2400,1,"{3573, 3532, 208, 3634, 63, 205}"
360,1,89,0,0.2010963,"\int \frac{\sqrt{d \tan (e+f x)}}{a+a \tan (e+f x)} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + a*Tan[e + f*x]),x]","-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}","-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a f}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a f}",1,"-((Sqrt[d]*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(a*f)) - (Sqrt[d]*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(Sqrt[2]*a*f)","A",6,5,25,0.2000,1,"{3572, 3532, 205, 3634, 63}"
361,1,81,0,0.2000008,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+a \tan (e+f x))} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a \sqrt{d} f}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} (\tan (e+f x)+1)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a \sqrt{d} f}","\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a \sqrt{d} f}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} (\tan (e+f x)+1)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a \sqrt{d} f}",1,"ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]]/(a*Sqrt[d]*f) + ArcTanh[(Sqrt[d]*(1 + Tan[e + f*x]))/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(Sqrt[2]*a*Sqrt[d]*f)","A",6,6,25,0.2400,1,"{3574, 3532, 208, 3634, 63, 205}"
362,1,111,0,0.3895996,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+a \tan (e+f x))} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a d^{3/2} f}-\frac{2}{a d f \sqrt{d \tan (e+f x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a d^{3/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a d^{3/2} f}-\frac{2}{a d f \sqrt{d \tan (e+f x)}}",1,"-(ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]]/(a*d^(3/2)*f)) + ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(Sqrt[2]*a*d^(3/2)*f) - 2/(a*d*f*Sqrt[d*Tan[e + f*x]])","A",7,6,25,0.2400,1,"{3569, 3653, 3532, 205, 3634, 63}"
363,1,135,0,0.4898278,"\int \frac{1}{(d \tan (e+f x))^{5/2} (a+a \tan (e+f x))} \, dx","Int[1/((d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x])),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a d^{5/2} f}+\frac{2}{a d^2 f \sqrt{d \tan (e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a d^{5/2} f}-\frac{2}{3 a d f (d \tan (e+f x))^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{a d^{5/2} f}+\frac{2}{a d^2 f \sqrt{d \tan (e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{\sqrt{2} a d^{5/2} f}-\frac{2}{3 a d f (d \tan (e+f x))^{3/2}}",1,"ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]]/(a*d^(5/2)*f) - ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(Sqrt[2]*a*d^(5/2)*f) - 2/(3*a*d*f*(d*Tan[e + f*x])^(3/2)) + 2/(a*d^2*f*Sqrt[d*Tan[e + f*x]])","A",10,10,25,0.4000,1,"{3569, 3649, 12, 16, 3573, 3532, 208, 3634, 63, 205}"
364,1,281,0,0.4997504,"\int \frac{(d \tan (e+f x))^{5/2}}{(a+a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + a*Tan[e + f*x])^2,x]","\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}+\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}-\frac{d^2 \sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}","\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}+\frac{d^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}-\frac{d^2 \sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}+\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}-\frac{d^{5/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}",1,"(3*d^(5/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*f) + (d^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) - (d^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) + (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) - (d^(5/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) - (d^2*Sqrt[d*Tan[e + f*x]])/(2*f*(a^2 + a^2*Tan[e + f*x]))","A",17,14,25,0.5600,1,"{3565, 3653, 12, 3476, 329, 211, 1165, 628, 1162, 617, 204, 3634, 63, 205}"
365,1,279,0,0.5088144,"\int \frac{(d \tan (e+f x))^{3/2}}{(a+a \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + a*Tan[e + f*x])^2,x]","-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}+\frac{d \sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}","-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}-\frac{d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}+\frac{d^{3/2} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}-\frac{d^{3/2} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}+\frac{d \sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}",1,"-(d^(3/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*f) - (d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) + (d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) + (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) - (d^(3/2)*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) + (d*Sqrt[d*Tan[e + f*x]])/(2*f*(a^2 + a^2*Tan[e + f*x]))","A",18,15,25,0.6000,1,"{3567, 3653, 12, 16, 3476, 329, 297, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
366,1,278,0,0.4767454,"\int \frac{\sqrt{d \tan (e+f x)}}{(a+a \tan (e+f x))^2} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + a*Tan[e + f*x])^2,x]","-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}-\frac{\sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}","-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 f}-\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 f}+\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 f}-\frac{\sqrt{d \tan (e+f x)}}{2 f \left(a^2 \tan (e+f x)+a^2\right)}-\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}+\frac{\sqrt{d} \log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 f}",1,"-(Sqrt[d]*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*f) - (Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) + (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]])/(2*Sqrt[2]*a^2*f) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]])/(4*Sqrt[2]*a^2*f) - Sqrt[d*Tan[e + f*x]]/(2*f*(a^2 + a^2*Tan[e + f*x]))","A",17,14,25,0.5600,1,"{3568, 3653, 12, 3476, 329, 211, 1165, 628, 1162, 617, 204, 3634, 63, 205}"
367,1,281,0,0.5255609,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+a \tan (e+f x))^2} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])^2),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{2 d f \left(a^2 \tan (e+f x)+a^2\right)}-\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 \sqrt{d} f}+\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 \sqrt{d} f}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 \sqrt{d} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 \sqrt{d} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 \sqrt{d} f}+\frac{\sqrt{d \tan (e+f x)}}{2 d f \left(a^2 \tan (e+f x)+a^2\right)}-\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 \sqrt{d} f}+\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 \sqrt{d} f}",1,"(3*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*Sqrt[d]*f) + ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*Sqrt[d]*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*Sqrt[d]*f) - Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*Sqrt[d]*f) + Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*Sqrt[d]*f) + Sqrt[d*Tan[e + f*x]]/(2*d*f*(a^2 + a^2*Tan[e + f*x]))","A",18,15,25,0.6000,1,"{3569, 3653, 12, 16, 3476, 329, 297, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
368,1,306,0,0.7301802,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+a \tan (e+f x))^2} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])^2),x]","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 d^{3/2} f}+\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{3/2} f}-\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{3/2} f}-\frac{5}{2 a^2 d f \sqrt{d \tan (e+f x)}}+\frac{1}{2 d f \left(a^2 \tan (e+f x)+a^2\right) \sqrt{d \tan (e+f x)}}","-\frac{5 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 d^{3/2} f}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 d^{3/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 d^{3/2} f}+\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{3/2} f}-\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{3/2} f}-\frac{5}{2 a^2 d f \sqrt{d \tan (e+f x)}}+\frac{1}{2 d f \left(a^2 \tan (e+f x)+a^2\right) \sqrt{d \tan (e+f x)}}",1,"(-5*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*d^(3/2)*f) + ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*d^(3/2)*f) - ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*d^(3/2)*f) + Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*d^(3/2)*f) - Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*d^(3/2)*f) - 5/(2*a^2*d*f*Sqrt[d*Tan[e + f*x]]) + 1/(2*d*f*Sqrt[d*Tan[e + f*x]]*(a^2 + a^2*Tan[e + f*x]))","A",18,15,25,0.6000,1,"{3569, 3649, 3653, 12, 3476, 329, 211, 1165, 628, 1162, 617, 204, 3634, 63, 205}"
369,1,331,0,0.9914512,"\int \frac{1}{(d \tan (e+f x))^{5/2} (a+a \tan (e+f x))^2} \, dx","Int[1/((d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x])^2),x]","\frac{7 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 d^{5/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 d^{5/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 d^{5/2} f}+\frac{9}{2 a^2 d^2 f \sqrt{d \tan (e+f x)}}+\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{5/2} f}-\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{5/2} f}+\frac{1}{2 d f \left(a^2 \tan (e+f x)+a^2\right) (d \tan (e+f x))^{3/2}}-\frac{7}{6 a^2 d f (d \tan (e+f x))^{3/2}}","\frac{7 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 a^2 d^{5/2} f}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{2 \sqrt{2} a^2 d^{5/2} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d \tan (e+f x)}}{\sqrt{d}}+1\right)}{2 \sqrt{2} a^2 d^{5/2} f}+\frac{9}{2 a^2 d^2 f \sqrt{d \tan (e+f x)}}+\frac{\log \left(\sqrt{d} \tan (e+f x)-\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{5/2} f}-\frac{\log \left(\sqrt{d} \tan (e+f x)+\sqrt{2} \sqrt{d \tan (e+f x)}+\sqrt{d}\right)}{4 \sqrt{2} a^2 d^{5/2} f}+\frac{1}{2 d f \left(a^2 \tan (e+f x)+a^2\right) (d \tan (e+f x))^{3/2}}-\frac{7}{6 a^2 d f (d \tan (e+f x))^{3/2}}",1,"(7*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(2*a^2*d^(5/2)*f) - ArcTan[1 - (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*d^(5/2)*f) + ArcTan[1 + (Sqrt[2]*Sqrt[d*Tan[e + f*x]])/Sqrt[d]]/(2*Sqrt[2]*a^2*d^(5/2)*f) + Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] - Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*d^(5/2)*f) - Log[Sqrt[d] + Sqrt[d]*Tan[e + f*x] + Sqrt[2]*Sqrt[d*Tan[e + f*x]]]/(4*Sqrt[2]*a^2*d^(5/2)*f) - 7/(6*a^2*d*f*(d*Tan[e + f*x])^(3/2)) + 9/(2*a^2*d^2*f*Sqrt[d*Tan[e + f*x]]) + 1/(2*d*f*(d*Tan[e + f*x])^(3/2)*(a^2 + a^2*Tan[e + f*x]))","A",20,16,25,0.6400,1,"{3569, 3649, 3653, 12, 16, 3476, 329, 297, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
370,1,189,0,0.7553989,"\int \frac{(d \tan (e+f x))^{9/2}}{(a+a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(9/2)/(a + a*Tan[e + f*x])^3,x]","-\frac{31 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{27 d^4 \sqrt{d \tan (e+f x)}}{8 a^3 f}-\frac{9 d^3 (d \tan (e+f x))^{3/2}}{8 a^3 f (\tan (e+f x)+1)}+\frac{d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d^2 (d \tan (e+f x))^{5/2}}{4 a f (a \tan (e+f x)+a)^2}","-\frac{31 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{27 d^4 \sqrt{d \tan (e+f x)}}{8 a^3 f}-\frac{9 d^3 (d \tan (e+f x))^{3/2}}{8 a^3 f (\tan (e+f x)+1)}+\frac{d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d^2 (d \tan (e+f x))^{5/2}}{4 a f (a \tan (e+f x)+a)^2}",1,"(-31*d^(9/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*f) + (d^(9/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(2*Sqrt[2]*a^3*f) + (27*d^4*Sqrt[d*Tan[e + f*x]])/(8*a^3*f) - (9*d^3*(d*Tan[e + f*x])^(3/2))/(8*a^3*f*(1 + Tan[e + f*x])) - (d^2*(d*Tan[e + f*x])^(5/2))/(4*a*f*(a + a*Tan[e + f*x])^2)","A",9,9,25,0.3600,1,"{3565, 3645, 3647, 3654, 3532, 208, 3634, 63, 205}"
371,1,165,0,0.6368706,"\int \frac{(d \tan (e+f x))^{7/2}}{(a+a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(7/2)/(a + a*Tan[e + f*x])^3,x]","\frac{11 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{7 d^3 \sqrt{d \tan (e+f x)}}{8 a^3 f (\tan (e+f x)+1)}-\frac{d^2 (d \tan (e+f x))^{3/2}}{4 a f (a \tan (e+f x)+a)^2}","\frac{11 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{7 d^3 \sqrt{d \tan (e+f x)}}{8 a^3 f (\tan (e+f x)+1)}-\frac{d^2 (d \tan (e+f x))^{3/2}}{4 a f (a \tan (e+f x)+a)^2}",1,"(11*d^(7/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*f) + (d^(7/2)*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(2*Sqrt[2]*a^3*f) - (7*d^3*Sqrt[d*Tan[e + f*x]])/(8*a^3*f*(1 + Tan[e + f*x])) - (d^2*(d*Tan[e + f*x])^(3/2))/(4*a*f*(a + a*Tan[e + f*x])^2)","A",8,7,25,0.2800,1,"{3565, 3645, 3653, 3532, 205, 3634, 63}"
372,1,164,0,0.5595634,"\int \frac{(d \tan (e+f x))^{5/2}}{(a+a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(5/2)/(a + a*Tan[e + f*x])^3,x]","\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{5 d^2 \sqrt{d \tan (e+f x)}}{8 a^3 f (\tan (e+f x)+1)}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d^2 \sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}","\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}+\frac{5 d^2 \sqrt{d \tan (e+f x)}}{8 a^3 f (\tan (e+f x)+1)}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d^2 \sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}",1,"(d^(5/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*f) - (d^(5/2)*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(2*Sqrt[2]*a^3*f) + (5*d^2*Sqrt[d*Tan[e + f*x]])/(8*a^3*f*(1 + Tan[e + f*x])) - (d^2*Sqrt[d*Tan[e + f*x]])/(4*a*f*(a + a*Tan[e + f*x])^2)","A",8,8,25,0.3200,1,"{3565, 3649, 3654, 3532, 208, 3634, 63, 205}"
373,1,164,0,0.5940451,"\int \frac{(d \tan (e+f x))^{3/2}}{(a+a \tan (e+f x))^3} \, dx","Int[(d*Tan[e + f*x])^(3/2)/(a + a*Tan[e + f*x])^3,x]","-\frac{5 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d \sqrt{d \tan (e+f x)}}{8 f \left(a^3 \tan (e+f x)+a^3\right)}+\frac{d \sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}","-\frac{5 d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{d \sqrt{d \tan (e+f x)}}{8 f \left(a^3 \tan (e+f x)+a^3\right)}+\frac{d \sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}",1,"(-5*d^(3/2)*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*f) - (d^(3/2)*ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(2*Sqrt[2]*a^3*f) + (d*Sqrt[d*Tan[e + f*x]])/(4*a*f*(a + a*Tan[e + f*x])^2) - (d*Sqrt[d*Tan[e + f*x]])/(8*f*(a^3 + a^3*Tan[e + f*x]))","A",8,7,25,0.2800,1,"{3567, 3649, 3653, 3532, 205, 3634, 63}"
374,1,161,0,0.5371224,"\int \frac{\sqrt{d \tan (e+f x)}}{(a+a \tan (e+f x))^3} \, dx","Int[Sqrt[d*Tan[e + f*x]]/(a + a*Tan[e + f*x])^3,x]","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}-\frac{3 \sqrt{d \tan (e+f x)}}{8 f \left(a^3 \tan (e+f x)+a^3\right)}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{\sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 f}-\frac{3 \sqrt{d \tan (e+f x)}}{8 f \left(a^3 \tan (e+f x)+a^3\right)}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 f}-\frac{\sqrt{d \tan (e+f x)}}{4 a f (a \tan (e+f x)+a)^2}",1,"(Sqrt[d]*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*f) + (Sqrt[d]*ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])])/(2*Sqrt[2]*a^3*f) - Sqrt[d*Tan[e + f*x]]/(4*a*f*(a + a*Tan[e + f*x])^2) - (3*Sqrt[d*Tan[e + f*x]])/(8*f*(a^3 + a^3*Tan[e + f*x]))","A",8,8,25,0.3200,1,"{3568, 3649, 3654, 3532, 208, 3634, 63, 205}"
375,1,165,0,0.619819,"\int \frac{1}{\sqrt{d \tan (e+f x)} (a+a \tan (e+f x))^3} \, dx","Int[1/(Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])^3),x]","\frac{11 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 \sqrt{d} f}+\frac{7 \sqrt{d \tan (e+f x)}}{8 a^3 d f (\tan (e+f x)+1)}+\frac{\sqrt{d \tan (e+f x)}}{4 a d f (a \tan (e+f x)+a)^2}","\frac{11 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 \sqrt{d} f}+\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 \sqrt{d} f}+\frac{7 \sqrt{d \tan (e+f x)}}{8 a^3 d f (\tan (e+f x)+1)}+\frac{\sqrt{d \tan (e+f x)}}{4 a d f (a \tan (e+f x)+a)^2}",1,"(11*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*Sqrt[d]*f) + ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(2*Sqrt[2]*a^3*Sqrt[d]*f) + (7*Sqrt[d*Tan[e + f*x]])/(8*a^3*d*f*(1 + Tan[e + f*x])) + Sqrt[d*Tan[e + f*x]]/(4*a*d*f*(a + a*Tan[e + f*x])^2)","A",8,7,25,0.2800,1,"{3569, 3649, 3653, 3532, 205, 3634, 63}"
376,1,189,0,0.7970981,"\int \frac{1}{(d \tan (e+f x))^{3/2} (a+a \tan (e+f x))^3} \, dx","Int[1/((d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])^3),x]","-\frac{31 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 d^{3/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 d^{3/2} f}-\frac{27}{8 a^3 d f \sqrt{d \tan (e+f x)}}+\frac{9}{8 a^3 d f (\tan (e+f x)+1) \sqrt{d \tan (e+f x)}}+\frac{1}{4 a d f (a \tan (e+f x)+a)^2 \sqrt{d \tan (e+f x)}}","-\frac{31 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 d^{3/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \tan (e+f x)+\sqrt{d}}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 d^{3/2} f}-\frac{27}{8 a^3 d f \sqrt{d \tan (e+f x)}}+\frac{9}{8 a^3 d f (\tan (e+f x)+1) \sqrt{d \tan (e+f x)}}+\frac{1}{4 a d f (a \tan (e+f x)+a)^2 \sqrt{d \tan (e+f x)}}",1,"(-31*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*d^(3/2)*f) - ArcTanh[(Sqrt[d] + Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(2*Sqrt[2]*a^3*d^(3/2)*f) - 27/(8*a^3*d*f*Sqrt[d*Tan[e + f*x]]) + 9/(8*a^3*d*f*Sqrt[d*Tan[e + f*x]]*(1 + Tan[e + f*x])) + 1/(4*a*d*f*Sqrt[d*Tan[e + f*x]]*(a + a*Tan[e + f*x])^2)","A",9,8,25,0.3200,1,"{3569, 3649, 3654, 3532, 208, 3634, 63, 205}"
377,1,215,0,1.0262112,"\int \frac{1}{(d \tan (e+f x))^{5/2} (a+a \tan (e+f x))^3} \, dx","Int[1/((d*Tan[e + f*x])^(5/2)*(a + a*Tan[e + f*x])^3),x]","\frac{59 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 d^{5/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 d^{5/2} f}+\frac{63}{8 a^3 d^2 f \sqrt{d \tan (e+f x)}}+\frac{11}{8 a^3 d f (\tan (e+f x)+1) (d \tan (e+f x))^{3/2}}-\frac{55}{24 a^3 d f (d \tan (e+f x))^{3/2}}+\frac{1}{4 a d f (a \tan (e+f x)+a)^2 (d \tan (e+f x))^{3/2}}","\frac{59 \tan ^{-1}\left(\frac{\sqrt{d \tan (e+f x)}}{\sqrt{d}}\right)}{8 a^3 d^{5/2} f}-\frac{\tan ^{-1}\left(\frac{\sqrt{d}-\sqrt{d} \tan (e+f x)}{\sqrt{2} \sqrt{d \tan (e+f x)}}\right)}{2 \sqrt{2} a^3 d^{5/2} f}+\frac{63}{8 a^3 d^2 f \sqrt{d \tan (e+f x)}}+\frac{11}{8 a^3 d f (\tan (e+f x)+1) (d \tan (e+f x))^{3/2}}-\frac{55}{24 a^3 d f (d \tan (e+f x))^{3/2}}+\frac{1}{4 a d f (a \tan (e+f x)+a)^2 (d \tan (e+f x))^{3/2}}",1,"(59*ArcTan[Sqrt[d*Tan[e + f*x]]/Sqrt[d]])/(8*a^3*d^(5/2)*f) - ArcTan[(Sqrt[d] - Sqrt[d]*Tan[e + f*x])/(Sqrt[2]*Sqrt[d*Tan[e + f*x]])]/(2*Sqrt[2]*a^3*d^(5/2)*f) - 55/(24*a^3*d*f*(d*Tan[e + f*x])^(3/2)) + 63/(8*a^3*d^2*f*Sqrt[d*Tan[e + f*x]]) + 11/(8*a^3*d*f*(d*Tan[e + f*x])^(3/2)*(1 + Tan[e + f*x])) + 1/(4*a*d*f*(d*Tan[e + f*x])^(3/2)*(a + a*Tan[e + f*x])^2)","A",10,8,25,0.3200,1,"{3569, 3649, 3650, 3653, 3532, 205, 3634, 63}"
378,1,264,0,0.5915618,"\int \tan ^5(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Tan[e + f*x]^5*Sqrt[1 + Tan[e + f*x]],x]","\frac{2 (\tan (e+f x)+1)^{3/2} \tan ^3(e+f x)}{9 f}-\frac{4 (\tan (e+f x)+1)^{3/2} \tan ^2(e+f x)}{21 f}-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{26 (\tan (e+f x)+1)^{3/2} \tan (e+f x)}{105 f}+\frac{52 (\tan (e+f x)+1)^{3/2}}{315 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}","\frac{2 (\tan (e+f x)+1)^{3/2} \tan ^3(e+f x)}{9 f}-\frac{4 (\tan (e+f x)+1)^{3/2} \tan ^2(e+f x)}{21 f}-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{26 (\tan (e+f x)+1)^{3/2} \tan (e+f x)}{105 f}+\frac{52 (\tan (e+f x)+1)^{3/2}}{315 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"-((Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f) - (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f + (2*Sqrt[1 + Tan[e + f*x]])/f + (52*(1 + Tan[e + f*x])^(3/2))/(315*f) - (26*Tan[e + f*x]*(1 + Tan[e + f*x])^(3/2))/(105*f) - (4*Tan[e + f*x]^2*(1 + Tan[e + f*x])^(3/2))/(21*f) + (2*Tan[e + f*x]^3*(1 + Tan[e + f*x])^(3/2))/(9*f)","A",11,10,21,0.4762,1,"{3566, 3647, 3648, 3630, 12, 3528, 3536, 3535, 203, 207}"
379,1,208,0,0.2643281,"\int \tan ^3(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Tan[e + f*x]^3*Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \tan (e+f x) (\tan (e+f x)+1)^{3/2}}{5 f}-\frac{4 (\tan (e+f x)+1)^{3/2}}{15 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \tan (e+f x) (\tan (e+f x)+1)^{3/2}}{5 f}-\frac{4 (\tan (e+f x)+1)^{3/2}}{15 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"(Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f + (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f - (2*Sqrt[1 + Tan[e + f*x]])/f - (4*(1 + Tan[e + f*x])^(3/2))/(15*f) + (2*Tan[e + f*x]*(1 + Tan[e + f*x])^(3/2))/(5*f)","A",9,8,21,0.3810,1,"{3566, 3630, 12, 3528, 3536, 3535, 203, 207}"
380,1,166,0,0.1621396,"\int \tan (e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Tan[e + f*x]*Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}","-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"-((Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f) - (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f + (2*Sqrt[1 + Tan[e + f*x]])/f","A",6,5,19,0.2632,1,"{3528, 3536, 3535, 203, 207}"
381,1,165,0,0.2545113,"\int \cot (e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"(Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f - (2*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/f + (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f","A",9,7,19,0.3684,1,"{3572, 3536, 3535, 203, 207, 3634, 63}"
382,1,221,0,0.5007005,"\int \cot ^3(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{9 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}","-\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{9 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}",1,"-((Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f) + (9*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(4*f) - (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f - (Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(4*f) - (Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(2*f)","A",11,9,21,0.4286,1,"{3568, 3649, 3653, 3536, 3535, 203, 207, 3634, 63}"
383,1,273,0,0.7150322,"\int \cot ^5(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Cot[e + f*x]^5*Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{139 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{24 f}+\frac{53 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{96 f}+\frac{11 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}","\frac{\sqrt{\frac{1}{2} \left(\sqrt{2}-1\right)} \tan ^{-1}\left(\frac{\left(2-\sqrt{2}\right) \tan (e+f x)-3 \sqrt{2}+4}{2 \sqrt{5 \sqrt{2}-7} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{139 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tanh ^{-1}\left(\frac{\left(2+\sqrt{2}\right) \tan (e+f x)+3 \sqrt{2}+4}{2 \sqrt{7+5 \sqrt{2}} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{24 f}+\frac{53 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{96 f}+\frac{11 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}",1,"(Sqrt[(-1 + Sqrt[2])/2]*ArcTan[(4 - 3*Sqrt[2] + (2 - Sqrt[2])*Tan[e + f*x])/(2*Sqrt[-7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f - (139*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(64*f) + (Sqrt[(1 + Sqrt[2])/2]*ArcTanh[(4 + 3*Sqrt[2] + (2 + Sqrt[2])*Tan[e + f*x])/(2*Sqrt[7 + 5*Sqrt[2]]*Sqrt[1 + Tan[e + f*x]])])/f + (11*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(64*f) + (53*Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(96*f) - (Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(24*f) - (Cot[e + f*x]^4*Sqrt[1 + Tan[e + f*x]])/(4*f)","A",13,9,21,0.4286,1,"{3568, 3649, 3653, 3536, 3535, 203, 207, 3634, 63}"
384,1,318,0,0.4335129,"\int \tan ^4(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Tan[e + f*x]^4*Sqrt[1 + Tan[e + f*x]],x]","\frac{2 (\tan (e+f x)+1)^{3/2} \tan ^2(e+f x)}{7 f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{8 (\tan (e+f x)+1)^{3/2} \tan (e+f x)}{35 f}-\frac{18 (\tan (e+f x)+1)^{3/2}}{35 f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}","\frac{2 (\tan (e+f x)+1)^{3/2} \tan ^2(e+f x)}{7 f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{8 (\tan (e+f x)+1)^{3/2} \tan (e+f x)}{35 f}-\frac{18 (\tan (e+f x)+1)^{3/2}}{35 f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}",1,"-((Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) - (18*(1 + Tan[e + f*x])^(3/2))/(35*f) - (8*Tan[e + f*x]*(1 + Tan[e + f*x])^(3/2))/(35*f) + (2*Tan[e + f*x]^2*(1 + Tan[e + f*x])^(3/2))/(7*f)","A",14,11,21,0.5238,1,"{3566, 3647, 3631, 3485, 700, 1127, 1161, 618, 204, 1164, 628}"
385,1,266,0,0.2273001,"\int \tan ^2(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Tan[e + f*x]^2*Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}","\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}",1,"(Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) + (2*(1 + Tan[e + f*x])^(3/2))/(3*f)","A",12,9,21,0.4286,1,"{3543, 3485, 700, 1127, 1161, 618, 204, 1164, 628}"
386,1,247,0,0.1889778,"\int \sqrt{1+\tan (e+f x)} \, dx","Int[Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}","-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}",1,"-((Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f)","A",11,8,12,0.6667,1,"{3485, 700, 1127, 1161, 618, 204, 1164, 628}"
387,1,288,0,0.3548737,"\int \cot ^2(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}","\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}",1,"(Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - ArcTanh[Sqrt[1 + Tan[e + f*x]]]/f - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) - (Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/f","A",16,13,21,0.6190,1,"{3568, 3653, 3485, 700, 1127, 1161, 618, 204, 1164, 628, 3634, 63, 207}"
388,1,346,0,0.6245286,"\int \cot ^4(e+f x) \sqrt{1+\tan (e+f x)} \, dx","Int[Cot[e + f*x]^4*Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{7 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{9 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}","-\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{\frac{1}{2} \left(1+\sqrt{2}\right)} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{2 \left(1+\sqrt{2}\right)} f}+\frac{7 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{9 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}",1,"-((Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[(1 + Sqrt[2])/2]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + (7*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(8*f) + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[2*(1 + Sqrt[2])]*f) + (9*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(8*f) - (Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(12*f) - (Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(3*f)","A",19,15,21,0.7143,1,"{3568, 3649, 3653, 21, 3485, 700, 1127, 1161, 618, 204, 1164, 628, 3634, 63, 207}"
389,1,369,0,0.5665176,"\int \tan ^5(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Tan[e + f*x]^5*(1 + Tan[e + f*x])^(3/2),x]","\frac{2 (\tan (e+f x)+1)^{5/2} \tan ^3(e+f x)}{11 f}-\frac{4 (\tan (e+f x)+1)^{5/2} \tan ^2(e+f x)}{33 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{50 (\tan (e+f x)+1)^{5/2} \tan (e+f x)}{231 f}+\frac{20 (\tan (e+f x)+1)^{5/2}}{231 f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}","\frac{2 (\tan (e+f x)+1)^{5/2} \tan ^3(e+f x)}{11 f}-\frac{4 (\tan (e+f x)+1)^{5/2} \tan ^2(e+f x)}{33 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{50 (\tan (e+f x)+1)^{5/2} \tan (e+f x)}{231 f}+\frac{20 (\tan (e+f x)+1)^{5/2}}{231 f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}",1,"(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + (2*Sqrt[1 + Tan[e + f*x]])/f + (2*(1 + Tan[e + f*x])^(3/2))/(3*f) + (20*(1 + Tan[e + f*x])^(5/2))/(231*f) - (50*Tan[e + f*x]*(1 + Tan[e + f*x])^(5/2))/(231*f) - (4*Tan[e + f*x]^2*(1 + Tan[e + f*x])^(5/2))/(33*f) + (2*Tan[e + f*x]^3*(1 + Tan[e + f*x])^(5/2))/(11*f)","A",19,13,21,0.6190,1,"{3566, 3647, 3648, 3630, 12, 3528, 3485, 708, 1094, 634, 618, 204, 628}"
390,1,315,0,0.3648961,"\int \tan ^3(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Tan[e + f*x]^3*(1 + Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 \tan (e+f x) (\tan (e+f x)+1)^{5/2}}{7 f}-\frac{4 (\tan (e+f x)+1)^{5/2}}{35 f}-\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 \tan (e+f x) (\tan (e+f x)+1)^{5/2}}{7 f}-\frac{4 (\tan (e+f x)+1)^{5/2}}{35 f}-\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}",1,"-((Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) - (2*Sqrt[1 + Tan[e + f*x]])/f - (2*(1 + Tan[e + f*x])^(3/2))/(3*f) - (4*(1 + Tan[e + f*x])^(5/2))/(35*f) + (2*Tan[e + f*x]*(1 + Tan[e + f*x])^(5/2))/(7*f)","A",17,11,21,0.5238,1,"{3566, 3630, 12, 3528, 3485, 708, 1094, 634, 618, 204, 628}"
391,1,271,0,0.2310555,"\int \tan (e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Tan[e + f*x]*(1 + Tan[e + f*x])^(3/2),x]","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{3/2}}{3 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}",1,"(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + (2*Sqrt[1 + Tan[e + f*x]])/f + (2*(1 + Tan[e + f*x])^(3/2))/(3*f)","A",14,9,19,0.4737,1,"{3528, 12, 3485, 708, 1094, 634, 618, 204, 628}"
392,1,253,0,0.282313,"\int \cot (e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]*(1 + Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}",1,"-((Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (2*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/f - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f)","A",16,12,19,0.6316,1,"{3573, 12, 3485, 708, 1094, 634, 618, 204, 628, 3634, 63, 207}"
393,1,307,0,0.4692671,"\int \cot ^3(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]^3*(1 + Tan[e + f*x])^(3/2),x]","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{5 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}-\frac{5 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{5 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}-\frac{5 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}",1,"(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f + (5*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(4*f) + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) - (5*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(4*f) - (Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(2*f)","A",18,14,21,0.6667,1,"{3567, 3650, 3653, 12, 3485, 708, 1094, 634, 618, 204, 628, 3634, 63, 207}"
394,1,361,0,0.6849307,"\int \cot ^5(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]^5*(1 + Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{83 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}-\frac{3 \sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{8 f}+\frac{15 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{32 f}+\frac{83 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}} f}-\frac{83 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}-\frac{3 \sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{8 f}+\frac{15 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{32 f}+\frac{83 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}",1,"-((Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/f - (83*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(64*f) - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(2*Sqrt[1 + Sqrt[2]]*f) + (83*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(64*f) + (15*Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(32*f) - (3*Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(8*f) - (Cot[e + f*x]^4*Sqrt[1 + Tan[e + f*x]])/(4*f)","A",20,15,21,0.7143,1,"{3567, 3650, 3649, 3653, 12, 3485, 708, 1094, 634, 618, 204, 628, 3634, 63, 207}"
395,1,227,0,0.3827713,"\int \tan ^4(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Tan[e + f*x]^4*(1 + Tan[e + f*x])^(3/2),x]","\frac{2 \tan ^2(e+f x) (\tan (e+f x)+1)^{5/2}}{9 f}-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{8 \tan (e+f x) (\tan (e+f x)+1)^{5/2}}{63 f}-\frac{22 (\tan (e+f x)+1)^{5/2}}{63 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}","\frac{2 \tan ^2(e+f x) (\tan (e+f x)+1)^{5/2}}{9 f}-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{8 \tan (e+f x) (\tan (e+f x)+1)^{5/2}}{63 f}-\frac{22 (\tan (e+f x)+1)^{5/2}}{63 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"-((Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f + (2*Sqrt[1 + Tan[e + f*x]])/f - (22*(1 + Tan[e + f*x])^(5/2))/(63*f) - (8*Tan[e + f*x]*(1 + Tan[e + f*x])^(5/2))/(63*f) + (2*Tan[e + f*x]^2*(1 + Tan[e + f*x])^(5/2))/(9*f)","A",10,9,21,0.4286,1,"{3566, 3647, 3631, 3482, 12, 3536, 3535, 203, 207}"
396,1,173,0,0.178385,"\int \tan ^2(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Tan[e + f*x]^2*(1 + Tan[e + f*x])^(3/2),x]","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{5/2}}{5 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 (\tan (e+f x)+1)^{5/2}}{5 f}-\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f + (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f - (2*Sqrt[1 + Tan[e + f*x]])/f + (2*(1 + Tan[e + f*x])^(5/2))/(5*f)","A",8,7,21,0.3333,1,"{3543, 3482, 12, 3536, 3535, 203, 207}"
397,1,156,0,0.1575212,"\int (1+\tan (e+f x))^{3/2} \, dx","Int[(1 + Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}",1,"-((Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f + (2*Sqrt[1 + Tan[e + f*x]])/f","A",7,6,12,0.5000,1,"{3482, 12, 3536, 3535, 203, 207}"
398,1,178,0,0.3049521,"\int \cot ^2(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]^2*(1 + Tan[e + f*x])^(3/2),x]","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{3 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{3 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}",1,"(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f - (3*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/f + (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f - (Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/f","A",11,9,21,0.4286,1,"{3567, 3654, 12, 3536, 3535, 203, 207, 3634, 63}"
399,1,238,0,0.5040362,"\int \cot ^4(e+f x) (1+\tan (e+f x))^{3/2} \, dx","Int[Cot[e + f*x]^4*(1 + Tan[e + f*x])^(3/2),x]","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{25 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}-\frac{7 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{7 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}+\frac{25 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}-\frac{7 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{7 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}",1,"-((Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f) + (25*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(8*f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/f + (7*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(8*f) - (7*Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(12*f) - (Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(3*f)","A",13,11,21,0.5238,1,"{3567, 3650, 3649, 3654, 12, 3536, 3535, 203, 207, 3634, 63}"
400,1,241,0,0.3735295,"\int \frac{\tan ^5(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Tan[e + f*x]^5/Sqrt[1 + Tan[e + f*x]],x]","\frac{2 \sqrt{\tan (e+f x)+1} \tan ^3(e+f x)}{7 f}-\frac{12 \sqrt{\tan (e+f x)+1} \tan ^2(e+f x)}{35 f}-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{22 \sqrt{\tan (e+f x)+1} \tan (e+f x)}{105 f}+\frac{44 \sqrt{\tan (e+f x)+1}}{105 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}","\frac{2 \sqrt{\tan (e+f x)+1} \tan ^3(e+f x)}{7 f}-\frac{12 \sqrt{\tan (e+f x)+1} \tan ^2(e+f x)}{35 f}-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{22 \sqrt{\tan (e+f x)+1} \tan (e+f x)}{105 f}+\frac{44 \sqrt{\tan (e+f x)+1}}{105 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}",1,"-(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) + (44*Sqrt[1 + Tan[e + f*x]])/(105*f) - (22*Tan[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(105*f) - (12*Tan[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(35*f) + (2*Tan[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(7*f)","A",10,9,21,0.4286,1,"{3566, 3647, 3648, 3630, 12, 3536, 3535, 203, 207}"
401,1,187,0,0.2078698,"\int \frac{\tan ^3(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Tan[e + f*x]^3/Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}+\frac{2 \tan (e+f x) \sqrt{\tan (e+f x)+1}}{3 f}-\frac{4 \sqrt{\tan (e+f x)+1}}{3 f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}+\frac{2 \tan (e+f x) \sqrt{\tan (e+f x)+1}}{3 f}-\frac{4 \sqrt{\tan (e+f x)+1}}{3 f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}",1,"(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) + (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (4*Sqrt[1 + Tan[e + f*x]])/(3*f) + (2*Tan[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(3*f)","A",8,7,21,0.3333,1,"{3566, 3630, 12, 3536, 3535, 203, 207}"
402,1,143,0,0.1159345,"\int \frac{\tan (e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Tan[e + f*x]/Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}",1,"-(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f)","A",5,4,19,0.2105,1,"{3536, 3535, 203, 207}"
403,1,161,0,0.2037953,"\int \frac{\cot (e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Cot[e + f*x]/Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{2 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}",1,"(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (2*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/f + (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f)","A",9,7,19,0.3684,1,"{3574, 3536, 3535, 203, 207, 3634, 63}"
404,1,215,0,0.3846055,"\int \frac{\cot ^3(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Cot[e + f*x]^3/Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}+\frac{5 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}+\frac{3 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}","-\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}+\frac{5 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{4 f}-\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{2 f}+\frac{3 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{4 f}",1,"-(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) + (5*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(4*f) - (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) + (3*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(4*f) - (Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(2*f)","A",12,10,21,0.4762,1,"{3569, 3649, 3654, 12, 3536, 3535, 203, 207, 3634, 63}"
405,1,269,0,0.5991406,"\int \frac{\cot ^5(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Cot[e + f*x]^5/Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{115 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}+\frac{7 \sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{24 f}+\frac{13 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{96 f}-\frac{13 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}","\frac{\sqrt{\sqrt{2}-1} \tan ^{-1}\left(\frac{\left(1-\sqrt{2}\right) \tan (e+f x)-2 \sqrt{2}+3}{\sqrt{2 \left(5 \sqrt{2}-7\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{115 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{64 f}+\frac{\sqrt{1+\sqrt{2}} \tanh ^{-1}\left(\frac{\left(1+\sqrt{2}\right) \tan (e+f x)+2 \sqrt{2}+3}{\sqrt{2 \left(7+5 \sqrt{2}\right)} \sqrt{\tan (e+f x)+1}}\right)}{2 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^4(e+f x)}{4 f}+\frac{7 \sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{24 f}+\frac{13 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{96 f}-\frac{13 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{64 f}",1,"(Sqrt[-1 + Sqrt[2]]*ArcTan[(3 - 2*Sqrt[2] + (1 - Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(-7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (115*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(64*f) + (Sqrt[1 + Sqrt[2]]*ArcTanh[(3 + 2*Sqrt[2] + (1 + Sqrt[2])*Tan[e + f*x])/(Sqrt[2*(7 + 5*Sqrt[2])]*Sqrt[1 + Tan[e + f*x]])])/(2*f) - (13*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(64*f) + (13*Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(96*f) + (7*Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(24*f) - (Cot[e + f*x]^4*Sqrt[1 + Tan[e + f*x]])/(4*f)","A",14,11,21,0.5238,1,"{3569, 3649, 3650, 3654, 12, 3536, 3535, 203, 207, 3634, 63}"
406,1,311,0,0.3564784,"\int \frac{\tan ^4(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Tan[e + f*x]^4/Sqrt[1 + Tan[e + f*x]],x]","\frac{2 \sqrt{\tan (e+f x)+1} \tan ^2(e+f x)}{5 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{8 \sqrt{\tan (e+f x)+1} \tan (e+f x)}{15 f}-\frac{14 \sqrt{\tan (e+f x)+1}}{15 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}","\frac{2 \sqrt{\tan (e+f x)+1} \tan ^2(e+f x)}{5 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{8 \sqrt{\tan (e+f x)+1} \tan (e+f x)}{15 f}-\frac{14 \sqrt{\tan (e+f x)+1}}{15 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}",1,"-(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) - (14*Sqrt[1 + Tan[e + f*x]])/(15*f) - (8*Tan[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(15*f) + (2*Tan[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(5*f)","A",14,10,21,0.4762,1,"{3566, 3647, 3631, 3485, 708, 1094, 634, 618, 204, 628}"
407,1,257,0,0.2068983,"\int \frac{\tan ^2(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Tan[e + f*x]^2/Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{2 \sqrt{\tan (e+f x)+1}}{f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}",1,"(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) + (2*Sqrt[1 + Tan[e + f*x]])/f","A",12,8,21,0.3810,1,"{3543, 3485, 708, 1094, 634, 618, 204, 628}"
408,1,240,0,0.1627786,"\int \frac{1}{\sqrt{1+\tan (e+f x)}} \, dx","Int[1/Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}",1,"-(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f)","A",11,7,12,0.5833,1,"{3485, 708, 1094, 634, 618, 204, 628}"
409,1,280,0,0.3989003,"\int \frac{\cot ^2(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Cot[e + f*x]^2/Sqrt[1 + Tan[e + f*x]],x]","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}","\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{f}-\frac{\sqrt{\tan (e+f x)+1} \cot (e+f x)}{f}",1,"(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) - (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) + ArcTanh[Sqrt[1 + Tan[e + f*x]]]/f + Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) - Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) - (Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/f","A",19,15,21,0.7143,1,"{3569, 3632, 21, 3573, 12, 3485, 708, 1094, 634, 618, 204, 628, 3634, 63, 207}"
410,1,339,0,0.5771985,"\int \frac{\cot ^4(e+f x)}{\sqrt{1+\tan (e+f x)}} \, dx","Int[Cot[e + f*x]^4/Sqrt[1 + Tan[e + f*x]],x]","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{3 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}+\frac{5 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{3 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}","-\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{\tan (e+f x)+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}+\frac{\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{\tan (e+f x)+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)}{2 f}-\frac{\log \left(\tan (e+f x)-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}+\frac{\log \left(\tan (e+f x)+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{\tan (e+f x)+1}+\sqrt{2}+1\right)}{4 \sqrt{1+\sqrt{2}} f}-\frac{3 \tanh ^{-1}\left(\sqrt{\tan (e+f x)+1}\right)}{8 f}-\frac{\sqrt{\tan (e+f x)+1} \cot ^3(e+f x)}{3 f}+\frac{5 \sqrt{\tan (e+f x)+1} \cot ^2(e+f x)}{12 f}+\frac{3 \sqrt{\tan (e+f x)+1} \cot (e+f x)}{8 f}",1,"-(Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) + (Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + Tan[e + f*x]])/Sqrt[2*(-1 + Sqrt[2])]])/(2*f) - (3*ArcTanh[Sqrt[1 + Tan[e + f*x]]])/(8*f) - Log[1 + Sqrt[2] + Tan[e + f*x] - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) + Log[1 + Sqrt[2] + Tan[e + f*x] + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + Tan[e + f*x]]]/(4*Sqrt[1 + Sqrt[2]]*f) + (3*Cot[e + f*x]*Sqrt[1 + Tan[e + f*x]])/(8*f) + (5*Cot[e + f*x]^2*Sqrt[1 + Tan[e + f*x]])/(12*f) - (Cot[e + f*x]^3*Sqrt[1 + Tan[e + f*x]])/(3*f)","A",19,15,21,0.7143,1,"{3569, 3649, 3650, 3653, 12, 3485, 708, 1094, 634, 618, 204, 628, 3634, 63, 207}"
411,1,161,0,0.1493498,"\int (d \tan (e+f x))^n (a+a \tan (e+f x))^m \, dx","Int[(d*Tan[e + f*x])^n*(a + a*Tan[e + f*x])^m,x]","\frac{(\tan (e+f x)+1)^{-m} (a \tan (e+f x)+a)^m (d \tan (e+f x))^{n+1} F_1(n+1;-m,1;n+2;-\tan (e+f x),-i \tan (e+f x))}{2 d f (n+1)}+\frac{(\tan (e+f x)+1)^{-m} (a \tan (e+f x)+a)^m (d \tan (e+f x))^{n+1} F_1(n+1;-m,1;n+2;-\tan (e+f x),i \tan (e+f x))}{2 d f (n+1)}","\frac{(\tan (e+f x)+1)^{-m} (a \tan (e+f x)+a)^m (d \tan (e+f x))^{n+1} F_1(n+1;-m,1;n+2;-\tan (e+f x),-i \tan (e+f x))}{2 d f (n+1)}+\frac{(\tan (e+f x)+1)^{-m} (a \tan (e+f x)+a)^m (d \tan (e+f x))^{n+1} F_1(n+1;-m,1;n+2;-\tan (e+f x),i \tan (e+f x))}{2 d f (n+1)}",1,"(AppellF1[1 + n, -m, 1, 2 + n, -Tan[e + f*x], (-I)*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*(a + a*Tan[e + f*x])^m)/(2*d*f*(1 + n)*(1 + Tan[e + f*x])^m) + (AppellF1[1 + n, -m, 1, 2 + n, -Tan[e + f*x], I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*(a + a*Tan[e + f*x])^m)/(2*d*f*(1 + n)*(1 + Tan[e + f*x])^m)","A",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
412,1,93,0,0.098645,"\int \tan ^5(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^5*(a + b*Tan[c + d*x]),x]","\frac{a \tan ^4(c+d x)}{4 d}-\frac{a \tan ^2(c+d x)}{2 d}-\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan ^5(c+d x)}{5 d}-\frac{b \tan ^3(c+d x)}{3 d}+\frac{b \tan (c+d x)}{d}-b x","\frac{a \tan ^4(c+d x)}{4 d}-\frac{a \tan ^2(c+d x)}{2 d}-\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan ^5(c+d x)}{5 d}-\frac{b \tan ^3(c+d x)}{3 d}+\frac{b \tan (c+d x)}{d}-b x",1,"-(b*x) - (a*Log[Cos[c + d*x]])/d + (b*Tan[c + d*x])/d - (a*Tan[c + d*x]^2)/(2*d) - (b*Tan[c + d*x]^3)/(3*d) + (a*Tan[c + d*x]^4)/(4*d) + (b*Tan[c + d*x]^5)/(5*d)","A",6,3,19,0.1579,1,"{3528, 3525, 3475}"
413,1,77,0,0.0785955,"\int \tan ^4(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^4*(a + b*Tan[c + d*x]),x]","\frac{a \tan ^3(c+d x)}{3 d}-\frac{a \tan (c+d x)}{d}+a x+\frac{b \tan ^4(c+d x)}{4 d}-\frac{b \tan ^2(c+d x)}{2 d}-\frac{b \log (\cos (c+d x))}{d}","\frac{a \tan ^3(c+d x)}{3 d}-\frac{a \tan (c+d x)}{d}+a x+\frac{b \tan ^4(c+d x)}{4 d}-\frac{b \tan ^2(c+d x)}{2 d}-\frac{b \log (\cos (c+d x))}{d}",1,"a*x - (b*Log[Cos[c + d*x]])/d - (a*Tan[c + d*x])/d - (b*Tan[c + d*x]^2)/(2*d) + (a*Tan[c + d*x]^3)/(3*d) + (b*Tan[c + d*x]^4)/(4*d)","A",5,3,19,0.1579,1,"{3528, 3525, 3475}"
414,1,60,0,0.0581332,"\int \tan ^3(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x]),x]","\frac{a \tan ^2(c+d x)}{2 d}+\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan ^3(c+d x)}{3 d}-\frac{b \tan (c+d x)}{d}+b x","\frac{a \tan ^2(c+d x)}{2 d}+\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan ^3(c+d x)}{3 d}-\frac{b \tan (c+d x)}{d}+b x",1,"b*x + (a*Log[Cos[c + d*x]])/d - (b*Tan[c + d*x])/d + (a*Tan[c + d*x]^2)/(2*d) + (b*Tan[c + d*x]^3)/(3*d)","A",4,3,19,0.1579,1,"{3528, 3525, 3475}"
415,1,44,0,0.0379417,"\int \tan ^2(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x]),x]","\frac{a \tan (c+d x)}{d}-a x+\frac{b \tan ^2(c+d x)}{2 d}+\frac{b \log (\cos (c+d x))}{d}","\frac{a \tan (c+d x)}{d}-a x+\frac{b \tan ^2(c+d x)}{2 d}+\frac{b \log (\cos (c+d x))}{d}",1,"-(a*x) + (b*Log[Cos[c + d*x]])/d + (a*Tan[c + d*x])/d + (b*Tan[c + d*x]^2)/(2*d)","A",3,3,19,0.1579,1,"{3528, 3525, 3475}"
416,1,29,0,0.0161197,"\int \tan (c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x]),x]","-\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan (c+d x)}{d}-b x","-\frac{a \log (\cos (c+d x))}{d}+\frac{b \tan (c+d x)}{d}-b x",1,"-(b*x) - (a*Log[Cos[c + d*x]])/d + (b*Tan[c + d*x])/d","A",2,2,17,0.1176,1,"{3525, 3475}"
417,1,17,0,0.0071293,"\int (a+b \tan (c+d x)) \, dx","Int[a + b*Tan[c + d*x],x]","a x-\frac{b \log (\cos (c+d x))}{d}","a x-\frac{b \log (\cos (c+d x))}{d}",1,"a*x - (b*Log[Cos[c + d*x]])/d","A",2,1,10,0.1000,1,"{3475}"
418,1,16,0,0.019953,"\int \cot (c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x]),x]","\frac{a \log (\sin (c+d x))}{d}+b x","\frac{a \log (\sin (c+d x))}{d}+b x",1,"b*x + (a*Log[Sin[c + d*x]])/d","A",2,2,17,0.1176,1,"{3531, 3475}"
419,1,29,0,0.0397291,"\int \cot ^2(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x]),x]","-\frac{a \cot (c+d x)}{d}-a x+\frac{b \log (\sin (c+d x))}{d}","-\frac{a \cot (c+d x)}{d}-a x+\frac{b \log (\sin (c+d x))}{d}",1,"-(a*x) - (a*Cot[c + d*x])/d + (b*Log[Sin[c + d*x]])/d","A",3,3,19,0.1579,1,"{3529, 3531, 3475}"
420,1,46,0,0.064159,"\int \cot ^3(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x]),x]","-\frac{a \cot ^2(c+d x)}{2 d}-\frac{a \log (\sin (c+d x))}{d}-\frac{b \cot (c+d x)}{d}-b x","-\frac{a \cot ^2(c+d x)}{2 d}-\frac{a \log (\sin (c+d x))}{d}-\frac{b \cot (c+d x)}{d}-b x",1,"-(b*x) - (b*Cot[c + d*x])/d - (a*Cot[c + d*x]^2)/(2*d) - (a*Log[Sin[c + d*x]])/d","A",4,3,19,0.1579,1,"{3529, 3531, 3475}"
421,1,60,0,0.0813487,"\int \cot ^4(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x]),x]","-\frac{a \cot ^3(c+d x)}{3 d}+\frac{a \cot (c+d x)}{d}+a x-\frac{b \cot ^2(c+d x)}{2 d}-\frac{b \log (\sin (c+d x))}{d}","-\frac{a \cot ^3(c+d x)}{3 d}+\frac{a \cot (c+d x)}{d}+a x-\frac{b \cot ^2(c+d x)}{2 d}-\frac{b \log (\sin (c+d x))}{d}",1,"a*x + (a*Cot[c + d*x])/d - (b*Cot[c + d*x]^2)/(2*d) - (a*Cot[c + d*x]^3)/(3*d) - (b*Log[Sin[c + d*x]])/d","A",5,3,19,0.1579,1,"{3529, 3531, 3475}"
422,1,75,0,0.1059948,"\int \cot ^5(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x]),x]","-\frac{a \cot ^4(c+d x)}{4 d}+\frac{a \cot ^2(c+d x)}{2 d}+\frac{a \log (\sin (c+d x))}{d}-\frac{b \cot ^3(c+d x)}{3 d}+\frac{b \cot (c+d x)}{d}+b x","-\frac{a \cot ^4(c+d x)}{4 d}+\frac{a \cot ^2(c+d x)}{2 d}+\frac{a \log (\sin (c+d x))}{d}-\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 + (a*Cot[c + d*x]^2)/(2*d) - (b*Cot[c + d*x]^3)/(3*d) - (a*Cot[c + d*x]^4)/(4*d) + (a*Log[Sin[c + d*x]])/d","A",6,3,19,0.1579,1,"{3529, 3531, 3475}"
423,1,93,0,0.1211252,"\int \cot ^6(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x]),x]","-\frac{a \cot ^5(c+d x)}{5 d}+\frac{a \cot ^3(c+d x)}{3 d}-\frac{a \cot (c+d x)}{d}-a x-\frac{b \cot ^4(c+d x)}{4 d}+\frac{b \cot ^2(c+d x)}{2 d}+\frac{b \log (\sin (c+d x))}{d}","-\frac{a \cot ^5(c+d x)}{5 d}+\frac{a \cot ^3(c+d x)}{3 d}-\frac{a \cot (c+d x)}{d}-a x-\frac{b \cot ^4(c+d x)}{4 d}+\frac{b \cot ^2(c+d x)}{2 d}+\frac{b \log (\sin (c+d x))}{d}",1,"-(a*x) - (a*Cot[c + d*x])/d + (b*Cot[c + d*x]^2)/(2*d) + (a*Cot[c + d*x]^3)/(3*d) - (b*Cot[c + d*x]^4)/(4*d) - (a*Cot[c + d*x]^5)/(5*d) + (b*Log[Sin[c + d*x]])/d","A",7,3,19,0.1579,1,"{3529, 3531, 3475}"
424,1,120,0,0.1675205,"\int \tan ^4(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^4*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \tan ^3(c+d x)}{3 d}-\frac{\left(a^2-b^2\right) \tan (c+d x)}{d}+x \left(a^2-b^2\right)+\frac{a b \tan ^4(c+d x)}{2 d}-\frac{a b \tan ^2(c+d x)}{d}-\frac{2 a b \log (\cos (c+d x))}{d}+\frac{b^2 \tan ^5(c+d x)}{5 d}","\frac{\left(a^2-b^2\right) \tan ^3(c+d x)}{3 d}-\frac{\left(a^2-b^2\right) \tan (c+d x)}{d}+x \left(a^2-b^2\right)+\frac{a b \tan ^4(c+d x)}{2 d}-\frac{a b \tan ^2(c+d x)}{d}-\frac{2 a b \log (\cos (c+d x))}{d}+\frac{b^2 \tan ^5(c+d x)}{5 d}",1,"(a^2 - b^2)*x - (2*a*b*Log[Cos[c + d*x]])/d - ((a^2 - b^2)*Tan[c + d*x])/d - (a*b*Tan[c + d*x]^2)/d + ((a^2 - b^2)*Tan[c + d*x]^3)/(3*d) + (a*b*Tan[c + d*x]^4)/(2*d) + (b^2*Tan[c + d*x]^5)/(5*d)","A",6,4,21,0.1905,1,"{3543, 3528, 3525, 3475}"
425,1,98,0,0.1275183,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \tan ^2(c+d x)}{2 d}+\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d}+\frac{2 a b \tan ^3(c+d x)}{3 d}-\frac{2 a b \tan (c+d x)}{d}+2 a b x+\frac{b^2 \tan ^4(c+d x)}{4 d}","\frac{\left(a^2-b^2\right) \tan ^2(c+d x)}{2 d}+\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d}+\frac{2 a b \tan ^3(c+d x)}{3 d}-\frac{2 a b \tan (c+d x)}{d}+2 a b x+\frac{b^2 \tan ^4(c+d x)}{4 d}",1,"2*a*b*x + ((a^2 - b^2)*Log[Cos[c + d*x]])/d - (2*a*b*Tan[c + d*x])/d + ((a^2 - b^2)*Tan[c + d*x]^2)/(2*d) + (2*a*b*Tan[c + d*x]^3)/(3*d) + (b^2*Tan[c + d*x]^4)/(4*d)","A",5,4,21,0.1905,1,"{3543, 3528, 3525, 3475}"
426,1,63,0,0.0515594,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^2,x]","-x \left(a^2-b^2\right)+\frac{(a+b \tan (c+d x))^3}{3 b d}+\frac{2 a b \log (\cos (c+d x))}{d}-\frac{b^2 \tan (c+d x)}{d}","-x \left(a^2-b^2\right)+\frac{(a+b \tan (c+d x))^3}{3 b d}+\frac{2 a b \log (\cos (c+d x))}{d}-\frac{b^2 \tan (c+d x)}{d}",1,"-((a^2 - b^2)*x) + (2*a*b*Log[Cos[c + d*x]])/d - (b^2*Tan[c + d*x])/d + (a + b*Tan[c + d*x])^3/(3*b*d)","A",3,3,21,0.1429,1,"{3543, 3477, 3475}"
427,1,58,0,0.0427957,"\int \tan (c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d}+\frac{(a+b \tan (c+d x))^2}{2 d}+\frac{a b \tan (c+d x)}{d}-2 a b x","-\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d}+\frac{(a+b \tan (c+d x))^2}{2 d}+\frac{a b \tan (c+d x)}{d}-2 a b x",1,"-2*a*b*x - ((a^2 - b^2)*Log[Cos[c + d*x]])/d + (a*b*Tan[c + d*x])/d + (a + b*Tan[c + d*x])^2/(2*d)","A",3,3,19,0.1579,1,"{3528, 3525, 3475}"
428,1,39,0,0.0182302,"\int (a+b \tan (c+d x))^2 \, dx","Int[(a + b*Tan[c + d*x])^2,x]","x \left(a^2-b^2\right)-\frac{2 a b \log (\cos (c+d x))}{d}+\frac{b^2 \tan (c+d x)}{d}","x \left(a^2-b^2\right)-\frac{2 a b \log (\cos (c+d x))}{d}+\frac{b^2 \tan (c+d x)}{d}",1,"(a^2 - b^2)*x - (2*a*b*Log[Cos[c + d*x]])/d + (b^2*Tan[c + d*x])/d","A",2,2,12,0.1667,1,"{3477, 3475}"
429,1,35,0,0.0367422,"\int \cot (c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^2,x]","\frac{a^2 \log (\sin (c+d x))}{d}+2 a b x-\frac{b^2 \log (\cos (c+d x))}{d}","\frac{a^2 \log (\sin (c+d x))}{d}+2 a b x-\frac{b^2 \log (\cos (c+d x))}{d}",1,"2*a*b*x - (b^2*Log[Cos[c + d*x]])/d + (a^2*Log[Sin[c + d*x]])/d","A",3,2,19,0.1053,1,"{3541, 3475}"
430,1,41,0,0.0645253,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2,x]","-x \left(a^2-b^2\right)-\frac{a^2 \cot (c+d x)}{d}+\frac{2 a b \log (\sin (c+d x))}{d}","-x \left(a^2-b^2\right)-\frac{a^2 \cot (c+d x)}{d}+\frac{2 a b \log (\sin (c+d x))}{d}",1,"-((a^2 - b^2)*x) - (a^2*Cot[c + d*x])/d + (2*a*b*Log[Sin[c + d*x]])/d","A",3,3,21,0.1429,1,"{3542, 3531, 3475}"
431,1,58,0,0.100025,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 \cot ^2(c+d x)}{2 d}-\frac{2 a b \cot (c+d x)}{d}-2 a b x","-\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 \cot ^2(c+d x)}{2 d}-\frac{2 a b \cot (c+d x)}{d}-2 a b x",1,"-2*a*b*x - (2*a*b*Cot[c + d*x])/d - (a^2*Cot[c + d*x]^2)/(2*d) - ((a^2 - b^2)*Log[Sin[c + d*x]])/d","A",4,4,21,0.1905,1,"{3542, 3529, 3531, 3475}"
432,1,78,0,0.1315269,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \cot (c+d x)}{d}+x \left(a^2-b^2\right)-\frac{a^2 \cot ^3(c+d x)}{3 d}-\frac{a b \cot ^2(c+d x)}{d}-\frac{2 a b \log (\sin (c+d x))}{d}","\frac{\left(a^2-b^2\right) \cot (c+d x)}{d}+x \left(a^2-b^2\right)-\frac{a^2 \cot ^3(c+d x)}{3 d}-\frac{a b \cot ^2(c+d x)}{d}-\frac{2 a b \log (\sin (c+d x))}{d}",1,"(a^2 - b^2)*x + ((a^2 - b^2)*Cot[c + d*x])/d - (a*b*Cot[c + d*x]^2)/d - (a^2*Cot[c + d*x]^3)/(3*d) - (2*a*b*Log[Sin[c + d*x]])/d","A",5,4,21,0.1905,1,"{3542, 3529, 3531, 3475}"
433,1,98,0,0.1561562,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 \cot ^4(c+d x)}{4 d}-\frac{2 a b \cot ^3(c+d x)}{3 d}+\frac{2 a b \cot (c+d x)}{d}+2 a b x","\frac{\left(a^2-b^2\right) \cot ^2(c+d x)}{2 d}+\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{d}-\frac{a^2 \cot ^4(c+d x)}{4 d}-\frac{2 a b \cot ^3(c+d x)}{3 d}+\frac{2 a b \cot (c+d x)}{d}+2 a b x",1,"2*a*b*x + (2*a*b*Cot[c + d*x])/d + ((a^2 - b^2)*Cot[c + d*x]^2)/(2*d) - (2*a*b*Cot[c + d*x]^3)/(3*d) - (a^2*Cot[c + d*x]^4)/(4*d) + ((a^2 - b^2)*Log[Sin[c + d*x]])/d","A",6,4,21,0.1905,1,"{3542, 3529, 3531, 3475}"
434,1,120,0,0.1900714,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-b^2\right) \cot ^3(c+d x)}{3 d}-\frac{\left(a^2-b^2\right) \cot (c+d x)}{d}-x \left(a^2-b^2\right)-\frac{a^2 \cot ^5(c+d x)}{5 d}-\frac{a b \cot ^4(c+d x)}{2 d}+\frac{a b \cot ^2(c+d x)}{d}+\frac{2 a b \log (\sin (c+d x))}{d}","\frac{\left(a^2-b^2\right) \cot ^3(c+d x)}{3 d}-\frac{\left(a^2-b^2\right) \cot (c+d x)}{d}-x \left(a^2-b^2\right)-\frac{a^2 \cot ^5(c+d x)}{5 d}-\frac{a b \cot ^4(c+d x)}{2 d}+\frac{a b \cot ^2(c+d x)}{d}+\frac{2 a b \log (\sin (c+d x))}{d}",1,"-((a^2 - b^2)*x) - ((a^2 - b^2)*Cot[c + d*x])/d + (a*b*Cot[c + d*x]^2)/d + ((a^2 - b^2)*Cot[c + d*x]^3)/(3*d) - (a*b*Cot[c + d*x]^4)/(2*d) - (a^2*Cot[c + d*x]^5)/(5*d) + (2*a*b*Log[Sin[c + d*x]])/d","A",7,4,21,0.1905,1,"{3542, 3529, 3531, 3475}"
435,1,147,0,0.1816107,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(a^2-b^2\right) \tan (c+d x)}{d}+\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d}+b x \left(3 a^2-b^2\right)-\frac{a (a+b \tan (c+d x))^4}{20 b^2 d}+\frac{\tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}-\frac{(a+b \tan (c+d x))^3}{3 d}-\frac{a (a+b \tan (c+d x))^2}{2 d}","-\frac{b \left(a^2-b^2\right) \tan (c+d x)}{d}+\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d}+b x \left(3 a^2-b^2\right)-\frac{a (a+b \tan (c+d x))^4}{20 b^2 d}+\frac{\tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}-\frac{(a+b \tan (c+d x))^3}{3 d}-\frac{a (a+b \tan (c+d x))^2}{2 d}",1,"b*(3*a^2 - b^2)*x + (a*(a^2 - 3*b^2)*Log[Cos[c + d*x]])/d - (b*(a^2 - b^2)*Tan[c + d*x])/d - (a*(a + b*Tan[c + d*x])^2)/(2*d) - (a + b*Tan[c + d*x])^3/(3*d) - (a*(a + b*Tan[c + d*x])^4)/(20*b^2*d) + (Tan[c + d*x]*(a + b*Tan[c + d*x])^4)/(5*b*d)","A",7,6,21,0.2857,1,"{3566, 3630, 12, 3528, 3525, 3475}"
436,1,94,0,0.0862305,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^3,x]","\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d}-a x \left(a^2-3 b^2\right)-\frac{2 a b^2 \tan (c+d x)}{d}+\frac{(a+b \tan (c+d x))^4}{4 b d}-\frac{b (a+b \tan (c+d x))^2}{2 d}","\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d}-a x \left(a^2-3 b^2\right)-\frac{2 a b^2 \tan (c+d x)}{d}+\frac{(a+b \tan (c+d x))^4}{4 b d}-\frac{b (a+b \tan (c+d x))^2}{2 d}",1,"-(a*(a^2 - 3*b^2)*x) + (b*(3*a^2 - b^2)*Log[Cos[c + d*x]])/d - (2*a*b^2*Tan[c + d*x])/d - (b*(a + b*Tan[c + d*x])^2)/(2*d) + (a + b*Tan[c + d*x])^4/(4*b*d)","A",4,4,21,0.1905,1,"{3543, 3482, 3525, 3475}"
437,1,97,0,0.0818862,"\int \tan (c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^3,x]","\frac{b \left(a^2-b^2\right) \tan (c+d x)}{d}-\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d}-b x \left(3 a^2-b^2\right)+\frac{(a+b \tan (c+d x))^3}{3 d}+\frac{a (a+b \tan (c+d x))^2}{2 d}","\frac{b \left(a^2-b^2\right) \tan (c+d x)}{d}-\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d}-b x \left(3 a^2-b^2\right)+\frac{(a+b \tan (c+d x))^3}{3 d}+\frac{a (a+b \tan (c+d x))^2}{2 d}",1,"-(b*(3*a^2 - b^2)*x) - (a*(a^2 - 3*b^2)*Log[Cos[c + d*x]])/d + (b*(a^2 - b^2)*Tan[c + d*x])/d + (a*(a + b*Tan[c + d*x])^2)/(2*d) + (a + b*Tan[c + d*x])^3/(3*d)","A",4,3,19,0.1579,1,"{3528, 3525, 3475}"
438,1,72,0,0.0513432,"\int (a+b \tan (c+d x))^3 \, dx","Int[(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d}+a x \left(a^2-3 b^2\right)+\frac{2 a b^2 \tan (c+d x)}{d}+\frac{b (a+b \tan (c+d x))^2}{2 d}","-\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d}+a x \left(a^2-3 b^2\right)+\frac{2 a b^2 \tan (c+d x)}{d}+\frac{b (a+b \tan (c+d x))^2}{2 d}",1,"a*(a^2 - 3*b^2)*x - (b*(3*a^2 - b^2)*Log[Cos[c + d*x]])/d + (2*a*b^2*Tan[c + d*x])/d + (b*(a + b*Tan[c + d*x])^2)/(2*d)","A",3,3,12,0.2500,1,"{3482, 3525, 3475}"
439,1,62,0,0.0759293,"\int \cot (c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^3,x]","b x \left(3 a^2-b^2\right)+\frac{a^3 \log (\sin (c+d x))}{d}+\frac{b^2 (a+b \tan (c+d x))}{d}-\frac{3 a b^2 \log (\cos (c+d x))}{d}","b x \left(3 a^2-b^2\right)+\frac{a^3 \log (\sin (c+d x))}{d}+\frac{b^2 (a+b \tan (c+d x))}{d}-\frac{3 a b^2 \log (\cos (c+d x))}{d}",1,"b*(3*a^2 - b^2)*x - (3*a*b^2*Log[Cos[c + d*x]])/d + (a^3*Log[Sin[c + d*x]])/d + (b^2*(a + b*Tan[c + d*x]))/d","A",4,3,19,0.1579,1,"{3566, 3624, 3475}"
440,1,69,0,0.0874544,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^3,x]","-a x \left(a^2-3 b^2\right)+\frac{3 a^2 b \log (\sin (c+d x))}{d}-\frac{a^2 \cot (c+d x) (a+b \tan (c+d x))}{d}-\frac{b^3 \log (\cos (c+d x))}{d}","-a x \left(a^2-3 b^2\right)+\frac{3 a^2 b \log (\sin (c+d x))}{d}-\frac{a^2 \cot (c+d x) (a+b \tan (c+d x))}{d}-\frac{b^3 \log (\cos (c+d x))}{d}",1,"-(a*(a^2 - 3*b^2)*x) - (b^3*Log[Cos[c + d*x]])/d + (3*a^2*b*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]*(a + b*Tan[c + d*x]))/d","A",4,3,21,0.1429,1,"{3565, 3624, 3475}"
441,1,83,0,0.1411536,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^3,x]","-\frac{a \left(a^2-3 b^2\right) \log (\sin (c+d x))}{d}-b x \left(3 a^2-b^2\right)-\frac{5 a^2 b \cot (c+d x)}{2 d}-\frac{a^2 \cot ^2(c+d x) (a+b \tan (c+d x))}{2 d}","-\frac{a \left(a^2-3 b^2\right) \log (\sin (c+d x))}{d}-b x \left(3 a^2-b^2\right)-\frac{5 a^2 b \cot (c+d x)}{2 d}-\frac{a^2 \cot ^2(c+d x) (a+b \tan (c+d x))}{2 d}",1,"-(b*(3*a^2 - b^2)*x) - (5*a^2*b*Cot[c + d*x])/(2*d) - (a*(a^2 - 3*b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^2*(a + b*Tan[c + d*x]))/(2*d)","A",4,4,21,0.1905,1,"{3565, 3628, 3531, 3475}"
442,1,104,0,0.1908413,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^3,x]","\frac{a \left(a^2-3 b^2\right) \cot (c+d x)}{d}-\frac{b \left(3 a^2-b^2\right) \log (\sin (c+d x))}{d}+a x \left(a^2-3 b^2\right)-\frac{7 a^2 b \cot ^2(c+d x)}{6 d}-\frac{a^2 \cot ^3(c+d x) (a+b \tan (c+d x))}{3 d}","\frac{a \left(a^2-3 b^2\right) \cot (c+d x)}{d}-\frac{b \left(3 a^2-b^2\right) \log (\sin (c+d x))}{d}+a x \left(a^2-3 b^2\right)-\frac{7 a^2 b \cot ^2(c+d x)}{6 d}-\frac{a^2 \cot ^3(c+d x) (a+b \tan (c+d x))}{3 d}",1,"a*(a^2 - 3*b^2)*x + (a*(a^2 - 3*b^2)*Cot[c + d*x])/d - (7*a^2*b*Cot[c + d*x]^2)/(6*d) - (b*(3*a^2 - b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^3*(a + b*Tan[c + d*x]))/(3*d)","A",5,5,21,0.2381,1,"{3565, 3628, 3529, 3531, 3475}"
443,1,130,0,0.2316623,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^3,x]","\frac{a \left(a^2-3 b^2\right) \cot ^2(c+d x)}{2 d}+\frac{b \left(3 a^2-b^2\right) \cot (c+d x)}{d}+\frac{a \left(a^2-3 b^2\right) \log (\sin (c+d x))}{d}+b x \left(3 a^2-b^2\right)-\frac{3 a^2 b \cot ^3(c+d x)}{4 d}-\frac{a^2 \cot ^4(c+d x) (a+b \tan (c+d x))}{4 d}","\frac{a \left(a^2-3 b^2\right) \cot ^2(c+d x)}{2 d}+\frac{b \left(3 a^2-b^2\right) \cot (c+d x)}{d}+\frac{a \left(a^2-3 b^2\right) \log (\sin (c+d x))}{d}+b x \left(3 a^2-b^2\right)-\frac{3 a^2 b \cot ^3(c+d x)}{4 d}-\frac{a^2 \cot ^4(c+d x) (a+b \tan (c+d x))}{4 d}",1,"b*(3*a^2 - b^2)*x + (b*(3*a^2 - b^2)*Cot[c + d*x])/d + (a*(a^2 - 3*b^2)*Cot[c + d*x]^2)/(2*d) - (3*a^2*b*Cot[c + d*x]^3)/(4*d) + (a*(a^2 - 3*b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^4*(a + b*Tan[c + d*x]))/(4*d)","A",6,5,21,0.2381,1,"{3565, 3628, 3529, 3531, 3475}"
444,1,157,0,0.2775356,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^3,x]","\frac{a \left(a^2-3 b^2\right) \cot ^3(c+d x)}{3 d}+\frac{b \left(3 a^2-b^2\right) \cot ^2(c+d x)}{2 d}-\frac{a \left(a^2-3 b^2\right) \cot (c+d x)}{d}+\frac{b \left(3 a^2-b^2\right) \log (\sin (c+d x))}{d}-a x \left(a^2-3 b^2\right)-\frac{11 a^2 b \cot ^4(c+d x)}{20 d}-\frac{a^2 \cot ^5(c+d x) (a+b \tan (c+d x))}{5 d}","\frac{a \left(a^2-3 b^2\right) \cot ^3(c+d x)}{3 d}+\frac{b \left(3 a^2-b^2\right) \cot ^2(c+d x)}{2 d}-\frac{a \left(a^2-3 b^2\right) \cot (c+d x)}{d}+\frac{b \left(3 a^2-b^2\right) \log (\sin (c+d x))}{d}-a x \left(a^2-3 b^2\right)-\frac{11 a^2 b \cot ^4(c+d x)}{20 d}-\frac{a^2 \cot ^5(c+d x) (a+b \tan (c+d x))}{5 d}",1,"-(a*(a^2 - 3*b^2)*x) - (a*(a^2 - 3*b^2)*Cot[c + d*x])/d + (b*(3*a^2 - b^2)*Cot[c + d*x]^2)/(2*d) + (a*(a^2 - 3*b^2)*Cot[c + d*x]^3)/(3*d) - (11*a^2*b*Cot[c + d*x]^4)/(20*d) + (b*(3*a^2 - b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^5*(a + b*Tan[c + d*x]))/(5*d)","A",7,5,21,0.2381,1,"{3565, 3628, 3529, 3531, 3475}"
445,1,181,0,0.2364072,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^4,x]","-\frac{\left(a^2-b^2\right) (a+b \tan (c+d x))^2}{2 d}-\frac{a b \left(a^2-3 b^2\right) \tan (c+d x)}{d}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d}+4 a b x \left(a^2-b^2\right)-\frac{a (a+b \tan (c+d x))^5}{30 b^2 d}+\frac{\tan (c+d x) (a+b \tan (c+d x))^5}{6 b d}-\frac{(a+b \tan (c+d x))^4}{4 d}-\frac{a (a+b \tan (c+d x))^3}{3 d}","-\frac{\left(a^2-b^2\right) (a+b \tan (c+d x))^2}{2 d}-\frac{a b \left(a^2-3 b^2\right) \tan (c+d x)}{d}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d}+4 a b x \left(a^2-b^2\right)-\frac{a (a+b \tan (c+d x))^5}{30 b^2 d}+\frac{\tan (c+d x) (a+b \tan (c+d x))^5}{6 b d}-\frac{(a+b \tan (c+d x))^4}{4 d}-\frac{a (a+b \tan (c+d x))^3}{3 d}",1,"4*a*b*(a^2 - b^2)*x + ((a^4 - 6*a^2*b^2 + b^4)*Log[Cos[c + d*x]])/d - (a*b*(a^2 - 3*b^2)*Tan[c + d*x])/d - ((a^2 - b^2)*(a + b*Tan[c + d*x])^2)/(2*d) - (a*(a + b*Tan[c + d*x])^3)/(3*d) - (a + b*Tan[c + d*x])^4/(4*d) - (a*(a + b*Tan[c + d*x])^5)/(30*b^2*d) + (Tan[c + d*x]*(a + b*Tan[c + d*x])^5)/(6*b*d)","A",8,6,21,0.2857,1,"{3566, 3630, 12, 3528, 3525, 3475}"
446,1,128,0,0.1408218,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^4,x]","-\frac{b^2 \left(3 a^2-b^2\right) \tan (c+d x)}{d}+\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{(a+b \tan (c+d x))^5}{5 b d}-\frac{b (a+b \tan (c+d x))^3}{3 d}-\frac{a b (a+b \tan (c+d x))^2}{d}","-\frac{b^2 \left(3 a^2-b^2\right) \tan (c+d x)}{d}+\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{(a+b \tan (c+d x))^5}{5 b d}-\frac{b (a+b \tan (c+d x))^3}{3 d}-\frac{a b (a+b \tan (c+d x))^2}{d}",1,"-((a^4 - 6*a^2*b^2 + b^4)*x) + (4*a*b*(a^2 - b^2)*Log[Cos[c + d*x]])/d - (b^2*(3*a^2 - b^2)*Tan[c + d*x])/d - (a*b*(a + b*Tan[c + d*x])^2)/d - (b*(a + b*Tan[c + d*x])^3)/(3*d) + (a + b*Tan[c + d*x])^5/(5*b*d)","A",5,5,21,0.2381,1,"{3543, 3482, 3528, 3525, 3475}"
447,1,130,0,0.1286866,"\int \tan (c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^4,x]","\frac{\left(a^2-b^2\right) (a+b \tan (c+d x))^2}{2 d}+\frac{a b \left(a^2-3 b^2\right) \tan (c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d}-4 a b x \left(a^2-b^2\right)+\frac{(a+b \tan (c+d x))^4}{4 d}+\frac{a (a+b \tan (c+d x))^3}{3 d}","\frac{\left(a^2-b^2\right) (a+b \tan (c+d x))^2}{2 d}+\frac{a b \left(a^2-3 b^2\right) \tan (c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d}-4 a b x \left(a^2-b^2\right)+\frac{(a+b \tan (c+d x))^4}{4 d}+\frac{a (a+b \tan (c+d x))^3}{3 d}",1,"-4*a*b*(a^2 - b^2)*x - ((a^4 - 6*a^2*b^2 + b^4)*Log[Cos[c + d*x]])/d + (a*b*(a^2 - 3*b^2)*Tan[c + d*x])/d + ((a^2 - b^2)*(a + b*Tan[c + d*x])^2)/(2*d) + (a*(a + b*Tan[c + d*x])^3)/(3*d) + (a + b*Tan[c + d*x])^4/(4*d)","A",5,3,19,0.1579,1,"{3528, 3525, 3475}"
448,1,103,0,0.1050841,"\int (a+b \tan (c+d x))^4 \, dx","Int[(a + b*Tan[c + d*x])^4,x]","\frac{b^2 \left(3 a^2-b^2\right) \tan (c+d x)}{d}-\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d}+x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{b (a+b \tan (c+d x))^3}{3 d}+\frac{a b (a+b \tan (c+d x))^2}{d}","\frac{b^2 \left(3 a^2-b^2\right) \tan (c+d x)}{d}-\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d}+x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{b (a+b \tan (c+d x))^3}{3 d}+\frac{a b (a+b \tan (c+d x))^2}{d}",1,"(a^4 - 6*a^2*b^2 + b^4)*x - (4*a*b*(a^2 - b^2)*Log[Cos[c + d*x]])/d + (b^2*(3*a^2 - b^2)*Tan[c + d*x])/d + (a*b*(a + b*Tan[c + d*x])^2)/d + (b*(a + b*Tan[c + d*x])^3)/(3*d)","A",4,4,12,0.3333,1,"{3482, 3528, 3525, 3475}"
449,1,92,0,0.1776308,"\int \cot (c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^4,x]","-\frac{b^2 \left(6 a^2-b^2\right) \log (\cos (c+d x))}{d}+4 a b x \left(a^2-b^2\right)+\frac{a^4 \log (\sin (c+d x))}{d}+\frac{3 a b^3 \tan (c+d x)}{d}+\frac{b^2 (a+b \tan (c+d x))^2}{2 d}","-\frac{b^2 \left(6 a^2-b^2\right) \log (\cos (c+d x))}{d}+4 a b x \left(a^2-b^2\right)+\frac{a^4 \log (\sin (c+d x))}{d}+\frac{3 a b^3 \tan (c+d x)}{d}+\frac{b^2 (a+b \tan (c+d x))^2}{2 d}",1,"4*a*b*(a^2 - b^2)*x - (b^2*(6*a^2 - b^2)*Log[Cos[c + d*x]])/d + (a^4*Log[Sin[c + d*x]])/d + (3*a*b^3*Tan[c + d*x])/d + (b^2*(a + b*Tan[c + d*x])^2)/(2*d)","A",5,4,19,0.2105,1,"{3566, 3637, 3624, 3475}"
450,1,97,0,0.175379,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^4,x]","\frac{b^2 \left(a^2+b^2\right) \tan (c+d x)}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{4 a^3 b \log (\sin (c+d x))}{d}-\frac{a^2 \cot (c+d x) (a+b \tan (c+d x))^2}{d}-\frac{4 a b^3 \log (\cos (c+d x))}{d}","\frac{b^2 \left(a^2+b^2\right) \tan (c+d x)}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)+\frac{4 a^3 b \log (\sin (c+d x))}{d}-\frac{a^2 \cot (c+d x) (a+b \tan (c+d x))^2}{d}-\frac{4 a b^3 \log (\cos (c+d x))}{d}",1,"-((a^4 - 6*a^2*b^2 + b^4)*x) - (4*a*b^3*Log[Cos[c + d*x]])/d + (4*a^3*b*Log[Sin[c + d*x]])/d + (b^2*(a^2 + b^2)*Tan[c + d*x])/d - (a^2*Cot[c + d*x]*(a + b*Tan[c + d*x])^2)/d","A",5,4,21,0.1905,1,"{3565, 3637, 3624, 3475}"
451,1,99,0,0.1992078,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 \left(a^2-6 b^2\right) \log (\sin (c+d x))}{d}-4 a b x \left(a^2-b^2\right)-\frac{3 a^3 b \cot (c+d x)}{d}-\frac{a^2 \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^4 \log (\cos (c+d x))}{d}","-\frac{a^2 \left(a^2-6 b^2\right) \log (\sin (c+d x))}{d}-4 a b x \left(a^2-b^2\right)-\frac{3 a^3 b \cot (c+d x)}{d}-\frac{a^2 \cot ^2(c+d x) (a+b \tan (c+d x))^2}{2 d}-\frac{b^4 \log (\cos (c+d x))}{d}",1,"-4*a*b*(a^2 - b^2)*x - (3*a^3*b*Cot[c + d*x])/d - (b^4*Log[Cos[c + d*x]])/d - (a^2*(a^2 - 6*b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^2*(a + b*Tan[c + d*x])^2)/(2*d)","A",5,4,21,0.1905,1,"{3565, 3635, 3624, 3475}"
452,1,117,0,0.2977122,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^4,x]","\frac{a^2 \left(3 a^2-17 b^2\right) \cot (c+d x)}{3 d}-\frac{4 a b \left(a^2-b^2\right) \log (\sin (c+d x))}{d}+x \left(-6 a^2 b^2+a^4+b^4\right)-\frac{4 a^3 b \cot ^2(c+d x)}{3 d}-\frac{a^2 \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}","\frac{a^2 \left(3 a^2-17 b^2\right) \cot (c+d x)}{3 d}-\frac{4 a b \left(a^2-b^2\right) \log (\sin (c+d x))}{d}+x \left(-6 a^2 b^2+a^4+b^4\right)-\frac{4 a^3 b \cot ^2(c+d x)}{3 d}-\frac{a^2 \cot ^3(c+d x) (a+b \tan (c+d x))^2}{3 d}",1,"(a^4 - 6*a^2*b^2 + b^4)*x + (a^2*(3*a^2 - 17*b^2)*Cot[c + d*x])/(3*d) - (4*a^3*b*Cot[c + d*x]^2)/(3*d) - (4*a*b*(a^2 - b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^3*(a + b*Tan[c + d*x])^2)/(3*d)","A",5,5,21,0.2381,1,"{3565, 3635, 3628, 3531, 3475}"
453,1,141,0,0.3416774,"\int \cot ^5(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^5*(a + b*Tan[c + d*x])^4,x]","\frac{a^2 \left(2 a^2-11 b^2\right) \cot ^2(c+d x)}{4 d}+\frac{4 a b \left(a^2-b^2\right) \cot (c+d x)}{d}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\sin (c+d x))}{d}+4 a b x \left(a^2-b^2\right)-\frac{5 a^3 b \cot ^3(c+d x)}{6 d}-\frac{a^2 \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}","\frac{a^2 \left(2 a^2-11 b^2\right) \cot ^2(c+d x)}{4 d}+\frac{4 a b \left(a^2-b^2\right) \cot (c+d x)}{d}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\sin (c+d x))}{d}+4 a b x \left(a^2-b^2\right)-\frac{5 a^3 b \cot ^3(c+d x)}{6 d}-\frac{a^2 \cot ^4(c+d x) (a+b \tan (c+d x))^2}{4 d}",1,"4*a*b*(a^2 - b^2)*x + (4*a*b*(a^2 - b^2)*Cot[c + d*x])/d + (a^2*(2*a^2 - 11*b^2)*Cot[c + d*x]^2)/(4*d) - (5*a^3*b*Cot[c + d*x]^3)/(6*d) + ((a^4 - 6*a^2*b^2 + b^4)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^4*(a + b*Tan[c + d*x])^2)/(4*d)","A",6,6,21,0.2857,1,"{3565, 3635, 3628, 3529, 3531, 3475}"
454,1,170,0,0.3829673,"\int \cot ^6(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^6*(a + b*Tan[c + d*x])^4,x]","\frac{a^2 \left(5 a^2-27 b^2\right) \cot ^3(c+d x)}{15 d}+\frac{2 a b \left(a^2-b^2\right) \cot ^2(c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \cot (c+d x)}{d}+\frac{4 a b \left(a^2-b^2\right) \log (\sin (c+d x))}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)-\frac{3 a^3 b \cot ^4(c+d x)}{5 d}-\frac{a^2 \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}","\frac{a^2 \left(5 a^2-27 b^2\right) \cot ^3(c+d x)}{15 d}+\frac{2 a b \left(a^2-b^2\right) \cot ^2(c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \cot (c+d x)}{d}+\frac{4 a b \left(a^2-b^2\right) \log (\sin (c+d x))}{d}-x \left(-6 a^2 b^2+a^4+b^4\right)-\frac{3 a^3 b \cot ^4(c+d x)}{5 d}-\frac{a^2 \cot ^5(c+d x) (a+b \tan (c+d x))^2}{5 d}",1,"-((a^4 - 6*a^2*b^2 + b^4)*x) - ((a^4 - 6*a^2*b^2 + b^4)*Cot[c + d*x])/d + (2*a*b*(a^2 - b^2)*Cot[c + d*x]^2)/d + (a^2*(5*a^2 - 27*b^2)*Cot[c + d*x]^3)/(15*d) - (3*a^3*b*Cot[c + d*x]^4)/(5*d) + (4*a*b*(a^2 - b^2)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^5*(a + b*Tan[c + d*x])^2)/(5*d)","A",7,6,21,0.2857,1,"{3565, 3635, 3628, 3529, 3531, 3475}"
455,1,198,0,0.4473654,"\int \cot ^7(c+d x) (a+b \tan (c+d x))^4 \, dx","Int[Cot[c + d*x]^7*(a + b*Tan[c + d*x])^4,x]","\frac{a^2 \left(3 a^2-16 b^2\right) \cot ^4(c+d x)}{12 d}+\frac{4 a b \left(a^2-b^2\right) \cot ^3(c+d x)}{3 d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \cot ^2(c+d x)}{2 d}-\frac{4 a b \left(a^2-b^2\right) \cot (c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\sin (c+d x))}{d}-4 a b x \left(a^2-b^2\right)-\frac{7 a^3 b \cot ^5(c+d x)}{15 d}-\frac{a^2 \cot ^6(c+d x) (a+b \tan (c+d x))^2}{6 d}","\frac{a^2 \left(3 a^2-16 b^2\right) \cot ^4(c+d x)}{12 d}+\frac{4 a b \left(a^2-b^2\right) \cot ^3(c+d x)}{3 d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \cot ^2(c+d x)}{2 d}-\frac{4 a b \left(a^2-b^2\right) \cot (c+d x)}{d}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\sin (c+d x))}{d}-4 a b x \left(a^2-b^2\right)-\frac{7 a^3 b \cot ^5(c+d x)}{15 d}-\frac{a^2 \cot ^6(c+d x) (a+b \tan (c+d x))^2}{6 d}",1,"-4*a*b*(a^2 - b^2)*x - (4*a*b*(a^2 - b^2)*Cot[c + d*x])/d - ((a^4 - 6*a^2*b^2 + b^4)*Cot[c + d*x]^2)/(2*d) + (4*a*b*(a^2 - b^2)*Cot[c + d*x]^3)/(3*d) + (a^2*(3*a^2 - 16*b^2)*Cot[c + d*x]^4)/(12*d) - (7*a^3*b*Cot[c + d*x]^5)/(15*d) - ((a^4 - 6*a^2*b^2 + b^4)*Log[Sin[c + d*x]])/d - (a^2*Cot[c + d*x]^6*(a + b*Tan[c + d*x])^2)/(6*d)","A",8,6,21,0.2857,1,"{3565, 3635, 3628, 3529, 3531, 3475}"
456,1,154,0,0.5828183,"\int \frac{\tan ^6(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^6/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2-b^2\right) \tan ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2-b^2\right) \tan (c+d x)}{b^4 d}+\frac{a^6 \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)}-\frac{b \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{a x}{a^2+b^2}-\frac{a \tan ^3(c+d x)}{3 b^2 d}+\frac{\tan ^4(c+d x)}{4 b d}","\frac{\left(a^2-b^2\right) \tan ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2-b^2\right) \tan (c+d x)}{b^4 d}+\frac{a^6 \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)}-\frac{b \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{a x}{a^2+b^2}-\frac{a \tan ^3(c+d x)}{3 b^2 d}+\frac{\tan ^4(c+d x)}{4 b d}",1,"-((a*x)/(a^2 + b^2)) - (b*Log[Cos[c + d*x]])/((a^2 + b^2)*d) + (a^6*Log[a + b*Tan[c + d*x]])/(b^5*(a^2 + b^2)*d) - (a*(a^2 - b^2)*Tan[c + d*x])/(b^4*d) + ((a^2 - b^2)*Tan[c + d*x]^2)/(2*b^3*d) - (a*Tan[c + d*x]^3)/(3*b^2*d) + Tan[c + d*x]^4/(4*b*d)","A",8,7,21,0.3333,1,"{3566, 3647, 3648, 3627, 3617, 31, 3475}"
457,1,125,0,0.3757349,"\int \frac{\tan ^5(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2-b^2\right) \tan (c+d x)}{b^3 d}-\frac{a^5 \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)}-\frac{a \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{b x}{a^2+b^2}-\frac{a \tan ^2(c+d x)}{2 b^2 d}+\frac{\tan ^3(c+d x)}{3 b d}","\frac{\left(a^2-b^2\right) \tan (c+d x)}{b^3 d}-\frac{a^5 \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)}-\frac{a \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{b x}{a^2+b^2}-\frac{a \tan ^2(c+d x)}{2 b^2 d}+\frac{\tan ^3(c+d x)}{3 b d}",1,"(b*x)/(a^2 + b^2) - (a*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a^5*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)*d) + ((a^2 - b^2)*Tan[c + d*x])/(b^3*d) - (a*Tan[c + d*x]^2)/(2*b^2*d) + Tan[c + d*x]^3/(3*b*d)","A",7,7,21,0.3333,1,"{3566, 3647, 3648, 3626, 3617, 31, 3475}"
458,1,97,0,0.2115953,"\int \frac{\tan ^4(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x]),x]","\frac{a^4 \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{b \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}-\frac{a \tan (c+d x)}{b^2 d}+\frac{\tan ^2(c+d x)}{2 b d}","\frac{a^4 \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)}+\frac{b \log (\cos (c+d x))}{d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}-\frac{a \tan (c+d x)}{b^2 d}+\frac{\tan ^2(c+d x)}{2 b d}",1,"(a*x)/(a^2 + b^2) + (b*Log[Cos[c + d*x]])/((a^2 + b^2)*d) + (a^4*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)*d) - (a*Tan[c + d*x])/(b^2*d) + Tan[c + d*x]^2/(2*b*d)","A",6,6,21,0.2857,1,"{3566, 3647, 3627, 3617, 31, 3475}"
459,1,79,0,0.1291133,"\int \frac{\tan ^3(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x]),x]","-\frac{a^3 \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}+\frac{a \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{b x}{a^2+b^2}+\frac{\tan (c+d x)}{b d}","-\frac{a^3 \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)}+\frac{a \log (\cos (c+d x))}{d \left(a^2+b^2\right)}-\frac{b x}{a^2+b^2}+\frac{\tan (c+d x)}{b d}",1,"-((b*x)/(a^2 + b^2)) + (a*Log[Cos[c + d*x]])/((a^2 + b^2)*d) - (a^3*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) + Tan[c + d*x]/(b*d)","A",5,5,21,0.2381,1,"{3566, 3626, 3617, 31, 3475}"
460,1,77,0,0.099732,"\int \frac{\tan ^2(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x]),x]","\frac{a^2 \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}+\frac{a^3 x}{b^2 \left(a^2+b^2\right)}-\frac{a x}{b^2}-\frac{\log (\cos (c+d x))}{b d}","\frac{a^2 \log (a \cos (c+d x)+b \sin (c+d x))}{b d \left(a^2+b^2\right)}-\frac{a x}{a^2+b^2}-\frac{\log (\cos (c+d x))}{b d}",1,"-((a*x)/b^2) + (a^3*x)/(b^2*(a^2 + b^2)) - Log[Cos[c + d*x]]/(b*d) + (a^2*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(b*(a^2 + b^2)*d)","A",4,4,21,0.1905,1,"{3541, 3475, 3484, 3530}"
461,1,46,0,0.0567776,"\int \frac{\tan (c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x]),x]","\frac{b x}{a^2+b^2}-\frac{a \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}","\frac{b x}{a^2+b^2}-\frac{a \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}",1,"(b*x)/(a^2 + b^2) - (a*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",2,2,19,0.1053,1,"{3531, 3530}"
462,1,45,0,0.043348,"\int \frac{1}{a+b \tan (c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(-1),x]","\frac{b \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}","\frac{b \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}",1,"(a*x)/(a^2 + b^2) + (b*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
463,1,66,0,0.0762826,"\int \frac{\cot (c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x]),x]","-\frac{b^2 \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{b x}{a^2+b^2}+\frac{\log (\sin (c+d x))}{a d}","-\frac{b^2 \log (a \cos (c+d x)+b \sin (c+d x))}{a d \left(a^2+b^2\right)}-\frac{b x}{a^2+b^2}+\frac{\log (\sin (c+d x))}{a d}",1,"-((b*x)/(a^2 + b^2)) + Log[Sin[c + d*x]]/(a*d) - (b^2*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a*(a^2 + b^2)*d)","A",3,3,19,0.1579,1,"{3571, 3530, 3475}"
464,1,81,0,0.1731795,"\int \frac{\cot ^2(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x]),x]","\frac{b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{a x}{a^2+b^2}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{\cot (c+d x)}{a d}","\frac{b^3 \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{a x}{a^2+b^2}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{\cot (c+d x)}{a d}",1,"-((a*x)/(a^2 + b^2)) - Cot[c + d*x]/(a*d) - (b*Log[Sin[c + d*x]])/(a^2*d) + (b^3*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)*d)","A",4,4,21,0.1905,1,"{3569, 3651, 3530, 3475}"
465,1,107,0,0.3138022,"\int \frac{\cot ^3(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^3/(a + b*Tan[c + d*x]),x]","-\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^4 \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{b x}{a^2+b^2}+\frac{b \cot (c+d x)}{a^2 d}-\frac{\cot ^2(c+d x)}{2 a d}","-\frac{\left(a^2-b^2\right) \log (\sin (c+d x))}{a^3 d}-\frac{b^4 \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)}+\frac{b x}{a^2+b^2}+\frac{b \cot (c+d x)}{a^2 d}-\frac{\cot ^2(c+d x)}{2 a d}",1,"(b*x)/(a^2 + b^2) + (b*Cot[c + d*x])/(a^2*d) - Cot[c + d*x]^2/(2*a*d) - ((a^2 - b^2)*Log[Sin[c + d*x]])/(a^3*d) - (b^4*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)*d)","A",5,5,21,0.2381,1,"{3569, 3649, 3652, 3530, 3475}"
466,1,133,0,0.4904722,"\int \frac{\cot ^4(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^4/(a + b*Tan[c + d*x]),x]","\frac{\left(a^2-b^2\right) \cot (c+d x)}{a^3 d}+\frac{b \left(a^2-b^2\right) \log (\sin (c+d x))}{a^4 d}+\frac{b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}+\frac{b \cot ^2(c+d x)}{2 a^2 d}-\frac{\cot ^3(c+d x)}{3 a d}","\frac{\left(a^2-b^2\right) \cot (c+d x)}{a^3 d}+\frac{b \left(a^2-b^2\right) \log (\sin (c+d x))}{a^4 d}+\frac{b^5 \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)}+\frac{a x}{a^2+b^2}+\frac{b \cot ^2(c+d x)}{2 a^2 d}-\frac{\cot ^3(c+d x)}{3 a d}",1,"(a*x)/(a^2 + b^2) + ((a^2 - b^2)*Cot[c + d*x])/(a^3*d) + (b*Cot[c + d*x]^2)/(2*a^2*d) - Cot[c + d*x]^3/(3*a*d) + (b*(a^2 - b^2)*Log[Sin[c + d*x]])/(a^4*d) + (b^5*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)*d)","A",6,6,21,0.2857,1,"{3569, 3649, 3650, 3651, 3530, 3475}"
467,1,239,0,0.7423084,"\int \frac{\tan ^6(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^6/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 \tan ^4(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(2 a^2+b^2\right) \tan ^2(c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{\left(4 a^2+b^2\right) \tan ^3(c+d x)}{3 b^2 d \left(a^2+b^2\right)}+\frac{\left(2 a^2 b^2+4 a^4-b^4\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)}-\frac{2 a^5 \left(2 a^2+3 b^2\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^2}-\frac{2 a b \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2 \tan ^4(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{a \left(2 a^2+b^2\right) \tan ^2(c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{\left(4 a^2+b^2\right) \tan ^3(c+d x)}{3 b^2 d \left(a^2+b^2\right)}+\frac{\left(2 a^2 b^2+4 a^4-b^4\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)}-\frac{2 a^5 \left(2 a^2+3 b^2\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^2}-\frac{2 a b \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}",1,"-(((a^2 - b^2)*x)/(a^2 + b^2)^2) - (2*a*b*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) - (2*a^5*(2*a^2 + 3*b^2)*Log[a + b*Tan[c + d*x]])/(b^5*(a^2 + b^2)^2*d) + ((4*a^4 + 2*a^2*b^2 - b^4)*Tan[c + d*x])/(b^4*(a^2 + b^2)*d) - (a*(2*a^2 + b^2)*Tan[c + d*x]^2)/(b^3*(a^2 + b^2)*d) + ((4*a^2 + b^2)*Tan[c + d*x]^3)/(3*b^2*(a^2 + b^2)*d) - (a^2*Tan[c + d*x]^4)/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",8,6,21,0.2857,1,"{3565, 3647, 3626, 3617, 31, 3475}"
468,1,197,0,0.5223501,"\int \frac{\tan ^5(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 \tan ^3(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(3 a^2+b^2\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)}-\frac{a \left(3 a^2+2 b^2\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{a^4 \left(3 a^2+5 b^2\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^2}-\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}","-\frac{a^2 \tan ^3(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(3 a^2+b^2\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)}-\frac{a \left(3 a^2+2 b^2\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{a^4 \left(3 a^2+5 b^2\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^2}-\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}",1,"(2*a*b*x)/(a^2 + b^2)^2 - ((a^2 - b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) + (a^4*(3*a^2 + 5*b^2)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^2*d) - (a*(3*a^2 + 2*b^2)*Tan[c + d*x])/(b^3*(a^2 + b^2)*d) + ((3*a^2 + b^2)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)*d) - (a^2*Tan[c + d*x]^3)/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",7,6,21,0.2857,1,"{3565, 3647, 3626, 3617, 31, 3475}"
469,1,155,0,0.2970894,"\int \frac{\tan ^4(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 \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^2\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}-\frac{2 a^3 \left(a^2+2 b^2\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{2 a b \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2 \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^2\right) \tan (c+d x)}{b^2 d \left(a^2+b^2\right)}-\frac{2 a^3 \left(a^2+2 b^2\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^2}+\frac{2 a b \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}",1,"((a^2 - b^2)*x)/(a^2 + b^2)^2 + (2*a*b*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) - (2*a^3*(a^2 + 2*b^2)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^2*d) + ((2*a^2 + b^2)*Tan[c + d*x])/(b^2*(a^2 + b^2)*d) - (a^2*Tan[c + d*x]^2)/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",6,6,21,0.2857,1,"{3565, 3647, 3626, 3617, 31, 3475}"
470,1,121,0,0.1618694,"\int \frac{\tan ^3(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2 \tan (c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{a^2 \left(a^2+3 b^2\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{2 a b x}{\left(a^2+b^2\right)^2}","\frac{a^3}{b^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{a^2 \left(a^2+3 b^2\right) \log (a+b \tan (c+d x))}{b^2 d \left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{2 a b x}{\left(a^2+b^2\right)^2}",1,"(-2*a*b*x)/(a^2 + b^2)^2 + ((a^2 - b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^2*d) + (a^2*(a^2 + 3*b^2)*Log[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)^2*d) - (a^2*Tan[c + d*x])/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",5,5,21,0.2381,1,"{3565, 3626, 3617, 31, 3475}"
471,1,88,0,0.1159154,"\int \frac{\tan ^2(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x])^2,x]","-\frac{a^2}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{2 a b \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\right)}{\left(a^2+b^2\right)^2}","-\frac{a^2}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{2 a b \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\right)}{\left(a^2+b^2\right)^2}",1,"-(((a^2 - b^2)*x)/(a^2 + b^2)^2) - (2*a*b*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) - a^2/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,21,0.1429,1,"{3542, 3531, 3530}"
472,1,82,0,0.0947094,"\int \frac{\tan (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x])^2,x]","\frac{a}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}","\frac{a}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}",1,"(2*a*b*x)/(a^2 + b^2)^2 - ((a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) + a/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,19,0.1579,1,"{3529, 3531, 3530}"
473,1,82,0,0.0810732,"\int \frac{1}{(a+b \tan (c+d x))^2} \, dx","Int[(a + b*Tan[c + d*x])^(-2),x]","-\frac{b}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{2 a b \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\right)}{\left(a^2+b^2\right)^2}","-\frac{b}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{2 a b \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\right)}{\left(a^2+b^2\right)^2}",1,"((a^2 - b^2)*x)/(a^2 + b^2)^2 + (2*a*b*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^2*d) - b/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",3,3,12,0.2500,1,"{3483, 3531, 3530}"
474,1,107,0,0.2153816,"\int \frac{\cot (c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x])^2,x]","\frac{b^2}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b^2 \left(3 a^2+b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\frac{2 a b x}{\left(a^2+b^2\right)^2}+\frac{\log (\sin (c+d x))}{a^2 d}","\frac{b^2}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{b^2 \left(3 a^2+b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\frac{2 a b x}{\left(a^2+b^2\right)^2}+\frac{\log (\sin (c+d x))}{a^2 d}",1,"(-2*a*b*x)/(a^2 + b^2)^2 + Log[Sin[c + d*x]]/(a^2*d) - (b^2*(3*a^2 + b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^2*(a^2 + b^2)^2*d) + b^2/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",4,4,19,0.2105,1,"{3569, 3651, 3530, 3475}"
475,1,150,0,0.3649788,"\int \frac{\cot ^2(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x])^2,x]","-\frac{b \left(a^2+2 b^2\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{2 b^3 \left(2 a^2+b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}-\frac{2 b \log (\sin (c+d x))}{a^3 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))}","-\frac{b \left(a^2+2 b^2\right)}{a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{2 b^3 \left(2 a^2+b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^2}-\frac{2 b \log (\sin (c+d x))}{a^3 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))}",1,"-(((a^2 - b^2)*x)/(a^2 + b^2)^2) - (2*b*Log[Sin[c + d*x]])/(a^3*d) + (2*b^3*(2*a^2 + b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^2*d) - (b*(a^2 + 2*b^2))/(a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) - Cot[c + d*x]/(a*d*(a + b*Tan[c + d*x]))","A",5,5,21,0.2381,1,"{3569, 3649, 3651, 3530, 3475}"
476,1,189,0,0.5728302,"\int \frac{\cot ^3(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^3/(a + b*Tan[c + d*x])^2,x]","\frac{b^2 \left(2 a^2+3 b^2\right)}{a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-3 b^2\right) \log (\sin (c+d x))}{a^4 d}-\frac{b^4 \left(5 a^2+3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}+\frac{3 b \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))}-\frac{\cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))}","\frac{b^2 \left(2 a^2+3 b^2\right)}{a^3 d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-3 b^2\right) \log (\sin (c+d x))}{a^4 d}-\frac{b^4 \left(5 a^2+3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^2}+\frac{2 a b x}{\left(a^2+b^2\right)^2}+\frac{3 b \cot (c+d x)}{2 a^2 d (a+b \tan (c+d x))}-\frac{\cot ^2(c+d x)}{2 a d (a+b \tan (c+d x))}",1,"(2*a*b*x)/(a^2 + b^2)^2 - ((a^2 - 3*b^2)*Log[Sin[c + d*x]])/(a^4*d) - (b^4*(5*a^2 + 3*b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^2*d) + (b^2*(2*a^2 + 3*b^2))/(a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])) + (3*b*Cot[c + d*x])/(2*a^2*d*(a + b*Tan[c + d*x])) - Cot[c + d*x]^2/(2*a*d*(a + b*Tan[c + d*x]))","A",6,6,21,0.2857,1,"{3569, 3649, 3650, 3651, 3530, 3475}"
477,1,283,0,0.8001372,"\int \frac{\tan ^6(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^6/(a + b*Tan[c + d*x])^3,x]","-\frac{2 a^2 \left(a^2+2 b^2\right) \tan ^3(c+d x)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^4(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(11 a^2 b^2+6 a^4+b^4\right) \tan ^2(c+d x)}{2 b^3 d \left(a^2+b^2\right)^2}-\frac{a \left(11 a^2 b^2+6 a^4+3 b^4\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)^2}+\frac{a^4 \left(17 a^2 b^2+6 a^4+15 b^4\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^3}-\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{2 a^2 \left(a^2+2 b^2\right) \tan ^3(c+d x)}{b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^4(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(11 a^2 b^2+6 a^4+b^4\right) \tan ^2(c+d x)}{2 b^3 d \left(a^2+b^2\right)^2}-\frac{a \left(11 a^2 b^2+6 a^4+3 b^4\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)^2}+\frac{a^4 \left(17 a^2 b^2+6 a^4+15 b^4\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^3}-\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}",1,"-((a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^3) - (b*(3*a^2 - b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a^4*(6*a^4 + 17*a^2*b^2 + 15*b^4)*Log[a + b*Tan[c + d*x]])/(b^5*(a^2 + b^2)^3*d) - (a*(6*a^4 + 11*a^2*b^2 + 3*b^4)*Tan[c + d*x])/(b^4*(a^2 + b^2)^2*d) + ((6*a^4 + 11*a^2*b^2 + b^4)*Tan[c + d*x]^2)/(2*b^3*(a^2 + b^2)^2*d) - (a^2*Tan[c + d*x]^4)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (2*a^2*(a^2 + 2*b^2)*Tan[c + d*x]^3)/(b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",8,7,21,0.3333,1,"{3565, 3645, 3647, 3626, 3617, 31, 3475}"
478,1,239,0,0.5553586,"\int \frac{\tan ^5(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 \left(3 a^2+7 b^2\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^3(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(6 a^2 b^2+3 a^4+b^4\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}-\frac{a^3 \left(9 a^2 b^2+3 a^4+10 b^4\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}-\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2 \left(3 a^2+7 b^2\right) \tan ^2(c+d x)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^3(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(6 a^2 b^2+3 a^4+b^4\right) \tan (c+d x)}{b^3 d \left(a^2+b^2\right)^2}-\frac{a^3 \left(9 a^2 b^2+3 a^4+10 b^4\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^3}-\frac{a \left(a^2-3 b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}",1,"(b*(3*a^2 - b^2)*x)/(a^2 + b^2)^3 - (a*(a^2 - 3*b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) - (a^3*(3*a^4 + 9*a^2*b^2 + 10*b^4)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^3*d) + ((3*a^4 + 6*a^2*b^2 + b^4)*Tan[c + d*x])/(b^3*(a^2 + b^2)^2*d) - (a^2*Tan[c + d*x]^3)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(3*a^2 + 7*b^2)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",7,7,21,0.3333,1,"{3565, 3645, 3647, 3626, 3617, 31, 3475}"
479,1,183,0,0.3141742,"\int \frac{\tan ^4(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 \tan ^2(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^3 \left(a^2+3 b^2\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a^2 \left(3 a^2 b^2+a^4+6 b^4\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2 \tan ^2(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^3 \left(a^2+3 b^2\right)}{b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{a^2 \left(3 a^2 b^2+a^4+6 b^4\right) \log (a+b \tan (c+d x))}{b^3 d \left(a^2+b^2\right)^3}+\frac{b \left(3 a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}",1,"(a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^3 + (b*(3*a^2 - b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^3*d) + (a^2*(a^4 + 3*a^2*b^2 + 6*b^4)*Log[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^3*d) - (a^2*Tan[c + d*x]^2)/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a^3*(a^2 + 3*b^2))/(b^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,6,21,0.2857,1,"{3565, 3635, 3626, 3617, 31, 3475}"
480,1,149,0,0.2273823,"\int \frac{\tan ^3(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 \left(a^2+5 b^2\right)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan (c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2-3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2 \left(a^2+5 b^2\right)}{2 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan (c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2-3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}",1,"-((b*(3*a^2 - b^2)*x)/(a^2 + b^2)^3) + (a*(a^2 - 3*b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - (a^2*Tan[c + d*x])/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(a^2 + 5*b^2))/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,21,0.1905,1,"{3565, 3628, 3531, 3530}"
481,1,129,0,0.2069337,"\int \frac{\tan ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{2 a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{a^2}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{2 a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \left(3 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}",1,"-((a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^3) - (b*(3*a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - a^2/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (2*a*b)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,21,0.1905,1,"{3542, 3529, 3531, 3530}"
482,1,129,0,0.1650849,"\int \frac{\tan (c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x])^3,x]","\frac{a}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2-b^2}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a \left(a^2-3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}","\frac{a}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^2-b^2}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a \left(a^2-3 b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}",1,"(b*(3*a^2 - b^2)*x)/(a^2 + b^2)^3 - (a*(a^2 - 3*b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) + a/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a^2 - b^2)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,3,19,0.1579,1,"{3529, 3531, 3530}"
483,1,122,0,0.1555445,"\int \frac{1}{(a+b \tan (c+d x))^3} \, dx","Int[(a + b*Tan[c + d*x])^(-3),x]","-\frac{2 a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}","-\frac{2 a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2-b^2\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^3}+\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}",1,"(a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^3 + (b*(3*a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^3*d) - b/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (2*a*b)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",4,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
484,1,168,0,0.4100405,"\int \frac{\cot (c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x])^3,x]","\frac{b^2 \left(3 a^2+b^2\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b^2}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{b^2 \left(3 a^2 b^2+6 a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^3}-\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}+\frac{\log (\sin (c+d x))}{a^3 d}","\frac{b^2 \left(3 a^2+b^2\right)}{a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b^2}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{b^2 \left(3 a^2 b^2+6 a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^3 d \left(a^2+b^2\right)^3}-\frac{b x \left(3 a^2-b^2\right)}{\left(a^2+b^2\right)^3}+\frac{\log (\sin (c+d x))}{a^3 d}",1,"-((b*(3*a^2 - b^2)*x)/(a^2 + b^2)^3) + Log[Sin[c + d*x]]/(a^3*d) - (b^2*(6*a^4 + 3*a^2*b^2 + b^4)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^3*(a^2 + b^2)^3*d) + b^2/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b^2*(3*a^2 + b^2))/(a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",5,5,19,0.2632,1,"{3569, 3649, 3651, 3530, 3475}"
485,1,211,0,0.6021355,"\int \frac{\cot ^2(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x])^3,x]","-\frac{b \left(6 a^2 b^2+a^4+3 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+3 b^2\right)}{2 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b^3 \left(9 a^2 b^2+10 a^4+3 b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}-\frac{3 b \log (\sin (c+d x))}{a^4 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^2}","-\frac{b \left(6 a^2 b^2+a^4+3 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+3 b^2\right)}{2 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{b^3 \left(9 a^2 b^2+10 a^4+3 b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^3}-\frac{a x \left(a^2-3 b^2\right)}{\left(a^2+b^2\right)^3}-\frac{3 b \log (\sin (c+d x))}{a^4 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^2}",1,"-((a*(a^2 - 3*b^2)*x)/(a^2 + b^2)^3) - (3*b*Log[Sin[c + d*x]])/(a^4*d) + (b^3*(10*a^4 + 9*a^2*b^2 + 3*b^4)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^3*d) - (b*(2*a^2 + 3*b^2))/(2*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - Cot[c + d*x]/(a*d*(a + b*Tan[c + d*x])^2) - (b*(a^4 + 6*a^2*b^2 + 3*b^4))/(a^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",6,5,21,0.2381,1,"{3569, 3649, 3651, 3530, 3475}"
486,1,315,0,0.8722894,"\int \frac{\tan ^6(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^6/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 \tan ^4(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{a^2 \left(2 a^2+5 b^2\right) \tan ^3(c+d x)}{3 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{2 a^2 \left(3 a^2 b^2+a^4+4 b^4\right) \tan ^2(c+d x)}{b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(12 a^4 b^2+13 a^2 b^4+4 a^6+b^6\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)^3}-\frac{4 a^3 \left(4 a^4 b^2+6 a^2 b^4+a^6+5 b^6\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^4}-\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2 \tan ^4(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{a^2 \left(2 a^2+5 b^2\right) \tan ^3(c+d x)}{3 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{2 a^2 \left(3 a^2 b^2+a^4+4 b^4\right) \tan ^2(c+d x)}{b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(12 a^4 b^2+13 a^2 b^4+4 a^6+b^6\right) \tan (c+d x)}{b^4 d \left(a^2+b^2\right)^3}-\frac{4 a^3 \left(4 a^4 b^2+6 a^2 b^4+a^6+5 b^6\right) \log (a+b \tan (c+d x))}{b^5 d \left(a^2+b^2\right)^4}-\frac{4 a b \left(a^2-b^2\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{x \left(-6 a^2 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}",1,"-(((a^4 - 6*a^2*b^2 + b^4)*x)/(a^2 + b^2)^4) - (4*a*b*(a^2 - b^2)*Log[Cos[c + d*x]])/((a^2 + b^2)^4*d) - (4*a^3*(a^6 + 4*a^4*b^2 + 6*a^2*b^4 + 5*b^6)*Log[a + b*Tan[c + d*x]])/(b^5*(a^2 + b^2)^4*d) + ((4*a^6 + 12*a^4*b^2 + 13*a^2*b^4 + b^6)*Tan[c + d*x])/(b^4*(a^2 + b^2)^3*d) - (a^2*Tan[c + d*x]^4)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (a^2*(2*a^2 + 5*b^2)*Tan[c + d*x]^3)/(3*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (2*a^2*(a^4 + 3*a^2*b^2 + 4*b^4)*Tan[c + d*x]^2)/(b^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",8,7,21,0.3333,1,"{3565, 3645, 3647, 3626, 3617, 31, 3475}"
487,1,256,0,0.5714737,"\int \frac{\tan ^5(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 \left(a^2+3 b^2\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 \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 \left(3 a^2 b^2+a^4+6 b^4\right)}{b^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a^2 \left(4 a^4 b^2+5 a^2 b^4+a^6+10 b^6\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^4}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2 \left(a^2+3 b^2\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 \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 \left(3 a^2 b^2+a^4+6 b^4\right)}{b^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a^2 \left(4 a^4 b^2+5 a^2 b^4+a^6+10 b^6\right) \log (a+b \tan (c+d x))}{b^4 d \left(a^2+b^2\right)^4}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (\cos (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}",1,"(4*a*b*(a^2 - b^2)*x)/(a^2 + b^2)^4 - ((a^4 - 6*a^2*b^2 + b^4)*Log[Cos[c + d*x]])/((a^2 + b^2)^4*d) + (a^2*(a^6 + 4*a^4*b^2 + 5*a^2*b^4 + 10*b^6)*Log[a + b*Tan[c + d*x]])/(b^4*(a^2 + b^2)^4*d) - (a^2*Tan[c + d*x]^3)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (a^2*(a^2 + 3*b^2)*Tan[c + d*x]^2)/(2*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (a^3*(a^4 + 3*a^2*b^2 + 6*b^4))/(b^4*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",7,7,21,0.3333,1,"{3565, 3645, 3635, 3626, 3617, 31, 3475}"
488,1,208,0,0.4091059,"\int \frac{\tan ^4(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 \left(a^2+4 b^2\right)}{3 b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a^2 \left(7 a^2 b^2+2 a^4+17 b^4\right)}{3 b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2 \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^3 \left(a^2+4 b^2\right)}{3 b^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a^2 \left(7 a^2 b^2+2 a^4+17 b^4\right)}{3 b^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}",1,"((a^4 - 6*a^2*b^2 + b^4)*x)/(a^2 + b^2)^4 + (4*a*b*(a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - (a^2*Tan[c + d*x]^2)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a^3*(a^2 + 4*b^2))/(3*b^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (a^2*(2*a^4 + 7*a^2*b^2 + 17*b^4))/(3*b^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,5,21,0.2381,1,"{3565, 3635, 3628, 3531, 3530}"
489,1,189,0,0.3247081,"\int \frac{\tan ^3(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2 \left(a^2+7 b^2\right)}{6 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a^2 \tan (c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{a \left(a^2-3 b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2 \left(a^2+7 b^2\right)}{6 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{a^2 \tan (c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{a \left(a^2-3 b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}-\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}",1,"(-4*a*b*(a^2 - b^2)*x)/(a^2 + b^2)^4 + ((a^4 - 6*a^2*b^2 + b^4)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - (a^2*Tan[c + d*x])/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (a^2*(a^2 + 7*b^2))/(6*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (a*(a^2 - 3*b^2))/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,5,21,0.2381,1,"{3565, 3628, 3529, 3531, 3530}"
490,1,169,0,0.2766317,"\int \frac{\tan ^2(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x])^4,x]","-\frac{a^2}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{a^2}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}",1,"-(((a^4 - 6*a^2*b^2 + b^4)*x)/(a^2 + b^2)^4) - (4*a*b*(a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - a^2/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a*b)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (b*(3*a^2 - b^2))/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,4,21,0.1905,1,"{3542, 3529, 3531, 3530}"
491,1,172,0,0.2317233,"\int \frac{\tan (c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x])^4,x]","\frac{a \left(a^2-3 b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^2-b^2}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}","\frac{a \left(a^2-3 b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{a}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{a^2-b^2}{2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{\left(-6 a^2 b^2+a^4+b^4\right) \log (a \cos (c+d x)+b \sin (c+d x))}{d \left(a^2+b^2\right)^4}+\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}",1,"(4*a*b*(a^2 - b^2)*x)/(a^2 + b^2)^4 - ((a^4 - 6*a^2*b^2 + b^4)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) + a/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (a^2 - b^2)/(2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (a*(a^2 - 3*b^2))/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,3,19,0.1579,1,"{3529, 3531, 3530}"
492,1,165,0,0.2286281,"\int \frac{1}{(a+b \tan (c+d x))^4} \, dx","Int[(a + b*Tan[c + d*x])^(-4),x]","-\frac{b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}","-\frac{b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{a b}{d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{4 a b \left(a^2-b^2\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}",1,"((a^4 - 6*a^2*b^2 + b^4)*x)/(a^2 + b^2)^4 + (4*a*b*(a^2 - b^2)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/((a^2 + b^2)^4*d) - b/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - (a*b)/((a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (b*(3*a^2 - b^2))/((a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",5,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
493,1,226,0,0.6507482,"\int \frac{\cot (c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x])^4,x]","\frac{b^2 \left(3 a^2 b^2+6 a^4+b^4\right)}{a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b^2 \left(3 a^2+b^2\right)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b^2}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{b^2 \left(5 a^4 b^2+4 a^2 b^4+10 a^6+b^6\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^4}-\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}+\frac{\log (\sin (c+d x))}{a^4 d}","\frac{b^2 \left(3 a^2 b^2+6 a^4+b^4\right)}{a^3 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}+\frac{b^2 \left(3 a^2+b^2\right)}{2 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}+\frac{b^2}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}-\frac{b^2 \left(5 a^4 b^2+4 a^2 b^4+10 a^6+b^6\right) \log (a \cos (c+d x)+b \sin (c+d x))}{a^4 d \left(a^2+b^2\right)^4}-\frac{4 a b x \left(a^2-b^2\right)}{\left(a^2+b^2\right)^4}+\frac{\log (\sin (c+d x))}{a^4 d}",1,"(-4*a*b*(a^2 - b^2)*x)/(a^2 + b^2)^4 + Log[Sin[c + d*x]]/(a^4*d) - (b^2*(10*a^6 + 5*a^4*b^2 + 4*a^2*b^4 + b^6)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^4*(a^2 + b^2)^4*d) + b^2/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) + (b^2*(3*a^2 + b^2))/(2*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) + (b^2*(6*a^4 + 3*a^2*b^2 + b^4))/(a^3*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",6,5,19,0.2632,1,"{3569, 3649, 3651, 3530, 3475}"
494,1,278,0,0.8531263,"\int \frac{\cot ^2(c+d x)}{(a+b \tan (c+d x))^4} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x])^4,x]","-\frac{b \left(13 a^4 b^2+12 a^2 b^4+a^6+4 b^6\right)}{a^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{b \left(4 a^2 b^2+a^4+2 b^4\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(3 a^2+4 b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{4 b^3 \left(6 a^4 b^2+4 a^2 b^4+5 a^6+b^6\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}-\frac{4 b \log (\sin (c+d x))}{a^5 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^3}","-\frac{b \left(13 a^4 b^2+12 a^2 b^4+a^6+4 b^6\right)}{a^4 d \left(a^2+b^2\right)^3 (a+b \tan (c+d x))}-\frac{b \left(4 a^2 b^2+a^4+2 b^4\right)}{a^3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^2}-\frac{b \left(3 a^2+4 b^2\right)}{3 a^2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^3}+\frac{4 b^3 \left(6 a^4 b^2+4 a^2 b^4+5 a^6+b^6\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 b^2+a^4+b^4\right)}{\left(a^2+b^2\right)^4}-\frac{4 b \log (\sin (c+d x))}{a^5 d}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^3}",1,"-(((a^4 - 6*a^2*b^2 + b^4)*x)/(a^2 + b^2)^4) - (4*b*Log[Sin[c + d*x]])/(a^5*d) + (4*b^3*(5*a^6 + 6*a^4*b^2 + 4*a^2*b^4 + b^6)*Log[a*Cos[c + d*x] + b*Sin[c + d*x]])/(a^5*(a^2 + b^2)^4*d) - (b*(3*a^2 + 4*b^2))/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^3) - Cot[c + d*x]/(a*d*(a + b*Tan[c + d*x])^3) - (b*(a^4 + 4*a^2*b^2 + 2*b^4))/(a^3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^2) - (b*(a^6 + 13*a^4*b^2 + 12*a^2*b^4 + 4*b^6))/(a^4*(a^2 + b^2)^3*d*(a + b*Tan[c + d*x]))","A",7,5,21,0.2381,1,"{3569, 3649, 3651, 3530, 3475}"
495,1,31,0,0.0402898,"\int \frac{1}{3+5 \tan (c+d x)} \, dx","Int[(3 + 5*Tan[c + d*x])^(-1),x]","\frac{5 \log (5 \sin (c+d x)+3 \cos (c+d x))}{34 d}+\frac{3 x}{34}","\frac{5 \log (5 \sin (c+d x)+3 \cos (c+d x))}{34 d}+\frac{3 x}{34}",1,"(3*x)/34 + (5*Log[3*Cos[c + d*x] + 5*Sin[c + d*x]])/(34*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
496,1,50,0,0.064283,"\int \frac{1}{(3+5 \tan (c+d x))^2} \, dx","Int[(3 + 5*Tan[c + d*x])^(-2),x]","-\frac{5}{34 d (5 \tan (c+d x)+3)}+\frac{15 \log (5 \sin (c+d x)+3 \cos (c+d x))}{578 d}-\frac{4 x}{289}","-\frac{5}{34 d (5 \tan (c+d x)+3)}+\frac{15 \log (5 \sin (c+d x)+3 \cos (c+d x))}{578 d}-\frac{4 x}{289}",1,"(-4*x)/289 + (15*Log[3*Cos[c + d*x] + 5*Sin[c + d*x]])/(578*d) - 5/(34*d*(3 + 5*Tan[c + d*x]))","A",3,3,12,0.2500,1,"{3483, 3531, 3530}"
497,1,69,0,0.0915674,"\int \frac{1}{(3+5 \tan (c+d x))^3} \, dx","Int[(3 + 5*Tan[c + d*x])^(-3),x]","-\frac{15}{578 d (5 \tan (c+d x)+3)}-\frac{5}{68 d (5 \tan (c+d x)+3)^2}+\frac{5 \log (5 \sin (c+d x)+3 \cos (c+d x))}{19652 d}-\frac{99 x}{19652}","-\frac{15}{578 d (5 \tan (c+d x)+3)}-\frac{5}{68 d (5 \tan (c+d x)+3)^2}+\frac{5 \log (5 \sin (c+d x)+3 \cos (c+d x))}{19652 d}-\frac{99 x}{19652}",1,"(-99*x)/19652 + (5*Log[3*Cos[c + d*x] + 5*Sin[c + d*x]])/(19652*d) - 5/(68*d*(3 + 5*Tan[c + d*x])^2) - 15/(578*d*(3 + 5*Tan[c + d*x]))","A",4,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
498,1,88,0,0.1200469,"\int \frac{1}{(3+5 \tan (c+d x))^4} \, dx","Int[(3 + 5*Tan[c + d*x])^(-4),x]","-\frac{5}{19652 d (5 \tan (c+d x)+3)}-\frac{15}{1156 d (5 \tan (c+d x)+3)^2}-\frac{5}{102 d (5 \tan (c+d x)+3)^3}-\frac{60 \log (5 \sin (c+d x)+3 \cos (c+d x))}{83521 d}-\frac{161 x}{334084}","-\frac{5}{19652 d (5 \tan (c+d x)+3)}-\frac{15}{1156 d (5 \tan (c+d x)+3)^2}-\frac{5}{102 d (5 \tan (c+d x)+3)^3}-\frac{60 \log (5 \sin (c+d x)+3 \cos (c+d x))}{83521 d}-\frac{161 x}{334084}",1,"(-161*x)/334084 - (60*Log[3*Cos[c + d*x] + 5*Sin[c + d*x]])/(83521*d) - 5/(102*d*(3 + 5*Tan[c + d*x])^3) - 15/(1156*d*(3 + 5*Tan[c + d*x])^2) - 5/(19652*d*(3 + 5*Tan[c + d*x]))","A",5,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
499,1,31,0,0.0374995,"\int \frac{1}{5+3 \tan (c+d x)} \, dx","Int[(5 + 3*Tan[c + d*x])^(-1),x]","\frac{3 \log (3 \sin (c+d x)+5 \cos (c+d x))}{34 d}+\frac{5 x}{34}","\frac{3 \log (3 \sin (c+d x)+5 \cos (c+d x))}{34 d}+\frac{5 x}{34}",1,"(5*x)/34 + (3*Log[5*Cos[c + d*x] + 3*Sin[c + d*x]])/(34*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
500,1,50,0,0.0637289,"\int \frac{1}{(5+3 \tan (c+d x))^2} \, dx","Int[(5 + 3*Tan[c + d*x])^(-2),x]","-\frac{3}{34 d (3 \tan (c+d x)+5)}+\frac{15 \log (3 \sin (c+d x)+5 \cos (c+d x))}{578 d}+\frac{4 x}{289}","-\frac{3}{34 d (3 \tan (c+d x)+5)}+\frac{15 \log (3 \sin (c+d x)+5 \cos (c+d x))}{578 d}+\frac{4 x}{289}",1,"(4*x)/289 + (15*Log[5*Cos[c + d*x] + 3*Sin[c + d*x]])/(578*d) - 3/(34*d*(5 + 3*Tan[c + d*x]))","A",3,3,12,0.2500,1,"{3483, 3531, 3530}"
501,1,69,0,0.0906826,"\int \frac{1}{(5+3 \tan (c+d x))^3} \, dx","Int[(5 + 3*Tan[c + d*x])^(-3),x]","-\frac{15}{578 d (3 \tan (c+d x)+5)}-\frac{3}{68 d (3 \tan (c+d x)+5)^2}+\frac{99 \log (3 \sin (c+d x)+5 \cos (c+d x))}{19652 d}-\frac{5 x}{19652}","-\frac{15}{578 d (3 \tan (c+d x)+5)}-\frac{3}{68 d (3 \tan (c+d x)+5)^2}+\frac{99 \log (3 \sin (c+d x)+5 \cos (c+d x))}{19652 d}-\frac{5 x}{19652}",1,"(-5*x)/19652 + (99*Log[5*Cos[c + d*x] + 3*Sin[c + d*x]])/(19652*d) - 3/(68*d*(5 + 3*Tan[c + d*x])^2) - 15/(578*d*(5 + 3*Tan[c + d*x]))","A",4,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
502,1,88,0,0.1178563,"\int \frac{1}{(5+3 \tan (c+d x))^4} \, dx","Int[(5 + 3*Tan[c + d*x])^(-4),x]","-\frac{99}{19652 d (3 \tan (c+d x)+5)}-\frac{15}{1156 d (3 \tan (c+d x)+5)^2}-\frac{1}{34 d (3 \tan (c+d x)+5)^3}+\frac{60 \log (3 \sin (c+d x)+5 \cos (c+d x))}{83521 d}-\frac{161 x}{334084}","-\frac{99}{19652 d (3 \tan (c+d x)+5)}-\frac{15}{1156 d (3 \tan (c+d x)+5)^2}-\frac{1}{34 d (3 \tan (c+d x)+5)^3}+\frac{60 \log (3 \sin (c+d x)+5 \cos (c+d x))}{83521 d}-\frac{161 x}{334084}",1,"(-161*x)/334084 + (60*Log[5*Cos[c + d*x] + 3*Sin[c + d*x]])/(83521*d) - 1/(34*d*(5 + 3*Tan[c + d*x])^3) - 15/(1156*d*(5 + 3*Tan[c + d*x])^2) - 99/(19652*d*(5 + 3*Tan[c + d*x]))","A",5,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
503,1,456,0,0.7036115,"\int \tan ^4(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^4*Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \left(8 a^2-35 b^2\right) (a+b \tan (c+d x))^{3/2}}{105 b^3 d}+\frac{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 \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 \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 \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{8 a \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{35 b^2 d}+\frac{2 \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{7 b d}","\frac{2 \left(8 a^2-35 b^2\right) (a+b \tan (c+d x))^{3/2}}{105 b^3 d}+\frac{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 \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 \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 \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{8 a \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{35 b^2 d}+\frac{2 \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2}}{7 b d}",1,"(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*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*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*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*(8*a^2 - 35*b^2)*(a + b*Tan[c + d*x])^(3/2))/(105*b^3*d) - (8*a*Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2))/(35*b^2*d) + (2*Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2))/(7*b*d)","A",14,10,23,0.4348,1,"{3566, 3647, 3631, 3485, 700, 1129, 634, 618, 206, 628}"
504,1,159,0,0.3338013,"\int \tan ^3(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{4 a (a+b \tan (c+d x))^{3/2}}{15 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{5 b d}-\frac{2 \sqrt{a+b \tan (c+d x)}}{d}+\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{4 a (a+b \tan (c+d x))^{3/2}}{15 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{3/2}}{5 b d}-\frac{2 \sqrt{a+b \tan (c+d x)}}{d}+\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(Sqrt[a - I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (Sqrt[a + I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*Sqrt[a + b*Tan[c + d*x]])/d - (4*a*(a + b*Tan[c + d*x])^(3/2))/(15*b^2*d) + (2*Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2))/(5*b*d)","A",11,8,23,0.3478,1,"{3566, 3630, 12, 3528, 3539, 3537, 63, 208}"
505,1,382,0,0.3063365,"\int \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{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 \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 \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 \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 (a+b \tan (c+d x))^{3/2}}{3 b d}","-\frac{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 \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 \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 \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 (a+b \tan (c+d x))^{3/2}}{3 b d}",1,"-((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*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*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*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*(a + b*Tan[c + d*x])^(3/2))/(3*b*d)","A",12,8,23,0.3478,1,"{3543, 3485, 700, 1129, 634, 618, 206, 628}"
506,1,106,0,0.1692998,"\int \tan (c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \sqrt{a+b \tan (c+d x)}}{d}-\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 \sqrt{a+b \tan (c+d x)}}{d}-\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"-((Sqrt[a - I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - (Sqrt[a + I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*Sqrt[a + b*Tan[c + d*x]])/d","A",8,5,21,0.2381,1,"{3528, 3539, 3537, 63, 208}"
507,1,358,0,0.2571431,"\int \sqrt{a+b \tan (c+d x)} \, dx","Int[Sqrt[a + b*Tan[c + d*x]],x]","\frac{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 \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 \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 \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 \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 \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 \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 \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*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*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*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*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",11,7,14,0.5000,1,"{3485, 700, 1129, 634, 618, 206, 628}"
508,1,116,0,0.2959858,"\int \cot (c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{\sqrt{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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + (Sqrt[a - I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (Sqrt[a + I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d","A",11,6,21,0.2857,1,"{3572, 3539, 3537, 63, 208, 3634}"
509,1,415,0,0.5234455,"\int \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{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 \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 \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 \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 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}-\frac{\cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}","-\frac{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 \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 \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 \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 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}-\frac{\cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}",1,"-((b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d)) - (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*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*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*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) - (Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/d","A",16,12,23,0.5217,1,"{3568, 3653, 3485, 700, 1129, 634, 618, 206, 628, 3634, 63, 208}"
510,1,189,0,0.6186793,"\int \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]],x]","\frac{\left(8 a^2+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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{\cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a d}","\frac{\left(8 a^2+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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{\sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{\cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a d}",1,"((8*a^2 + b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(3/2)*d) - (Sqrt[a - I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (Sqrt[a + I*b]*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (b*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*a*d) - (Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",13,8,23,0.3478,1,"{3568, 3649, 3653, 3539, 3537, 63, 208, 3634}"
511,1,209,0,0.4527537,"\int \tan ^4(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^4*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 \left(8 a^2-63 b^2\right) (a+b \tan (c+d x))^{5/2}}{315 b^3 d}-\frac{8 a \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{63 b^2 d}+\frac{2 \tan ^2(c+d x) (a+b \tan (c+d x))^{5/2}}{9 b d}+\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 \left(8 a^2-63 b^2\right) (a+b \tan (c+d x))^{5/2}}{315 b^3 d}-\frac{8 a \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{63 b^2 d}+\frac{2 \tan ^2(c+d x) (a+b \tan (c+d x))^{5/2}}{9 b d}+\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((-I)*(a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (I*(a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b*Sqrt[a + b*Tan[c + d*x]])/d + (2*(8*a^2 - 63*b^2)*(a + b*Tan[c + d*x])^(5/2))/(315*b^3*d) - (8*a*Tan[c + d*x]*(a + b*Tan[c + d*x])^(5/2))/(63*b^2*d) + (2*Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(5/2))/(9*b*d)","A",11,8,23,0.3478,1,"{3566, 3647, 3631, 3482, 3539, 3537, 63, 208}"
512,1,181,0,0.3700824,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^(3/2),x]","-\frac{4 a (a+b \tan (c+d x))^{5/2}}{35 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{7 b d}-\frac{2 (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{4 a (a+b \tan (c+d x))^{5/2}}{35 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{5/2}}{7 b d}-\frac{2 (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{d}+\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*a*Sqrt[a + b*Tan[c + d*x]])/d - (2*(a + b*Tan[c + d*x])^(3/2))/(3*d) - (4*a*(a + b*Tan[c + d*x])^(5/2))/(35*b^2*d) + (2*Tan[c + d*x]*(a + b*Tan[c + d*x])^(5/2))/(7*b*d)","A",12,8,23,0.3478,1,"{3566, 3630, 12, 3528, 3539, 3537, 63, 208}"
513,1,135,0,0.244483,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 (a+b \tan (c+d x))^{5/2}}{5 b d}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 (a+b \tan (c+d x))^{5/2}}{5 b d}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(I*(a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (I*(a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*b*Sqrt[a + b*Tan[c + d*x]])/d + (2*(a + b*Tan[c + d*x])^(5/2))/(5*b*d)","A",9,6,23,0.2609,1,"{3543, 3482, 3539, 3537, 63, 208}"
514,1,128,0,0.2286089,"\int \tan (c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 a \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{2 a \sqrt{a+b \tan (c+d x)}}{d}-\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"-(((a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - ((a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*a*Sqrt[a + b*Tan[c + d*x]])/d + (2*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",9,5,21,0.2381,1,"{3528, 3539, 3537, 63, 208}"
515,1,111,0,0.1740974,"\int (a+b \tan (c+d x))^{3/2} \, dx","Int[(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{3/2} \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{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((-I)*(a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (I*(a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b*Sqrt[a + b*Tan[c + d*x]])/d","A",8,5,14,0.3571,1,"{3482, 3539, 3537, 63, 208}"
516,1,116,0,0.3134385,"\int \cot (c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{(a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(-2*a^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + ((a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d","A",11,6,21,0.2857,1,"{3573, 3539, 3537, 63, 208, 3634}"
517,1,149,0,0.4390236,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(3/2),x]","\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{i (a+i b)^{3/2} \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{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{i (a+i b)^{3/2} \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,"(-3*Sqrt[a]*b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + (I*(a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (I*(a + I*b)^(3/2)*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",12,7,23,0.3043,1,"{3567, 3653, 3539, 3537, 63, 208, 3634}"
518,1,189,0,0.6915517,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(3/2),x]","\frac{\left(8 a^2-3 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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{5 b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}","\frac{\left(8 a^2-3 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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{(a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{a \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{5 b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}",1,"((8*a^2 - 3*b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*Sqrt[a]*d) - ((a - I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(3/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (5*b*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",13,8,23,0.3478,1,"{3567, 3649, 3653, 3539, 3537, 63, 208, 3634}"
519,1,211,0,0.4711412,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 \left(a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{d}-\frac{4 a (a+b \tan (c+d x))^{7/2}}{63 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{7/2}}{9 b d}-\frac{2 (a+b \tan (c+d x))^{5/2}}{5 d}-\frac{2 a (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{2 \left(a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{d}-\frac{4 a (a+b \tan (c+d x))^{7/2}}{63 b^2 d}+\frac{2 \tan (c+d x) (a+b \tan (c+d x))^{7/2}}{9 b d}-\frac{2 (a+b \tan (c+d x))^{5/2}}{5 d}-\frac{2 a (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (2*(a^2 - b^2)*Sqrt[a + b*Tan[c + d*x]])/d - (2*a*(a + b*Tan[c + d*x])^(3/2))/(3*d) - (2*(a + b*Tan[c + d*x])^(5/2))/(5*d) - (4*a*(a + b*Tan[c + d*x])^(7/2))/(63*b^2*d) + (2*Tan[c + d*x]*(a + b*Tan[c + d*x])^(7/2))/(9*b*d)","A",13,8,23,0.3478,1,"{3566, 3630, 12, 3528, 3539, 3537, 63, 208}"
520,1,158,0,0.3047897,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 (a+b \tan (c+d x))^{7/2}}{7 b d}-\frac{2 b (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{4 a b \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 (a+b \tan (c+d x))^{7/2}}{7 b d}-\frac{2 b (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{4 a b \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(I*(a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (I*(a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (4*a*b*Sqrt[a + b*Tan[c + d*x]])/d - (2*b*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*(a + b*Tan[c + d*x])^(7/2))/(7*b*d)","A",10,7,23,0.3043,1,"{3543, 3482, 3528, 3539, 3537, 63, 208}"
521,1,158,0,0.2862469,"\int \tan (c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 \left(a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{2 a (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 \left(a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 (a+b \tan (c+d x))^{5/2}}{5 d}+\frac{2 a (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"-(((a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d) - ((a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*(a^2 - b^2)*Sqrt[a + b*Tan[c + d*x]])/d + (2*a*(a + b*Tan[c + d*x])^(3/2))/(3*d) + (2*(a + b*Tan[c + d*x])^(5/2))/(5*d)","A",10,5,21,0.2381,1,"{3528, 3539, 3537, 63, 208}"
522,1,134,0,0.2405795,"\int (a+b \tan (c+d x))^{5/2} \, dx","Int[(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b (a+b \tan (c+d x))^{3/2}}{3 d}+\frac{4 a b \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{5/2} \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{4 a b \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((-I)*(a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (I*(a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (4*a*b*Sqrt[a + b*Tan[c + d*x]])/d + (2*b*(a + b*Tan[c + d*x])^(3/2))/(3*d)","A",9,6,14,0.4286,1,"{3482, 3528, 3539, 3537, 63, 208}"
523,1,138,0,0.4945063,"\int \cot (c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 b^2 \sqrt{a+b \tan (c+d x)}}{d}+\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}+\frac{2 b^2 \sqrt{a+b \tan (c+d x)}}{d}+\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(-2*a^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + ((a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + ((a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b^2*Sqrt[a + b*Tan[c + d*x]])/d","A",12,7,21,0.3333,1,"{3566, 3653, 3539, 3537, 63, 208, 3634}"
524,1,151,0,0.5077856,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(5/2),x]","-\frac{5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","-\frac{5 a^{3/2} b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{d}-\frac{a^2 \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{d}+\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}-\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"(-5*a^(3/2)*b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/d + (I*(a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - (I*(a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (a^2*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/d","A",12,7,23,0.3043,1,"{3565, 3653, 3539, 3537, 63, 208, 3634}"
525,1,192,0,0.7713752,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^(5/2),x]","\frac{\sqrt{a} \left(8 a^2-15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{a^2 \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{9 a b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}","\frac{\sqrt{a} \left(8 a^2-15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 d}-\frac{a^2 \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{(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} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{9 a b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 d}",1,"(Sqrt[a]*(8*a^2 - 15*b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*d) - ((a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d - ((a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d - (9*a*b*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*d) - (a^2*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",13,8,23,0.3478,1,"{3565, 3649, 3653, 3539, 3537, 63, 208, 3634}"
526,1,237,0,1.0665035,"\int \cot ^4(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^4*(a + b*Tan[c + d*x])^(5/2),x]","\frac{5 b \left(8 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 \sqrt{a} d}+\frac{\left(8 a^2-11 b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 d}-\frac{a^2 \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{13 a b \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}","\frac{5 b \left(8 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{8 \sqrt{a} d}+\frac{\left(8 a^2-11 b^2\right) \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{8 d}-\frac{a^2 \cot ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}-\frac{13 a b \cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}",1,"(5*b*(8*a^2 - b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(8*Sqrt[a]*d) - (I*(a - I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (I*(a + I*b)^(5/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + ((8*a^2 - 11*b^2)*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(8*d) - (13*a*b*Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(12*d) - (a^2*Cot[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",14,8,23,0.3478,1,"{3565, 3649, 3653, 3539, 3537, 63, 208, 3634}"
527,1,167,0,0.3500486,"\int (a+b \tan (c+d x))^{7/2} \, dx","Int[(a + b*Tan[c + d*x])^(7/2),x]","\frac{2 b \left(3 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{4 a b (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}","\frac{2 b \left(3 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{4 a b (a+b \tan (c+d x))^{3/2}}{3 d}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d}",1,"((-I)*(a - I*b)^(7/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/d + (I*(a + I*b)^(7/2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/d + (2*b*(3*a^2 - b^2)*Sqrt[a + b*Tan[c + d*x]])/d + (4*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",10,6,14,0.4286,1,"{3482, 3528, 3539, 3537, 63, 208}"
528,1,229,0,0.556136,"\int \frac{\tan ^5(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^5/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \left(24 a^2-35 b^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{105 b^3 d}-\frac{4 a \left(24 a^2-35 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 b^4 d}-\frac{12 a \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{35 b^2 d}+\frac{2 \tan ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{7 b d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","\frac{2 \left(24 a^2-35 b^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{105 b^3 d}-\frac{4 a \left(24 a^2-35 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 b^4 d}-\frac{12 a \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{35 b^2 d}+\frac{2 \tan ^3(c+d x) \sqrt{a+b \tan (c+d x)}}{7 b d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/(Sqrt[a - I*b]*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/(Sqrt[a + I*b]*d) - (4*a*(24*a^2 - 35*b^2)*Sqrt[a + b*Tan[c + d*x]])/(105*b^4*d) + (2*(24*a^2 - 35*b^2)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(105*b^3*d) - (12*a*Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(35*b^2*d) + (2*Tan[c + d*x]^3*Sqrt[a + b*Tan[c + d*x]])/(7*b*d)","A",12,9,23,0.3913,1,"{3566, 3647, 3648, 3630, 12, 3539, 3537, 63, 208}"
529,1,500,0,0.6625641,"\int \frac{\tan ^4(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^4/Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \left(8 a^2-15 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 b^3 d}-\frac{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 \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 \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 \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{8 a \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{15 b^2 d}+\frac{2 \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b d}","\frac{2 \left(8 a^2-15 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 b^3 d}-\frac{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 \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 \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 \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{8 a \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{15 b^2 d}+\frac{2 \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b d}",1,"(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*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*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*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) + (2*(8*a^2 - 15*b^2)*Sqrt[a + b*Tan[c + d*x]])/(15*b^3*d) - (8*a*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(15*b^2*d) + (2*Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(5*b*d)","A",14,10,23,0.4348,1,"{3566, 3647, 3631, 3485, 708, 1094, 634, 618, 206, 628}"
530,1,140,0,0.2517323,"\int \frac{\tan ^3(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^3/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{4 a \sqrt{a+b \tan (c+d x)}}{3 b^2 d}+\frac{2 \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","-\frac{4 a \sqrt{a+b \tan (c+d x)}}{3 b^2 d}+\frac{2 \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/(Sqrt[a - I*b]*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/(Sqrt[a + I*b]*d) - (4*a*Sqrt[a + b*Tan[c + d*x]])/(3*b^2*d) + (2*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b*d)","A",10,7,23,0.3043,1,"{3566, 3630, 12, 3539, 3537, 63, 208}"
531,1,424,0,0.3345315,"\int \frac{\tan ^2(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^2/Sqrt[a + b*Tan[c + d*x]],x]","\frac{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 \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 \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 \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{2 \sqrt{a+b \tan (c+d x)}}{b d}","\frac{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 \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 \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 \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{2 \sqrt{a+b \tan (c+d x)}}{b d}",1,"-((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*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*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*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) + (2*Sqrt[a + b*Tan[c + d*x]])/(b*d)","A",12,8,23,0.3478,1,"{3543, 3485, 708, 1094, 634, 618, 206, 628}"
532,1,87,0,0.1370441,"\int \frac{\tan (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/(Sqrt[a - I*b]*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/(Sqrt[a + I*b]*d)","A",7,4,21,0.1905,1,"{3539, 3537, 63, 208}"
533,1,402,0,0.2781964,"\int \frac{1}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[1/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{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 \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 \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 \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 \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 \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 \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 \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*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*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*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*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",11,7,14,0.5000,1,"{3485, 708, 1094, 634, 618, 206, 628}"
534,1,116,0,0.2643381,"\int \frac{\cot (c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Cot[c + d*x]/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}",1,"(-2*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/(Sqrt[a - I*b]*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/(Sqrt[a + I*b]*d)","A",11,6,21,0.2857,1,"{3574, 3539, 3537, 63, 208, 3634}"
535,1,461,0,0.6131813,"\int \frac{\cot ^2(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^2/Sqrt[a + b*Tan[c + d*x]],x]","\frac{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 \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 \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 \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 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{\cot (c+d x) \sqrt{a+b \tan (c+d x)}}{a d}","\frac{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 \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 \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 \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 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{\cot (c+d x) \sqrt{a+b \tan (c+d x)}}{a d}",1,"(b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) - (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*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*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*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) - (Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(a*d)","A",17,13,23,0.5652,1,"{3569, 3653, 12, 3485, 708, 1094, 634, 618, 206, 628, 3634, 63, 208}"
536,1,194,0,0.5771798,"\int \frac{\cot ^3(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^3/Sqrt[a + b*Tan[c + d*x]],x]","\frac{\left(8 a^2-3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}+\frac{3 b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a^2 d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{\cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 a d}","\frac{\left(8 a^2-3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{5/2} d}+\frac{3 b \cot (c+d x) \sqrt{a+b \tan (c+d x)}}{4 a^2 d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d \sqrt{a-i b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d \sqrt{a+i b}}-\frac{\cot ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{2 a d}",1,"((8*a^2 - 3*b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(5/2)*d) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/(Sqrt[a - I*b]*d) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/(Sqrt[a + I*b]*d) + (3*b*Cot[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(4*a^2*d) - (Cot[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(2*a*d)","A",14,9,23,0.3913,1,"{3569, 3649, 3654, 12, 3539, 3537, 63, 208, 3634}"
537,1,282,0,0.6949925,"\int \frac{\tan ^5(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \tan ^3(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \left(6 a^2+b^2\right) \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b^2 d \left(a^2+b^2\right)}-\frac{2 a \left(8 a^2+3 b^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{5 b^3 d \left(a^2+b^2\right)}+\frac{2 \left(6 a^2 b^2+16 a^4-5 b^4\right) \sqrt{a+b \tan (c+d x)}}{5 b^4 d \left(a^2+b^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\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^2 \tan ^3(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \left(6 a^2+b^2\right) \tan ^2(c+d x) \sqrt{a+b \tan (c+d x)}}{5 b^2 d \left(a^2+b^2\right)}-\frac{2 a \left(8 a^2+3 b^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{5 b^3 d \left(a^2+b^2\right)}+\frac{2 \left(6 a^2 b^2+16 a^4-5 b^4\right) \sqrt{a+b \tan (c+d x)}}{5 b^4 d \left(a^2+b^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(3/2)*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(3/2)*d) - (2*a^2*Tan[c + d*x]^3)/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + (2*(16*a^4 + 6*a^2*b^2 - 5*b^4)*Sqrt[a + b*Tan[c + d*x]])/(5*b^4*(a^2 + b^2)*d) - (2*a*(8*a^2 + 3*b^2)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(5*b^3*(a^2 + b^2)*d) + (2*(6*a^2 + b^2)*Tan[c + d*x]^2*Sqrt[a + b*Tan[c + d*x]])/(5*b^2*(a^2 + b^2)*d)","A",11,7,23,0.3043,1,"{3565, 3647, 3630, 3539, 3537, 63, 208}"
538,1,226,0,0.4509515,"\int \frac{\tan ^4(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \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^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^2 d \left(a^2+b^2\right)}-\frac{2 a \left(8 a^2+5 b^2\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i \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^2 \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^2\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^2 d \left(a^2+b^2\right)}-\frac{2 a \left(8 a^2+5 b^2\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"((-I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*a^2*Tan[c + d*x]^2)/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) - (2*a*(8*a^2 + 5*b^2)*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)*d) + (2*(4*a^2 + b^2)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b^2*(a^2 + b^2)*d)","A",10,7,23,0.3043,1,"{3565, 3647, 3630, 3539, 3537, 63, 208}"
539,1,165,0,0.3111153,"\int \frac{\tan ^3(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \tan (c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \left(2 a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{\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^2 \tan (c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \left(2 a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(3/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(3/2)*d) - (2*a^2*Tan[c + d*x])/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + (2*(2*a^2 + b^2)*Sqrt[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d)","A",9,6,23,0.2609,1,"{3565, 3630, 3539, 3537, 63, 208}"
540,1,125,0,0.2276341,"\int \frac{\tan ^2(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{i \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^2}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"(I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*a^2)/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,23,0.2174,1,"{3542, 3539, 3537, 63, 208}"
541,1,116,0,0.194266,"\int \frac{\tan (c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 a}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\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}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(3/2)*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(3/2)*d) + (2*a)/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,21,0.2381,1,"{3529, 3539, 3537, 63, 208}"
542,1,120,0,0.1691744,"\int \frac{1}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[(a + b*Tan[c + d*x])^(-3/2),x]","-\frac{2 b}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i \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}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"((-I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (2*b)/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,5,14,0.3571,1,"{3483, 3539, 3537, 63, 208}"
543,1,150,0,0.4661248,"\int \frac{\cot (c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b^2}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{\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}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}",1,"(-2*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(3/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(3/2)*d) + (2*b^2)/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",12,7,21,0.3333,1,"{3569, 3653, 3539, 3537, 63, 208, 3634}"
544,1,192,0,0.6346088,"\int \frac{\cot ^2(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{b \left(a^2+3 b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{\cot (c+d x)}{a d \sqrt{a+b \tan (c+d x)}}","-\frac{b \left(a^2+3 b^2\right)}{a^2 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{\cot (c+d x)}{a d \sqrt{a+b \tan (c+d x)}}",1,"(3*b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(3/2)*d) - (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(3/2)*d) - (b*(a^2 + 3*b^2))/(a^2*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) - Cot[c + d*x]/(a*d*Sqrt[a + b*Tan[c + d*x]])","A",13,8,23,0.3478,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
545,1,241,0,0.8523113,"\int \frac{\cot ^3(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^3/(a + b*Tan[c + d*x])^(3/2),x]","\frac{b^2 \left(7 a^2+15 b^2\right)}{4 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(8 a^2-15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d}+\frac{5 b \cot (c+d x)}{4 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{\cot ^2(c+d x)}{2 a d \sqrt{a+b \tan (c+d x)}}","\frac{b^2 \left(7 a^2+15 b^2\right)}{4 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(8 a^2-15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{7/2} d}+\frac{5 b \cot (c+d x)}{4 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{3/2}}-\frac{\cot ^2(c+d x)}{2 a d \sqrt{a+b \tan (c+d x)}}",1,"((8*a^2 - 15*b^2)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(4*a^(7/2)*d) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(3/2)*d) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(3/2)*d) + (b^2*(7*a^2 + 15*b^2))/(4*a^3*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + (5*b*Cot[c + d*x])/(4*a^2*d*Sqrt[a + b*Tan[c + d*x]]) - Cot[c + d*x]^2/(2*a*d*Sqrt[a + b*Tan[c + d*x]])","A",14,9,23,0.3913,1,"{3569, 3649, 3650, 3653, 3539, 3537, 63, 208, 3634}"
546,1,291,0,0.7856549,"\int \frac{\tan ^5(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^5/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{4 a^2 \left(a^2+2 b^2\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(15 a^2 b^2+8 a^4+b^4\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)^2}-\frac{4 a \left(15 a^2 b^2+8 a^4+4 b^4\right) \sqrt{a+b \tan (c+d x)}}{3 b^4 d \left(a^2+b^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{\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 \tan ^3(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{4 a^2 \left(a^2+2 b^2\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(15 a^2 b^2+8 a^4+b^4\right) \tan (c+d x) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)^2}-\frac{4 a \left(15 a^2 b^2+8 a^4+4 b^4\right) \sqrt{a+b \tan (c+d x)}}{3 b^4 d \left(a^2+b^2\right)^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(5/2)*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(5/2)*d) - (2*a^2*Tan[c + d*x]^3)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (4*a^2*(a^2 + 2*b^2)*Tan[c + d*x]^2)/(b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]]) - (4*a*(8*a^4 + 15*a^2*b^2 + 4*b^4)*Sqrt[a + b*Tan[c + d*x]])/(3*b^4*(a^2 + b^2)^2*d) + (2*(8*a^4 + 15*a^2*b^2 + b^4)*Tan[c + d*x]*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)^2*d)","A",11,8,23,0.3478,1,"{3565, 3645, 3647, 3630, 3539, 3537, 63, 208}"
547,1,226,0,0.4947886,"\int \frac{\tan ^4(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^4/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 a^3 \left(2 a^2+5 b^2\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+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{i \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 \tan ^2(c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 a^3 \left(2 a^2+5 b^2\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+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{3 b^3 d \left(a^2+b^2\right)}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"((-I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (2*a^2*Tan[c + d*x]^2)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (4*a^3*(2*a^2 + 5*b^2))/(3*b^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]]) + (2*(4*a^2 + 3*b^2)*Sqrt[a + b*Tan[c + d*x]])/(3*b^3*(a^2 + b^2)*d)","A",10,7,23,0.3043,1,"{3565, 3635, 3630, 3539, 3537, 63, 208}"
548,1,172,0,0.3678913,"\int \frac{\tan ^3(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^3/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{4 a^2 \left(a^2+4 b^2\right)}{3 b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 a^2 \tan (c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","-\frac{4 a^2 \left(a^2+4 b^2\right)}{3 b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 a^2 \tan (c+d x)}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(5/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(5/2)*d) - (2*a^2*Tan[c + d*x])/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (4*a^2*(a^2 + 4*b^2))/(3*b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,23,0.2609,1,"{3565, 3628, 3539, 3537, 63, 208}"
549,1,157,0,0.3180837,"\int \frac{\tan ^2(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^2/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 a b}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{i \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}{3 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 a b}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"(I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (2*a^2)/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (4*a*b)/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,23,0.2609,1,"{3542, 3529, 3539, 3537, 63, 208}"
550,1,155,0,0.2661614,"\int \frac{\tan (c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 a}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(a^2-b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{\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}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{2 \left(a^2-b^2\right)}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"-(ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(5/2)*d)) - ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(5/2)*d) + (2*a)/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*(a^2 - b^2))/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,21,0.2381,1,"{3529, 3539, 3537, 63, 208}"
551,1,152,0,0.2493372,"\int \frac{1}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[(a + b*Tan[c + d*x])^(-5/2),x]","-\frac{4 a b}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}","-\frac{4 a b}{d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"((-I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (2*b)/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (4*a*b)/((a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,6,14,0.4286,1,"{3483, 3529, 3539, 3537, 63, 208}"
552,1,195,0,0.7326846,"\int \frac{\cot (c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]/(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 b^2 \left(3 a^2+b^2\right)}{a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 b^2}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{\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^2 \left(3 a^2+b^2\right)}{a^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 b^2}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{5/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}",1,"(-2*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(5/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]]/((a - I*b)^(5/2)*d) + ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]]/((a + I*b)^(5/2)*d) + (2*b^2)/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*b^2*(3*a^2 + b^2))/(a^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",13,8,21,0.3810,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
553,1,245,0,0.9413239,"\int \frac{\cot ^2(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]^2/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{b \left(3 a^2+5 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 b^2+a^4+5 b^4\right)}{a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}","-\frac{b \left(3 a^2+5 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 b^2+a^4+5 b^4\right)}{a^3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{5/2}}-\frac{\cot (c+d x)}{a d (a+b \tan (c+d x))^{3/2}}",1,"(5*b*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a]])/(a^(7/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(5/2)*d) - (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(5/2)*d) - (b*(3*a^2 + 5*b^2))/(3*a^2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - Cot[c + d*x]/(a*d*(a + b*Tan[c + d*x])^(3/2)) - (b*(a^4 + 10*a^2*b^2 + 5*b^4))/(a^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",14,8,23,0.3478,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
554,1,194,0,0.3888071,"\int \frac{1}{(a+b \tan (c+d x))^{7/2}} \, dx","Int[(a + b*Tan[c + d*x])^(-7/2),x]","-\frac{2 b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 \sqrt{a+b \tan (c+d x)}}-\frac{4 a b}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^{3/2}}-\frac{2 b}{5 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{7/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{7/2}}","-\frac{2 b \left(3 a^2-b^2\right)}{d \left(a^2+b^2\right)^3 \sqrt{a+b \tan (c+d x)}}-\frac{4 a b}{3 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))^{3/2}}-\frac{2 b}{5 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a-i b}}\right)}{d (a-i b)^{7/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{a+i b}}\right)}{d (a+i b)^{7/2}}",1,"((-I)*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a - I*b]])/((a - I*b)^(7/2)*d) + (I*ArcTanh[Sqrt[a + b*Tan[c + d*x]]/Sqrt[a + I*b]])/((a + I*b)^(7/2)*d) - (2*b)/(5*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(5/2)) - (4*a*b)/(3*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^2 - b^2))/((a^2 + b^2)^3*d*Sqrt[a + b*Tan[c + d*x]])","A",10,6,14,0.4286,1,"{3483, 3529, 3539, 3537, 63, 208}"
555,1,202,0,0.1607736,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x]),x]","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 a \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b \tan ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{2 b \sqrt{\tan (c+d x)}}{d}","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 a \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b \tan ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{2 b \sqrt{\tan (c+d x)}}{d}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a + 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 + (2*a*Tan[c + d*x]^(3/2))/(3*d) + (2*b*Tan[c + d*x]^(5/2))/(5*d)","A",13,8,21,0.3810,1,"{3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
556,1,184,0,0.1373574,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x)) \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]),x]","\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 a \sqrt{\tan (c+d x)}}{d}+\frac{2 b \tan ^{\frac{3}{2}}(c+d x)}{3 d}","\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 a \sqrt{\tan (c+d x)}}{d}+\frac{2 b \tan ^{\frac{3}{2}}(c+d x)}{3 d}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*a*Sqrt[Tan[c + d*x]])/d + (2*b*Tan[c + d*x]^(3/2))/(3*d)","A",12,8,21,0.3810,1,"{3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
557,1,166,0,0.1130958,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x)) \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]),x]","-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b \sqrt{\tan (c+d x)}}{d}","-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b \sqrt{\tan (c+d x)}}{d}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a + 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",11,8,21,0.3810,1,"{3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
558,1,150,0,0.0922042,"\int \frac{a+b \tan (c+d x)}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[Tan[c + d*x]],x]","-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d)","A",10,7,21,0.3333,1,"{3534, 1168, 1162, 617, 204, 1165, 628}"
559,1,166,0,0.1141644,"\int \frac{a+b \tan (c+d x)}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])/Tan[c + d*x]^(3/2),x]","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{d \sqrt{\tan (c+d x)}}","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{d \sqrt{\tan (c+d x)}}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a)/(d*Sqrt[Tan[c + d*x]])","A",11,8,21,0.3810,1,"{3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
560,1,184,0,0.1369265,"\int \frac{a+b \tan (c+d x)}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])/Tan[c + d*x]^(5/2),x]","\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b}{d \sqrt{\tan (c+d x)}}","\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b}{d \sqrt{\tan (c+d x)}}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a)/(3*d*Tan[c + d*x]^(3/2)) - (2*b)/(d*Sqrt[Tan[c + d*x]])","A",12,8,21,0.3810,1,"{3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
561,1,202,0,0.1526056,"\int \frac{a+b \tan (c+d x)}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])/Tan[c + d*x]^(7/2),x]","-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 a}{d \sqrt{\tan (c+d x)}}-\frac{2 b}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{2 a}{d \sqrt{\tan (c+d x)}}-\frac{2 b}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a)/(5*d*Tan[c + d*x]^(5/2)) - (2*b)/(3*d*Tan[c + d*x]^(3/2)) + (2*a)/(d*Sqrt[Tan[c + d*x]])","A",13,8,21,0.3810,1,"{3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
562,1,268,0,0.2557797,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2,x]","\frac{2 \left(a^2-b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \tan ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 a b \sqrt{\tan (c+d x)}}{d}+\frac{2 b^2 \tan ^{\frac{7}{2}}(c+d x)}{7 d}","\frac{2 \left(a^2-b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \tan ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 a b \sqrt{\tan (c+d x)}}{d}+\frac{2 b^2 \tan ^{\frac{7}{2}}(c+d x)}{7 d}",1,"((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (4*a*b*Sqrt[Tan[c + d*x]])/d + (2*(a^2 - b^2)*Tan[c + d*x]^(3/2))/(3*d) + (4*a*b*Tan[c + d*x]^(5/2))/(5*d) + (2*b^2*Tan[c + d*x]^(7/2))/(7*d)","A",14,9,23,0.3913,1,"{3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
563,1,249,0,0.2206157,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b^2 \tan ^{\frac{5}{2}}(c+d x)}{5 d}","\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b^2 \tan ^{\frac{5}{2}}(c+d x)}{5 d}",1,"((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*(a^2 - b^2)*Sqrt[Tan[c + d*x]])/d + (4*a*b*Tan[c + d*x]^(3/2))/(3*d) + (2*b^2*Tan[c + d*x]^(5/2))/(5*d)","A",13,9,23,0.3913,1,"{3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
564,1,223,0,0.1836563,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2 \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \sqrt{\tan (c+d x)}}{d}+\frac{2 b^2 \tan ^{\frac{3}{2}}(c+d x)}{3 d}","-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{4 a b \sqrt{\tan (c+d x)}}{d}+\frac{2 b^2 \tan ^{\frac{3}{2}}(c+d x)}{3 d}",1,"-(((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (4*a*b*Sqrt[Tan[c + d*x]])/d + (2*b^2*Tan[c + d*x]^(3/2))/(3*d)","A",12,9,23,0.3913,1,"{3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
565,1,204,0,0.1471218,"\int \frac{(a+b \tan (c+d x))^2}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^2/Sqrt[Tan[c + d*x]],x]","-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \sqrt{\tan (c+d x)}}{d}","-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \sqrt{\tan (c+d x)}}{d}",1,"-(((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b^2*Sqrt[Tan[c + d*x]])/d","A",11,8,23,0.3478,1,"{3543, 3534, 1168, 1162, 617, 204, 1165, 628}"
566,1,204,0,0.1618992,"\int \frac{(a+b \tan (c+d x))^2}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^2/Tan[c + d*x]^(3/2),x]","\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2}{d \sqrt{\tan (c+d x)}}","\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{2 a^2}{d \sqrt{\tan (c+d x)}}",1,"((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2)/(d*Sqrt[Tan[c + d*x]])","A",11,8,23,0.3478,1,"{3542, 3534, 1168, 1162, 617, 204, 1165, 628}"
567,1,223,0,0.1960314,"\int \frac{(a+b \tan (c+d x))^2}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^2/Tan[c + d*x]^(5/2),x]","\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\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 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{4 a b}{d \sqrt{\tan (c+d x)}}","\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\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 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{4 a b}{d \sqrt{\tan (c+d x)}}",1,"((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2)/(3*d*Tan[c + d*x]^(3/2)) - (4*a*b)/(d*Sqrt[Tan[c + d*x]])","A",12,9,23,0.3913,1,"{3542, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
568,1,249,0,0.2117277,"\int \frac{(a+b \tan (c+d x))^2}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^2/Tan[c + d*x]^(7/2),x]","-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2-b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\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 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{4 a b}{3 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 \left(a^2-b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\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 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{4 a b}{3 d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*a^2)/(5*d*Tan[c + d*x]^(5/2)) - (4*a*b)/(3*d*Tan[c + d*x]^(3/2)) + (2*(a^2 - b^2))/(d*Sqrt[Tan[c + d*x]])","A",13,9,23,0.3913,1,"{3542, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
569,1,328,0,0.4583186,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3,x]","\frac{2 b \left(3 a^2-b^2\right) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a \left(a^2-3 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 b \left(3 a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \tan ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))}{9 d}+\frac{40 a b^2 \tan ^{\frac{7}{2}}(c+d x)}{63 d}","\frac{2 b \left(3 a^2-b^2\right) \tan ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a \left(a^2-3 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 b \left(3 a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \tan ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))}{9 d}+\frac{40 a b^2 \tan ^{\frac{7}{2}}(c+d x)}{63 d}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (2*b*(3*a^2 - b^2)*Sqrt[Tan[c + d*x]])/d + (2*a*(a^2 - 3*b^2)*Tan[c + d*x]^(3/2))/(3*d) + (2*b*(3*a^2 - b^2)*Tan[c + d*x]^(5/2))/(5*d) + (40*a*b^2*Tan[c + d*x]^(7/2))/(63*d) + (2*b^2*Tan[c + d*x]^(7/2)*(a + b*Tan[c + d*x]))/(9*d)","A",15,10,23,0.4348,1,"{3566, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
570,1,299,0,0.4023418,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3,x]","\frac{2 b \left(3 a^2-b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(a^2-3 b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))}{7 d}+\frac{32 a b^2 \tan ^{\frac{5}{2}}(c+d x)}{35 d}","\frac{2 b \left(3 a^2-b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(a^2-3 b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))}{7 d}+\frac{32 a b^2 \tan ^{\frac{5}{2}}(c+d x)}{35 d}",1,"((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*a*(a^2 - 3*b^2)*Sqrt[Tan[c + d*x]])/d + (2*b*(3*a^2 - b^2)*Tan[c + d*x]^(3/2))/(3*d) + (32*a*b^2*Tan[c + d*x]^(5/2))/(35*d) + (2*b^2*Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x]))/(7*d)","A",14,10,23,0.4348,1,"{3566, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
571,1,272,0,0.3567354,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^3 \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^3,x]","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{8 a b^2 \tan ^{\frac{3}{2}}(c+d x)}{5 d}+\frac{2 b^2 \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}{5 d}","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right) \sqrt{\tan (c+d x)}}{d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{8 a b^2 \tan ^{\frac{3}{2}}(c+d x)}{5 d}+\frac{2 b^2 \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}{5 d}",1,"-(((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*(3*a^2 - b^2)*Sqrt[Tan[c + d*x]])/d + (8*a*b^2*Tan[c + d*x]^(3/2))/(5*d) + (2*b^2*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]))/(5*d)","A",13,10,23,0.4348,1,"{3566, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
572,1,245,0,0.3043046,"\int \frac{(a+b \tan (c+d x))^3}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^3/Sqrt[Tan[c + d*x]],x]","-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}{3 d}+\frac{16 a b^2 \sqrt{\tan (c+d x)}}{3 d}","-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{2 b^2 \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}{3 d}+\frac{16 a b^2 \sqrt{\tan (c+d x)}}{3 d}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (16*a*b^2*Sqrt[Tan[c + d*x]])/(3*d) + (2*b^2*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))/(3*d)","A",12,9,23,0.3913,1,"{3566, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
573,1,245,0,0.3079605,"\int \frac{(a+b \tan (c+d x))^3}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Tan[c + d*x]^(3/2),x]","\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{d \sqrt{\tan (c+d x)}}","\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{d \sqrt{\tan (c+d x)}}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + (2*b*(a^2 + b^2)*Sqrt[Tan[c + d*x]])/d - (2*a^2*(a + b*Tan[c + d*x]))/(d*Sqrt[Tan[c + d*x]])","A",12,9,23,0.3913,1,"{3565, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
574,1,245,0,0.3117173,"\int \frac{(a+b \tan (c+d x))^3}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Tan[c + d*x]^(5/2),x]","\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b \tan (c+d x))}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{16 a^2 b}{3 d \sqrt{\tan (c+d x)}}","\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b \tan (c+d x))}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{16 a^2 b}{3 d \sqrt{\tan (c+d x)}}",1,"((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (16*a^2*b)/(3*d*Sqrt[Tan[c + d*x]]) - (2*a^2*(a + b*Tan[c + d*x]))/(3*d*Tan[c + d*x]^(3/2))","A",12,9,23,0.3913,1,"{3565, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
575,1,270,0,0.3473625,"\int \frac{(a+b \tan (c+d x))^3}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Tan[c + d*x]^(7/2),x]","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{8 a^2 b}{5 d \tan ^{\frac{3}{2}}(c+d x)}","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\tan (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{8 a^2 b}{5 d \tan ^{\frac{3}{2}}(c+d x)}",1,"-(((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (8*a^2*b)/(5*d*Tan[c + d*x]^(3/2)) + (2*a*(a^2 - 3*b^2))/(d*Sqrt[Tan[c + d*x]]) - (2*a^2*(a + b*Tan[c + d*x]))/(5*d*Tan[c + d*x]^(5/2))","A",13,10,23,0.4348,1,"{3565, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
576,1,299,0,0.3815281,"\int \frac{(a+b \tan (c+d x))^3}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Tan[c + d*x]^(9/2),x]","\frac{2 a \left(a^2-3 b^2\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right)}{d \sqrt{\tan (c+d x)}}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b \tan (c+d x))}{7 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{32 a^2 b}{35 d \tan ^{\frac{5}{2}}(c+d x)}","\frac{2 a \left(a^2-3 b^2\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right)}{d \sqrt{\tan (c+d x)}}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b \tan (c+d x))}{7 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{32 a^2 b}{35 d \tan ^{\frac{5}{2}}(c+d x)}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (32*a^2*b)/(35*d*Tan[c + d*x]^(5/2)) + (2*a*(a^2 - 3*b^2))/(3*d*Tan[c + d*x]^(3/2)) + (2*b*(3*a^2 - b^2))/(d*Sqrt[Tan[c + d*x]]) - (2*a^2*(a + b*Tan[c + d*x]))/(7*d*Tan[c + d*x]^(7/2))","A",14,10,23,0.4348,1,"{3565, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
577,1,326,0,0.4588345,"\int \frac{(a+b \tan (c+d x))^3}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Tan[c + d*x]^(11/2),x]","\frac{2 a \left(a^2-3 b^2\right)}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\tan (c+d x)}}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{9 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{40 a^2 b}{63 d \tan ^{\frac{7}{2}}(c+d x)}","\frac{2 a \left(a^2-3 b^2\right)}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b \left(3 a^2-b^2\right)}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\tan (c+d x)}}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\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+b \tan (c+d x))}{9 d \tan ^{\frac{9}{2}}(c+d x)}-\frac{40 a^2 b}{63 d \tan ^{\frac{7}{2}}(c+d x)}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) - (40*a^2*b)/(63*d*Tan[c + d*x]^(7/2)) + (2*a*(a^2 - 3*b^2))/(5*d*Tan[c + d*x]^(5/2)) + (2*b*(3*a^2 - b^2))/(3*d*Tan[c + d*x]^(3/2)) - (2*a*(a^2 - 3*b^2))/(d*Sqrt[Tan[c + d*x]]) - (2*a^2*(a + b*Tan[c + d*x]))/(9*d*Tan[c + d*x]^(9/2))","A",15,10,23,0.4348,1,"{3565, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
578,1,150,0,0.0965201,"\int \frac{a+b \tan (c+d x)}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[Tan[c + d*x]],x]","-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d}-\frac{(a-b) \log \left(\tan (c+d x)-\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\tan (c+d x)+\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*d)","A",10,7,21,0.3333,1,"{3534, 1168, 1162, 617, 204, 1165, 628}"
579,1,162,0,0.1103482,"\int \frac{a+b \tan (c+d x)}{\sqrt{-\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[-Tan[c + d*x]],x]","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{-\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(-\tan (c+d x)-\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(-\tan (c+d x)+\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{2 \sqrt{2} d}","\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{-\tan (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{\sqrt{2} d}+\frac{(a+b) \log \left(-\tan (c+d x)-\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(-\tan (c+d x)+\sqrt{2} \sqrt{-\tan (c+d x)}+1\right)}{2 \sqrt{2} d}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[-Tan[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[-Tan[c + d*x]]])/(Sqrt[2]*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[-Tan[c + d*x]] - Tan[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[-Tan[c + d*x]] - Tan[c + d*x]])/(2*Sqrt[2]*d)","A",10,7,23,0.3043,1,"{3534, 1168, 1162, 617, 204, 1165, 628}"
580,1,208,0,0.1452766,"\int \frac{a+b \tan (c+d x)}{\sqrt{e \tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[e*Tan[c + d*x]],x]","-\frac{(a+b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e \tan (c+d x)}}{\sqrt{e}}\right)}{\sqrt{2} d \sqrt{e}}+\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e \tan (c+d x)}}{\sqrt{e}}+1\right)}{\sqrt{2} d \sqrt{e}}-\frac{(a-b) \log \left(\sqrt{e} \tan (c+d x)-\sqrt{2} \sqrt{e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}+\frac{(a-b) \log \left(\sqrt{e} \tan (c+d x)+\sqrt{2} \sqrt{e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}","-\frac{(a+b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{e \tan (c+d x)}}{\sqrt{e}}\right)}{\sqrt{2} d \sqrt{e}}+\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{e \tan (c+d x)}}{\sqrt{e}}+1\right)}{\sqrt{2} d \sqrt{e}}-\frac{(a-b) \log \left(\sqrt{e} \tan (c+d x)-\sqrt{2} \sqrt{e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}+\frac{(a-b) \log \left(\sqrt{e} \tan (c+d x)+\sqrt{2} \sqrt{e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}",1,"-(((a + b)*ArcTan[1 - (Sqrt[2]*Sqrt[e*Tan[c + d*x]])/Sqrt[e]])/(Sqrt[2]*d*Sqrt[e])) + ((a + b)*ArcTan[1 + (Sqrt[2]*Sqrt[e*Tan[c + d*x]])/Sqrt[e]])/(Sqrt[2]*d*Sqrt[e]) - ((a - b)*Log[Sqrt[e] + Sqrt[e]*Tan[c + d*x] - Sqrt[2]*Sqrt[e*Tan[c + d*x]]])/(2*Sqrt[2]*d*Sqrt[e]) + ((a - b)*Log[Sqrt[e] + Sqrt[e]*Tan[c + d*x] + Sqrt[2]*Sqrt[e*Tan[c + d*x]]])/(2*Sqrt[2]*d*Sqrt[e])","A",10,7,23,0.3043,1,"{3534, 1168, 1162, 617, 204, 1165, 628}"
581,1,214,0,0.1417378,"\int \frac{a+b \tan (c+d x)}{\sqrt{-e \tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[-(e*Tan[c + d*x])],x]","\frac{(a-b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{-e \tan (c+d x)}}{\sqrt{e}}\right)}{\sqrt{2} d \sqrt{e}}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-e \tan (c+d x)}}{\sqrt{e}}+1\right)}{\sqrt{2} d \sqrt{e}}+\frac{(a+b) \log \left(-\sqrt{e} \tan (c+d x)-\sqrt{2} \sqrt{-e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}-\frac{(a+b) \log \left(-\sqrt{e} \tan (c+d x)+\sqrt{2} \sqrt{-e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}","\frac{(a-b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{-e \tan (c+d x)}}{\sqrt{e}}\right)}{\sqrt{2} d \sqrt{e}}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-e \tan (c+d x)}}{\sqrt{e}}+1\right)}{\sqrt{2} d \sqrt{e}}+\frac{(a+b) \log \left(-\sqrt{e} \tan (c+d x)-\sqrt{2} \sqrt{-e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}-\frac{(a+b) \log \left(-\sqrt{e} \tan (c+d x)+\sqrt{2} \sqrt{-e \tan (c+d x)}+\sqrt{e}\right)}{2 \sqrt{2} d \sqrt{e}}",1,"((a - b)*ArcTan[1 - (Sqrt[2]*Sqrt[-(e*Tan[c + d*x])])/Sqrt[e]])/(Sqrt[2]*d*Sqrt[e]) - ((a - b)*ArcTan[1 + (Sqrt[2]*Sqrt[-(e*Tan[c + d*x])])/Sqrt[e]])/(Sqrt[2]*d*Sqrt[e]) + ((a + b)*Log[Sqrt[e] - Sqrt[e]*Tan[c + d*x] - Sqrt[2]*Sqrt[-(e*Tan[c + d*x])]])/(2*Sqrt[2]*d*Sqrt[e]) - ((a + b)*Log[Sqrt[e] - Sqrt[e]*Tan[c + d*x] + Sqrt[2]*Sqrt[-(e*Tan[c + d*x])]])/(2*Sqrt[2]*d*Sqrt[e])","A",10,7,24,0.2917,1,"{3534, 1168, 1162, 617, 204, 1165, 628}"
582,1,300,0,0.8181355,"\int \frac{\tan ^{\frac{9}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(9/2)/(a + b*Tan[c + d*x]),x]","-\frac{2 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{7/2} d \left(a^2+b^2\right)}-\frac{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \left(a^2-b^2\right) \sqrt{\tan (c+d x)}}{b^3 d}+\frac{(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-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 \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d}+\frac{2 \tan ^{\frac{5}{2}}(c+d x)}{5 b d}","-\frac{2 a^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{7/2} d \left(a^2+b^2\right)}-\frac{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \left(a^2-b^2\right) \sqrt{\tan (c+d x)}}{b^3 d}+\frac{(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-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 \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d}+\frac{2 \tan ^{\frac{5}{2}}(c+d x)}{5 b d}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(9/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(7/2)*(a^2 + b^2)*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((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^2 - b^2)*Sqrt[Tan[c + d*x]])/(b^3*d) - (2*a*Tan[c + d*x]^(3/2))/(3*b^2*d) + (2*Tan[c + d*x]^(5/2))/(5*b*d)","A",17,14,23,0.6087,1,"{3566, 3647, 3648, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
583,1,271,0,0.5715408,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(7/2)/(a + b*Tan[c + d*x]),x]","\frac{2 a^{7/2} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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+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 \sqrt{\tan (c+d x)}}{b^2 d}+\frac{2 \tan ^{\frac{3}{2}}(c+d x)}{3 b d}","\frac{2 a^{7/2} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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+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 \sqrt{\tan (c+d x)}}{b^2 d}+\frac{2 \tan ^{\frac{3}{2}}(c+d x)}{3 b d}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(7/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(5/2)*(a^2 + b^2)*d) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((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*Sqrt[Tan[c + d*x]])/(b^2*d) + (2*Tan[c + d*x]^(3/2))/(3*b*d)","A",16,13,23,0.5652,1,"{3566, 3647, 3654, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
584,1,250,0,0.4188772,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(5/2)/(a + b*Tan[c + d*x]),x]","-\frac{2 a^{5/2} \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{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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-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 \sqrt{\tan (c+d x)}}{b d}","-\frac{2 a^{5/2} \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{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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-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 \sqrt{\tan (c+d x)}}{b d}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(5/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(3/2)*(a^2 + b^2)*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + (2*Sqrt[Tan[c + d*x]])/(b*d)","A",15,12,23,0.5217,1,"{3566, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
585,1,232,0,0.2470921,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(3/2)/(a + b*Tan[c + d*x]),x]","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}+\frac{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}+\frac{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(3/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[b]*(a^2 + b^2)*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",14,11,23,0.4783,1,"{3573, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
586,1,232,0,0.2478117,"\int \frac{\sqrt{\tan (c+d x)}}{a+b \tan (c+d x)} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + b*Tan[c + d*x]),x]","-\frac{(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+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} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{d \left(a^2+b^2\right)}+\frac{(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-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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{d \left(a^2+b^2\right)}+\frac{(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-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)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/((a^2 + b^2)*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",14,11,23,0.4783,1,"{3572, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
587,1,232,0,0.248706,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])),x]","\frac{2 b^{3/2} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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+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} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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+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)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[a]*(a^2 + b^2)*d) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a + b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",14,11,23,0.4783,1,"{3574, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
588,1,250,0,0.4149627,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","-\frac{2 b^{5/2} \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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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-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-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 d \sqrt{\tan (c+d x)}}","-\frac{2 b^{5/2} \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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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-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-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 d \sqrt{\tan (c+d x)}}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(5/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(3/2)*(a^2 + b^2)*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((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*d*Sqrt[Tan[c + d*x]])","A",15,12,23,0.5217,1,"{3569, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
589,1,271,0,0.5748418,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","\frac{2 b^{7/2} \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{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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^2 d \sqrt{\tan (c+d x)}}-\frac{2}{3 a d \tan ^{\frac{3}{2}}(c+d x)}","\frac{2 b^{7/2} \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{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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+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^2 d \sqrt{\tan (c+d x)}}-\frac{2}{3 a d \tan ^{\frac{3}{2}}(c+d x)}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(7/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(5/2)*(a^2 + b^2)*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - 2/(3*a*d*Tan[c + d*x]^(3/2)) + (2*b)/(a^2*d*Sqrt[Tan[c + d*x]])","A",16,13,23,0.5652,1,"{3569, 3649, 3654, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
590,1,300,0,0.7945754,"\int \frac{1}{\tan ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(7/2)*(a + b*Tan[c + d*x])),x]","-\frac{2 b^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d \left(a^2+b^2\right)}-\frac{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \left(a^2-b^2\right)}{a^3 d \sqrt{\tan (c+d x)}}+\frac{(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-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 a^2 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2}{5 a d \tan ^{\frac{5}{2}}(c+d x)}","-\frac{2 b^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{a^{7/2} d \left(a^2+b^2\right)}-\frac{(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+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{2 \left(a^2-b^2\right)}{a^3 d \sqrt{\tan (c+d x)}}+\frac{(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-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 a^2 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2}{5 a d \tan ^{\frac{5}{2}}(c+d x)}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(9/2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(7/2)*(a^2 + b^2)*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - 2/(5*a*d*Tan[c + d*x]^(5/2)) + (2*b)/(3*a^2*d*Tan[c + d*x]^(3/2)) + (2*(a^2 - b^2))/(a^3*d*Sqrt[Tan[c + d*x]])","A",17,14,23,0.6087,1,"{3569, 3649, 3650, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
591,1,399,0,1.012409,"\int \frac{\tan ^{\frac{9}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(9/2)/(a + b*Tan[c + d*x])^2,x]","\frac{a^{7/2} \left(5 a^2+9 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{7/2} d \left(a^2+b^2\right)^2}-\frac{a^2 \tan ^{\frac{5}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(5 a^2+2 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d \left(a^2+b^2\right)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a \left(5 a^2+4 b^2\right) \sqrt{\tan (c+d x)}}{b^3 d \left(a^2+b^2\right)}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^{7/2} \left(5 a^2+9 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{b^{7/2} d \left(a^2+b^2\right)^2}-\frac{a^2 \tan ^{\frac{5}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(5 a^2+2 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d \left(a^2+b^2\right)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a \left(5 a^2+4 b^2\right) \sqrt{\tan (c+d x)}}{b^3 d \left(a^2+b^2\right)}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (a^(7/2)*(5*a^2 + 9*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(7/2)*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - (a*(5*a^2 + 4*b^2)*Sqrt[Tan[c + d*x]])/(b^3*(a^2 + b^2)*d) + ((5*a^2 + 2*b^2)*Tan[c + d*x]^(3/2))/(3*b^2*(a^2 + b^2)*d) - (a^2*Tan[c + d*x]^(5/2))/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",17,13,23,0.5652,1,"{3565, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
592,1,358,0,0.7478375,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(7/2)/(a + b*Tan[c + d*x])^2,x]","-\frac{a^{5/2} \left(3 a^2+7 b^2\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^2 \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+2 b^2\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{5/2} \left(3 a^2+7 b^2\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^2 \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+2 b^2\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (a^(5/2)*(3*a^2 + 7*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(5/2)*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((3*a^2 + 2*b^2)*Sqrt[Tan[c + d*x]])/(b^2*(a^2 + b^2)*d) - (a^2*Tan[c + d*x]^(3/2))/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3565, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
593,1,318,0,0.5050387,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(5/2)/(a + b*Tan[c + d*x])^2,x]","\frac{a^{3/2} \left(a^2+5 b^2\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{\left(a^2+2 a b-b^2\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+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a^2 \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+5 b^2\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{\left(a^2+2 a b-b^2\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+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}-\frac{a^2 \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (a^(3/2)*(a^2 + 5*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(b^(3/2)*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - (a^2*Sqrt[Tan[c + d*x]])/(b*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,23,0.5217,1,"{3565, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
594,1,312,0,0.447421,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Tan[c + d*x]^(3/2)/(a + b*Tan[c + d*x])^2,x]","\frac{\sqrt{a} \left(a^2-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)^2}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{a \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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{\sqrt{a} \left(a^2-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{b} d \left(a^2+b^2\right)^2}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^2}+\frac{a \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (Sqrt[a]*(a^2 - 3*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[b]*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + (a*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,23,0.5217,1,"{3567, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
595,1,316,0,0.432909,"\int \frac{\sqrt{\tan (c+d x)}}{(a+b \tan (c+d x))^2} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + b*Tan[c + d*x])^2,x]","-\frac{\sqrt{b} \left(3 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)^2}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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{\sqrt{b} \left(3 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d \left(a^2+b^2\right)^2}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) (a+b \tan (c+d x))}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (Sqrt[b]*(3*a^2 - b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(Sqrt[a]*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - (b*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,23,0.5217,1,"{3568, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
596,1,317,0,0.497854,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^2} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2),x]","\frac{b^{3/2} \left(5 a^2+b^2\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{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^2 \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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(5 a^2+b^2\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{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^2 \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) (a+b \tan (c+d x))}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (b^(3/2)*(5*a^2 + b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(3/2)*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + (b^2*Sqrt[Tan[c + d*x]])/(a*(a^2 + b^2)*d*(a + b*Tan[c + d*x]))","A",15,12,23,0.5217,1,"{3569, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
597,1,358,0,0.7626162,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2),x]","-\frac{b^{5/2} \left(7 a^2+3 b^2\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+2 a b-b^2\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+2 a b-b^2\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^2}{a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}-\frac{2 a^2+3 b^2}{a^2 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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(7 a^2+3 b^2\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+2 a b-b^2\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+2 a b-b^2\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^2}{a d \left(a^2+b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))}-\frac{2 a^2+3 b^2}{a^2 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (b^(5/2)*(7*a^2 + 3*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(5/2)*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*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 + 3*b^2)/(a^2*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]) + b^2/(a*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
598,1,397,0,1.000645,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2),x]","\frac{b^{7/2} \left(9 a^2+5 b^2\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^2}{a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+5 b^2}{3 a^2 d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \left(4 a^2+5 b^2\right)}{a^3 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{7/2} \left(9 a^2+5 b^2\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^2}{a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+5 b^2}{3 a^2 d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \left(4 a^2+5 b^2\right)}{a^3 d \left(a^2+b^2\right) \sqrt{\tan (c+d x)}}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (b^(7/2)*(9*a^2 + 5*b^2)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(a^(7/2)*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*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 + 5*b^2)/(3*a^2*(a^2 + b^2)*d*Tan[c + d*x]^(3/2)) + (b*(4*a^2 + 5*b^2))/(a^3*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]) + b^2/(a*(a^2 + b^2)*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]))","A",17,13,23,0.5652,1,"{3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
599,1,493,0,1.4024178,"\int \frac{\tan ^{\frac{11}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^(11/2)/(a + b*Tan[c + d*x])^3,x]","\frac{a^{7/2} \left(102 a^2 b^2+35 a^4+99 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{9/2} d \left(a^2+b^2\right)^3}-\frac{a^2 \left(7 a^2+15 b^2\right) \tan ^{\frac{5}{2}}(c+d x)}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^{\frac{7}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(67 a^2 b^2+35 a^4+8 b^4\right) \tan ^{\frac{3}{2}}(c+d x)}{12 b^3 d \left(a^2+b^2\right)^2}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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 \left(67 a^2 b^2+35 a^4+24 b^4\right) \sqrt{\tan (c+d x)}}{4 b^4 d \left(a^2+b^2\right)^2}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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^{7/2} \left(102 a^2 b^2+35 a^4+99 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{9/2} d \left(a^2+b^2\right)^3}-\frac{a^2 \left(7 a^2+15 b^2\right) \tan ^{\frac{5}{2}}(c+d x)}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{a^2 \tan ^{\frac{7}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(67 a^2 b^2+35 a^4+8 b^4\right) \tan ^{\frac{3}{2}}(c+d x)}{12 b^3 d \left(a^2+b^2\right)^2}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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 \left(67 a^2 b^2+35 a^4+24 b^4\right) \sqrt{\tan (c+d x)}}{4 b^4 d \left(a^2+b^2\right)^2}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (a^(7/2)*(35*a^4 + 102*a^2*b^2 + 99*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(9/2)*(a^2 + b^2)^3*d) + ((a - b)*(a^2 + 4*a*b + b^2)*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^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - (a*(35*a^4 + 67*a^2*b^2 + 24*b^4)*Sqrt[Tan[c + d*x]])/(4*b^4*(a^2 + b^2)^2*d) + ((35*a^4 + 67*a^2*b^2 + 8*b^4)*Tan[c + d*x]^(3/2))/(12*b^3*(a^2 + b^2)^2*d) - (a^2*Tan[c + d*x]^(7/2))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(7*a^2 + 15*b^2)*Tan[c + d*x]^(5/2))/(4*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",18,14,23,0.6087,1,"{3565, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
600,1,444,0,1.0864726,"\int \frac{\tan ^{\frac{9}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^(9/2)/(a + b*Tan[c + d*x])^3,x]","-\frac{a^{5/2} \left(46 a^2 b^2+15 a^4+63 b^4\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{a^2 \left(5 a^2+13 b^2\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{a^2 \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-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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(31 a^2 b^2+15 a^4+8 b^4\right) \sqrt{\tan (c+d x)}}{4 b^3 d \left(a^2+b^2\right)^2}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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^{5/2} \left(46 a^2 b^2+15 a^4+63 b^4\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{a^2 \left(5 a^2+13 b^2\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{a^2 \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-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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(31 a^2 b^2+15 a^4+8 b^4\right) \sqrt{\tan (c+d x)}}{4 b^3 d \left(a^2+b^2\right)^2}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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 - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (a^(5/2)*(15*a^4 + 46*a^2*b^2 + 63*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(7/2)*(a^2 + b^2)^3*d) + ((a + b)*(a^2 - 4*a*b + b^2)*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^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((15*a^4 + 31*a^2*b^2 + 8*b^4)*Sqrt[Tan[c + d*x]])/(4*b^3*(a^2 + b^2)^2*d) - (a^2*Tan[c + d*x]^(5/2))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(5*a^2 + 13*b^2)*Tan[c + d*x]^(3/2))/(4*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",17,14,23,0.6087,1,"{3565, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
601,1,396,0,0.8386854,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^(7/2)/(a + b*Tan[c + d*x])^3,x]","-\frac{a^2 \tan ^{\frac{3}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^{3/2} \left(6 a^2 b^2+3 a^4+35 b^4\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(3 a^2+11 b^2\right) \sqrt{\tan (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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^2 \tan ^{\frac{3}{2}}(c+d x)}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a^{3/2} \left(6 a^2 b^2+3 a^4+35 b^4\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(3 a^2+11 b^2\right) \sqrt{\tan (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (a^(3/2)*(3*a^4 + 6*a^2*b^2 + 35*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(5/2)*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*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^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - (a^2*Tan[c + d*x]^(3/2))/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (a^2*(3*a^2 + 11*b^2)*Sqrt[Tan[c + d*x]])/(4*b^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3565, 3645, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
602,1,390,0,0.8732523,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^(5/2)/(a + b*Tan[c + d*x])^3,x]","\frac{\sqrt{a} \left(18 a^2 b^2+a^4-15 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{3/2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \sqrt{\tan (c+d x)}}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2+9 b^2\right) \sqrt{\tan (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{a} \left(18 a^2 b^2+a^4-15 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 b^{3/2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \sqrt{\tan (c+d x)}}{2 b d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{a \left(a^2+9 b^2\right) \sqrt{\tan (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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 - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (Sqrt[a]*(a^4 + 18*a^2*b^2 - 15*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*b^(3/2)*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*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^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - (a^2*Sqrt[Tan[c + d*x]])/(2*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (a*(a^2 + 9*b^2)*Sqrt[Tan[c + d*x]])/(4*b*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3565, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
603,1,385,0,0.8051961,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Tan[c + d*x]^(3/2)/(a + b*Tan[c + d*x])^3,x]","\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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 b^2+3 a^4+3 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^3}+\frac{a \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2-5 b^2\right) \sqrt{\tan (c+d x)}}{4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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 b^2+3 a^4+3 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 \sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^3}+\frac{a \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{\left(3 a^2-5 b^2\right) \sqrt{\tan (c+d x)}}{4 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + ((3*a^4 - 26*a^2*b^2 + 3*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*Sqrt[a]*Sqrt[b]*(a^2 + b^2)^3*d) + ((a - b)*(a^2 + 4*a*b + b^2)*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^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + (a*Sqrt[Tan[c + d*x]])/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + ((3*a^2 - 5*b^2)*Sqrt[Tan[c + d*x]])/(4*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3567, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
604,1,389,0,0.7701934,"\int \frac{\sqrt{\tan (c+d x)}}{(a+b \tan (c+d x))^3} \, dx","Int[Sqrt[Tan[c + d*x]]/(a + b*Tan[c + d*x])^3,x]","-\frac{\sqrt{b} \left(-18 a^2 b^2+15 a^4-b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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(7 a^2-b^2\right) \sqrt{\tan (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{b} \left(-18 a^2 b^2+15 a^4-b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{3/2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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(7 a^2-b^2\right) \sqrt{\tan (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}-\frac{b \sqrt{\tan (c+d x)}}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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 - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (Sqrt[b]*(15*a^4 - 18*a^2*b^2 - b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(3/2)*(a^2 + b^2)^3*d) + ((a + b)*(a^2 - 4*a*b + b^2)*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^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - (b*Sqrt[Tan[c + d*x]])/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) - (b*(7*a^2 - b^2)*Sqrt[Tan[c + d*x]])/(4*a*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3568, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
605,1,396,0,0.8355233,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^3} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^3),x]","\frac{b^{3/2} \left(6 a^2 b^2+35 a^4+3 b^4\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{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(11 a^2+3 b^2\right) \sqrt{\tan (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b^2 \sqrt{\tan (c+d x)}}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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(6 a^2 b^2+35 a^4+3 b^4\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{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(11 a^2+3 b^2\right) \sqrt{\tan (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a+b \tan (c+d x))}+\frac{b^2 \sqrt{\tan (c+d x)}}{2 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^2}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (b^(3/2)*(35*a^4 + 6*a^2*b^2 + 3*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(5/2)*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*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^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Tan[c + d*x]] + Tan[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + (b^2*Sqrt[Tan[c + d*x]])/(2*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^2) + (b^2*(11*a^2 + 3*b^2)*Sqrt[Tan[c + d*x]])/(4*a^2*(a^2 + b^2)^2*d*(a + b*Tan[c + d*x]))","A",16,13,23,0.5652,1,"{3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
606,1,444,0,1.0973587,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{b^{5/2} \left(46 a^2 b^2+63 a^4+15 b^4\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{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \left(13 a^2+5 b^2\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^2}{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 b^2+8 a^4+15 b^4}{4 a^3 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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^{5/2} \left(46 a^2 b^2+63 a^4+15 b^4\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{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \left(13 a^2+5 b^2\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^2}{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 b^2+8 a^4+15 b^4}{4 a^3 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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 - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (b^(5/2)*(63*a^4 + 46*a^2*b^2 + 15*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(7/2)*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*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^2 - 4*a*b + b^2)*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 + 31*a^2*b^2 + 15*b^4)/(4*a^3*(a^2 + b^2)^2*d*Sqrt[Tan[c + d*x]]) + b^2/(2*a*(a^2 + b^2)*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^2) + (b^2*(13*a^2 + 5*b^2))/(4*a^2*(a^2 + b^2)^2*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x]))","A",17,13,23,0.5652,1,"{3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
607,1,493,0,1.4023135,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3),x]","\frac{b^{7/2} \left(102 a^2 b^2+99 a^4+35 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{9/2} d \left(a^2+b^2\right)^3}+\frac{b^2 \left(15 a^2+7 b^2\right)}{4 a^2 d \left(a^2+b^2\right)^2 \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}+\frac{b^2}{2 a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{67 a^2 b^2+8 a^4+35 b^4}{12 a^3 d \left(a^2+b^2\right)^2 \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \left(67 a^2 b^2+24 a^4+35 b^4\right)}{4 a^4 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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^{7/2} \left(102 a^2 b^2+99 a^4+35 b^4\right) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a}}\right)}{4 a^{9/2} d \left(a^2+b^2\right)^3}+\frac{b^2 \left(15 a^2+7 b^2\right)}{4 a^2 d \left(a^2+b^2\right)^2 \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))}+\frac{b^2}{2 a d \left(a^2+b^2\right) \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{67 a^2 b^2+8 a^4+35 b^4}{12 a^3 d \left(a^2+b^2\right)^2 \tan ^{\frac{3}{2}}(c+d x)}+\frac{b \left(67 a^2 b^2+24 a^4+35 b^4\right)}{4 a^4 d \left(a^2+b^2\right)^2 \sqrt{\tan (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Tan[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (b^(7/2)*(99*a^4 + 102*a^2*b^2 + 35*b^4)*ArcTan[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a]])/(4*a^(9/2)*(a^2 + b^2)^3*d) + ((a - b)*(a^2 + 4*a*b + b^2)*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^2 + 4*a*b + b^2)*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 + 67*a^2*b^2 + 35*b^4)/(12*a^3*(a^2 + b^2)^2*d*Tan[c + d*x]^(3/2)) + (b*(24*a^4 + 67*a^2*b^2 + 35*b^4))/(4*a^4*(a^2 + b^2)^2*d*Sqrt[Tan[c + d*x]]) + b^2/(2*a*(a^2 + b^2)*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2) + (b^2*(15*a^2 + 7*b^2))/(4*a^2*(a^2 + b^2)^2*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x]))","A",18,13,23,0.5652,1,"{3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
608,1,231,0,1.5991311,"\int \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{\left(a^2+8 b^2\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} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 b d}-\frac{a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b d}+\frac{\sqrt{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{\left(a^2+8 b^2\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} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 b d}-\frac{a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b d}+\frac{\sqrt{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}",1,"-((Sqrt[I*a - b]*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) - ((a^2 + 8*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*b^(3/2)*d) + (Sqrt[I*a + b]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (a*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*b*d) + (Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(2*b*d)","A",14,10,25,0.4000,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
609,1,184,0,0.6954413,"\int \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]],x]","\frac{i \sqrt{-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{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}+\frac{i \sqrt{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{i \sqrt{-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{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}+\frac{i \sqrt{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}",1,"(I*Sqrt[I*a - b]*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (a*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) + (I*Sqrt[I*a + b]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",13,10,25,0.4000,1,"{3570, 3655, 6725, 63, 217, 206, 910, 93, 205, 208}"
610,1,151,0,0.5103757,"\int \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)} \, dx","Int[Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]],x]","\frac{\sqrt{-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 \sqrt{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} \tanh ^{-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} \tan ^{-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} \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} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"(Sqrt[I*a - b]*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (Sqrt[I*a + b]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d","A",11,9,25,0.3600,1,"{3575, 906, 63, 217, 206, 6725, 93, 205, 208}"
611,1,115,0,0.1256349,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{\tan (c+d x)}} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Sqrt[Tan[c + d*x]],x]","-\frac{i \sqrt{-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{i \sqrt{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{i \sqrt{-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{i \sqrt{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}",1,"((-I)*Sqrt[I*a - b]*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (I*Sqrt[I*a + b]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d","A",7,5,25,0.2000,1,"{3575, 910, 93, 205, 208}"
612,1,139,0,0.4430293,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Tan[c + d*x]^(3/2),x]","-\frac{\sqrt{-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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{\sqrt{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{\sqrt{-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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{\sqrt{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}",1,"-((Sqrt[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]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",8,6,25,0.2400,1,"{3568, 3616, 3615, 93, 203, 206}"
613,1,181,0,0.3485606,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Tan[c + d*x]^(5/2),x]","\frac{i \sqrt{-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 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{i \sqrt{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{i \sqrt{-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 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{3 a d \sqrt{\tan (c+d x)}}+\frac{i \sqrt{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}",1,"(I*Sqrt[I*a - b]*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (I*Sqrt[I*a + b]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*Sqrt[a + b*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (2*b*Sqrt[a + b*Tan[c + d*x]])/(3*a*d*Sqrt[Tan[c + d*x]])","A",10,8,25,0.3200,1,"{3568, 3649, 21, 3575, 910, 93, 205, 208}"
614,1,221,0,0.8070381,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Tan[c + d*x]^(7/2),x]","\frac{2 \left(15 a^2+2 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \sqrt{\tan (c+d x)}}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{-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 \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{\sqrt{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 \left(15 a^2+2 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^2 d \sqrt{\tan (c+d x)}}-\frac{2 b \sqrt{a+b \tan (c+d x)}}{15 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{-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 \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{\sqrt{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}",1,"(Sqrt[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]*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*Sqrt[a + b*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (2*b*Sqrt[a + b*Tan[c + d*x]])/(15*a*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2 + 2*b^2)*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d*Sqrt[Tan[c + d*x]])","A",10,7,25,0.2800,1,"{3568, 3649, 3616, 3615, 93, 203, 206}"
615,1,280,0,1.9476039,"\int \tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2),x]","-\frac{\left(a^2+8 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 b d}-\frac{a \left(a^2+24 b^2\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{i (-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{3 b d}-\frac{a \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{12 b d}-\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{\left(a^2+8 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 b d}-\frac{a \left(a^2+24 b^2\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{i (-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{3 b d}-\frac{a \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{12 b d}-\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"(I*(I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (a*(a^2 + 24*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(8*b^(3/2)*d) - (I*(I*a + b)^(3/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((a^2 + 8*b^2)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(8*b*d) - (a*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(12*b*d) + (Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2))/(3*b*d)","A",15,10,25,0.4000,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
616,1,226,0,1.4965691,"\int \tan ^{\frac{3}{2}}(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])^(3/2),x]","\frac{\left(3 a^2-8 b^2\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{(-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 d}+\frac{3 a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","\frac{\left(3 a^2-8 b^2\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{(-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{2 d}+\frac{3 a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"((I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((3*a^2 - 8*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*Sqrt[b]*d) + ((I*a + b)^(3/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (3*a*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*d) + (Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(2*d)","A",14,10,25,0.4000,1,"{3570, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
617,1,186,0,1.201023,"\int \sqrt{\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])^(3/2),x]","-\frac{i (-b+i a)^{3/2} \tan ^{-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{3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","-\frac{i (-b+i a)^{3/2} \tan ^{-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{3 a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"((-I)*(I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (3*a*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (I*(I*a + b)^(3/2)*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",13,9,25,0.3600,1,"{3570, 3655, 6725, 63, 217, 206, 93, 205, 208}"
618,1,152,0,0.5552847,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Sqrt[Tan[c + d*x]],x]","\frac{2 b^{3/2} \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} \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} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","\frac{2 b^{3/2} \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} \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} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(3/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d","A",12,9,25,0.3600,1,"{3575, 910, 63, 217, 206, 6725, 93, 205, 208}"
619,1,145,0,0.467372,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(3/2),x]","\frac{i (-b+i a)^{3/2} \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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","\frac{i (-b+i a)^{3/2} \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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}-\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"(I*(I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (I*(I*a + b)^(3/2)*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",8,6,25,0.2400,1,"{3567, 3616, 3615, 93, 203, 206}"
620,1,173,0,0.6511511,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(5/2),x]","\frac{(-b+i a)^{3/2} \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 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{8 b \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(b+i a)^{3/2} \tanh ^{-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} \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 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{8 b \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}+\frac{(b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"((I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((I*a + b)^(3/2)*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)) - (8*b*Sqrt[a + b*Tan[c + d*x]])/(3*d*Sqrt[Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3567, 3649, 3616, 3615, 93, 203, 206}"
621,1,224,0,0.8745336,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(7/2),x]","\frac{2 \left(5 a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{5 a d \sqrt{\tan (c+d x)}}-\frac{i (-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{4 b \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","\frac{2 \left(5 a^2-b^2\right) \sqrt{a+b \tan (c+d x)}}{5 a d \sqrt{\tan (c+d x)}}-\frac{i (-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{4 b \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{i (b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"((-I)*(I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (I*(I*a + b)^(3/2)*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)) - (4*b*Sqrt[a + b*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(3/2)) + (2*(5*a^2 - b^2)*Sqrt[a + b*Tan[c + d*x]])/(5*a*d*Sqrt[Tan[c + d*x]])","A",10,7,25,0.2800,1,"{3567, 3649, 3616, 3615, 93, 203, 206}"
622,1,266,0,1.1389571,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Tan[c + d*x]^(9/2),x]","\frac{2 \left(35 a^2-3 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 b \left(70 a^2+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{16 b \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}","\frac{2 \left(35 a^2-3 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{4 b \left(70 a^2+3 b^2\right) \sqrt{a+b \tan (c+d x)}}{105 a^2 d \sqrt{\tan (c+d x)}}-\frac{(-b+i a)^{3/2} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}-\frac{16 b \sqrt{a+b \tan (c+d x)}}{35 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{2 a \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(b+i a)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"-(((I*a - b)^(3/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) - ((I*a + b)^(3/2)*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)) - (16*b*Sqrt[a + b*Tan[c + d*x]])/(35*d*Tan[c + d*x]^(5/2)) + (2*(35*a^2 - 3*b^2)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d*Tan[c + d*x]^(3/2)) + (4*b*(70*a^2 + 3*b^2)*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d*Sqrt[Tan[c + d*x]])","A",11,7,25,0.2800,1,"{3567, 3649, 3616, 3615, 93, 203, 206}"
623,1,332,0,2.5782721,"\int \tan ^{\frac{5}{2}}(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])^(5/2),x]","-\frac{\left(5 a^2+48 b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{96 b d}-\frac{a \left(5 a^2+112 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{64 b d}-\frac{\left(240 a^2 b^2+5 a^4-128 b^4\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} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{7/2}}{4 b d}-\frac{a \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{24 b d}-\frac{(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)}{d}","-\frac{\left(5 a^2+48 b^2\right) \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}{96 b d}-\frac{a \left(5 a^2+112 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{64 b d}-\frac{\left(240 a^2 b^2+5 a^4-128 b^4\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} \tan ^{-1}\left(\frac{\sqrt{-b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{7/2}}{4 b d}-\frac{a \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}}{24 b d}-\frac{(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)}{d}",1,"((I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((5*a^4 + 240*a^2*b^2 - 128*b^4)*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)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (a*(5*a^2 + 112*b^2)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(64*b*d) - ((5*a^2 + 48*b^2)*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2))/(96*b*d) - (a*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2))/(24*b*d) + (Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(7/2))/(4*b*d)","A",16,10,25,0.4000,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
624,1,277,0,2.1942136,"\int \tan ^{\frac{3}{2}}(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])^(5/2),x]","\frac{\left(11 a^2-8 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 d}+\frac{5 a \left(a^2-8 b^2\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^2 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (-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)}{d}+\frac{13 a b \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}-\frac{i (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)}{d}","\frac{\left(11 a^2-8 b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{8 d}+\frac{5 a \left(a^2-8 b^2\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^2 \tan ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (-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)}{d}+\frac{13 a b \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{12 d}-\frac{i (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)}{d}",1,"((-I)*(I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (5*a*(a^2 - 8*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(8*Sqrt[b]*d) - (I*(I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + ((11*a^2 - 8*b^2)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(8*d) + (13*a*b*Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(12*d) + (b^2*Tan[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",15,10,25,0.4000,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
625,1,231,0,1.8937755,"\int \sqrt{\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])^(5/2),x]","\frac{\sqrt{b} \left(15 a^2-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{b^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{(-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)}{d}+\frac{9 a b \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(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)}{d}","\frac{\sqrt{b} \left(15 a^2-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 d}+\frac{b^2 \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 d}-\frac{(-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)}{d}+\frac{9 a b \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 d}+\frac{(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)}{d}",1,"-(((I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + (Sqrt[b]*(15*a^2 - 8*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*d) + ((I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (9*a*b*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*d) + (b^2*Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(2*d)","A",14,10,25,0.4000,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
626,1,188,0,1.3912988,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Sqrt[Tan[c + d*x]],x]","\frac{b^2 \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{i (-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)}{d}+\frac{i (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)}{d}","\frac{b^2 \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{5 a b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}+\frac{i (-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)}{d}+\frac{i (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)}{d}",1,"(I*(I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (5*a*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (I*(I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (b^2*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",13,9,25,0.3600,1,"{3566, 3655, 6725, 63, 217, 206, 93, 205, 208}"
627,1,183,0,1.3745373,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(3/2),x]","-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{5/2} \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} \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} \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^2 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\tan (c+d x)}}+\frac{2 b^{5/2} \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} \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} \tanh ^{-1}\left(\frac{\sqrt{b+i a} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{d}",1,"((I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Tan[c + d*x]])","A",13,9,25,0.3600,1,"{3565, 3655, 6725, 63, 217, 206, 93, 205, 208}"
628,1,182,0,0.7533782,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\tan ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(5/2),x]","-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{i (-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)}{d}-\frac{14 a b \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{i (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)}{d}","-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{3 d \tan ^{\frac{3}{2}}(c+d x)}-\frac{i (-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)}{d}-\frac{14 a b \sqrt{a+b \tan (c+d x)}}{3 d \sqrt{\tan (c+d x)}}-\frac{i (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)}{d}",1,"((-I)*(I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (I*(I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + b*Tan[c + d*x]])/(3*d*Tan[c + d*x]^(3/2)) - (14*a*b*Sqrt[a + b*Tan[c + d*x]])/(3*d*Sqrt[Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3565, 3649, 3616, 3615, 93, 203, 206}"
629,1,219,0,0.994674,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\tan ^{\frac{7}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(7/2),x]","\frac{2 \left(15 a^2-23 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{(-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)}{d}-\frac{22 a b \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(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)}{d}","\frac{2 \left(15 a^2-23 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{5 d \tan ^{\frac{5}{2}}(c+d x)}-\frac{(-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)}{d}-\frac{22 a b \sqrt{a+b \tan (c+d x)}}{15 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{(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)}{d}",1,"-(((I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d) + ((I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + b*Tan[c + d*x]])/(5*d*Tan[c + d*x]^(5/2)) - (22*a*b*Sqrt[a + b*Tan[c + d*x]])/(15*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2 - 23*b^2)*Sqrt[a + b*Tan[c + d*x]])/(15*d*Sqrt[Tan[c + d*x]])","A",10,7,25,0.2800,1,"{3565, 3649, 3616, 3615, 93, 203, 206}"
630,1,270,0,1.2938099,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\tan ^{\frac{9}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(9/2),x]","\frac{2 \left(7 a^2-9 b^2\right) \sqrt{a+b \tan (c+d x)}}{21 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 b \left(49 a^2-3 b^2\right) \sqrt{a+b \tan (c+d x)}}{21 a d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}+\frac{i (-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)}{d}-\frac{6 a b \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{i (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)}{d}","\frac{2 \left(7 a^2-9 b^2\right) \sqrt{a+b \tan (c+d x)}}{21 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 b \left(49 a^2-3 b^2\right) \sqrt{a+b \tan (c+d x)}}{21 a d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{7}{2}}(c+d x)}+\frac{i (-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)}{d}-\frac{6 a b \sqrt{a+b \tan (c+d x)}}{7 d \tan ^{\frac{5}{2}}(c+d x)}+\frac{i (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)}{d}",1,"(I*(I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d + (I*(I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + b*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(7/2)) - (6*a*b*Sqrt[a + b*Tan[c + d*x]])/(7*d*Tan[c + d*x]^(5/2)) + (2*(7*a^2 - 9*b^2)*Sqrt[a + b*Tan[c + d*x]])/(21*d*Tan[c + d*x]^(3/2)) + (2*b*(49*a^2 - 3*b^2)*Sqrt[a + b*Tan[c + d*x]])/(21*a*d*Sqrt[Tan[c + d*x]])","A",11,7,25,0.2800,1,"{3565, 3649, 3616, 3615, 93, 203, 206}"
631,1,318,0,1.5632055,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\tan ^{\frac{11}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Tan[c + d*x]^(11/2),x]","\frac{2 b \left(231 a^2-5 b^2\right) \sqrt{a+b \tan (c+d x)}}{315 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2-25 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 b^2+315 a^4-10 b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}+\frac{(-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)}{d}-\frac{38 a b \sqrt{a+b \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(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)}{d}","\frac{2 b \left(231 a^2-5 b^2\right) \sqrt{a+b \tan (c+d x)}}{315 a d \tan ^{\frac{3}{2}}(c+d x)}+\frac{2 \left(21 a^2-25 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 b^2+315 a^4-10 b^4\right) \sqrt{a+b \tan (c+d x)}}{315 a^2 d \sqrt{\tan (c+d x)}}-\frac{2 a^2 \sqrt{a+b \tan (c+d x)}}{9 d \tan ^{\frac{9}{2}}(c+d x)}+\frac{(-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)}{d}-\frac{38 a b \sqrt{a+b \tan (c+d x)}}{63 d \tan ^{\frac{7}{2}}(c+d x)}-\frac{(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)}{d}",1,"((I*a - b)^(5/2)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - ((I*a + b)^(5/2)*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/d - (2*a^2*Sqrt[a + b*Tan[c + d*x]])/(9*d*Tan[c + d*x]^(9/2)) - (38*a*b*Sqrt[a + b*Tan[c + d*x]])/(63*d*Tan[c + d*x]^(7/2)) + (2*(21*a^2 - 25*b^2)*Sqrt[a + b*Tan[c + d*x]])/(105*d*Tan[c + d*x]^(5/2)) + (2*b*(231*a^2 - 5*b^2)*Sqrt[a + b*Tan[c + d*x]])/(315*a*d*Tan[c + d*x]^(3/2)) - (2*(315*a^4 - 483*a^2*b^2 - 10*b^4)*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d*Sqrt[Tan[c + d*x]])","A",12,7,25,0.2800,1,"{3565, 3649, 3616, 3615, 93, 203, 206}"
632,1,232,0,0.9893457,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(7/2)/Sqrt[a + b*Tan[c + d*x]],x]","\frac{\left(3 a^2-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{5/2} d}-\frac{3 a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b^2 d}+\frac{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 b d}+\frac{\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{\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{\left(3 a^2-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{4 b^{5/2} d}-\frac{3 a \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{4 b^2 d}+\frac{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{2 b d}+\frac{\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{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a - b]*d) + ((3*a^2 - 8*b^2)*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(4*b^(5/2)*d) + ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a + b]*d) - (3*a*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(4*b^2*d) + (Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(2*b*d)","A",14,11,25,0.4400,1,"{3566, 3647, 3656, 6725, 63, 217, 206, 912, 93, 205, 208}"
633,1,188,0,0.7095904,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(5/2)/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{i \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{\sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b d}+\frac{i \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 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}-\frac{i \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{\sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b d}+\frac{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) - (a*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(3/2)*d) + (I*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) + (Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(b*d)","A",13,10,25,0.4000,1,"{3566, 3655, 6725, 63, 217, 206, 910, 93, 205, 208}"
634,1,152,0,0.1714333,"\int \frac{\tan ^{\frac{3}{2}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(3/2)/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{\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 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\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{\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 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{\sqrt{b} d}-\frac{\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,"-(ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a - b]*d)) + (2*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[b]*d) - ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a + b]*d)","A",12,9,25,0.3600,1,"{3575, 910, 63, 217, 206, 912, 93, 205, 208}"
635,1,115,0,0.1296803,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[a + b*Tan[c + d*x]],x]","\frac{i \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 \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 \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 \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) - (I*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d)","A",7,5,25,0.2000,1,"{3575, 910, 93, 205, 208}"
636,1,109,0,0.1262385,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{\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{\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{\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{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a - b]*d) + ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a + b]*d)","A",7,5,25,0.2000,1,"{3575, 912, 93, 205, 208}"
637,1,147,0,0.1975704,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]),x]","-\frac{i \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 \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{i \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 \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 \sqrt{a+b \tan (c+d x)}}{a d \sqrt{\tan (c+d x)}}+\frac{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) + (I*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*Sqrt[a + b*Tan[c + d*x]])/(a*d*Sqrt[Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3569, 12, 3575, 910, 93, 205, 208}"
638,1,180,0,0.3481554,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{4 b \sqrt{a+b \tan (c+d x)}}{3 a^2 d \sqrt{\tan (c+d x)}}-\frac{\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 \sqrt{a+b \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\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{4 b \sqrt{a+b \tan (c+d x)}}{3 a^2 d \sqrt{\tan (c+d x)}}-\frac{\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 \sqrt{a+b \tan (c+d x)}}{3 a d \tan ^{\frac{3}{2}}(c+d x)}-\frac{\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,"-(ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a - b]*d)) - ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/(Sqrt[I*a + b]*d) - (2*Sqrt[a + b*Tan[c + d*x]])/(3*a*d*Tan[c + d*x]^(3/2)) + (4*b*Sqrt[a + b*Tan[c + d*x]])/(3*a^2*d*Sqrt[Tan[c + d*x]])","A",10,8,25,0.3200,1,"{3569, 3649, 12, 3575, 912, 93, 205, 208}"
639,1,229,0,0.5007207,"\int \frac{1}{\tan ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{2 \left(15 a^2-8 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^3 d \sqrt{\tan (c+d x)}}+\frac{8 b \sqrt{a+b \tan (c+d x)}}{15 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{i \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 \sqrt{a+b \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{i \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 \left(15 a^2-8 b^2\right) \sqrt{a+b \tan (c+d x)}}{15 a^3 d \sqrt{\tan (c+d x)}}+\frac{8 b \sqrt{a+b \tan (c+d x)}}{15 a^2 d \tan ^{\frac{3}{2}}(c+d x)}+\frac{i \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 \sqrt{a+b \tan (c+d x)}}{5 a d \tan ^{\frac{5}{2}}(c+d x)}-\frac{i \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a - b]*d) - (I*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(Sqrt[I*a + b]*d) - (2*Sqrt[a + b*Tan[c + d*x]])/(5*a*d*Tan[c + d*x]^(5/2)) + (8*b*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d*Tan[c + d*x]^(3/2)) + (2*(15*a^2 - 8*b^2)*Sqrt[a + b*Tan[c + d*x]])/(15*a^3*d*Sqrt[Tan[c + d*x]])","A",11,9,25,0.3600,1,"{3569, 3649, 3650, 12, 3575, 910, 93, 205, 208}"
640,1,250,0,1.5496298,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(7/2)/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(3 a^2+b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}+\frac{i \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{i \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^2 \tan ^{\frac{3}{2}}(c+d x)}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{\left(3 a^2+b^2\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right)}-\frac{3 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}+\frac{i \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{i \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) - (3*a*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(5/2)*d) + (I*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^2*Tan[c + d*x]^(3/2))/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]]) + ((3*a^2 + b^2)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d)","A",14,10,25,0.4000,1,"{3565, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
641,1,195,0,1.2378356,"\int \frac{\tan ^{\frac{5}{2}}(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^(5/2)/(a + b*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}+\frac{\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{\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^2 \sqrt{\tan (c+d x)}}{b d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{3/2} d}+\frac{\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{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(3/2)*d) + (2*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(3/2)*d) - 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^2*Sqrt[Tan[c + d*x]])/(b*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",13,9,25,0.3600,1,"{3565, 3655, 6725, 63, 217, 206, 93, 205, 208}"
642,1,154,0,0.4569644,"\int \frac{\tan ^{\frac{3}{2}}(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])^(3/2),x]","\frac{2 a \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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{\tan (c+d x)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) - (I*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*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,6,25,0.2400,1,"{3567, 3616, 3615, 93, 203, 206}"
643,1,149,0,0.4532284,"\int \frac{\sqrt{\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])^(3/2),x]","-\frac{2 b \sqrt{\tan (c+d x)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{\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{\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)}}{d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}-\frac{\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{\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,"-(ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(3/2)*d)) + 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*Sqrt[Tan[c + d*x]])/((a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,6,25,0.2400,1,"{3568, 3616, 3615, 93, 203, 206}"
644,1,159,0,0.4656836,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 b^2 \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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^2 \sqrt{\tan (c+d x)}}{a d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) + (I*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^2*Sqrt[Tan[c + d*x]])/(a*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",8,6,25,0.2400,1,"{3569, 3616, 3615, 93, 203, 206}"
645,1,193,0,0.6444994,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 b \left(a^2+2 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{\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{2}{a d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{\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 \left(a^2+2 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{\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{2}{a d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(3/2)*d) - 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*d*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) - (2*b*(a^2 + 2*b^2)*Sqrt[Tan[c + d*x]])/(a^2*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3569, 3649, 3616, 3615, 93, 203, 206}"
646,1,241,0,0.8299334,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 b^2 \left(5 a^2+8 b^2\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{8 b}{3 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{i \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{2}{3 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}-\frac{i \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^2 \left(5 a^2+8 b^2\right) \sqrt{\tan (c+d x)}}{3 a^3 d \left(a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}+\frac{8 b}{3 a^2 d \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{i \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{2}{3 a d \tan ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}-\frac{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(3/2)*d) - (I*ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a + b)^(3/2)*d) - 2/(3*a*d*Tan[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]) + (8*b)/(3*a^2*d*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) + (2*b^2*(5*a^2 + 8*b^2)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)*d*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{3569, 3649, 3650, 3616, 3615, 93, 203, 206}"
647,1,317,0,2.1049233,"\int \frac{\tan ^{\frac{9}{2}}(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(9/2)/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \tan ^{\frac{5}{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(5 a^2+11 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{\left(10 a^2 b^2+5 a^4+b^4\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b^3 d \left(a^2+b^2\right)^2}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{7/2} d}-\frac{i \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{i \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^2 \tan ^{\frac{5}{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(5 a^2+11 b^2\right) \tan ^{\frac{3}{2}}(c+d x)}{3 b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{\left(10 a^2 b^2+5 a^4+b^4\right) \sqrt{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}{b^3 d \left(a^2+b^2\right)^2}-\frac{5 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{7/2} d}-\frac{i \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{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) - (5*a*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(7/2)*d) + (I*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^2*Tan[c + d*x]^(5/2))/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*a^2*(5*a^2 + 11*b^2)*Tan[c + d*x]^(3/2))/(3*b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]]) + ((5*a^4 + 10*a^2*b^2 + b^4)*Sqrt[Tan[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(b^3*(a^2 + b^2)^2*d)","A",15,11,25,0.4400,1,"{3565, 3645, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
648,1,251,0,1.7568863,"\int \frac{\tan ^{\frac{7}{2}}(c+d x)}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Tan[c + d*x]^(7/2)/(a + b*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \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^2 \left(a^2+3 b^2\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}-\frac{\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{\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^2 \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^2 \left(a^2+3 b^2\right) \sqrt{\tan (c+d x)}}{b^2 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}}\right)}{b^{5/2} d}-\frac{\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{\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,"-(ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(5/2)*d)) + (2*ArcTanh[(Sqrt[b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/(b^(5/2)*d) - 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^2*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^2 + 3*b^2)*Sqrt[Tan[c + d*x]])/(b^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",14,10,25,0.4000,1,"{3565, 3645, 3655, 6725, 63, 217, 206, 93, 205, 208}"
649,1,214,0,0.7508949,"\int \frac{\tan ^{\frac{5}{2}}(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])^(5/2),x]","-\frac{2 a^2 \sqrt{\tan (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+7 b^2\right) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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^2 \sqrt{\tan (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+7 b^2\right) \sqrt{\tan (c+d x)}}{3 b d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) - (I*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^2*Sqrt[Tan[c + d*x]])/(3*b*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(a^2 + 7*b^2)*Sqrt[Tan[c + d*x]])/(3*b*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3565, 3649, 3616, 3615, 93, 203, 206}"
650,1,199,0,0.6762325,"\int \frac{\tan ^{\frac{3}{2}}(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])^(5/2),x]","\frac{2 a \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 \left(a^2-2 b^2\right) \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{\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{\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{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}+\frac{4 \left(a^2-2 b^2\right) \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}+\frac{\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{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(5/2)*d) + 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*Sqrt[Tan[c + d*x]])/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (4*(a^2 - 2*b^2)*Sqrt[Tan[c + d*x]])/(3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3567, 3649, 3616, 3615, 93, 203, 206}"
651,1,211,0,0.7048569,"\int \frac{\sqrt{\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])^(5/2),x]","-\frac{2 b \left(5 a^2-b^2\right) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{i \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{i \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 \left(5 a^2-b^2\right) \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right)^2 \sqrt{a+b \tan (c+d x)}}-\frac{2 b \sqrt{\tan (c+d x)}}{3 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{i \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{i \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)*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) + (I*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*Sqrt[Tan[c + d*x]])/(3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(5*a^2 - b^2)*Sqrt[Tan[c + d*x]])/(3*a*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3568, 3649, 3616, 3615, 93, 203, 206}"
652,1,212,0,0.7257872,"\int \frac{1}{\sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{4 b^2 \left(4 a^2+b^2\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{2 b^2 \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{\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{\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{4 b^2 \left(4 a^2+b^2\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{2 b^2 \sqrt{\tan (c+d x)}}{3 a d \left(a^2+b^2\right) (a+b \tan (c+d x))^{3/2}}-\frac{\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{\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,"-(ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(5/2)*d)) - 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^2*Sqrt[Tan[c + d*x]])/(3*a*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (4*b^2*(4*a^2 + b^2)*Sqrt[Tan[c + d*x]])/(3*a^2*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{3569, 3649, 3616, 3615, 93, 203, 206}"
653,1,265,0,0.9590646,"\int \frac{1}{\tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)),x]","-\frac{2 b \left(3 a^2+4 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{2 b \left(17 a^2 b^2+3 a^4+8 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{i \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{2}{a d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{i \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 \left(3 a^2+4 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{2 b \left(17 a^2 b^2+3 a^4+8 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{i \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{2}{a d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{i \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*ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]])/((I*a - b)^(5/2)*d) - (I*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*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^2 + 4*b^2)*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 + 17*a^2*b^2 + 8*b^4)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",10,7,25,0.2800,1,"{3569, 3649, 3616, 3615, 93, 203, 206}"
654,1,298,0,1.180631,"\int \frac{1}{\tan ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Tan[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{4 b^2 \left(15 a^2 b^2+4 a^4+8 b^4\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^2 \left(7 a^2+8 b^2\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{4 b}{a^2 d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{\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{2}{3 a d \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}+\frac{\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{4 b^2 \left(15 a^2 b^2+4 a^4+8 b^4\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^2 \left(7 a^2+8 b^2\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{4 b}{a^2 d \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{\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{2}{3 a d \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}}+\frac{\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,"ArcTan[(Sqrt[I*a - b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a - b)^(5/2)*d) + ArcTanh[(Sqrt[I*a + b]*Sqrt[Tan[c + d*x]])/Sqrt[a + b*Tan[c + d*x]]]/((I*a + b)^(5/2)*d) - 2/(3*a*d*Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)) + (4*b)/(a^2*d*Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*b^2*(7*a^2 + 8*b^2)*Sqrt[Tan[c + d*x]])/(3*a^3*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(3/2)) + (4*b^2*(4*a^4 + 15*a^2*b^2 + 8*b^4)*Sqrt[Tan[c + d*x]])/(3*a^4*(a^2 + b^2)^2*d*Sqrt[a + b*Tan[c + d*x]])","A",11,8,25,0.3200,1,"{3569, 3649, 3650, 3616, 3615, 93, 203, 206}"
655,1,89,0,0.1228899,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{2+3 \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[2 + 3*Tan[c + d*x]]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3-2 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3+2 i} d}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3-2 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3+2 i} d}",1,"ArcTanh[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 + 3*Tan[c + d*x]]]/(Sqrt[3 - 2*I]*d) + ArcTanh[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 + 3*Tan[c + d*x]]]/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 208}"
656,1,89,0,0.1064329,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{-2+3 \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[-2 + 3*Tan[c + d*x]]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}","\frac{\tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}",1,"ArcTanh[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 + 3*Tan[c + d*x]]]/(Sqrt[3 - 2*I]*d) + ArcTanh[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 + 3*Tan[c + d*x]]]/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 208}"
657,1,89,0,0.1075055,"\int \frac{1}{\sqrt{2-3 \tan (c+d x)} \sqrt{\tan (c+d x)}} \, dx","Int[1/(Sqrt[2 - 3*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3-2 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3+2 i} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3-2 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3+2 i} d}",1,"ArcTan[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 - 3*Tan[c + d*x]]]/(Sqrt[3 - 2*I]*d) + ArcTan[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 - 3*Tan[c + d*x]]]/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 205}"
658,1,89,0,0.1064502,"\int \frac{1}{\sqrt{-2-3 \tan (c+d x)} \sqrt{\tan (c+d x)}} \, dx","Int[1/(Sqrt[-2 - 3*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}",1,"ArcTan[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 - 3*Tan[c + d*x]]]/(Sqrt[3 - 2*I]*d) + ArcTan[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 - 3*Tan[c + d*x]]]/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 205}"
659,1,89,0,0.1176605,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{3+2 \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[3 + 2*Tan[c + d*x]]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2-3 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2+3 i} d}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2-3 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2+3 i} d}",1,"ArcTanh[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 + 2*Tan[c + d*x]]]/(Sqrt[2 - 3*I]*d) + ArcTanh[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 + 2*Tan[c + d*x]]]/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 208}"
660,1,89,0,0.1034892,"\int \frac{1}{\sqrt{3-2 \tan (c+d x)} \sqrt{\tan (c+d x)}} \, dx","Int[1/(Sqrt[3 - 2*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2-3 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2+3 i} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2-3 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2+3 i} d}",1,"ArcTan[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 - 2*Tan[c + d*x]]]/(Sqrt[2 - 3*I]*d) + ArcTan[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 - 2*Tan[c + d*x]]]/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 205}"
661,1,89,0,0.0994763,"\int \frac{1}{\sqrt{\tan (c+d x)} \sqrt{-3+2 \tan (c+d x)}} \, dx","Int[1/(Sqrt[Tan[c + d*x]]*Sqrt[-3 + 2*Tan[c + d*x]]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}",1,"ArcTanh[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 + 2*Tan[c + d*x]]]/(Sqrt[2 - 3*I]*d) + ArcTanh[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 + 2*Tan[c + d*x]]]/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 208}"
662,1,89,0,0.1010336,"\int \frac{1}{\sqrt{-3-2 \tan (c+d x)} \sqrt{\tan (c+d x)}} \, dx","Int[1/(Sqrt[-3 - 2*Tan[c + d*x]]*Sqrt[Tan[c + d*x]]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}+\frac{\tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}",1,"ArcTan[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 - 2*Tan[c + d*x]]]/(Sqrt[2 - 3*I]*d) + ArcTan[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 - 2*Tan[c + d*x]]]/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 912, 93, 205}"
663,1,95,0,0.098205,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{2+3 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[2 + 3*Tan[c + d*x]],x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3-2 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3+2 i} d}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3-2 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)+2}}\right)}{\sqrt{3+2 i} d}",1,"(I*ArcTanh[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 + 3*Tan[c + d*x]]])/(Sqrt[3 - 2*I]*d) - (I*ArcTanh[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 + 3*Tan[c + d*x]]])/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 208}"
664,1,95,0,0.0967733,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{-2+3 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[-2 + 3*Tan[c + d*x]],x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}",1,"((-I)*ArcTanh[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 + 3*Tan[c + d*x]]])/(Sqrt[3 - 2*I]*d) + (I*ArcTanh[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 + 3*Tan[c + d*x]]])/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 208}"
665,1,95,0,0.098106,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[2 - 3*Tan[c + d*x]],x]","\frac{i \tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3+2 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3-2 i} d}","\frac{i \tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3+2 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{2-3 \tan (c+d x)}}\right)}{\sqrt{3-2 i} d}",1,"((-I)*ArcTan[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 - 3*Tan[c + d*x]]])/(Sqrt[3 - 2*I]*d) + (I*ArcTan[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[2 - 3*Tan[c + d*x]]])/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 205}"
666,1,95,0,0.0984915,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{-2-3 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[-2 - 3*Tan[c + d*x]],x]","\frac{i \tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}","\frac{i \tan ^{-1}\left(\frac{\sqrt{3-2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3-2 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{3+2 i} \sqrt{\tan (c+d x)}}{\sqrt{-3 \tan (c+d x)-2}}\right)}{\sqrt{3+2 i} d}",1,"(I*ArcTan[(Sqrt[3 - 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 - 3*Tan[c + d*x]]])/(Sqrt[3 - 2*I]*d) - (I*ArcTan[(Sqrt[3 + 2*I]*Sqrt[Tan[c + d*x]])/Sqrt[-2 - 3*Tan[c + d*x]]])/(Sqrt[3 + 2*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 205}"
667,1,95,0,0.0949088,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{3+2 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[3 + 2*Tan[c + d*x]],x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2-3 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2+3 i} d}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2-3 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)+3}}\right)}{\sqrt{2+3 i} d}",1,"(I*ArcTanh[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 + 2*Tan[c + d*x]]])/(Sqrt[2 - 3*I]*d) - (I*ArcTanh[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 + 2*Tan[c + d*x]]])/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 208}"
668,1,95,0,0.096192,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[3 - 2*Tan[c + d*x]],x]","\frac{i \tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2+3 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2-3 i} d}","\frac{i \tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2+3 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{3-2 \tan (c+d x)}}\right)}{\sqrt{2-3 i} d}",1,"((-I)*ArcTan[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 - 2*Tan[c + d*x]]])/(Sqrt[2 - 3*I]*d) + (I*ArcTan[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[3 - 2*Tan[c + d*x]]])/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 205}"
669,1,95,0,0.0930203,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{-3+2 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[-3 + 2*Tan[c + d*x]],x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}",1,"((-I)*ArcTanh[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 + 2*Tan[c + d*x]]])/(Sqrt[2 - 3*I]*d) + (I*ArcTanh[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 + 2*Tan[c + d*x]]])/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 208}"
670,1,95,0,0.093505,"\int \frac{\sqrt{\tan (c+d x)}}{\sqrt{-3-2 \tan (c+d x)}} \, dx","Int[Sqrt[Tan[c + d*x]]/Sqrt[-3 - 2*Tan[c + d*x]],x]","\frac{i \tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}","\frac{i \tan ^{-1}\left(\frac{\sqrt{2-3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2-3 i} d}-\frac{i \tan ^{-1}\left(\frac{\sqrt{2+3 i} \sqrt{\tan (c+d x)}}{\sqrt{-2 \tan (c+d x)-3}}\right)}{\sqrt{2+3 i} d}",1,"(I*ArcTan[(Sqrt[2 - 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 - 2*Tan[c + d*x]]])/(Sqrt[2 - 3*I]*d) - (I*ArcTan[(Sqrt[2 + 3*I]*Sqrt[Tan[c + d*x]])/Sqrt[-3 - 2*Tan[c + d*x]]])/(Sqrt[2 + 3*I]*d)","A",7,4,25,0.1600,1,"{3575, 910, 93, 205}"
671,1,466,0,0.6892277,"\int \frac{\tan ^{\frac{5}{3}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(5/3)/(a + b*Tan[c + d*x]),x]","-\frac{\sqrt{3} a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3} d \left(a^2+b^2\right)}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 b^{2/3} d \left(a^2+b^2\right)}+\frac{a^{5/3} \log (a+b \tan (c+d x))}{2 b^{2/3} d \left(a^2+b^2\right)}","-\frac{\sqrt{3} a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3} d \left(a^2+b^2\right)}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 b^{2/3} d \left(a^2+b^2\right)}+\frac{a^{5/3} \log (a+b \tan (c+d x))}{2 b^{2/3} d \left(a^2+b^2\right)}",1,"-(b*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) + (b*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) - (Sqrt[3]*a^(5/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tan[c + d*x]^(1/3))/(Sqrt[3]*a^(1/3))])/(b^(2/3)*(a^2 + b^2)*d) + (Sqrt[3]*a*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(2*(a^2 + b^2)*d) + (b*ArcTan[Tan[c + d*x]^(1/3)])/((a^2 + b^2)*d) - (3*a^(5/3)*Log[a^(1/3) + b^(1/3)*Tan[c + d*x]^(1/3)])/(2*b^(2/3)*(a^2 + b^2)*d) - (a*Log[1 + Tan[c + d*x]^(2/3)])/(2*(a^2 + b^2)*d) + (Sqrt[3]*b*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) - (Sqrt[3]*b*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (a^(5/3)*Log[a + b*Tan[c + d*x]])/(2*b^(2/3)*(a^2 + b^2)*d) + (a*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(4*(a^2 + b^2)*d)","A",32,18,23,0.7826,1,"{3574, 3528, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203, 3634, 50, 56, 617}"
672,1,465,0,0.5408776,"\int \frac{\sqrt[3]{\tan (c+d x)}}{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^(1/3)/(a + b*Tan[c + d*x]),x]","-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}+\frac{\sqrt{3} \sqrt[3]{a} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{d \left(a^2+b^2\right)}-\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 \sqrt[3]{a} b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{\sqrt[3]{a} b^{2/3} \log (a+b \tan (c+d x))}{2 d \left(a^2+b^2\right)}","-\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}+\frac{\sqrt{3} \sqrt[3]{a} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{d \left(a^2+b^2\right)}-\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 \sqrt[3]{a} b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}+\frac{\sqrt[3]{a} b^{2/3} \log (a+b \tan (c+d x))}{2 d \left(a^2+b^2\right)}",1,"-(b*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) + (b*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) + (Sqrt[3]*a^(1/3)*b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tan[c + d*x]^(1/3))/(Sqrt[3]*a^(1/3))])/((a^2 + b^2)*d) - (Sqrt[3]*a*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(2*(a^2 + b^2)*d) + (b*ArcTan[Tan[c + d*x]^(1/3)])/((a^2 + b^2)*d) - (3*a^(1/3)*b^(2/3)*Log[a^(1/3) + b^(1/3)*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) - (a*Log[1 + Tan[c + d*x]^(2/3)])/(2*(a^2 + b^2)*d) - (Sqrt[3]*b*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (Sqrt[3]*b*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (a^(1/3)*b^(2/3)*Log[a + b*Tan[c + d*x]])/(2*(a^2 + b^2)*d) + (a*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(4*(a^2 + b^2)*d)","A",30,18,23,0.7826,1,"{3574, 3528, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31, 3634, 50, 58, 617}"
673,1,467,0,0.5777284,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} (a+b \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(1/3)*(a + b*Tan[c + d*x])),x]","-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 \sqrt[3]{a} d \left(a^2+b^2\right)}+\frac{b^{4/3} \log (a+b \tan (c+d x))}{2 \sqrt[3]{a} d \left(a^2+b^2\right)}","-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}-\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 \sqrt[3]{a} d \left(a^2+b^2\right)}+\frac{b^{4/3} \log (a+b \tan (c+d x))}{2 \sqrt[3]{a} d \left(a^2+b^2\right)}",1,"(b*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) - (b*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) - (Sqrt[3]*b^(4/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tan[c + d*x]^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(1/3)*(a^2 + b^2)*d) - (Sqrt[3]*a*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(2*(a^2 + b^2)*d) - (b*ArcTan[Tan[c + d*x]^(1/3)])/((a^2 + b^2)*d) - (3*b^(4/3)*Log[a^(1/3) + b^(1/3)*Tan[c + d*x]^(1/3)])/(2*a^(1/3)*(a^2 + b^2)*d) + (a*Log[1 + Tan[c + d*x]^(2/3)])/(2*(a^2 + b^2)*d) - (Sqrt[3]*b*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (Sqrt[3]*b*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (b^(4/3)*Log[a + b*Tan[c + d*x]])/(2*a^(1/3)*(a^2 + b^2)*d) - (a*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(4*(a^2 + b^2)*d)","A",28,16,23,0.6957,1,"{3574, 3538, 3476, 329, 275, 200, 31, 634, 618, 204, 628, 295, 203, 3634, 56, 617}"
674,1,525,0,0.558197,"\int \frac{1}{\tan ^{\frac{5}{3}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Tan[c + d*x]^(5/3)*(a + b*Tan[c + d*x])),x]","\frac{\sqrt{3} b^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} d \left(a^2+b^2\right)}-\frac{3 b^2}{2 a d \left(a^2+b^2\right) \tan ^{\frac{2}{3}}(c+d x)}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{3 a}{2 d \left(a^2+b^2\right) \tan ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 b^{8/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 a^{5/3} d \left(a^2+b^2\right)}+\frac{b^{8/3} \log (a+b \tan (c+d x))}{2 a^{5/3} d \left(a^2+b^2\right)}","\frac{\sqrt{3} b^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sqrt[3]{\tan (c+d x)}}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{5/3} d \left(a^2+b^2\right)}-\frac{3 b^2}{2 a d \left(a^2+b^2\right) \tan ^{\frac{2}{3}}(c+d x)}+\frac{b \tan ^{-1}\left(\sqrt{3}-2 \sqrt[3]{\tan (c+d x)}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(2 \sqrt[3]{\tan (c+d x)}+\sqrt{3}\right)}{2 d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}\left(\sqrt[3]{\tan (c+d x)}\right)}{d \left(a^2+b^2\right)}+\frac{\sqrt{3} a \tan ^{-1}\left(\frac{1-2 \tan ^{\frac{2}{3}}(c+d x)}{\sqrt{3}}\right)}{2 d \left(a^2+b^2\right)}-\frac{3 a}{2 d \left(a^2+b^2\right) \tan ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)-\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}-\frac{\sqrt{3} b \log \left(\tan ^{\frac{2}{3}}(c+d x)+\sqrt{3} \sqrt[3]{\tan (c+d x)}+1\right)}{4 d \left(a^2+b^2\right)}+\frac{a \log \left(\tan ^{\frac{2}{3}}(c+d x)+1\right)}{2 d \left(a^2+b^2\right)}-\frac{a \log \left(\tan ^{\frac{4}{3}}(c+d x)-\tan ^{\frac{2}{3}}(c+d x)+1\right)}{4 d \left(a^2+b^2\right)}-\frac{3 b^{8/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sqrt[3]{\tan (c+d x)}\right)}{2 a^{5/3} d \left(a^2+b^2\right)}+\frac{b^{8/3} \log (a+b \tan (c+d x))}{2 a^{5/3} d \left(a^2+b^2\right)}",1,"(b*ArcTan[Sqrt[3] - 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) - (b*ArcTan[Sqrt[3] + 2*Tan[c + d*x]^(1/3)])/(2*(a^2 + b^2)*d) + (Sqrt[3]*b^(8/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tan[c + d*x]^(1/3))/(Sqrt[3]*a^(1/3))])/(a^(5/3)*(a^2 + b^2)*d) + (Sqrt[3]*a*ArcTan[(1 - 2*Tan[c + d*x]^(2/3))/Sqrt[3]])/(2*(a^2 + b^2)*d) - (b*ArcTan[Tan[c + d*x]^(1/3)])/((a^2 + b^2)*d) - (3*b^(8/3)*Log[a^(1/3) + b^(1/3)*Tan[c + d*x]^(1/3)])/(2*a^(5/3)*(a^2 + b^2)*d) + (a*Log[1 + Tan[c + d*x]^(2/3)])/(2*(a^2 + b^2)*d) + (Sqrt[3]*b*Log[1 - Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) - (Sqrt[3]*b*Log[1 + Sqrt[3]*Tan[c + d*x]^(1/3) + Tan[c + d*x]^(2/3)])/(4*(a^2 + b^2)*d) + (b^(8/3)*Log[a + b*Tan[c + d*x]])/(2*a^(5/3)*(a^2 + b^2)*d) - (a*Log[1 - Tan[c + d*x]^(2/3) + Tan[c + d*x]^(4/3)])/(4*(a^2 + b^2)*d) - (3*a)/(2*(a^2 + b^2)*d*Tan[c + d*x]^(2/3)) - (3*b^2)/(2*a*(a^2 + b^2)*d*Tan[c + d*x]^(2/3))","A",30,18,23,0.7826,1,"{3574, 3529, 3538, 3476, 329, 209, 634, 618, 204, 628, 203, 275, 292, 31, 3634, 51, 58, 617}"
675,1,163,0,0.2642254,"\int \frac{\tan ^{\frac{4}{3}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(4/3)/Sqrt[a + b*Tan[c + d*x]],x]","\frac{3 \tan ^{\frac{7}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{7}{3};1,\frac{1}{2};\frac{10}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{14 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{7}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{7}{3};1,\frac{1}{2};\frac{10}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{14 d \sqrt{a+b \tan (c+d x)}}","\frac{3 \tan ^{\frac{7}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{7}{3};1,\frac{1}{2};\frac{10}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{14 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{7}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{7}{3};1,\frac{1}{2};\frac{10}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{14 d \sqrt{a+b \tan (c+d x)}}",1,"(3*AppellF1[7/3, 1, 1/2, 10/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(7/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(14*d*Sqrt[a + b*Tan[c + d*x]]) + (3*AppellF1[7/3, 1, 1/2, 10/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(7/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(14*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 511, 510}"
676,1,163,0,0.2630647,"\int \frac{\tan ^{\frac{2}{3}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(2/3)/Sqrt[a + b*Tan[c + d*x]],x]","\frac{3 \tan ^{\frac{5}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{5}{3};1,\frac{1}{2};\frac{8}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{10 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{5}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{5}{3};1,\frac{1}{2};\frac{8}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{10 d \sqrt{a+b \tan (c+d x)}}","\frac{3 \tan ^{\frac{5}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{5}{3};1,\frac{1}{2};\frac{8}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{10 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{5}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{5}{3};1,\frac{1}{2};\frac{8}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{10 d \sqrt{a+b \tan (c+d x)}}",1,"(3*AppellF1[5/3, 1, 1/2, 8/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(5/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(10*d*Sqrt[a + b*Tan[c + d*x]]) + (3*AppellF1[5/3, 1, 1/2, 8/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(5/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(10*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 511, 510}"
677,1,163,0,0.2542549,"\int \frac{\sqrt[3]{\tan (c+d x)}}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^(1/3)/Sqrt[a + b*Tan[c + d*x]],x]","\frac{3 \tan ^{\frac{4}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{8 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{4}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{8 d \sqrt{a+b \tan (c+d x)}}","\frac{3 \tan ^{\frac{4}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{8 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{4}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{8 d \sqrt{a+b \tan (c+d x)}}",1,"(3*AppellF1[4/3, 1, 1/2, 7/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(4/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(8*d*Sqrt[a + b*Tan[c + d*x]]) + (3*AppellF1[4/3, 1, 1/2, 7/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(4/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(8*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 511, 510}"
678,1,163,0,0.2323289,"\int \frac{1}{\sqrt[3]{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(1/3)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{3 \tan ^{\frac{2}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{4 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{2}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{4 d \sqrt{a+b \tan (c+d x)}}","\frac{3 \tan ^{\frac{2}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{4 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \tan ^{\frac{2}{3}}(c+d x) \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{4 d \sqrt{a+b \tan (c+d x)}}",1,"(3*AppellF1[2/3, 1, 1/2, 5/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(2/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(4*d*Sqrt[a + b*Tan[c + d*x]]) + (3*AppellF1[2/3, 1, 1/2, 5/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(2/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(4*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 511, 510}"
679,1,163,0,0.2092617,"\int \frac{1}{\tan ^{\frac{2}{3}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(2/3)*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{3 \sqrt[3]{\tan (c+d x)} \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \sqrt[3]{\tan (c+d x)} \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt{a+b \tan (c+d x)}}","\frac{3 \sqrt[3]{\tan (c+d x)} \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt{a+b \tan (c+d x)}}+\frac{3 \sqrt[3]{\tan (c+d x)} \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt{a+b \tan (c+d x)}}",1,"(3*AppellF1[1/3, 1, 1/2, 4/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*Sqrt[a + b*Tan[c + d*x]]) + (3*AppellF1[1/3, 1, 1/2, 4/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Tan[c + d*x]^(1/3)*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 430, 429}"
680,1,163,0,0.2609912,"\int \frac{1}{\tan ^{\frac{4}{3}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Tan[c + d*x]^(4/3)*Sqrt[a + b*Tan[c + d*x]]),x]","-\frac{3 \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt[3]{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{3 \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt[3]{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}","-\frac{3 \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt[3]{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{3 \sqrt{\frac{b \tan (c+d x)}{a}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};i \tan (c+d x),-\frac{b \tan (c+d x)}{a}\right)}{2 d \sqrt[3]{\tan (c+d x)} \sqrt{a+b \tan (c+d x)}}",1,"(-3*AppellF1[-1/3, 1, 1/2, 2/3, (-I)*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*Tan[c + d*x]^(1/3)*Sqrt[a + b*Tan[c + d*x]]) - (3*AppellF1[-1/3, 1, 1/2, 2/3, I*Tan[c + d*x], -((b*Tan[c + d*x])/a)]*Sqrt[1 + (b*Tan[c + d*x])/a])/(2*d*Tan[c + d*x]^(1/3)*Sqrt[a + b*Tan[c + d*x]])","A",9,5,25,0.2000,1,"{3575, 912, 130, 511, 510}"
681,1,525,0,0.7818698,"\int \tan ^4(e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Tan[e + f*x]^4*(c + d*Tan[e + f*x])^(1/3),x]","\frac{3 \left(9 c^2-35 d^2\right) (c+d \tan (e+f x))^{4/3}}{140 d^3 f}-\frac{\sqrt{3} \sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 d f}+\frac{\sqrt{3} \sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 d f}-\frac{9 c \tan (e+f x) (c+d \tan (e+f x))^{4/3}}{35 d^2 f}+\frac{3 \sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 d f}-\frac{3 \sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 d f}+\frac{\sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 d f}-\frac{\sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 d f}-\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}-\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}+\frac{3 \tan ^2(e+f x) (c+d \tan (e+f x))^{4/3}}{10 d f}","\frac{3 \left(9 c^2-35 d^2\right) (c+d \tan (e+f x))^{4/3}}{140 d^3 f}-\frac{\sqrt{3} \sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 d f}+\frac{\sqrt{3} \sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 d f}-\frac{9 c \tan (e+f x) (c+d \tan (e+f x))^{4/3}}{35 d^2 f}+\frac{3 \sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 d f}-\frac{3 \sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 d f}+\frac{\sqrt{-d^2} \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 d f}-\frac{\sqrt{-d^2} \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 d f}-\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}-\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}+\frac{3 \tan ^2(e+f x) (c+d \tan (e+f x))^{4/3}}{10 d f}",1,"-((c - Sqrt[-d^2])^(1/3)*x)/4 - ((c + Sqrt[-d^2])^(1/3)*x)/4 - (Sqrt[3]*Sqrt[-d^2]*(c - Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*d*f) + (Sqrt[3]*Sqrt[-d^2]*(c + Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c + Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*d*f) + (Sqrt[-d^2]*(c - Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*d*f) - (Sqrt[-d^2]*(c + Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*d*f) + (3*Sqrt[-d^2]*(c - Sqrt[-d^2])^(1/3)*Log[(c - Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*d*f) - (3*Sqrt[-d^2]*(c + Sqrt[-d^2])^(1/3)*Log[(c + Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*d*f) + (3*(9*c^2 - 35*d^2)*(c + d*Tan[e + f*x])^(4/3))/(140*d^3*f) - (9*c*Tan[e + f*x]*(c + d*Tan[e + f*x])^(4/3))/(35*d^2*f) + (3*Tan[e + f*x]^2*(c + d*Tan[e + f*x])^(4/3))/(10*d*f)","A",16,10,23,0.4348,1,"{3566, 3647, 3631, 3485, 712, 50, 57, 617, 204, 31}"
682,1,373,0,0.5578035,"\int \tan ^3(e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Tan[e + f*x]^3*(c + d*Tan[e + f*x])^(1/3),x]","-\frac{9 c (c+d \tan (e+f x))^{4/3}}{28 d^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{\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 \tan (e+f x) (c+d \tan (e+f x))^{4/3}}{7 d f}-\frac{3 \sqrt[3]{c+d \tan (e+f x)}}{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{9 c (c+d \tan (e+f x))^{4/3}}{28 d^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{\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 \tan (e+f x) (c+d \tan (e+f x))^{4/3}}{7 d f}-\frac{3 \sqrt[3]{c+d \tan (e+f x)}}{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) - (3*(c + d*Tan[e + f*x])^(1/3))/f - (9*c*(c + d*Tan[e + f*x])^(4/3))/(28*d^2*f) + (3*Tan[e + f*x]*(c + d*Tan[e + f*x])^(4/3))/(7*d*f)","A",15,10,23,0.4348,1,"{3566, 3630, 12, 3528, 3539, 3537, 57, 617, 204, 31}"
683,1,439,0,0.3131671,"\int \tan ^2(e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Tan[e + f*x]^2*(c + d*Tan[e + f*x])^(1/3),x]","-\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}+\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}+\frac{3 (c+d \tan (e+f x))^{4/3}}{4 d f}","-\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}+\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}+\frac{3 (c+d \tan (e+f x))^{4/3}}{4 d f}",1,"((c - Sqrt[-d^2])^(1/3)*x)/4 + ((c + Sqrt[-d^2])^(1/3)*x)/4 - (Sqrt[3]*d*(c - Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) + (Sqrt[3]*d*(c + Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c + Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) + (d*(c - Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) - (d*(c + Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) + (3*d*(c - Sqrt[-d^2])^(1/3)*Log[(c - Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f) - (3*d*(c + Sqrt[-d^2])^(1/3)*Log[(c + Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f) + (3*(c + d*Tan[e + f*x])^(4/3))/(4*d*f)","A",14,8,23,0.3478,1,"{3543, 3485, 712, 50, 57, 617, 204, 31}"
684,1,318,0,0.2997198,"\int \tan (e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Tan[e + f*x]*(c + d*Tan[e + f*x])^(1/3),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+d \tan (e+f x)}}{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+d \tan (e+f x)}}{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) + (3*(c + d*Tan[e + f*x])^(1/3))/f","A",12,7,21,0.3333,1,"{3528, 3539, 3537, 57, 617, 204, 31}"
685,1,415,0,0.2461005,"\int \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^(1/3),x]","\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}-\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}-\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}","\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}-\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}-\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}",1,"-((c - Sqrt[-d^2])^(1/3)*x)/4 - ((c + Sqrt[-d^2])^(1/3)*x)/4 + (Sqrt[3]*d*(c - Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) - (Sqrt[3]*d*(c + Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c + Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) - (d*(c - Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) + (d*(c + Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) - (3*d*(c - Sqrt[-d^2])^(1/3)*Log[(c - Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f) + (3*d*(c + Sqrt[-d^2])^(1/3)*Log[(c + Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f)","A",13,7,14,0.5000,1,"{3485, 712, 50, 57, 617, 204, 31}"
686,1,402,0,0.4775613,"\int \cot (e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Cot[e + f*x]*(c + d*Tan[e + f*x])^(1/3),x]","-\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{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{\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} \log \left(\sqrt[3]{c}-\sqrt[3]{c+d \tan (e+f x)}\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]{c} \log (\tan (e+f x))}{2 f}","-\frac{\sqrt{3} \sqrt[3]{c} \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{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{\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} \log \left(\sqrt[3]{c}-\sqrt[3]{c+d \tan (e+f x)}\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]{c} \log (\tan (e+f x))}{2 f}",1,"(-I/4)*(c - I*d)^(1/3)*x + (I/4)*(c + I*d)^(1/3)*x - (Sqrt[3]*c^(1/3)*ArcTan[(c^(1/3) + 2*(c + d*Tan[e + f*x])^(1/3))/(Sqrt[3]*c^(1/3))])/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) + (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) - (c^(1/3)*Log[Tan[e + f*x]])/(2*f) + (3*c^(1/3)*Log[c^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(2*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",19,10,21,0.4762,1,"{3574, 3528, 3539, 3537, 57, 617, 204, 31, 3634, 50}"
687,1,546,0,0.5815057,"\int \cot ^2(e+f x) \sqrt[3]{c+d \tan (e+f x)} \, dx","Int[Cot[e + f*x]^2*(c + d*Tan[e + f*x])^(1/3),x]","-\frac{d \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} f}-\frac{d \log (\tan (e+f x))}{6 c^{2/3} f}+\frac{d \log \left(\sqrt[3]{c}-\sqrt[3]{c+d \tan (e+f x)}\right)}{2 c^{2/3} f}-\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}+\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}-\frac{\cot (e+f x) \sqrt[3]{c+d \tan (e+f x)}}{f}","-\frac{d \tan ^{-1}\left(\frac{2 \sqrt[3]{c+d \tan (e+f x)}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} f}-\frac{d \log (\tan (e+f x))}{6 c^{2/3} f}+\frac{d \log \left(\sqrt[3]{c}-\sqrt[3]{c+d \tan (e+f x)}\right)}{2 c^{2/3} f}-\frac{\sqrt{3} d \sqrt[3]{c-\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c-\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{\sqrt{3} d \sqrt[3]{c+\sqrt{-d^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{c+d \tan (e+f x)}}{\sqrt[3]{c+\sqrt{-d^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-d^2} f}+\frac{3 d \sqrt[3]{c-\sqrt{-d^2}} \log \left(\sqrt[3]{c-\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}-\frac{3 d \sqrt[3]{c+\sqrt{-d^2}} \log \left(\sqrt[3]{c+\sqrt{-d^2}}-\sqrt[3]{c+d \tan (e+f x)}\right)}{4 \sqrt{-d^2} f}+\frac{d \sqrt[3]{c-\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}-\frac{d \sqrt[3]{c+\sqrt{-d^2}} \log (\cos (e+f x))}{4 \sqrt{-d^2} f}+\frac{1}{4} x \sqrt[3]{c-\sqrt{-d^2}}+\frac{1}{4} x \sqrt[3]{c+\sqrt{-d^2}}-\frac{\cot (e+f x) \sqrt[3]{c+d \tan (e+f x)}}{f}",1,"((c - Sqrt[-d^2])^(1/3)*x)/4 + ((c + Sqrt[-d^2])^(1/3)*x)/4 - (d*ArcTan[(c^(1/3) + 2*(c + d*Tan[e + f*x])^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*f) - (Sqrt[3]*d*(c - Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c - Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) + (Sqrt[3]*d*(c + Sqrt[-d^2])^(1/3)*ArcTan[(1 + (2*(c + d*Tan[e + f*x])^(1/3))/(c + Sqrt[-d^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-d^2]*f) + (d*(c - Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) - (d*(c + Sqrt[-d^2])^(1/3)*Log[Cos[e + f*x]])/(4*Sqrt[-d^2]*f) - (d*Log[Tan[e + f*x]])/(6*c^(2/3)*f) + (d*Log[c^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(2*c^(2/3)*f) + (3*d*(c - Sqrt[-d^2])^(1/3)*Log[(c - Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f) - (3*d*(c + Sqrt[-d^2])^(1/3)*Log[(c + Sqrt[-d^2])^(1/3) - (c + d*Tan[e + f*x])^(1/3)])/(4*Sqrt[-d^2]*f) - (Cot[e + f*x]*(c + d*Tan[e + f*x])^(1/3))/f","A",20,10,23,0.4348,1,"{3568, 3653, 3485, 712, 50, 57, 617, 204, 31, 3634}"
688,1,329,0,0.3760905,"\int (a+b \tan (c+d x))^{5/3} \, dx","Int[(a + b*Tan[c + d*x])^(5/3),x]","\frac{i \sqrt{3} (a-i b)^{5/3} \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{i \sqrt{3} (a+i b)^{5/3} \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 b (a+b \tan (c+d x))^{2/3}}{2 d}+\frac{3 i (a-i b)^{5/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 i (a+i b)^{5/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}+\frac{i (a-i b)^{5/3} \log (\cos (c+d x))}{4 d}-\frac{i (a+i b)^{5/3} \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{5/3}-\frac{1}{4} x (a+i b)^{5/3}","\frac{i \sqrt{3} (a-i b)^{5/3} \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{i \sqrt{3} (a+i b)^{5/3} \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 b (a+b \tan (c+d x))^{2/3}}{2 d}+\frac{3 i (a-i b)^{5/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 i (a+i b)^{5/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}+\frac{i (a-i b)^{5/3} \log (\cos (c+d x))}{4 d}-\frac{i (a+i b)^{5/3} \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{5/3}-\frac{1}{4} x (a+i b)^{5/3}",1,"-((a - I*b)^(5/3)*x)/4 - ((a + I*b)^(5/3)*x)/4 + ((I/2)*Sqrt[3]*(a - I*b)^(5/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/d - ((I/2)*Sqrt[3]*(a + I*b)^(5/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/d + ((I/4)*(a - I*b)^(5/3)*Log[Cos[c + d*x]])/d - ((I/4)*(a + I*b)^(5/3)*Log[Cos[c + d*x]])/d + (((3*I)/4)*(a - I*b)^(5/3)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/d - (((3*I)/4)*(a + I*b)^(5/3)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/d + (3*b*(a + b*Tan[c + d*x])^(2/3))/(2*d)","A",12,7,14,0.5000,1,"{3482, 3539, 3537, 55, 617, 204, 31}"
689,1,327,0,0.3604445,"\int (a+b \tan (c+d x))^{4/3} \, dx","Int[(a + b*Tan[c + d*x])^(4/3),x]","-\frac{i \sqrt{3} (a-i b)^{4/3} \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{i \sqrt{3} (a+i b)^{4/3} \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 b \sqrt[3]{a+b \tan (c+d x)}}{d}+\frac{3 i (a-i b)^{4/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 i (a+i b)^{4/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}+\frac{i (a-i b)^{4/3} \log (\cos (c+d x))}{4 d}-\frac{i (a+i b)^{4/3} \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{4/3}-\frac{1}{4} x (a+i b)^{4/3}","-\frac{i \sqrt{3} (a-i b)^{4/3} \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{i \sqrt{3} (a+i b)^{4/3} \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 b \sqrt[3]{a+b \tan (c+d x)}}{d}+\frac{3 i (a-i b)^{4/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d}-\frac{3 i (a+i b)^{4/3} \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d}+\frac{i (a-i b)^{4/3} \log (\cos (c+d x))}{4 d}-\frac{i (a+i b)^{4/3} \log (\cos (c+d x))}{4 d}-\frac{1}{4} x (a-i b)^{4/3}-\frac{1}{4} x (a+i b)^{4/3}",1,"-((a - I*b)^(4/3)*x)/4 - ((a + I*b)^(4/3)*x)/4 - ((I/2)*Sqrt[3]*(a - I*b)^(4/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/d + ((I/2)*Sqrt[3]*(a + I*b)^(4/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/d + ((I/4)*(a - I*b)^(4/3)*Log[Cos[c + d*x]])/d - ((I/4)*(a + I*b)^(4/3)*Log[Cos[c + d*x]])/d + (((3*I)/4)*(a - I*b)^(4/3)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/d - (((3*I)/4)*(a + I*b)^(4/3)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/d + (3*b*(a + b*Tan[c + d*x])^(1/3))/d","A",12,7,14,0.5000,1,"{3482, 3539, 3537, 57, 617, 204, 31}"
690,1,415,0,0.3816126,"\int (a+b \tan (c+d x))^{2/3} \, dx","Int[(a + b*Tan[c + d*x])^(2/3),x]","-\frac{\sqrt{3} b \left(a-\sqrt{-b^2}\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}+\frac{\sqrt{3} b \left(a+\sqrt{-b^2}\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{3 b \left(a-\sqrt{-b^2}\right)^{2/3} \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}+\frac{3 b \left(a+\sqrt{-b^2}\right)^{2/3} \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}-\frac{b \left(a-\sqrt{-b^2}\right)^{2/3} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}+\frac{b \left(a+\sqrt{-b^2}\right)^{2/3} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}-\frac{1}{4} x \left(a-\sqrt{-b^2}\right)^{2/3}-\frac{1}{4} x \left(a+\sqrt{-b^2}\right)^{2/3}","-\frac{\sqrt{3} b \left(a-\sqrt{-b^2}\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}+\frac{\sqrt{3} b \left(a+\sqrt{-b^2}\right)^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{3 b \left(a-\sqrt{-b^2}\right)^{2/3} \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}+\frac{3 b \left(a+\sqrt{-b^2}\right)^{2/3} \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}-\frac{b \left(a-\sqrt{-b^2}\right)^{2/3} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}+\frac{b \left(a+\sqrt{-b^2}\right)^{2/3} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}-\frac{1}{4} x \left(a-\sqrt{-b^2}\right)^{2/3}-\frac{1}{4} x \left(a+\sqrt{-b^2}\right)^{2/3}",1,"-((a - Sqrt[-b^2])^(2/3)*x)/4 - ((a + Sqrt[-b^2])^(2/3)*x)/4 - (Sqrt[3]*b*(a - Sqrt[-b^2])^(2/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*d) + (Sqrt[3]*b*(a + Sqrt[-b^2])^(2/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*d) - (b*(a - Sqrt[-b^2])^(2/3)*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*d) + (b*(a + Sqrt[-b^2])^(2/3)*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*d) - (3*b*(a - Sqrt[-b^2])^(2/3)*Log[(a - Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*d) + (3*b*(a + Sqrt[-b^2])^(2/3)*Log[(a + Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*d)","A",13,7,14,0.5000,1,"{3485, 712, 50, 55, 617, 204, 31}"
691,1,415,0,0.2917095,"\int \sqrt[3]{a+b \tan (c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(1/3),x]","\frac{\sqrt{3} b \sqrt[3]{a-\sqrt{-b^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{\sqrt{3} b \sqrt[3]{a+\sqrt{-b^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{3 b \sqrt[3]{a-\sqrt{-b^2}} \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}+\frac{3 b \sqrt[3]{a+\sqrt{-b^2}} \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}-\frac{b \sqrt[3]{a-\sqrt{-b^2}} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}+\frac{b \sqrt[3]{a+\sqrt{-b^2}} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}-\frac{1}{4} x \sqrt[3]{a-\sqrt{-b^2}}-\frac{1}{4} x \sqrt[3]{a+\sqrt{-b^2}}","\frac{\sqrt{3} b \sqrt[3]{a-\sqrt{-b^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{\sqrt{3} b \sqrt[3]{a+\sqrt{-b^2}} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d}-\frac{3 b \sqrt[3]{a-\sqrt{-b^2}} \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}+\frac{3 b \sqrt[3]{a+\sqrt{-b^2}} \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d}-\frac{b \sqrt[3]{a-\sqrt{-b^2}} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}+\frac{b \sqrt[3]{a+\sqrt{-b^2}} \log (\cos (c+d x))}{4 \sqrt{-b^2} d}-\frac{1}{4} x \sqrt[3]{a-\sqrt{-b^2}}-\frac{1}{4} x \sqrt[3]{a+\sqrt{-b^2}}",1,"-((a - Sqrt[-b^2])^(1/3)*x)/4 - ((a + Sqrt[-b^2])^(1/3)*x)/4 + (Sqrt[3]*b*(a - Sqrt[-b^2])^(1/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*d) - (Sqrt[3]*b*(a + Sqrt[-b^2])^(1/3)*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*d) - (b*(a - Sqrt[-b^2])^(1/3)*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*d) + (b*(a + Sqrt[-b^2])^(1/3)*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*d) - (3*b*(a - Sqrt[-b^2])^(1/3)*Log[(a - Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*d) + (3*b*(a + Sqrt[-b^2])^(1/3)*Log[(a + Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*d)","A",13,7,14,0.5000,1,"{3485, 712, 50, 57, 617, 204, 31}"
692,1,415,0,0.2635207,"\int \frac{1}{\sqrt[3]{a+b \tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^(-1/3),x]","-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{3 b \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{3 b \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{x}{4 \sqrt[3]{a-\sqrt{-b^2}}}-\frac{x}{4 \sqrt[3]{a+\sqrt{-b^2}}}","-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{3 b \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{3 b \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \sqrt[3]{a-\sqrt{-b^2}}}+\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \sqrt[3]{a+\sqrt{-b^2}}}-\frac{x}{4 \sqrt[3]{a-\sqrt{-b^2}}}-\frac{x}{4 \sqrt[3]{a+\sqrt{-b^2}}}",1,"-x/(4*(a - Sqrt[-b^2])^(1/3)) - x/(4*(a + Sqrt[-b^2])^(1/3)) - (Sqrt[3]*b*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])^(1/3)*d) + (Sqrt[3]*b*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])^(1/3)*d) - (b*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*(a - Sqrt[-b^2])^(1/3)*d) + (b*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*(a + Sqrt[-b^2])^(1/3)*d) - (3*b*Log[(a - Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*(a - Sqrt[-b^2])^(1/3)*d) + (3*b*Log[(a + Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*(a + Sqrt[-b^2])^(1/3)*d)","A",11,6,14,0.4286,1,"{3485, 712, 55, 617, 204, 31}"
693,1,415,0,0.2711494,"\int \frac{1}{(a+b \tan (c+d x))^{2/3}} \, dx","Int[(a + b*Tan[c + d*x])^(-2/3),x]","\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{3 b \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}+\frac{3 b \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}+\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{x}{4 \left(a-\sqrt{-b^2}\right)^{2/3}}-\frac{x}{4 \left(a+\sqrt{-b^2}\right)^{2/3}}","\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a-\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}-\frac{\sqrt{3} b \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{a+b \tan (c+d x)}}{\sqrt[3]{a+\sqrt{-b^2}}}+1}{\sqrt{3}}\right)}{2 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{3 b \log \left(\sqrt[3]{a-\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}+\frac{3 b \log \left(\sqrt[3]{a+\sqrt{-b^2}}-\sqrt[3]{a+b \tan (c+d x)}\right)}{4 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \left(a-\sqrt{-b^2}\right)^{2/3}}+\frac{b \log (\cos (c+d x))}{4 \sqrt{-b^2} d \left(a+\sqrt{-b^2}\right)^{2/3}}-\frac{x}{4 \left(a-\sqrt{-b^2}\right)^{2/3}}-\frac{x}{4 \left(a+\sqrt{-b^2}\right)^{2/3}}",1,"-x/(4*(a - Sqrt[-b^2])^(2/3)) - x/(4*(a + Sqrt[-b^2])^(2/3)) + (Sqrt[3]*b*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])^(2/3)*d) - (Sqrt[3]*b*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + Sqrt[-b^2])^(1/3))/Sqrt[3]])/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])^(2/3)*d) - (b*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*(a - Sqrt[-b^2])^(2/3)*d) + (b*Log[Cos[c + d*x]])/(4*Sqrt[-b^2]*(a + Sqrt[-b^2])^(2/3)*d) - (3*b*Log[(a - Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*(a - Sqrt[-b^2])^(2/3)*d) + (3*b*Log[(a + Sqrt[-b^2])^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/(4*Sqrt[-b^2]*(a + Sqrt[-b^2])^(2/3)*d)","A",11,6,14,0.4286,1,"{3485, 712, 57, 617, 204, 31}"
694,1,336,0,0.3577559,"\int \frac{1}{(a+b \tan (c+d x))^{4/3}} \, dx","Int[(a + b*Tan[c + d*x])^(-4/3),x]","-\frac{3 b}{d \left(a^2+b^2\right) \sqrt[3]{a+b \tan (c+d x)}}+\frac{i \sqrt{3} \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)^{4/3}}-\frac{i \sqrt{3} \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)^{4/3}}+\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{4/3}}-\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{4/3}}+\frac{i \log (\cos (c+d x))}{4 d (a-i b)^{4/3}}-\frac{i \log (\cos (c+d x))}{4 d (a+i b)^{4/3}}-\frac{x}{4 (a-i b)^{4/3}}-\frac{x}{4 (a+i b)^{4/3}}","-\frac{3 b}{d \left(a^2+b^2\right) \sqrt[3]{a+b \tan (c+d x)}}+\frac{i \sqrt{3} \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)^{4/3}}-\frac{i \sqrt{3} \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)^{4/3}}+\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{4/3}}-\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{4/3}}+\frac{i \log (\cos (c+d x))}{4 d (a-i b)^{4/3}}-\frac{i \log (\cos (c+d x))}{4 d (a+i b)^{4/3}}-\frac{x}{4 (a-i b)^{4/3}}-\frac{x}{4 (a+i b)^{4/3}}",1,"-x/(4*(a - I*b)^(4/3)) - x/(4*(a + I*b)^(4/3)) + ((I/2)*Sqrt[3]*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/((a - I*b)^(4/3)*d) - ((I/2)*Sqrt[3]*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/((a + I*b)^(4/3)*d) + ((I/4)*Log[Cos[c + d*x]])/((a - I*b)^(4/3)*d) - ((I/4)*Log[Cos[c + d*x]])/((a + I*b)^(4/3)*d) + (((3*I)/4)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/((a - I*b)^(4/3)*d) - (((3*I)/4)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/((a + I*b)^(4/3)*d) - (3*b)/((a^2 + b^2)*d*(a + b*Tan[c + d*x])^(1/3))","A",12,7,14,0.5000,1,"{3483, 3539, 3537, 55, 617, 204, 31}"
695,1,338,0,0.3611533,"\int \frac{1}{(a+b \tan (c+d x))^{5/3}} \, dx","Int[(a + b*Tan[c + d*x])^(-5/3),x]","-\frac{3 b}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{2/3}}-\frac{i \sqrt{3} \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)^{5/3}}+\frac{i \sqrt{3} \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)^{5/3}}+\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{5/3}}-\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{5/3}}+\frac{i \log (\cos (c+d x))}{4 d (a-i b)^{5/3}}-\frac{i \log (\cos (c+d x))}{4 d (a+i b)^{5/3}}-\frac{x}{4 (a-i b)^{5/3}}-\frac{x}{4 (a+i b)^{5/3}}","-\frac{3 b}{2 d \left(a^2+b^2\right) (a+b \tan (c+d x))^{2/3}}-\frac{i \sqrt{3} \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)^{5/3}}+\frac{i \sqrt{3} \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)^{5/3}}+\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a-i b}\right)}{4 d (a-i b)^{5/3}}-\frac{3 i \log \left(-\sqrt[3]{a+b \tan (c+d x)}+\sqrt[3]{a+i b}\right)}{4 d (a+i b)^{5/3}}+\frac{i \log (\cos (c+d x))}{4 d (a-i b)^{5/3}}-\frac{i \log (\cos (c+d x))}{4 d (a+i b)^{5/3}}-\frac{x}{4 (a-i b)^{5/3}}-\frac{x}{4 (a+i b)^{5/3}}",1,"-x/(4*(a - I*b)^(5/3)) - x/(4*(a + I*b)^(5/3)) - ((I/2)*Sqrt[3]*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a - I*b)^(1/3))/Sqrt[3]])/((a - I*b)^(5/3)*d) + ((I/2)*Sqrt[3]*ArcTan[(1 + (2*(a + b*Tan[c + d*x])^(1/3))/(a + I*b)^(1/3))/Sqrt[3]])/((a + I*b)^(5/3)*d) + ((I/4)*Log[Cos[c + d*x]])/((a - I*b)^(5/3)*d) - ((I/4)*Log[Cos[c + d*x]])/((a + I*b)^(5/3)*d) + (((3*I)/4)*Log[(a - I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/((a - I*b)^(5/3)*d) - (((3*I)/4)*Log[(a + I*b)^(1/3) - (a + b*Tan[c + d*x])^(1/3)])/((a + I*b)^(5/3)*d) - (3*b)/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x])^(2/3))","A",12,7,14,0.5000,1,"{3483, 3539, 3537, 57, 617, 204, 31}"
696,1,261,0,0.640625,"\int (d \tan (e+f x))^n (a+b \tan (e+f x))^4 \, dx","Int[(d*Tan[e + f*x])^n*(a + b*Tan[e + f*x])^4,x]","\frac{4 a b \left(a^2-b^2\right) (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}-\frac{b^2 \left(b^2 (n+3)-a^2 (5 n+17)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+3)}+\frac{b^2 (a+b \tan (e+f x))^2 (d \tan (e+f x))^{n+1}}{d f (n+3)}+\frac{2 a b^3 (n+4) \tan (e+f x) (d \tan (e+f x))^{n+1}}{d f (n+2) (n+3)}","\frac{4 a b \left(a^2-b^2\right) (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{\left(-6 a^2 b^2+a^4+b^4\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}-\frac{b^2 \left(b^2 (n+3)-a^2 (5 n+17)\right) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+3)}+\frac{b^2 (a+b \tan (e+f x))^2 (d \tan (e+f x))^{n+1}}{d f (n+3)}+\frac{2 a b^3 (n+4) \tan (e+f x) (d \tan (e+f x))^{n+1}}{d f (n+2) (n+3)}",1,"-((b^2*(b^2*(3 + n) - a^2*(17 + 5*n))*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*(3 + n))) + ((a^4 - 6*a^2*b^2 + b^4)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) + (2*a*b^3*(4 + n)*Tan[e + f*x]*(d*Tan[e + f*x])^(1 + n))/(d*f*(2 + n)*(3 + n)) + (4*a*b*(a^2 - b^2)*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(d^2*f*(2 + n)) + (b^2*(d*Tan[e + f*x])^(1 + n)*(a + b*Tan[e + f*x])^2)/(d*f*(3 + n))","A",8,6,23,0.2609,1,"{3566, 3637, 3630, 3538, 3476, 364}"
697,1,198,0,0.2810344,"\int (d \tan (e+f x))^n (a+b \tan (e+f x))^3 \, dx","Int[(d*Tan[e + f*x])^n*(a + b*Tan[e + f*x])^3,x]","\frac{b \left(3 a^2-b^2\right) (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{a \left(a^2-3 b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{a b^2 (2 n+5) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2)}+\frac{b^2 (a+b \tan (e+f x)) (d \tan (e+f x))^{n+1}}{d f (n+2)}","\frac{b \left(3 a^2-b^2\right) (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{a \left(a^2-3 b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{a b^2 (2 n+5) (d \tan (e+f x))^{n+1}}{d f (n+1) (n+2)}+\frac{b^2 (a+b \tan (e+f x)) (d \tan (e+f x))^{n+1}}{d f (n+2)}",1,"(a*b^2*(5 + 2*n)*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n)) + (a*(a^2 - 3*b^2)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) + (b*(3*a^2 - b^2)*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(d^2*f*(2 + n)) + (b^2*(d*Tan[e + f*x])^(1 + n)*(a + b*Tan[e + f*x]))/(d*f*(2 + n))","A",7,5,23,0.2174,1,"{3566, 3630, 3538, 3476, 364}"
698,1,140,0,0.1476384,"\int (d \tan (e+f x))^n (a+b \tan (e+f x))^2 \, dx","Int[(d*Tan[e + f*x])^n*(a + b*Tan[e + f*x])^2,x]","\frac{\left(a^2-b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{2 a b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{b^2 (d \tan (e+f x))^{n+1}}{d f (n+1)}","\frac{\left(a^2-b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{2 a b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}+\frac{b^2 (d \tan (e+f x))^{n+1}}{d f (n+1)}",1,"(b^2*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) + ((a^2 - b^2)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) + (2*a*b*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(d^2*f*(2 + n))","A",6,4,23,0.1739,1,"{3543, 3538, 3476, 364}"
699,1,103,0,0.0786746,"\int (d \tan (e+f x))^n (a+b \tan (e+f x)) \, dx","Int[(d*Tan[e + f*x])^n*(a + b*Tan[e + f*x]),x]","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}","\frac{a (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1)}+\frac{b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2)}",1,"(a*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n)) + (b*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/(d^2*f*(2 + n))","A",5,3,21,0.1429,1,"{3538, 3476, 364}"
700,1,181,0,0.2637116,"\int \frac{(d \tan (e+f x))^n}{a+b \tan (e+f x)} \, dx","Int[(d*Tan[e + f*x])^n/(a + b*Tan[e + f*x]),x]","-\frac{b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)}+\frac{a (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1) \left(a^2+b^2\right)}+\frac{b^2 (d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{b \tan (e+f x)}{a}\right)}{a d f (n+1) \left(a^2+b^2\right)}","-\frac{b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)}+\frac{a (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1) \left(a^2+b^2\right)}+\frac{b^2 (d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{b \tan (e+f x)}{a}\right)}{a d f (n+1) \left(a^2+b^2\right)}",1,"(a*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/((a^2 + b^2)*d*f*(1 + n)) + (b^2*Hypergeometric2F1[1, 1 + n, 2 + n, -((b*Tan[e + f*x])/a)]*(d*Tan[e + f*x])^(1 + n))/(a*(a^2 + b^2)*d*f*(1 + n)) - (b*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/((a^2 + b^2)*d^2*f*(2 + n))","A",8,6,23,0.2609,1,"{3574, 3538, 3476, 364, 3634, 64}"
701,1,252,0,0.5360102,"\int \frac{(d \tan (e+f x))^n}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Tan[e + f*x])^n/(a + b*Tan[e + f*x])^2,x]","-\frac{2 a b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1) \left(a^2+b^2\right)^2}+\frac{b^2 \left(a^2 (2-n)-b^2 n\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{b \tan (e+f x)}{a}\right)}{a^2 d f (n+1) \left(a^2+b^2\right)^2}+\frac{b^2 (d \tan (e+f x))^{n+1}}{a d f \left(a^2+b^2\right) (a+b \tan (e+f x))}","-\frac{2 a b (d \tan (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\tan ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\tan ^2(e+f x)\right)}{d f (n+1) \left(a^2+b^2\right)^2}+\frac{b^2 \left(a^2 (2-n)-b^2 n\right) (d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{b \tan (e+f x)}{a}\right)}{a^2 d f (n+1) \left(a^2+b^2\right)^2}+\frac{b^2 (d \tan (e+f x))^{n+1}}{a d f \left(a^2+b^2\right) (a+b \tan (e+f x))}",1,"((a^2 - b^2)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(1 + n))/((a^2 + b^2)^2*d*f*(1 + n)) + (b^2*(a^2*(2 - n) - b^2*n)*Hypergeometric2F1[1, 1 + n, 2 + n, -((b*Tan[e + f*x])/a)]*(d*Tan[e + f*x])^(1 + n))/(a^2*(a^2 + b^2)^2*d*f*(1 + n)) - (2*a*b*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Tan[e + f*x]^2]*(d*Tan[e + f*x])^(2 + n))/((a^2 + b^2)^2*d^2*f*(2 + n)) + (b^2*(d*Tan[e + f*x])^(1 + n))/(a*(a^2 + b^2)*d*f*(a + b*Tan[e + f*x]))","A",9,7,23,0.3043,1,"{3569, 3653, 3538, 3476, 364, 3634, 64}"
702,1,175,0,0.2005252,"\int \tan ^m(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Tan[c + d*x]^m*(a + b*Tan[c + d*x])^(3/2),x]","\frac{a \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 \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 \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 \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*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*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",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
703,1,173,0,0.1866973,"\int \tan ^m(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Tan[c + d*x]^m*Sqrt[a + b*Tan[c + d*x]],x]","\frac{\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{\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{\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{\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,"(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]) + (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",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
704,1,173,0,0.1826991,"\int \frac{\tan ^m(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Tan[c + d*x]^m/Sqrt[a + b*Tan[c + d*x]],x]","\frac{\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{\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{\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{\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,"(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]]) + (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",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
705,1,179,0,0.2018515,"\int \frac{\tan ^m(c+d x)}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Tan[c + d*x]^m/(a + b*Tan[c + d*x])^(3/2),x]","\frac{\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{\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{\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{\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,"(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]]) + (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",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
706,1,179,0,0.1809844,"\int (d \tan (e+f x))^n (a+b \tan (e+f x))^m \, dx","Int[(d*Tan[e + f*x])^n*(a + b*Tan[e + f*x])^m,x]","\frac{(d \tan (e+f x))^{n+1} (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(n+1;-m,1;n+2;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 d f (n+1)}+\frac{(d \tan (e+f x))^{n+1} (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(n+1;-m,1;n+2;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 d f (n+1)}","\frac{(d \tan (e+f x))^{n+1} (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(n+1;-m,1;n+2;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 d f (n+1)}+\frac{(d \tan (e+f x))^{n+1} (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(n+1;-m,1;n+2;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 d f (n+1)}",1,"(AppellF1[1 + n, -m, 1, 2 + n, -((b*Tan[e + f*x])/a), (-I)*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*(a + b*Tan[e + f*x])^m)/(2*d*f*(1 + n)*(1 + (b*Tan[e + f*x])/a)^m) + (AppellF1[1 + n, -m, 1, 2 + n, -((b*Tan[e + f*x])/a), I*Tan[e + f*x]]*(d*Tan[e + f*x])^(1 + n)*(a + b*Tan[e + f*x])^m)/(2*d*f*(1 + n)*(1 + (b*Tan[e + f*x])/a)^m)","A",7,4,23,0.1739,1,"{3575, 912, 135, 133}"
707,1,297,0,0.5195692,"\int \tan ^4(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Tan[c + d*x]^4*(a + b*Tan[c + d*x])^n,x]","\frac{\left(2 a^2-b^2 (n+2) (n+3)\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1) (n+2) (n+3)}-\frac{\sqrt{-b^2} (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{2 b d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{\sqrt{-b^2} (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{2 b d (n+1) \left(a+\sqrt{-b^2}\right)}-\frac{2 a \tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+2) (n+3)}+\frac{\tan ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+3)}","\frac{\left(2 a^2-b^2 (n+2) (n+3)\right) (a+b \tan (c+d x))^{n+1}}{b^3 d (n+1) (n+2) (n+3)}-\frac{\sqrt{-b^2} (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a-\sqrt{-b^2}}\right)}{2 b d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{\sqrt{-b^2} (a+b \tan (c+d x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{a+b \tan (c+d x)}{a+\sqrt{-b^2}}\right)}{2 b d (n+1) \left(a+\sqrt{-b^2}\right)}-\frac{2 a \tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b^2 d (n+2) (n+3)}+\frac{\tan ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+3)}",1,"((2*a^2 - b^2*(2 + n)*(3 + n))*(a + b*Tan[c + d*x])^(1 + n))/(b^3*d*(1 + n)*(2 + n)*(3 + n)) - (Sqrt[-b^2]*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*b*(a - Sqrt[-b^2])*d*(1 + n)) + (Sqrt[-b^2]*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*b*(a + Sqrt[-b^2])*d*(1 + n)) - (2*a*Tan[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b^2*d*(2 + n)*(3 + n)) + (Tan[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(3 + n))","A",8,6,21,0.2857,1,"{3566, 3647, 3631, 3485, 712, 68}"
708,1,192,0,0.277299,"\int \tan ^3(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Tan[c + d*x]^3*(a + b*Tan[c + d*x])^n,x]","-\frac{a (a+b \tan (c+d x))^{n+1}}{b^2 d (n+1) (n+2)}+\frac{(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+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{\tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+2)}","-\frac{a (a+b \tan (c+d x))^{n+1}}{b^2 d (n+1) (n+2)}+\frac{(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+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{\tan (c+d x) (a+b \tan (c+d x))^{n+1}}{b d (n+2)}",1,"-((a*(a + b*Tan[c + d*x])^(1 + n))/(b^2*d*(1 + n)*(2 + n))) + (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)) + (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)) + (Tan[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(b*d*(2 + n))","A",8,6,21,0.2857,1,"{3566, 3630, 12, 3539, 3537, 68}"
709,1,193,0,0.1484128,"\int \tan ^2(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Tan[c + d*x]^2*(a + b*Tan[c + d*x])^n,x]","-\frac{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}+\frac{(a+b \tan (c+d x))^{n+1}}{b d (n+1)}","-\frac{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}+\frac{(a+b \tan (c+d x))^{n+1}}{b d (n+1)}",1,"(a + b*Tan[c + d*x])^(1 + n)/(b*d*(1 + n)) - (b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])*d*(1 + n)) + (b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])*d*(1 + n))","A",6,4,21,0.1905,1,"{3543, 3485, 712, 68}"
710,1,127,0,0.1145541,"\int \tan (c+d x) (a+b \tan (c+d x))^n \, dx","Int[Tan[c + d*x]*(a + b*Tan[c + d*x])^n,x]","-\frac{(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+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+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+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,"-(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)) - (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",5,3,19,0.1579,1,"{3539, 3537, 68}"
711,1,167,0,0.1037337,"\int (a+b \tan (c+d x))^n \, dx","Int[(a + b*Tan[c + d*x])^n,x]","\frac{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}-\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}","\frac{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}-\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}",1,"(b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])*d*(1 + n)) - (b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])*d*(1 + n))","A",5,3,12,0.2500,1,"{3485, 712, 68}"
712,1,175,0,0.2099941,"\int \cot (c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cot[c + d*x]*(a + b*Tan[c + d*x])^n,x]","\frac{(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+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+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{(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+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+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,"(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)) + (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)) - (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",8,6,19,0.3158,1,"{3574, 3539, 3537, 68, 3634, 65}"
713,1,245,0,0.3618706,"\int \cot ^2(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cot[c + d*x]^2*(a + b*Tan[c + d*x])^n,x]","-\frac{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{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}-\frac{\cot (c+d x) (a+b \tan (c+d x))^{n+1}}{a d}","-\frac{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{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-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a-\sqrt{-b^2}\right)}+\frac{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+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} d (n+1) \left(a+\sqrt{-b^2}\right)}-\frac{\cot (c+d x) (a+b \tan (c+d x))^{n+1}}{a d}",1,"-((Cot[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(a*d)) - (b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a - Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])*d*(1 + n)) + (b*Hypergeometric2F1[1, 1 + n, 2 + n, (a + b*Tan[c + d*x])/(a + Sqrt[-b^2])]*(a + b*Tan[c + d*x])^(1 + n))/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])*d*(1 + n)) - (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",10,8,21,0.3810,1,"{3569, 3653, 12, 3485, 712, 68, 3634, 65}"
714,1,261,0,0.5613518,"\int \cot ^3(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cot[c + d*x]^3*(a + b*Tan[c + d*x])^n,x]","\frac{\left(2 a^2+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{b (1-n) \cot (c+d x) (a+b \tan (c+d x))^{n+1}}{2 a^2 d}-\frac{(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+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{\cot ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{2 a d}","\frac{\left(2 a^2+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{b (1-n) \cot (c+d x) (a+b \tan (c+d x))^{n+1}}{2 a^2 d}-\frac{(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+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{\cot ^2(c+d x) (a+b \tan (c+d x))^{n+1}}{2 a d}",1,"(b*(1 - n)*Cot[c + d*x]*(a + b*Tan[c + d*x])^(1 + n))/(2*a^2*d) - (Cot[c + d*x]^2*(a + b*Tan[c + d*x])^(1 + n))/(2*a*d) - (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)) - (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 + 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",11,9,21,0.4286,1,"{3569, 3649, 3654, 12, 3539, 3537, 68, 3634, 65}"
715,1,159,0,0.223886,"\int \tan ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Tan[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n,x]","\frac{\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{\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{\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{\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,"(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) + (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",9,5,23,0.2174,1,"{3575, 912, 130, 511, 510}"
716,1,159,0,0.2210124,"\int \sqrt{\tan (c+d x)} (a+b \tan (c+d x))^n \, dx","Int[Sqrt[Tan[c + d*x]]*(a + b*Tan[c + d*x])^n,x]","\frac{\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{\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{\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{\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,"(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) + (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",9,5,23,0.2174,1,"{3575, 912, 130, 511, 510}"
717,1,153,0,0.1903106,"\int \frac{(a+b \tan (c+d x))^n}{\sqrt{\tan (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^n/Sqrt[Tan[c + d*x]],x]","\frac{\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{\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{\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{\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,"(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) + (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",9,5,23,0.2174,1,"{3575, 912, 130, 430, 429}"
718,1,155,0,0.2248935,"\int \frac{(a+b \tan (c+d x))^n}{\tan ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^n/Tan[c + d*x]^(3/2),x]","-\frac{(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+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+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+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,"-((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)) - (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",9,5,23,0.2174,1,"{3575, 912, 130, 511, 510}"
719,1,65,0,0.1028281,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 a \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 i a \sqrt{\cot (c+d x)}}{d}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 i a \sqrt{\cot (c+d x)}}{d}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-2*(-1)^(3/4)*a*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - ((2*I)*a*Sqrt[Cot[c + d*x]])/d - (2*a*Cot[c + d*x]^(3/2))/(3*d)","A",5,4,24,0.1667,1,"{3673, 3528, 3533, 208}"
720,1,45,0,0.0784045,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x]),x]","-\frac{2 a \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a \sqrt{\cot (c+d x)}}{d}-\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-2*(-1)^(1/4)*a*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a*Sqrt[Cot[c + d*x]])/d","A",4,4,24,0.1667,1,"{3673, 3528, 3533, 208}"
721,1,28,0,0.0522558,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x]),x]","\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(2*(-1)^(3/4)*a*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d","A",3,3,24,0.1250,1,"{3673, 3533, 208}"
722,1,47,0,0.0775335,"\int \frac{a+i a \tan (c+d x)}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])/Sqrt[Cot[c + d*x]],x]","\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a}{d \sqrt{\cot (c+d x)}}","\frac{2 \sqrt[4]{-1} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}+\frac{2 i a}{d \sqrt{\cot (c+d x)}}",1,"(2*(-1)^(1/4)*a*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + ((2*I)*a)/(d*Sqrt[Cot[c + d*x]])","A",4,4,24,0.1667,1,"{3673, 3529, 3533, 208}"
723,1,65,0,0.0997634,"\int \frac{a+i a \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])/Cot[c + d*x]^(3/2),x]","\frac{2 i a}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a}{d \sqrt{\cot (c+d x)}}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","\frac{2 i a}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a}{d \sqrt{\cot (c+d x)}}-\frac{2 (-1)^{3/4} a \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-2*(-1)^(3/4)*a*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (((2*I)/3)*a)/(d*Cot[c + d*x]^(3/2)) + (2*a)/(d*Sqrt[Cot[c + d*x]])","A",5,4,24,0.1667,1,"{3673, 3529, 3533, 208}"
724,1,91,0,0.1723783,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^2,x]","-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 i a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{4 a^2 \sqrt{\cot (c+d x)}}{d}+\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 i a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{4 a^2 \sqrt{\cot (c+d x)}}{d}+\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(4*(-1)^(1/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (4*a^2*Sqrt[Cot[c + d*x]])/d - (((4*I)/3)*a^2*Cot[c + d*x]^(3/2))/d - (2*a^2*Cot[c + d*x]^(5/2))/(5*d)","A",6,5,26,0.1923,1,"{3673, 3543, 3528, 3533, 208}"
725,1,71,0,0.1395835,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2,x]","-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 i a^2 \sqrt{\cot (c+d x)}}{d}-\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 i a^2 \sqrt{\cot (c+d x)}}{d}-\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-4*(-1)^(3/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - ((4*I)*a^2*Sqrt[Cot[c + d*x]])/d - (2*a^2*Cot[c + d*x]^(3/2))/(3*d)","A",5,5,26,0.1923,1,"{3673, 3543, 3528, 3533, 208}"
726,1,49,0,0.1127761,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2,x]","-\frac{2 a^2 \sqrt{\cot (c+d x)}}{d}-\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a^2 \sqrt{\cot (c+d x)}}{d}-\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-4*(-1)^(1/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2*Sqrt[Cot[c + d*x]])/d","A",4,4,26,0.1538,1,"{3673, 3543, 3533, 208}"
727,1,49,0,0.1153636,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^2 \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^2,x]","\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a^2}{d \sqrt{\cot (c+d x)}}","\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 a^2}{d \sqrt{\cot (c+d x)}}",1,"(4*(-1)^(3/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2)/(d*Sqrt[Cot[c + d*x]])","A",4,4,26,0.1538,1,"{3673, 3542, 3533, 208}"
728,1,71,0,0.1434454,"\int \frac{(a+i a \tan (c+d x))^2}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^2/Sqrt[Cot[c + d*x]],x]","-\frac{2 a^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{4 i a^2}{d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 a^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{4 i a^2}{d \sqrt{\cot (c+d x)}}+\frac{4 \sqrt[4]{-1} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(4*(-1)^(1/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2)/(3*d*Cot[c + d*x]^(3/2)) + ((4*I)*a^2)/(d*Sqrt[Cot[c + d*x]])","A",5,5,26,0.1923,1,"{3673, 3542, 3529, 3533, 208}"
729,1,91,0,0.1706957,"\int \frac{(a+i a \tan (c+d x))^2}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^2/Cot[c + d*x]^(3/2),x]","\frac{4 i a^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2}{d \sqrt{\cot (c+d x)}}-\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","\frac{4 i a^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 a^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{4 a^2}{d \sqrt{\cot (c+d x)}}-\frac{4 (-1)^{3/4} a^2 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-4*(-1)^(3/4)*a^2*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*a^2)/(5*d*Cot[c + d*x]^(5/2)) + (((4*I)/3)*a^2)/(d*Cot[c + d*x]^(3/2)) + (4*a^2)/(d*Sqrt[Cot[c + d*x]])","A",6,5,26,0.1923,1,"{3673, 3542, 3529, 3533, 208}"
730,1,106,0,0.2013846,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^3,x]","-\frac{8 i a^3 \cot ^{\frac{3}{2}}(c+d x)}{5 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \left(a^3 \cot (c+d x)+i a^3\right)}{5 d}+\frac{8 a^3 \sqrt{\cot (c+d x)}}{d}+\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{8 i a^3 \cot ^{\frac{3}{2}}(c+d x)}{5 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \left(a^3 \cot (c+d x)+i a^3\right)}{5 d}+\frac{8 a^3 \sqrt{\cot (c+d x)}}{d}+\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(8*(-1)^(1/4)*a^3*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d + (8*a^3*Sqrt[Cot[c + d*x]])/d - (((8*I)/5)*a^3*Cot[c + d*x]^(3/2))/d - (2*Cot[c + d*x]^(3/2)*(I*a^3 + a^3*Cot[c + d*x]))/(5*d)","A",6,6,26,0.2308,1,"{3673, 3556, 3592, 3528, 3533, 208}"
731,1,88,0,0.1699498,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^3,x]","-\frac{16 i a^3 \sqrt{\cot (c+d x)}}{3 d}-\frac{2 \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{3 d}-\frac{8 (-1)^{3/4} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{16 i a^3 \sqrt{\cot (c+d x)}}{3 d}-\frac{2 \sqrt{\cot (c+d x)} \left(a^3 \cot (c+d x)+i a^3\right)}{3 d}-\frac{8 (-1)^{3/4} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(-8*(-1)^(3/4)*a^3*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (((16*I)/3)*a^3*Sqrt[Cot[c + d*x]])/d - (2*Sqrt[Cot[c + d*x]]*(I*a^3 + a^3*Cot[c + d*x]))/(3*d)","A",5,5,26,0.1923,1,"{3673, 3556, 3592, 3533, 208}"
732,1,64,0,0.1182748,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3,x]","-\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{d \sqrt{\cot (c+d x)}}","-\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{d \sqrt{\cot (c+d x)}}",1,"(-8*(-1)^(1/4)*a^3*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (2*(I*a^3 + a^3*Cot[c + d*x]))/(d*Sqrt[Cot[c + d*x]])","A",5,5,26,0.1923,1,"{3673, 3553, 12, 3533, 208}"
733,1,86,0,0.1863536,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^3 \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^3,x]","-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{16 a^3}{3 d \sqrt{\cot (c+d x)}}+\frac{8 (-1)^{3/4} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{16 a^3}{3 d \sqrt{\cot (c+d x)}}+\frac{8 (-1)^{3/4} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(8*(-1)^(3/4)*a^3*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (16*a^3)/(3*d*Sqrt[Cot[c + d*x]]) - (2*(I*a^3 + a^3*Cot[c + d*x]))/(3*d*Cot[c + d*x]^(3/2))","A",5,5,26,0.1923,1,"{3673, 3553, 3591, 3533, 208}"
734,1,106,0,0.2201574,"\int \frac{(a+i a \tan (c+d x))^3}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^3/Sqrt[Cot[c + d*x]],x]","-\frac{8 a^3}{5 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 i a^3}{d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}","-\frac{8 a^3}{5 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{2 \left(a^3 \cot (c+d x)+i a^3\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 i a^3}{d \sqrt{\cot (c+d x)}}+\frac{8 \sqrt[4]{-1} a^3 \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{d}",1,"(8*(-1)^(1/4)*a^3*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/d - (8*a^3)/(5*d*Cot[c + d*x]^(3/2)) + ((8*I)*a^3)/(d*Sqrt[Cot[c + d*x]]) - (2*(I*a^3 + a^3*Cot[c + d*x]))/(5*d*Cot[c + d*x]^(5/2))","A",6,6,26,0.2308,1,"{3673, 3553, 3591, 3529, 3533, 208}"
735,1,220,0,0.2364856,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x]),x]","\frac{\cot ^{\frac{3}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{5 \sqrt{\cot (c+d x)}}{2 a d}-\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{\cot ^{\frac{3}{2}}(c+d x)}{2 d (a \cot (c+d x)+i a)}-\frac{5 \sqrt{\cot (c+d x)}}{2 a d}-\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{5}{8}-\frac{3 i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}+\frac{\left(\frac{5}{4}+\frac{3 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((-5/4 - (3*I)/4)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) + ((5/4 + (3*I)/4)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - (5*Sqrt[Cot[c + d*x]])/(2*a*d) + Cot[c + d*x]^(3/2)/(2*d*(I*a + a*Cot[c + d*x])) - ((5/8 - (3*I)/8)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) + ((5/8 - (3*I)/8)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",13,10,26,0.3846,1,"{3673, 3550, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
736,1,200,0,0.2044013,"\int \frac{\sqrt{\cot (c+d x)}}{a+i a \tan (c+d x)} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + I*a*Tan[c + d*x]),x]","\frac{\sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","\frac{\sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{8}+\frac{i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{4}-\frac{i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((3/4 - I/4)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((3/4 - I/4)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) + Sqrt[Cot[c + d*x]]/(2*d*(I*a + a*Cot[c + d*x])) - ((3/8 + I/8)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) + ((3/8 + I/8)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",12,9,26,0.3462,1,"{3673, 3550, 3534, 1168, 1162, 617, 204, 1165, 628}"
737,1,68,0,0.127321,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])),x]","\frac{\sqrt[4]{-1} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{2 a d}+\frac{i \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}","\frac{\sqrt[4]{-1} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{2 a d}+\frac{i \sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}",1,"((-1)^(1/4)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/(2*a*d) + ((I/2)*Sqrt[Cot[c + d*x]])/(d*(I*a + a*Cot[c + d*x]))","A",4,4,26,0.1538,1,"{3673, 3549, 3533, 208}"
738,1,200,0,0.2035032,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])),x]","-\frac{\sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) \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{3 i}{8}\right) \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{3 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","-\frac{\sqrt{\cot (c+d x)}}{2 d (a \cot (c+d x)+i a)}-\frac{\left(\frac{1}{8}+\frac{3 i}{8}\right) \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{3 i}{8}\right) \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{3 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{1}{4}-\frac{3 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((1/4 - (3*I)/4)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((1/4 - (3*I)/4)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - Sqrt[Cot[c + d*x]]/(2*d*(I*a + a*Cot[c + d*x])) - ((1/8 + (3*I)/8)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) + ((1/8 + (3*I)/8)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",12,9,26,0.3462,1,"{3673, 3552, 3534, 1168, 1162, 617, 204, 1165, 628}"
739,1,222,0,0.2391809,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])),x]","-\frac{5 i}{2 a d \sqrt{\cot (c+d x)}}-\frac{1}{2 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)}+\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}","-\frac{5 i}{2 a d \sqrt{\cot (c+d x)}}-\frac{1}{2 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)}+\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{8}-\frac{5 i}{8}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}+\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a d}-\frac{\left(\frac{3}{4}+\frac{5 i}{4}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a d}",1,"((3/4 + (5*I)/4)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((3/4 + (5*I)/4)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a*d) - ((5*I)/2)/(a*d*Sqrt[Cot[c + d*x]]) - 1/(2*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])) + ((3/8 - (5*I)/8)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d) - ((3/8 - (5*I)/8)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a*d)","A",13,10,26,0.3846,1,"{3673, 3552, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
740,1,252,0,0.3690429,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x])^2,x]","\frac{7 \cot ^{\frac{3}{2}}(c+d x)}{8 a^2 d (\cot (c+d x)+i)}-\frac{25 \sqrt{\cot (c+d x)}}{8 a^2 d}-\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\cot ^{\frac{5}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}","\frac{7 \cot ^{\frac{3}{2}}(c+d x)}{8 a^2 d (\cot (c+d x)+i)}-\frac{25 \sqrt{\cot (c+d x)}}{8 a^2 d}-\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{32}-\frac{21 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{16}+\frac{21 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\cot ^{\frac{5}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}",1,"((-25/16 - (21*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + ((25/16 + (21*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) - (25*Sqrt[Cot[c + d*x]])/(8*a^2*d) + (7*Cot[c + d*x]^(3/2))/(8*a^2*d*(I + Cot[c + d*x])) + Cot[c + d*x]^(5/2)/(4*d*(I*a + a*Cot[c + d*x])^2) - ((25/32 - (21*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((25/32 - (21*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",14,11,26,0.4231,1,"{3673, 3558, 3595, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
741,1,232,0,0.3306221,"\int \frac{\sqrt{\cot (c+d x)}}{(a+i a \tan (c+d x))^2} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + I*a*Tan[c + d*x])^2,x]","\frac{5 \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}-\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}","\frac{5 \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}-\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{9}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{4 d (a \cot (c+d x)+i a)^2}",1,"((9/16 - (5*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) - ((9/16 - (5*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (5*Sqrt[Cot[c + d*x]])/(8*a^2*d*(I + Cot[c + d*x])) + Cot[c + d*x]^(3/2)/(4*d*(I*a + a*Cot[c + d*x])^2) - ((9/32 + (5*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((9/32 + (5*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",13,10,26,0.3846,1,"{3673, 3558, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
742,1,234,0,0.3375499,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^2} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^2),x]","\frac{3 i \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \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{3 i}{32}\right) \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{3 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}","\frac{3 i \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}+\frac{3 i}{32}\right) \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{3 i}{32}\right) \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{3 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{1}{16}-\frac{3 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}",1,"((1/16 - (3*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) - ((1/16 - (3*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (((3*I)/8)*Sqrt[Cot[c + d*x]])/(a^2*d*(I + Cot[c + d*x])) + Sqrt[Cot[c + d*x]]/(4*d*(I*a + a*Cot[c + d*x])^2) + ((1/32 + (3*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) - ((1/32 + (3*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",13,10,26,0.3846,1,"{3673, 3558, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
743,1,234,0,0.3089228,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{\sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) \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{3 i}{32}\right) \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{3 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{i \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}","\frac{\sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}+\frac{\left(\frac{1}{32}-\frac{3 i}{32}\right) \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{3 i}{32}\right) \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{3 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{1}{16}+\frac{3 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{i \sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}",1,"((-1/16 - (3*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + ((1/16 + (3*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + Sqrt[Cot[c + d*x]]/(8*a^2*d*(I + Cot[c + d*x])) + ((I/4)*Sqrt[Cot[c + d*x]])/(d*(I*a + a*Cot[c + d*x])^2) + ((1/32 - (3*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) - ((1/32 - (3*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",13,10,26,0.3846,1,"{3673, 3557, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
744,1,234,0,0.329752,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^2),x]","\frac{5 i \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}-\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}","\frac{5 i \sqrt{\cot (c+d x)}}{8 a^2 d (\cot (c+d x)+i)}-\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{32}-\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{9}{16}+\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{\sqrt{\cot (c+d x)}}{4 d (a \cot (c+d x)+i a)^2}",1,"((-9/16 - (5*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + ((9/16 + (5*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) + (((5*I)/8)*Sqrt[Cot[c + d*x]])/(a^2*d*(I + Cot[c + d*x])) - Sqrt[Cot[c + d*x]]/(4*d*(I*a + a*Cot[c + d*x])^2) - ((9/32 - (5*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((9/32 - (5*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",13,10,26,0.3846,1,"{3673, 3559, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
745,1,254,0,0.3731634,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^2),x]","-\frac{25}{8 a^2 d \sqrt{\cot (c+d x)}}+\frac{7 i}{8 a^2 d \sqrt{\cot (c+d x)} (\cot (c+d x)+i)}-\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{1}{4 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}","-\frac{25}{8 a^2 d \sqrt{\cot (c+d x)}}+\frac{7 i}{8 a^2 d \sqrt{\cot (c+d x)} (\cot (c+d x)+i)}-\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{32}+\frac{21 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}+\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^2 d}-\frac{\left(\frac{25}{16}-\frac{21 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^2 d}-\frac{1}{4 d \sqrt{\cot (c+d x)} (a \cot (c+d x)+i a)^2}",1,"((25/16 - (21*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) - ((25/16 - (21*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^2*d) - 25/(8*a^2*d*Sqrt[Cot[c + d*x]]) + ((7*I)/8)/(a^2*d*Sqrt[Cot[c + d*x]]*(I + Cot[c + d*x])) - 1/(4*d*Sqrt[Cot[c + d*x]]*(I*a + a*Cot[c + d*x])^2) - ((25/32 + (21*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d) + ((25/32 + (21*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^2*d)","A",14,11,26,0.4231,1,"{3673, 3559, 3596, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
746,1,273,0,0.4685109,"\int \frac{\sqrt{\cot (c+d x)}}{(a+i a \tan (c+d x))^3} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + I*a*Tan[c + d*x])^3,x]","\frac{5 \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\cot ^{\frac{5}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{3 a d (a \cot (c+d x)+i a)^2}","\frac{5 \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{7}{32}+\frac{5 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{7}{16}-\frac{5 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{\cot ^{\frac{5}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{3 a d (a \cot (c+d x)+i a)^2}",1,"((7/16 - (5*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) - ((7/16 - (5*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + Cot[c + d*x]^(5/2)/(6*d*(I*a + a*Cot[c + d*x])^3) + Cot[c + d*x]^(3/2)/(3*a*d*(I*a + a*Cot[c + d*x])^2) + (5*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) - ((7/32 + (5*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d) + ((7/32 + (5*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d)","A",14,10,26,0.3846,1,"{3673, 3558, 3595, 3534, 1168, 1162, 617, 204, 1165, 628}"
747,1,267,0,0.4574979,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^3} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^3),x]","\frac{i \sqrt{\cot (c+d x)}}{4 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{i \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{i \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{i \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{8 \sqrt{2} a^3 d}+\frac{i \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a^3 d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{\sqrt{\cot (c+d x)}}{4 a d (a \cot (c+d x)+i a)^2}","\frac{i \sqrt{\cot (c+d x)}}{4 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{i \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{i \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{i \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{8 \sqrt{2} a^3 d}+\frac{i \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a^3 d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{6 d (a \cot (c+d x)+i a)^3}+\frac{\sqrt{\cot (c+d x)}}{4 a d (a \cot (c+d x)+i a)^2}",1,"((-I/8)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + ((I/8)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + Cot[c + d*x]^(3/2)/(6*d*(I*a + a*Cot[c + d*x])^3) + Sqrt[Cot[c + d*x]]/(4*a*d*(I*a + a*Cot[c + d*x])^2) + ((I/4)*Sqrt[Cot[c + d*x]])/(d*(I*a^3 + a^3*Cot[c + d*x])) + ((I/16)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d) - ((I/16)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d)","A",16,13,26,0.5000,1,"{3673, 3558, 3595, 3596, 12, 3476, 329, 297, 1162, 617, 204, 1165, 628}"
748,1,141,0,0.3032639,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^3),x]","\frac{\sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{(-1)^{3/4} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{8 a^3 d}+\frac{i \sqrt{\cot (c+d x)}}{6 a d (a \cot (c+d x)+i a)^2}+\frac{\sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}","\frac{\sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}-\frac{(-1)^{3/4} \tanh ^{-1}\left((-1)^{3/4} \sqrt{\cot (c+d x)}\right)}{8 a^3 d}+\frac{i \sqrt{\cot (c+d x)}}{6 a d (a \cot (c+d x)+i a)^2}+\frac{\sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}",1,"-((-1)^(3/4)*ArcTanh[(-1)^(3/4)*Sqrt[Cot[c + d*x]]])/(8*a^3*d) + Sqrt[Cot[c + d*x]]/(6*d*(I*a + a*Cot[c + d*x])^3) + ((I/6)*Sqrt[Cot[c + d*x]])/(a*d*(I*a + a*Cot[c + d*x])^2) + Sqrt[Cot[c + d*x]]/(8*d*(I*a^3 + a^3*Cot[c + d*x]))","A",7,7,26,0.2692,1,"{3673, 3558, 3596, 12, 3549, 3533, 208}"
749,1,222,0,0.3067147,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^3),x]","-\frac{\log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{\log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{8 \sqrt{2} a^3 d}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a^3 d}+\frac{\sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}+\frac{i \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}","-\frac{\log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}+\frac{\log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{16 \sqrt{2} a^3 d}-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{8 \sqrt{2} a^3 d}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{8 \sqrt{2} a^3 d}+\frac{\sqrt{\cot (c+d x)}}{12 a d (a \cot (c+d x)+i a)^2}+\frac{i \sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}",1,"-ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]]/(8*Sqrt[2]*a^3*d) + ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]]/(8*Sqrt[2]*a^3*d) + ((I/6)*Sqrt[Cot[c + d*x]])/(d*(I*a + a*Cot[c + d*x])^3) + Sqrt[Cot[c + d*x]]/(12*a*d*(I*a + a*Cot[c + d*x])^2) - Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]]/(16*Sqrt[2]*a^3*d) + Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]]/(16*Sqrt[2]*a^3*d)","A",15,12,26,0.4615,1,"{3673, 3557, 3596, 21, 3476, 329, 211, 1165, 628, 1162, 617, 204}"
750,1,275,0,0.4651335,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^3),x]","\frac{5 \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{i \sqrt{\cot (c+d x)}}{3 a d (a \cot (c+d x)+i a)^2}-\frac{\sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}","\frac{5 \sqrt{\cot (c+d x)}}{8 d \left(a^3 \cot (c+d x)+i a^3\right)}+\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{5}{32}+\frac{7 i}{32}\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}-\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} a^3 d}+\frac{\left(\frac{5}{16}-\frac{7 i}{16}\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} a^3 d}+\frac{i \sqrt{\cot (c+d x)}}{3 a d (a \cot (c+d x)+i a)^2}-\frac{\sqrt{\cot (c+d x)}}{6 d (a \cot (c+d x)+i a)^3}",1,"((-5/16 + (7*I)/16)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) + ((5/16 - (7*I)/16)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*a^3*d) - Sqrt[Cot[c + d*x]]/(6*d*(I*a + a*Cot[c + d*x])^3) + ((I/3)*Sqrt[Cot[c + d*x]])/(a*d*(I*a + a*Cot[c + d*x])^2) + (5*Sqrt[Cot[c + d*x]])/(8*d*(I*a^3 + a^3*Cot[c + d*x])) + ((5/32 + (7*I)/32)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d) - ((5/32 + (7*I)/32)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(Sqrt[2]*a^3*d)","A",14,10,26,0.3846,1,"{3673, 3559, 3596, 3534, 1168, 1162, 617, 204, 1165, 628}"
751,1,174,0,0.4878729,"\int \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{2 i \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{26 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(1+i) \sqrt{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 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}-\frac{2 i \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{15 d}+\frac{26 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{15 d}-\frac{(1+i) \sqrt{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}",1,"((-1 - I)*Sqrt[a]*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 + (26*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(15*d) - (((2*I)/15)*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/(5*d)","A",7,6,28,0.2143,1,"{4241, 3561, 3598, 12, 3544, 205}"
752,1,140,0,0.3353235,"\int \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{2 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{(1-i) \sqrt{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 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{2 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{3 d}-\frac{(1-i) \sqrt{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}",1,"((-1 + I)*Sqrt[a]*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)/3)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*d)","A",6,6,28,0.2143,1,"{4241, 3561, 3598, 12, 3544, 205}"
753,1,102,0,0.1945938,"\int \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(1+i) \sqrt{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 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","\frac{(1+i) \sqrt{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 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"((1 + I)*Sqrt[a]*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*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",4,4,28,0.1429,1,"{4241, 3548, 3544, 205}"
754,1,69,0,0.1296956,"\int \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)} \, dx","Int[Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{(1-i) \sqrt{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{(1-i) \sqrt{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}",1,"((1 - I)*Sqrt[a]*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",3,3,28,0.1071,1,"{4241, 3544, 205}"
755,1,144,0,0.326973,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\sqrt{\cot (c+d x)}} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Sqrt[Cot[c + d*x]],x]","-\frac{2 (-1)^{3/4} \sqrt{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{(1+i) \sqrt{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} \sqrt{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{(1+i) \sqrt{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}",1,"(-2*(-1)^(3/4)*Sqrt[a]*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]*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",8,8,28,0.2857,1,"{4241, 3563, 3544, 205, 3599, 63, 217, 203}"
756,1,175,0,0.4066142,"\int \frac{\sqrt{a+i a \tan (c+d x)}}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[Sqrt[a + I*a*Tan[c + d*x]]/Cot[c + d*x]^(3/2),x]","-\frac{\sqrt[4]{-1} \sqrt{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{\sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}-\frac{(1-i) \sqrt{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{\sqrt[4]{-1} \sqrt{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{\sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}-\frac{(1-i) \sqrt{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}",1,"-(((-1)^(1/4)*Sqrt[a]*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]*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 + Sqrt[a + I*a*Tan[c + d*x]]/(d*Sqrt[Cot[c + d*x]])","A",10,10,28,0.3571,1,"{4241, 3560, 21, 3555, 3544, 205, 3599, 63, 217, 203}"
757,1,218,0,0.6521379,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 i a^2 \cot ^{\frac{3}{2}}(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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{4 i a \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}+\frac{12 a \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{5 d}","-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}-\frac{2 i a^2 \cot ^{\frac{3}{2}}(c+d x)}{5 d \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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{4 i a \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{5 d}+\frac{12 a \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{5 d}",1,"((-2 - 2*I)*a^(3/2)*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)/5)*a^2*Cot[c + d*x]^(3/2))/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (2*a^2*Cot[c + d*x]^(5/2))/(5*d*Sqrt[a + I*a*Tan[c + d*x]]) + (12*a*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(5*d) - (((4*I)/5)*a*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/d","A",8,7,28,0.2500,1,"{4241, 3553, 3596, 3598, 12, 3544, 205}"
758,1,139,0,0.2832492,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{(2-2 i) a^{3/2} \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 \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i a \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}","-\frac{(2-2 i) a^{3/2} \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 \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 i a \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}",1,"((-2 + 2*I)*a^(3/2)*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*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",5,5,28,0.1786,1,"{4241, 3548, 3545, 3544, 205}"
759,1,103,0,0.209593,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{(2+2 i) a^{3/2} \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{(2+2 i) a^{3/2} \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,"((2 + 2*I)*a^(3/2)*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",4,4,28,0.1429,1,"{4241, 3545, 3544, 205}"
760,1,144,0,0.3406917,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2} \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{2 \sqrt[4]{-1} a^{3/2} \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} \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} \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} \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}",1,"(2*(-1)^(1/4)*a^(3/2)*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)*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",8,8,28,0.2857,1,"{4241, 3555, 3544, 205, 3599, 63, 217, 203}"
761,1,216,0,0.6122864,"\int \frac{(a+i a \tan (c+d x))^{3/2}}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(3/2)/Sqrt[Cot[c + d*x]],x]","-\frac{a^2}{d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{3 (-1)^{3/4} a^{3/2} \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{i a^2}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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^2}{d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{3 (-1)^{3/4} a^{3/2} \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{i a^2}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{(2+2 i) a^{3/2} \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}",1,"(-3*(-1)^(3/4)*a^(3/2)*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)*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/(d*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) + (I*a^2)/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",10,10,28,0.3571,1,"{4241, 3556, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
762,1,222,0,0.6458408,"\int \cot ^{\frac{9}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(9/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{2 a^2 \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}-\frac{6 i a^2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}+\frac{32 a^2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{104 i a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{(4-4 i) a^{5/2} \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^2 \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}-\frac{6 i a^2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{7 d}+\frac{32 a^2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{104 i a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{21 d}+\frac{(4-4 i) a^{5/2} \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}",1,"((4 - 4*I)*a^(5/2)*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 + (((104*I)/21)*a^2*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d + (32*a^2*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(21*d) - (((6*I)/7)*a^2*Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*a^2*Cot[c + d*x]^(7/2)*Sqrt[a + I*a*Tan[c + d*x]])/(7*d)","A",8,6,28,0.2143,1,"{4241, 3553, 3598, 12, 3544, 205}"
763,1,176,0,0.352847,"\int \cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{4 a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(4+4 i) a^{5/2} \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 i a \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}","\frac{4 a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(4+4 i) a^{5/2} \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 i a \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}{3 d}-\frac{2 \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}{5 d}",1,"((-4 - 4*I)*a^(5/2)*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*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (((2*I)/3)*a*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/d - (2*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2))/(5*d)","A",6,5,28,0.1786,1,"{4241, 3548, 3545, 3544, 205}"
764,1,142,0,0.2760938,"\int \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{4 i a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(4-4 i) a^{5/2} \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) (a+i a \tan (c+d x))^{3/2}}{3 d}","-\frac{4 i a^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}-\frac{(4-4 i) a^{5/2} \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) (a+i a \tan (c+d x))^{3/2}}{3 d}",1,"((-4 + 4*I)*a^(5/2)*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*I)*a^2*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d - (2*a*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2))/(3*d)","A",5,4,28,0.1429,1,"{4241, 3545, 3544, 205}"
765,1,179,0,0.4750678,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{2 (-1)^{3/4} a^{5/2} \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^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} \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} \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^2 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{d}+\frac{(4+4 i) a^{5/2} \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}",1,"(2*(-1)^(3/4)*a^(5/2)*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)*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*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/d","A",9,9,28,0.3214,1,"{4241, 3553, 3601, 3544, 205, 3599, 63, 217, 203}"
766,1,179,0,0.4653809,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2} \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{5 \sqrt[4]{-1} a^{5/2} \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 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{(4-4 i) a^{5/2} \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{5 \sqrt[4]{-1} a^{5/2} \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 \sqrt{a+i a \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{(4-4 i) a^{5/2} \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}",1,"(5*(-1)^(1/4)*a^(5/2)*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)*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*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",9,9,28,0.3214,1,"{4241, 3556, 3601, 3544, 205, 3599, 63, 217, 203}"
767,1,222,0,0.5997575,"\int \frac{(a+i a \tan (c+d x))^{5/2}}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^(5/2)/Sqrt[Cot[c + d*x]],x]","-\frac{a^2 \sqrt{a+i a \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{23 (-1)^{3/4} a^{5/2} \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{9 i a^2 \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}-\frac{(4+4 i) a^{5/2} \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^2 \sqrt{a+i a \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{23 (-1)^{3/4} a^{5/2} \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{9 i a^2 \sqrt{a+i a \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}-\frac{(4+4 i) a^{5/2} \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}",1,"(-23*(-1)^(3/4)*a^(5/2)*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)*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*Sqrt[a + I*a*Tan[c + d*x]])/(2*d*Cot[c + d*x]^(3/2)) + (((9*I)/4)*a^2*Sqrt[a + I*a*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",10,10,28,0.3571,1,"{4241, 3556, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
768,1,181,0,0.4749864,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^(5/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{5 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \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) \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 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{3 a d}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{d \sqrt{a+i a \tan (c+d x)}}+\frac{7 i \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) \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)*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) + Cot[c + d*x]^(3/2)/(d*Sqrt[a + I*a*Tan[c + d*x]]) + (((7*I)/3)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d) - (5*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(3*a*d)","A",7,6,28,0.2143,1,"{4241, 3559, 3598, 12, 3544, 205}"
769,1,140,0,0.3291962,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^(3/2)/Sqrt[a + I*a*Tan[c + d*x]],x]","-\frac{3 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\sqrt{\cot (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{3 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{a d}+\frac{\sqrt{\cot (c+d x)}}{d \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)*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) + Sqrt[Cot[c + d*x]]/(d*Sqrt[a + I*a*Tan[c + d*x]]) - (3*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a*d)","A",6,6,28,0.2143,1,"{4241, 3559, 3598, 12, 3544, 205}"
770,1,105,0,0.2567585,"\int \frac{\sqrt{\cot (c+d x)}}{\sqrt{a+i a \tan (c+d x)}} \, dx","Int[Sqrt[Cot[c + d*x]]/Sqrt[a + I*a*Tan[c + d*x]],x]","\frac{1}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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{1}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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)*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) + 1/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,28,0.1786,1,"{4241, 3548, 3546, 3544, 205}"
771,1,108,0,0.1944387,"\int \frac{1}{\sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]]),x]","\frac{i}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{i}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)*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/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",4,4,28,0.1429,1,"{4241, 3546, 3544, 205}"
772,1,180,0,0.4488192,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{2 \sqrt[4]{-1} \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{1}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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} \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{1}{d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}-\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \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,"(-2*(-1)^(1/4)*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)*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) - 1/(d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",9,9,28,0.3214,1,"{4241, 3558, 3601, 3544, 205, 3599, 63, 217, 203}"
773,1,217,0,0.5835515,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*Sqrt[a + I*a*Tan[c + d*x]]),x]","-\frac{1}{d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{(-1)^{3/4} \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{2 i \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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{1}{d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{(-1)^{3/4} \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{2 i \sqrt{a+i a \tan (c+d x)}}{a d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \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)^(3/4)*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)*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) - 1/(d*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - ((2*I)*Sqrt[a + I*a*Tan[c + d*x]])/(a*d*Sqrt[Cot[c + d*x]])","A",10,10,28,0.3571,1,"{4241, 3558, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
774,1,221,0,0.6493011,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^(5/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{7 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{13 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{5 \cot ^{\frac{3}{2}}(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}","-\frac{7 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}+\frac{13 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{2 a^2 d}-\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{5 \cot ^{\frac{3}{2}}(c+d x)}{2 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((-1/4 + I/4)*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) + Cot[c + d*x]^(3/2)/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (5*Cot[c + d*x]^(3/2))/(2*a*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((13*I)/2)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a^2*d) - (7*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d)","A",8,7,28,0.2500,1,"{4241, 3559, 3596, 3598, 12, 3544, 205}"
775,1,182,0,0.5004335,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Cot[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x])^(3/2),x]","-\frac{25 \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) \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{11 \sqrt{\cot (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\sqrt{\cot (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}","-\frac{25 \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) \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{11 \sqrt{\cot (c+d x)}}{6 a d \sqrt{a+i a \tan (c+d x)}}+\frac{\sqrt{\cot (c+d x)}}{3 d (a+i a \tan (c+d x))^{3/2}}",1,"((1/4 + I/4)*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) + Sqrt[Cot[c + d*x]]/(3*d*(a + I*a*Tan[c + d*x])^(3/2)) + (11*Sqrt[Cot[c + d*x]])/(6*a*d*Sqrt[a + I*a*Tan[c + d*x]]) - (25*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(6*a^2*d)","A",7,7,28,0.2500,1,"{4241, 3559, 3596, 3598, 12, 3544, 205}"
776,1,145,0,0.3499042,"\int \frac{\sqrt{\cot (c+d x)}}{(a+i a \tan (c+d x))^{3/2}} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + I*a*Tan[c + d*x])^(3/2),x]","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{7}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{7}{6 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}+\frac{1}{3 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}",1,"((1/4 - I/4)*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) + 1/(3*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + 7/(6*a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",6,6,28,0.2143,1,"{4241, 3559, 3596, 12, 3544, 205}"
777,1,147,0,0.2781746,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \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{1}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{i}{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) \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{1}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{i}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 - I/4)*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) + 1/(3*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + (I/2)/(a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",5,5,28,0.1786,1,"{4241, 3547, 3546, 3544, 205}"
778,1,147,0,0.2732098,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(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) \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{i}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{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) \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{i}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"((-1/4 + I/4)*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/3)/(d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + 1/(2*a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",5,4,28,0.1429,1,"{4241, 3546, 3544, 205}"
779,1,221,0,0.6069049,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","\frac{2 (-1)^{3/4} \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{\left(\frac{1}{4}+\frac{i}{4}\right) \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{1}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{3 i}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}","\frac{2 (-1)^{3/4} \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{\left(\frac{1}{4}+\frac{i}{4}\right) \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{1}{3 d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{3 i}{2 a d \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}",1,"(2*(-1)^(3/4)*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)*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) - 1/(3*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + ((3*I)/2)/(a*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",10,10,28,0.3571,1,"{4241, 3558, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
780,1,258,0,0.7484636,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(3/2)),x]","-\frac{3 \sqrt[4]{-1} \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{7 \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{13 i}{6 a d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{1}{3 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}","-\frac{3 \sqrt[4]{-1} \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{7 \sqrt{a+i a \tan (c+d x)}}{2 a^2 d \sqrt{\cot (c+d x)}}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \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{13 i}{6 a d \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}-\frac{1}{3 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}",1,"(-3*(-1)^(1/4)*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)*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) - 1/(3*d*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(3/2)) + ((13*I)/6)/(a*d*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]]) - (7*Sqrt[a + I*a*Tan[c + d*x]])/(2*a^2*d*Sqrt[Cot[c + d*x]])","A",11,11,28,0.3929,1,"{4241, 3558, 3595, 3597, 3601, 3544, 205, 3599, 63, 217, 203}"
781,1,258,0,0.8079188,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]^(5/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{361 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{89 \cot ^{\frac{3}{2}}(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{707 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \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 \cot ^{\frac{3}{2}}(c+d x)}{10 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}","-\frac{361 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{89 \cot ^{\frac{3}{2}}(c+d x)}{20 a^2 d \sqrt{a+i a \tan (c+d x)}}+\frac{707 i \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}-\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \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 \cot ^{\frac{3}{2}}(c+d x)}{10 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\cot ^{\frac{3}{2}}(c+d x)}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 + I/8)*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) + Cot[c + d*x]^(3/2)/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (7*Cot[c + d*x]^(3/2))/(10*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (89*Cot[c + d*x]^(3/2))/(20*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) + (((707*I)/60)*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(a^3*d) - (361*Cot[c + d*x]^(3/2)*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d)","A",9,7,28,0.2500,1,"{4241, 3559, 3596, 3598, 12, 3544, 205}"
782,1,219,0,0.667005,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Cot[c + d*x]^(3/2)/(a + I*a*Tan[c + d*x])^(5/2),x]","-\frac{317 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{151 \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) \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{17 \sqrt{\cot (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\sqrt{\cot (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}","-\frac{317 \sqrt{\cot (c+d x)} \sqrt{a+i a \tan (c+d x)}}{60 a^3 d}+\frac{151 \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) \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{17 \sqrt{\cot (c+d x)}}{30 a d (a+i a \tan (c+d x))^{3/2}}+\frac{\sqrt{\cot (c+d x)}}{5 d (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 + I/8)*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) + Sqrt[Cot[c + d*x]]/(5*d*(a + I*a*Tan[c + d*x])^(5/2)) + (17*Sqrt[Cot[c + d*x]])/(30*a*d*(a + I*a*Tan[c + d*x])^(3/2)) + (151*Sqrt[Cot[c + d*x]])/(60*a^2*d*Sqrt[a + I*a*Tan[c + d*x]]) - (317*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])/(60*a^3*d)","A",8,7,28,0.2500,1,"{4241, 3559, 3596, 3598, 12, 3544, 205}"
783,1,182,0,0.5147866,"\int \frac{\sqrt{\cot (c+d x)}}{(a+i a \tan (c+d x))^{5/2}} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + I*a*Tan[c + d*x])^(5/2),x]","\frac{67}{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) \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{13}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}","\frac{67}{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) \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{13}{30 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 - I/8)*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) + 1/(5*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + 13/(30*a*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) + 67/(60*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",7,6,28,0.2143,1,"{4241, 3559, 3596, 12, 3544, 205}"
784,1,188,0,0.5049943,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{i}{20 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) \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{i}{10 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}","-\frac{i}{20 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) \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{i}{10 a d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 - I/8)*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/5)/(d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(5/2)) + (I/10)/(a*d*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^(3/2)) - (I/20)/(a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",7,6,28,0.2143,1,"{4241, 3557, 3596, 12, 3544, 205}"
785,1,184,0,0.3572699,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{1}{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) \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{i}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","\frac{1}{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) \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{i}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{1}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"((-1/8 + I/8)*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) + 1/(5*d*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)) + (I/6)/(a*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + 1/(4*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",6,5,28,0.1786,1,"{4241, 3547, 3546, 3544, 205}"
786,1,186,0,0.3552464,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","-\frac{i}{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) \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{1}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","-\frac{i}{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) \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{1}{6 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}+\frac{i}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"((1/8 + I/8)*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/5)/(d*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)) + 1/(6*a*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) - (I/4)/(a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",6,4,28,0.1429,1,"{4241, 3546, 3544, 205}"
787,1,258,0,0.7901754,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + I*a*Tan[c + d*x])^(5/2)),x]","\frac{2 \sqrt[4]{-1} \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{7}{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) \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{i}{2 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}-\frac{1}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}","\frac{2 \sqrt[4]{-1} \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{7}{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) \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{i}{2 a d \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^{3/2}}-\frac{1}{5 d \cot ^{\frac{5}{2}}(c+d x) (a+i a \tan (c+d x))^{5/2}}",1,"(2*(-1)^(1/4)*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)*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) - 1/(5*d*Cot[c + d*x]^(5/2)*(a + I*a*Tan[c + d*x])^(5/2)) + (I/2)/(a*d*Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^(3/2)) + 7/(4*a^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + I*a*Tan[c + d*x]])","A",11,10,28,0.3571,1,"{4241, 3558, 3595, 3601, 3544, 205, 3599, 63, 217, 203}"
788,1,139,0,0.3645053,"\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^3 \, dx","Int[(d*Cot[e + f*x])^n*(a + I*a*Tan[e + f*x])^3,x]","-\frac{4 i a^3 d^2 (d \cot (e+f x))^{n-2} \, _2F_1(1,n-2;n-1;-i \cot (e+f x))}{f (2-n)}+\frac{d^2 \left(a^3 \cot (e+f x)+i a^3\right) (d \cot (e+f x))^{n-2}}{f (1-n)}+\frac{i a^3 d^2 (1-2 n) (d \cot (e+f x))^{n-2}}{f (1-n) (2-n)}","-\frac{4 i a^3 d^2 (d \cot (e+f x))^{n-2} \, _2F_1(1,n-2;n-1;-i \cot (e+f x))}{f (2-n)}+\frac{d^2 \left(a^3 \cot (e+f x)+i a^3\right) (d \cot (e+f x))^{n-2}}{f (1-n)}+\frac{i a^3 d^2 (1-2 n) (d \cot (e+f x))^{n-2}}{f (1-n) (2-n)}",1,"(I*a^3*d^2*(1 - 2*n)*(d*Cot[e + f*x])^(-2 + n))/(f*(1 - n)*(2 - n)) + (d^2*(d*Cot[e + f*x])^(-2 + n)*(I*a^3 + a^3*Cot[e + f*x]))/(f*(1 - n)) - ((4*I)*a^3*d^2*(d*Cot[e + f*x])^(-2 + n)*Hypergeometric2F1[1, -2 + n, -1 + n, (-I)*Cot[e + f*x]])/(f*(2 - n))","A",6,6,26,0.2308,1,"{3673, 3556, 3592, 3537, 12, 64}"
789,1,72,0,0.1771858,"\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^2 \, dx","Int[(d*Cot[e + f*x])^n*(a + I*a*Tan[e + f*x])^2,x]","\frac{a^2 d (d \cot (e+f x))^{n-1}}{f (1-n)}-\frac{2 a^2 d (d \cot (e+f x))^{n-1} \, _2F_1(1,n-1;n;-i \cot (e+f x))}{f (1-n)}","\frac{a^2 d (d \cot (e+f x))^{n-1}}{f (1-n)}-\frac{2 a^2 d (d \cot (e+f x))^{n-1} \, _2F_1(1,n-1;n;-i \cot (e+f x))}{f (1-n)}",1,"(a^2*d*(d*Cot[e + f*x])^(-1 + n))/(f*(1 - n)) - (2*a^2*d*(d*Cot[e + f*x])^(-1 + n)*Hypergeometric2F1[1, -1 + n, n, (-I)*Cot[e + f*x]])/(f*(1 - n))","A",5,5,26,0.1923,1,"{3673, 3543, 3537, 12, 64}"
790,1,37,0,0.0713237,"\int (d \cot (e+f x))^n (a+i a \tan (e+f x)) \, dx","Int[(d*Cot[e + f*x])^n*(a + I*a*Tan[e + f*x]),x]","-\frac{i a (d \cot (e+f x))^n \, _2F_1(1,n;n+1;-i \cot (e+f x))}{f n}","-\frac{i a (d \cot (e+f x))^n \, _2F_1(1,n;n+1;-i \cot (e+f x))}{f n}",1,"((-I)*a*(d*Cot[e + f*x])^n*Hypergeometric2F1[1, n, 1 + n, (-I)*Cot[e + f*x]])/(f*n)","A",3,3,24,0.1250,1,"{3673, 3537, 64}"
791,1,157,0,0.2549635,"\int \frac{(d \cot (e+f x))^n}{a+i a \tan (e+f x)} \, dx","Int[(d*Cot[e + f*x])^n/(a + I*a*Tan[e + f*x]),x]","-\frac{i n (d \cot (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\cot ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(n+1) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{2 a d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+2}}{2 d^2 f (a \cot (e+f x)+i a)}","-\frac{i n (d \cot (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\cot ^2(e+f x)\right)}{2 a d^2 f (n+2)}+\frac{(n+1) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{2 a d^3 f (n+3)}-\frac{(d \cot (e+f x))^{n+2}}{2 d^2 f (a \cot (e+f x)+i a)}",1,"-(d*Cot[e + f*x])^(2 + n)/(2*d^2*f*(I*a + a*Cot[e + f*x])) - ((I/2)*n*(d*Cot[e + f*x])^(2 + n)*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Cot[e + f*x]^2])/(a*d^2*f*(2 + n)) + ((1 + n)*(d*Cot[e + f*x])^(3 + n)*Hypergeometric2F1[1, (3 + n)/2, (5 + n)/2, -Cot[e + f*x]^2])/(2*a*d^3*f*(3 + n))","A",7,5,26,0.1923,1,"{3673, 3552, 3538, 3476, 364}"
792,1,202,0,0.4963073,"\int \frac{(d \cot (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx","Int[(d*Cot[e + f*x])^n/(a + I*a*Tan[e + f*x])^2,x]","\frac{(n+1)^2 (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{4 a^2 d^3 f (n+3)}+\frac{i n (n+2) (d \cot (e+f x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\cot ^2(e+f x)\right)}{4 a^2 d^4 f (n+4)}-\frac{i n (d \cot (e+f x))^{n+3}}{4 a^2 d^3 f (\cot (e+f x)+i)}-\frac{(d \cot (e+f x))^{n+3}}{4 d^3 f (a \cot (e+f x)+i a)^2}","\frac{(n+1)^2 (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{4 a^2 d^3 f (n+3)}+\frac{i n (n+2) (d \cot (e+f x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\cot ^2(e+f x)\right)}{4 a^2 d^4 f (n+4)}-\frac{i n (d \cot (e+f x))^{n+3}}{4 a^2 d^3 f (\cot (e+f x)+i)}-\frac{(d \cot (e+f x))^{n+3}}{4 d^3 f (a \cot (e+f x)+i a)^2}",1,"((-I/4)*n*(d*Cot[e + f*x])^(3 + n))/(a^2*d^3*f*(I + Cot[e + f*x])) - (d*Cot[e + f*x])^(3 + n)/(4*d^3*f*(I*a + a*Cot[e + f*x])^2) + ((1 + n)^2*(d*Cot[e + f*x])^(3 + n)*Hypergeometric2F1[1, (3 + n)/2, (5 + n)/2, -Cot[e + f*x]^2])/(4*a^2*d^3*f*(3 + n)) + ((I/4)*n*(2 + n)*(d*Cot[e + f*x])^(4 + n)*Hypergeometric2F1[1, (4 + n)/2, (6 + n)/2, -Cot[e + f*x]^2])/(a^2*d^4*f*(4 + n))","A",8,6,26,0.2308,1,"{3673, 3559, 3596, 3538, 3476, 364}"
793,1,95,0,0.1644149,"\int (d \cot (e+f x))^n (a+i a \tan (e+f x))^m \, dx","Int[(d*Cot[e + f*x])^n*(a + I*a*Tan[e + f*x])^m,x]","\frac{\tan (e+f x) (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (d \cot (e+f x))^n F_1(1-n;1-m,1;2-n;-i \tan (e+f x),i \tan (e+f x))}{f (1-n)}","\frac{\tan (e+f x) (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m (d \cot (e+f x))^n F_1(1-n;1-m,1;2-n;-i \tan (e+f x),i \tan (e+f x))}{f (1-n)}",1,"(AppellF1[1 - n, 1 - m, 1, 2 - n, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*(d*Cot[e + f*x])^n*Tan[e + f*x]*(a + I*a*Tan[e + f*x])^m)/(f*(1 - n)*(1 + I*Tan[e + f*x])^m)","A",4,4,26,0.1538,1,"{4241, 3564, 135, 133}"
794,1,79,0,0.1726336,"\int \cot ^{\frac{3}{2}}(c+d x) (a+i a \tan (c+d x))^n \, dx","Int[Cot[c + d*x]^(3/2)*(a + I*a*Tan[c + d*x])^n,x]","-\frac{2 \sqrt{\cot (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{1}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}","-\frac{2 \sqrt{\cot (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{1}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{d}",1,"(-2*AppellF1[-1/2, 1 - n, 1, 1/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(d*(1 + I*Tan[c + d*x])^n)","A",5,5,26,0.1923,1,"{4241, 3564, 130, 511, 510}"
795,1,79,0,0.1465672,"\int \sqrt{\cot (c+d x)} (a+i a \tan (c+d x))^n \, dx","Int[Sqrt[Cot[c + d*x]]*(a + I*a*Tan[c + d*x])^n,x]","\frac{2 (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+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)}}",1,"(2*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)","A",5,5,26,0.1923,1,"{4241, 3564, 130, 430, 429}"
796,1,81,0,0.1641358,"\int \frac{(a+i a \tan (c+d x))^n}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + I*a*Tan[c + d*x])^n/Sqrt[Cot[c + d*x]],x]","\frac{2 (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{3}{2};1-n,1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{2 (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{3}{2};1-n,1;\frac{5}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"(2*AppellF1[3/2, 1 - n, 1, 5/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(3*d*Cot[c + d*x]^(3/2)*(1 + I*Tan[c + d*x])^n)","A",5,5,26,0.1923,1,"{4241, 3564, 130, 511, 510}"
797,1,81,0,0.1634897,"\int \frac{(a+i a \tan (c+d x))^n}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + I*a*Tan[c + d*x])^n/Cot[c + d*x]^(3/2),x]","\frac{2 (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{5}{2};1-n,1;\frac{7}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 (1+i \tan (c+d x))^{-n} (a+i a \tan (c+d x))^n F_1\left(\frac{5}{2};1-n,1;\frac{7}{2};-i \tan (c+d x),i \tan (c+d x)\right)}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"(2*AppellF1[5/2, 1 - n, 1, 7/2, (-I)*Tan[c + d*x], I*Tan[c + d*x]]*(a + I*a*Tan[c + d*x])^n)/(5*d*Cot[c + d*x]^(5/2)*(1 + I*Tan[c + d*x])^n)","A",5,5,26,0.1923,1,"{4241, 3564, 130, 511, 510}"
798,1,202,0,0.1830651,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x]),x]","\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \cot ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a \sqrt{\cot (c+d x)}}{d}-\frac{2 b \cot ^{\frac{3}{2}}(c+d x)}{3 d}","\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \cot ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{2 a \sqrt{\cot (c+d x)}}{d}-\frac{2 b \cot ^{\frac{3}{2}}(c+d x)}{3 d}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*a*Sqrt[Cot[c + d*x]])/d - (2*b*Cot[c + d*x]^(3/2))/(3*d) - (2*a*Cot[c + d*x]^(5/2))/(5*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,9,21,0.4286,1,"{3673, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
799,1,184,0,0.1601411,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x]),x]","\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 b \sqrt{\cot (c+d x)}}{d}","\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{2 b \sqrt{\cot (c+d x)}}{d}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*b*Sqrt[Cot[c + d*x]])/d - (2*a*Cot[c + d*x]^(3/2))/(3*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,9,21,0.4286,1,"{3673, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
800,1,166,0,0.1322373,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x)) \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x]),x]","-\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \sqrt{\cot (c+d x)}}{d}","-\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a \sqrt{\cot (c+d x)}}{d}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a*Sqrt[Cot[c + d*x]])/d - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,21,0.4286,1,"{3673, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
801,1,150,0,0.112356,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x)) \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x]),x]","-\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}","-\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",11,8,21,0.3810,1,"{3673, 3534, 1168, 1162, 617, 204, 1165, 628}"
802,1,166,0,0.133518,"\int \frac{a+b \tan (c+d x)}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])/Sqrt[Cot[c + d*x]],x]","\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-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{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-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)}}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b)/(d*Sqrt[Cot[c + d*x]]) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,21,0.4286,1,"{3673, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
803,1,184,0,0.1543132,"\int \frac{a+b \tan (c+d x)}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])/Cot[c + d*x]^(3/2),x]","\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a}{d \sqrt{\cot (c+d x)}}+\frac{2 b}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{(a-b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a}{d \sqrt{\cot (c+d x)}}+\frac{2 b}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b)/(3*d*Cot[c + d*x]^(3/2)) + (2*a)/(d*Sqrt[Cot[c + d*x]]) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,9,21,0.4286,1,"{3673, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
804,1,202,0,0.1784448,"\int \frac{a+b \tan (c+d x)}{\cot ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])/Cot[c + d*x]^(5/2),x]","-\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b}{5 d \cot ^{\frac{5}{2}}(c+d x)}-\frac{2 b}{d \sqrt{\cot (c+d x)}}","-\frac{(a+b) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 a}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b}{5 d \cot ^{\frac{5}{2}}(c+d x)}-\frac{2 b}{d \sqrt{\cot (c+d x)}}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b)/(5*d*Cot[c + d*x]^(5/2)) + (2*a)/(3*d*Cot[c + d*x]^(3/2)) - (2*b)/(d*Sqrt[Cot[c + d*x]]) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,9,21,0.4286,1,"{3673, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
805,1,268,0,0.2877299,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^2,x]","\frac{2 \left(a^2-b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{7}{2}}(c+d x)}{7 d}-\frac{4 a b \cot ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{4 a b \sqrt{\cot (c+d x)}}{d}","\frac{2 \left(a^2-b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{7}{2}}(c+d x)}{7 d}-\frac{4 a b \cot ^{\frac{5}{2}}(c+d x)}{5 d}+\frac{4 a b \sqrt{\cot (c+d x)}}{d}",1,"((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (4*a*b*Sqrt[Cot[c + d*x]])/d + (2*(a^2 - b^2)*Cot[c + d*x]^(3/2))/(3*d) - (4*a*b*Cot[c + d*x]^(5/2))/(5*d) - (2*a^2*Cot[c + d*x]^(7/2))/(7*d) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,10,23,0.4348,1,"{3673, 3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
806,1,249,0,0.2683142,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^2,x]","\frac{2 \left(a^2-b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 a b \cot ^{\frac{3}{2}}(c+d x)}{3 d}","\frac{2 \left(a^2-b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x)}{5 d}-\frac{4 a b \cot ^{\frac{3}{2}}(c+d x)}{3 d}",1,"((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*(a^2 - b^2)*Sqrt[Cot[c + d*x]])/d - (4*a*b*Cot[c + d*x]^(3/2))/(3*d) - (2*a^2*Cot[c + d*x]^(5/2))/(5*d) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,10,23,0.4348,1,"{3673, 3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
807,1,223,0,0.2110868,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2,x]","\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 a b \sqrt{\cot (c+d x)}}{d}","\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x)}{3 d}-\frac{4 a b \sqrt{\cot (c+d x)}}{d}",1,"-(((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (4*a*b*Sqrt[Cot[c + d*x]])/d - (2*a^2*Cot[c + d*x]^(3/2))/(3*d) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,23,0.4348,1,"{3673, 3543, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
808,1,204,0,0.1822851,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2 \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \sqrt{\cot (c+d x)}}{d}","-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \sqrt{\cot (c+d x)}}{d}",1,"-(((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a^2*Sqrt[Cot[c + d*x]])/d - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,23,0.3913,1,"{3673, 3543, 3534, 1168, 1162, 617, 204, 1165, 628}"
809,1,204,0,0.1757221,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^2 \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^2,x]","-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2}{d \sqrt{\cot (c+d x)}}","-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2}{d \sqrt{\cot (c+d x)}}",1,"((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2)/(d*Sqrt[Cot[c + d*x]]) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",12,9,23,0.3913,1,"{3673, 3542, 3534, 1168, 1162, 617, 204, 1165, 628}"
810,1,223,0,0.2170791,"\int \frac{(a+b \tan (c+d x))^2}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^2/Sqrt[Cot[c + d*x]],x]","\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2}{3 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2)/(3*d*Cot[c + d*x]^(3/2)) + (4*a*b)/(d*Sqrt[Cot[c + d*x]]) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,23,0.4348,1,"{3673, 3542, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
811,1,249,0,0.2479822,"\int \frac{(a+b \tan (c+d x))^2}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^2/Cot[c + d*x]^(3/2),x]","\frac{2 \left(a^2-b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 \left(a^2-b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 b^2}{5 d \cot ^{\frac{5}{2}}(c+d x)}",1,"-(((a^2 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2)/(5*d*Cot[c + d*x]^(5/2)) + (4*a*b)/(3*d*Cot[c + d*x]^(3/2)) + (2*(a^2 - b^2))/(d*Sqrt[Cot[c + d*x]]) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,10,23,0.4348,1,"{3673, 3542, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
812,1,268,0,0.2857688,"\int \frac{(a+b \tan (c+d x))^2}{\cot ^{\frac{5}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^2/Cot[c + d*x]^(5/2),x]","\frac{2 \left(a^2-b^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{5 d \cot ^{\frac{5}{2}}(c+d x)}-\frac{4 a b}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}","\frac{2 \left(a^2-b^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{\left(a^2+2 a b-b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{\left(a^2-2 a b-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{4 a b}{5 d \cot ^{\frac{5}{2}}(c+d x)}-\frac{4 a b}{d \sqrt{\cot (c+d x)}}+\frac{2 b^2}{7 d \cot ^{\frac{7}{2}}(c+d x)}",1,"-(((a^2 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b^2)/(7*d*Cot[c + d*x]^(7/2)) + (4*a*b)/(5*d*Cot[c + d*x]^(5/2)) + (2*(a^2 - b^2))/(3*d*Cot[c + d*x]^(3/2)) - (4*a*b)/(d*Sqrt[Cot[c + d*x]]) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,10,23,0.4348,1,"{3673, 3542, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
813,1,299,0,0.4382234,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^3,x]","\frac{2 a \left(a^2-3 b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b \left(3 a^2-b^2\right) \sqrt{\cot (c+d x)}}{d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x) (a \cot (c+d x)+b)}{7 d}-\frac{32 a^2 b \cot ^{\frac{5}{2}}(c+d x)}{35 d}","\frac{2 a \left(a^2-3 b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 d}+\frac{2 b \left(3 a^2-b^2\right) \sqrt{\cot (c+d x)}}{d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x) (a \cot (c+d x)+b)}{7 d}-\frac{32 a^2 b \cot ^{\frac{5}{2}}(c+d x)}{35 d}",1,"((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*b*(3*a^2 - b^2)*Sqrt[Cot[c + d*x]])/d + (2*a*(a^2 - 3*b^2)*Cot[c + d*x]^(3/2))/(3*d) - (32*a^2*b*Cot[c + d*x]^(5/2))/(35*d) - (2*a^2*Cot[c + d*x]^(5/2)*(b + a*Cot[c + d*x]))/(7*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,11,23,0.4783,1,"{3673, 3566, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
814,1,270,0,0.3839039,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^3,x]","\frac{2 a \left(a^2-3 b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{8 a^2 b \cot ^{\frac{3}{2}}(c+d x)}{5 d}-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)}{5 d}","\frac{2 a \left(a^2-3 b^2\right) \sqrt{\cot (c+d x)}}{d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{8 a^2 b \cot ^{\frac{3}{2}}(c+d x)}{5 d}-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x) (a \cot (c+d x)+b)}{5 d}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (2*a*(a^2 - 3*b^2)*Sqrt[Cot[c + d*x]])/d - (8*a^2*b*Cot[c + d*x]^(3/2))/(5*d) - (2*a^2*Cot[c + d*x]^(3/2)*(b + a*Cot[c + d*x]))/(5*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,23,0.4783,1,"{3673, 3566, 3630, 3528, 3534, 1168, 1162, 617, 204, 1165, 628}"
815,1,245,0,0.3508953,"\int \cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3,x]","\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}{3 d}-\frac{16 a^2 b \sqrt{\cot (c+d x)}}{3 d}","\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}-\frac{2 a^2 \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}{3 d}-\frac{16 a^2 b \sqrt{\cot (c+d x)}}{3 d}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (16*a^2*b*Sqrt[Cot[c + d*x]])/(3*d) - (2*a^2*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x]))/(3*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,23,0.4348,1,"{3673, 3566, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
816,1,245,0,0.3431694,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3 \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3,x]","-\frac{2 a \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{d \sqrt{\cot (c+d x)}}","-\frac{2 a \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}{d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{d \sqrt{\cot (c+d x)}}",1,"-(((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - (2*a*(a^2 + b^2)*Sqrt[Cot[c + d*x]])/d + (2*b^2*(b + a*Cot[c + d*x]))/(d*Sqrt[Cot[c + d*x]]) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,23,0.4348,1,"{3673, 3565, 3630, 3534, 1168, 1162, 617, 204, 1165, 628}"
817,1,245,0,0.3416489,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^3 \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^3,x]","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{16 a b^2}{3 d \sqrt{\cot (c+d x)}}","-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{16 a b^2}{3 d \sqrt{\cot (c+d x)}}",1,"((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (16*a*b^2)/(3*d*Sqrt[Cot[c + d*x]]) + (2*b^2*(b + a*Cot[c + d*x]))/(3*d*Cot[c + d*x]^(3/2)) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",13,10,23,0.4348,1,"{3673, 3565, 3628, 3534, 1168, 1162, 617, 204, 1165, 628}"
818,1,272,0,0.3925369,"\int \frac{(a+b \tan (c+d x))^3}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^3/Sqrt[Cot[c + d*x]],x]","\frac{2 b \left(3 a^2-b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 a b^2}{5 d \cot ^{\frac{3}{2}}(c+d x)}","\frac{2 b \left(3 a^2-b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{5 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{8 a b^2}{5 d \cot ^{\frac{3}{2}}(c+d x)}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (8*a*b^2)/(5*d*Cot[c + d*x]^(3/2)) + (2*b*(3*a^2 - b^2))/(d*Sqrt[Cot[c + d*x]]) + (2*b^2*(b + a*Cot[c + d*x]))/(5*d*Cot[c + d*x]^(5/2)) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",14,11,23,0.4783,1,"{3673, 3565, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
819,1,299,0,0.4426675,"\int \frac{(a+b \tan (c+d x))^3}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^3/Cot[c + d*x]^(3/2),x]","\frac{2 b \left(3 a^2-b^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{7 d \cot ^{\frac{7}{2}}(c+d x)}+\frac{32 a b^2}{35 d \cot ^{\frac{5}{2}}(c+d x)}","\frac{2 b \left(3 a^2-b^2\right)}{3 d \cot ^{\frac{3}{2}}(c+d x)}+\frac{2 a \left(a^2-3 b^2\right)}{d \sqrt{\cot (c+d x)}}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)-\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \log \left(\cot (c+d x)+\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{2 \sqrt{2} d}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d}+\frac{2 b^2 (a \cot (c+d x)+b)}{7 d \cot ^{\frac{7}{2}}(c+d x)}+\frac{32 a b^2}{35 d \cot ^{\frac{5}{2}}(c+d x)}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*d) + (32*a*b^2)/(35*d*Cot[c + d*x]^(5/2)) + (2*b*(3*a^2 - b^2))/(3*d*Cot[c + d*x]^(3/2)) + (2*a*(a^2 - 3*b^2))/(d*Sqrt[Cot[c + d*x]]) + (2*b^2*(b + a*Cot[c + d*x]))/(7*d*Cot[c + d*x]^(7/2)) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*d)","A",15,11,23,0.4783,1,"{3673, 3565, 3628, 3529, 3534, 1168, 1162, 617, 204, 1165, 628}"
820,1,271,0,0.6726999,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(5/2)/(a + b*Tan[c + d*x]),x]","\frac{(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+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^{7/2} \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{(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-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 \sqrt{\cot (c+d x)}}{a^2 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d}","\frac{(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+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^{7/2} \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{(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-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 \sqrt{\cot (c+d x)}}{a^2 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(7/2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(5/2)*(a^2 + b^2)*d) + (2*b*Sqrt[Cot[c + d*x]])/(a^2*d) - (2*Cot[c + d*x]^(3/2))/(3*a*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",17,14,23,0.6087,1,"{3673, 3566, 3647, 3654, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
821,1,250,0,0.4852548,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(3/2)/(a + b*Tan[c + d*x]),x]","-\frac{(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-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} \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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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{\cot (c+d x)}}{a d}","-\frac{(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-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} \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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}+\frac{(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{\cot (c+d x)}}{a d}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*b^(5/2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(3/2)*(a^2 + b^2)*d) - (2*Sqrt[Cot[c + d*x]])/(a*d) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",16,13,23,0.5652,1,"{3673, 3566, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
822,1,232,0,0.3005856,"\int \frac{\sqrt{\cot (c+d x)}}{a+b \tan (c+d x)} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + b*Tan[c + d*x]),x]","-\frac{(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+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} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}","-\frac{(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+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} \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-b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(a-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}",1,"((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*b^(3/2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[a]*(a^2 + b^2)*d) - ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,23,0.5217,1,"{3673, 3573, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
823,1,232,0,0.2942023,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])),x]","\frac{(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-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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{d \left(a^2+b^2\right)}","\frac{(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-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+b) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)}-\frac{(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} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{d \left(a^2+b^2\right)}",1,"((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/((a^2 + b^2)*d) + ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,23,0.5217,1,"{3673, 3572, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
824,1,232,0,0.2975611,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])),x]","\frac{(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+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} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}-\frac{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}","\frac{(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+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} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)}-\frac{(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-b) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)}",1,"-(((a - b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a - b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) - (2*a^(3/2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[b]*(a^2 + b^2)*d) + ((a + b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) - ((a + b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",15,12,23,0.5217,1,"{3673, 3574, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
825,1,250,0,0.49386,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])),x]","-\frac{(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-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} \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{(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+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 d \sqrt{\cot (c+d x)}}","-\frac{(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-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} \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{(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+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 d \sqrt{\cot (c+d x)}}",1,"-(((a + b)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d)) + ((a + b)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)*d) + (2*a^(5/2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(3/2)*(a^2 + b^2)*d) + 2/(b*d*Sqrt[Cot[c + d*x]]) - ((a - b)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d) + ((a - b)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)*d)","A",16,13,23,0.5652,1,"{3673, 3569, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
826,1,398,0,1.0974586,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^(5/2)/(a + b*Tan[c + d*x])^2,x]","\frac{b^2 \cot ^{\frac{5}{2}}(c+d x)}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(2 a^2+5 b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 a^2 d \left(a^2+b^2\right)}+\frac{b \left(4 a^2+5 b^2\right) \sqrt{\cot (c+d x)}}{a^3 d \left(a^2+b^2\right)}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{7/2} \left(9 a^2+5 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{7/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^2 \cot ^{\frac{5}{2}}(c+d x)}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(2 a^2+5 b^2\right) \cot ^{\frac{3}{2}}(c+d x)}{3 a^2 d \left(a^2+b^2\right)}+\frac{b \left(4 a^2+5 b^2\right) \sqrt{\cot (c+d x)}}{a^3 d \left(a^2+b^2\right)}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{7/2} \left(9 a^2+5 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{a^{7/2} d \left(a^2+b^2\right)^2}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (b^(7/2)*(9*a^2 + 5*b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(7/2)*(a^2 + b^2)^2*d) + (b*(4*a^2 + 5*b^2)*Sqrt[Cot[c + d*x]])/(a^3*(a^2 + b^2)*d) - ((2*a^2 + 5*b^2)*Cot[c + d*x]^(3/2))/(3*a^2*(a^2 + b^2)*d) + (b^2*Cot[c + d*x]^(5/2))/(a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",18,14,23,0.6087,1,"{3673, 3565, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
827,1,357,0,0.8197944,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{(a+b \tan (c+d x))^2} \, dx","Int[Cot[c + d*x]^(3/2)/(a + b*Tan[c + d*x])^2,x]","\frac{b^2 \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+3 b^2\right) \sqrt{\cot (c+d x)}}{a^2 d \left(a^2+b^2\right)}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^{5/2} \left(7 a^2+3 b^2\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+2 a b-b^2\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+2 a b-b^2\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^2 \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+3 b^2\right) \sqrt{\cot (c+d x)}}{a^2 d \left(a^2+b^2\right)}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^{5/2} \left(7 a^2+3 b^2\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+2 a b-b^2\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+2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (b^(5/2)*(7*a^2 + 3*b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(5/2)*(a^2 + b^2)^2*d) - ((2*a^2 + 3*b^2)*Sqrt[Cot[c + d*x]])/(a^2*(a^2 + b^2)*d) + (b^2*Cot[c + d*x]^(3/2))/(a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",17,14,23,0.6087,1,"{3673, 3565, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
828,1,318,0,0.5697195,"\int \frac{\sqrt{\cot (c+d x)}}{(a+b \tan (c+d x))^2} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + b*Tan[c + d*x])^2,x]","\frac{b^2 \sqrt{\cot (c+d x)}}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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(5 a^2+b^2\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{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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^2 \sqrt{\cot (c+d x)}}{a d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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(5 a^2+b^2\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{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (b^(3/2)*(5*a^2 + b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(a^(3/2)*(a^2 + b^2)^2*d) + (b^2*Sqrt[Cot[c + d*x]])/(a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,23,0.5652,1,"{3673, 3565, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
829,1,315,0,0.508131,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^2} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^2),x]","-\frac{b \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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{\sqrt{b} \left(3 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} d \left(a^2+b^2\right)^2}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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{\sqrt{b} \left(3 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a} d \left(a^2+b^2\right)^2}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (Sqrt[b]*(3*a^2 - b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[a]*(a^2 + b^2)^2*d) - (b*Sqrt[Cot[c + d*x]])/((a^2 + b^2)*d*(b + a*Cot[c + d*x])) + ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,23,0.5652,1,"{3673, 3567, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
830,1,313,0,0.4900098,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^2),x]","\frac{a \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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{\sqrt{a} \left(a^2-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)^2}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 \sqrt{\cot (c+d x)}}{d \left(a^2+b^2\right) (a \cot (c+d x)+b)}+\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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{\sqrt{a} \left(a^2-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d \left(a^2+b^2\right)^2}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (Sqrt[a]*(a^2 - 3*b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(Sqrt[b]*(a^2 + b^2)^2*d) + (a*Sqrt[Cot[c + d*x]])/((a^2 + b^2)*d*(b + a*Cot[c + d*x])) + ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,23,0.5652,1,"{3673, 3568, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
831,1,319,0,0.5751695,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^2),x]","-\frac{a^2 \sqrt{\cot (c+d x)}}{b d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+5 b^2\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{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^2 \sqrt{\cot (c+d x)}}{b d \left(a^2+b^2\right) (a \cot (c+d x)+b)}-\frac{\left(a^2-2 a b-b^2\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^2-2 a b-b^2\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+5 b^2\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{\left(a^2+2 a b-b^2\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+2 a b-b^2\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 + 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d)) + ((a^2 + 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - (a^(3/2)*(a^2 + 5*b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(3/2)*(a^2 + b^2)^2*d) - (a^2*Sqrt[Cot[c + d*x]])/(b*(a^2 + b^2)*d*(b + a*Cot[c + d*x])) - ((a^2 - 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 - 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",16,13,23,0.5652,1,"{3673, 3569, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
832,1,357,0,0.8453001,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^2} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^2),x]","-\frac{a^2}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}+\frac{3 a^2+2 b^2}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{5/2} \left(3 a^2+7 b^2\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^2-2 a b-b^2\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^2-2 a b-b^2\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^2}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a \cot (c+d x)+b)}+\frac{3 a^2+2 b^2}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}-\frac{\left(a^2+2 a b-b^2\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+2 a b-b^2\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^{5/2} \left(3 a^2+7 b^2\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^2-2 a b-b^2\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^2-2 a b-b^2\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 - 2*a*b - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) - ((a^2 - 2*a*b - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^2*d) + (a^(5/2)*(3*a^2 + 7*b^2)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(b^(5/2)*(a^2 + b^2)^2*d) + (3*a^2 + 2*b^2)/(b^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]) - a^2/(b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(b + a*Cot[c + d*x])) - ((a^2 + 2*a*b - b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d) + ((a^2 + 2*a*b - b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^2*d)","A",17,14,23,0.6087,1,"{3673, 3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
833,1,493,0,1.5618157,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]^(5/2)/(a + b*Tan[c + d*x])^3,x]","\frac{b^2 \left(15 a^2+7 b^2\right) \cot ^{\frac{5}{2}}(c+d x)}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{b^2 \cot ^{\frac{7}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(67 a^2 b^2+8 a^4+35 b^4\right) \cot ^{\frac{3}{2}}(c+d x)}{12 a^3 d \left(a^2+b^2\right)^2}+\frac{b \left(67 a^2 b^2+24 a^4+35 b^4\right) \sqrt{\cot (c+d x)}}{4 a^4 d \left(a^2+b^2\right)^2}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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{b^{7/2} \left(102 a^2 b^2+99 a^4+35 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{9/2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(15 a^2+7 b^2\right) \cot ^{\frac{5}{2}}(c+d x)}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{b^2 \cot ^{\frac{7}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(67 a^2 b^2+8 a^4+35 b^4\right) \cot ^{\frac{3}{2}}(c+d x)}{12 a^3 d \left(a^2+b^2\right)^2}+\frac{b \left(67 a^2 b^2+24 a^4+35 b^4\right) \sqrt{\cot (c+d x)}}{4 a^4 d \left(a^2+b^2\right)^2}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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{b^{7/2} \left(102 a^2 b^2+99 a^4+35 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{9/2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (b^(7/2)*(99*a^4 + 102*a^2*b^2 + 35*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(9/2)*(a^2 + b^2)^3*d) + (b*(24*a^4 + 67*a^2*b^2 + 35*b^4)*Sqrt[Cot[c + d*x]])/(4*a^4*(a^2 + b^2)^2*d) - ((8*a^4 + 67*a^2*b^2 + 35*b^4)*Cot[c + d*x]^(3/2))/(12*a^3*(a^2 + b^2)^2*d) + (b^2*Cot[c + d*x]^(7/2))/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + (b^2*(15*a^2 + 7*b^2)*Cot[c + d*x]^(5/2))/(4*a^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",19,15,23,0.6522,1,"{3673, 3565, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
834,1,444,0,1.2127677,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{(a+b \tan (c+d x))^3} \, dx","Int[Cot[c + d*x]^(3/2)/(a + b*Tan[c + d*x])^3,x]","\frac{b^2 \left(13 a^2+5 b^2\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{b^2 \cot ^{\frac{5}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(31 a^2 b^2+8 a^4+15 b^4\right) \sqrt{\cot (c+d x)}}{4 a^3 d \left(a^2+b^2\right)^2}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{b^{5/2} \left(46 a^2 b^2+63 a^4+15 b^4\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{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \left(13 a^2+5 b^2\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{b^2 \cot ^{\frac{5}{2}}(c+d x)}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{\left(31 a^2 b^2+8 a^4+15 b^4\right) \sqrt{\cot (c+d x)}}{4 a^3 d \left(a^2+b^2\right)^2}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{b^{5/2} \left(46 a^2 b^2+63 a^4+15 b^4\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{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (b^(5/2)*(63*a^4 + 46*a^2*b^2 + 15*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(7/2)*(a^2 + b^2)^3*d) - ((8*a^4 + 31*a^2*b^2 + 15*b^4)*Sqrt[Cot[c + d*x]])/(4*a^3*(a^2 + b^2)^2*d) + (b^2*Cot[c + d*x]^(5/2))/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + (b^2*(13*a^2 + 5*b^2)*Cot[c + d*x]^(3/2))/(4*a^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",18,15,23,0.6522,1,"{3673, 3565, 3645, 3647, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
835,1,396,0,0.9258714,"\int \frac{\sqrt{\cot (c+d x)}}{(a+b \tan (c+d x))^3} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + b*Tan[c + d*x])^3,x]","\frac{b^2 \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^2 \left(11 a^2+3 b^2\right) \sqrt{\cot (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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{b^{3/2} \left(6 a^2 b^2+35 a^4+3 b^4\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{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \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^2 \left(11 a^2+3 b^2\right) \sqrt{\cot (c+d x)}}{4 a^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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{b^{3/2} \left(6 a^2 b^2+35 a^4+3 b^4\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{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (b^(3/2)*(35*a^4 + 6*a^2*b^2 + 3*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(5/2)*(a^2 + b^2)^3*d) + (b^2*Cot[c + d*x]^(3/2))/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + (b^2*(11*a^2 + 3*b^2)*Sqrt[Cot[c + d*x]])/(4*a^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,23,0.6087,1,"{3673, 3565, 3645, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
836,1,392,0,0.9759478,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^3} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^3),x]","\frac{b^2 \sqrt{\cot (c+d x)}}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{b \left(9 a^2+b^2\right) \sqrt{\cot (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{b} \left(-18 a^2 b^2+15 a^4-b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{3/2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\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^2 \sqrt{\cot (c+d x)}}{2 a d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{b \left(9 a^2+b^2\right) \sqrt{\cot (c+d x)}}{4 a d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{b} \left(-18 a^2 b^2+15 a^4-b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 a^{3/2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) + (Sqrt[b]*(15*a^4 - 18*a^2*b^2 - b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*a^(3/2)*(a^2 + b^2)^3*d) + (b^2*Sqrt[Cot[c + d*x]])/(2*a*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) - (b*(9*a^2 + b^2)*Sqrt[Cot[c + d*x]])/(4*a*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,23,0.6087,1,"{3673, 3565, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
837,1,385,0,0.8949718,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{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^2-3 b^2\right) \sqrt{\cot (c+d x)}}{4 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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 b^2+3 a^4+3 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^3}","-\frac{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^2-3 b^2\right) \sqrt{\cot (c+d x)}}{4 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a+b) \left(a^2-4 a b+b^2\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 b^2+3 a^4+3 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{a} \sqrt{b} d \left(a^2+b^2\right)^3}",1,"-(((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((3*a^4 - 26*a^2*b^2 + 3*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*Sqrt[a]*Sqrt[b]*(a^2 + b^2)^3*d) - (b*Sqrt[Cot[c + d*x]])/(2*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) + ((5*a^2 - 3*b^2)*Sqrt[Cot[c + d*x]])/(4*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,23,0.6087,1,"{3673, 3567, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
838,1,385,0,0.862727,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{a \left(a^2-7 b^2\right) \sqrt{\cot (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{a \sqrt{\cot (c+d x)}}{2 d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{a} \left(18 a^2 b^2+a^4-15 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\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^2-7 b^2\right) \sqrt{\cot (c+d x)}}{4 b d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}+\frac{a \sqrt{\cot (c+d x)}}{2 d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{(a+b) \left(a^2-4 a b+b^2\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+b) \left(a^2-4 a b+b^2\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{\sqrt{a} \left(18 a^2 b^2+a^4-15 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{\cot (c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d \left(a^2+b^2\right)^3}-\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}+\frac{(a-b) \left(a^2+4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"-(((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d)) + ((a - b)*(a^2 + 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (Sqrt[a]*(a^4 + 18*a^2*b^2 - 15*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*(a^2 + b^2)^3*d) + (a*Sqrt[Cot[c + d*x]])/(2*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) - (a*(a^2 - 7*b^2)*Sqrt[Cot[c + d*x]])/(4*b*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a + b)*(a^2 - 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,23,0.6087,1,"{3673, 3568, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
839,1,396,0,0.9358573,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^3} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^3),x]","-\frac{a^2 \left(3 a^2+11 b^2\right) \sqrt{\cot (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{a^2 \sqrt{\cot (c+d x)}}{2 b d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 b^2+3 a^4+35 b^4\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\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^2 \left(3 a^2+11 b^2\right) \sqrt{\cot (c+d x)}}{4 b^2 d \left(a^2+b^2\right)^2 (a \cot (c+d x)+b)}-\frac{a^2 \sqrt{\cot (c+d x)}}{2 b d \left(a^2+b^2\right) (a \cot (c+d x)+b)^2}-\frac{(a-b) \left(a^2+4 a b+b^2\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-b) \left(a^2+4 a b+b^2\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 b^2+3 a^4+35 b^4\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+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\cot (c+d x)}\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}-\frac{(a+b) \left(a^2-4 a b+b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\cot (c+d x)}+1\right)}{\sqrt{2} d \left(a^2+b^2\right)^3}",1,"((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - ((a + b)*(a^2 - 4*a*b + b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Cot[c + d*x]]])/(Sqrt[2]*(a^2 + b^2)^3*d) - (a^(3/2)*(3*a^4 + 6*a^2*b^2 + 35*b^4)*ArcTan[(Sqrt[a]*Sqrt[Cot[c + d*x]])/Sqrt[b]])/(4*b^(5/2)*(a^2 + b^2)^3*d) - (a^2*Sqrt[Cot[c + d*x]])/(2*b*(a^2 + b^2)*d*(b + a*Cot[c + d*x])^2) - (a^2*(3*a^2 + 11*b^2)*Sqrt[Cot[c + d*x]])/(4*b^2*(a^2 + b^2)^2*d*(b + a*Cot[c + d*x])) - ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 - Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d) + ((a - b)*(a^2 + 4*a*b + b^2)*Log[1 + Sqrt[2]*Sqrt[Cot[c + d*x]] + Cot[c + d*x]])/(2*Sqrt[2]*(a^2 + b^2)^3*d)","A",17,14,23,0.6087,1,"{3673, 3569, 3649, 3653, 3534, 1168, 1162, 617, 204, 1165, 628, 3634, 63, 205}"
840,1,261,0,0.9026238,"\int \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]],x]","\frac{2 \left(15 a^2+2 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^2 d}-\frac{2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{2 b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a d}+\frac{\sqrt{-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} \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 \left(15 a^2+2 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 a^2 d}-\frac{2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{2 b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 a d}+\frac{\sqrt{-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} \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}",1,"(Sqrt[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]*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 + 2*b^2)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*a^2*d) - (2*b*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*a*d) - (2*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d)","A",11,8,25,0.3200,1,"{4241, 3568, 3649, 3616, 3615, 93, 203, 206}"
841,1,221,0,0.43408,"\int \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{i \sqrt{-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 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a d}+\frac{i \sqrt{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 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{i \sqrt{-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 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a d}+\frac{i \sqrt{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}",1,"(I*Sqrt[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*Sqrt[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*b*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*a*d) - (2*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",11,9,25,0.3600,1,"{4241, 3568, 3649, 21, 3575, 910, 93, 205, 208}"
842,1,179,0,0.484787,"\int \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)} \, dx","Int[Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{\sqrt{-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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{\sqrt{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{\sqrt{-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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{\sqrt{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}",1,"-((Sqrt[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]*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*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",9,7,25,0.2800,1,"{4241, 3568, 3616, 3615, 93, 203, 206}"
843,1,155,0,0.1915516,"\int \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)} \, dx","Int[Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]],x]","-\frac{i \sqrt{-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{i \sqrt{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{i \sqrt{-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{i \sqrt{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}",1,"((-I)*Sqrt[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*Sqrt[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",8,6,25,0.2400,1,"{4241, 3575, 910, 93, 205, 208}"
844,1,211,0,0.5829315,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\sqrt{\cot (c+d x)}} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Sqrt[Cot[c + d*x]],x]","\frac{\sqrt{-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 \sqrt{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} \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{\sqrt{-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 \sqrt{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} \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}",1,"(Sqrt[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]*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]*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",12,10,25,0.4000,1,"{4241, 3575, 906, 63, 217, 206, 6725, 93, 205, 208}"
845,1,244,0,0.7057842,"\int \frac{\sqrt{a+b \tan (c+d x)}}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[Sqrt[a + b*Tan[c + d*x]]/Cot[c + d*x]^(3/2),x]","\frac{i \sqrt{-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{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{a \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{i \sqrt{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{i \sqrt{-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{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{a \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{i \sqrt{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}",1,"(I*Sqrt[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 + (a*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*Sqrt[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 + Sqrt[a + b*Tan[c + d*x]]/(d*Sqrt[Cot[c + d*x]])","A",14,11,25,0.4400,1,"{4241, 3570, 3655, 6725, 63, 217, 206, 910, 93, 205, 208}"
846,1,306,0,1.227405,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 \left(35 a^2-3 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{4 b \left(70 a^2+3 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^2 d}-\frac{2 a \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}-\frac{16 b \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}-\frac{(-b+i a)^{3/2} \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} \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 \left(35 a^2-3 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 a d}+\frac{4 b \left(70 a^2+3 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{105 a^2 d}-\frac{2 a \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}-\frac{16 b \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{35 d}-\frac{(-b+i a)^{3/2} \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} \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}",1,"-(((I*a - b)^(3/2)*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)*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*b*(70*a^2 + 3*b^2)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(105*a^2*d) + (2*(35*a^2 - 3*b^2)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(105*a*d) - (16*b*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(35*d) - (2*a*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(7*d)","A",12,8,25,0.3200,1,"{4241, 3567, 3649, 3616, 3615, 93, 203, 206}"
847,1,264,0,0.9466385,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{3/2} \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 \left(5 a^2-b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{5 a d}-\frac{2 a \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{4 b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{i (-b+i a)^{3/2} \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{i (b+i a)^{3/2} \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 \left(5 a^2-b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{5 a d}-\frac{2 a \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{4 b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{i (-b+i a)^{3/2} \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{i (b+i a)^{3/2} \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}",1,"((-I)*(I*a - b)^(3/2)*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*(I*a + b)^(3/2)*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*(5*a^2 - b^2)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(5*a*d) - (4*b*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d) - (2*a*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d)","A",11,8,25,0.3200,1,"{4241, 3567, 3649, 3616, 3615, 93, 203, 206}"
848,1,213,0,0.7254286,"\int \cot ^{\frac{5}{2}}(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])^(3/2),x]","-\frac{2 a \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{(-b+i a)^{3/2} \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 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{(b+i a)^{3/2} \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{(-b+i a)^{3/2} \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 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}+\frac{(b+i a)^{3/2} \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}",1,"((I*a - b)^(3/2)*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)*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 - (8*b*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*d) - (2*a*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",10,8,25,0.3200,1,"{4241, 3567, 3649, 3616, 3615, 93, 203, 206}"
849,1,185,0,0.5375051,"\int \cot ^{\frac{3}{2}}(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])^(3/2),x]","\frac{i (-b+i a)^{3/2} \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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (b+i a)^{3/2} \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{i (-b+i a)^{3/2} \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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}-\frac{i (b+i a)^{3/2} \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}",1,"(I*(I*a - b)^(3/2)*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*(I*a + b)^(3/2)*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",9,7,25,0.2800,1,"{4241, 3567, 3616, 3615, 93, 203, 206}"
850,1,212,0,0.7311383,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2} \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b^{3/2} \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} \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} \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 b^{3/2} \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} \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} \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}",1,"-(((I*a - b)^(3/2)*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^(3/2)*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)*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",13,10,25,0.4000,1,"{4241, 3575, 910, 63, 217, 206, 6725, 93, 205, 208}"
851,1,246,0,1.2385662,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Sqrt[Cot[c + d*x]],x]","-\frac{i (-b+i a)^{3/2} \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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{3 a \sqrt{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{i (b+i a)^{3/2} \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{i (-b+i a)^{3/2} \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 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{3 a \sqrt{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{i (b+i a)^{3/2} \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}",1,"((-I)*(I*a - b)^(3/2)*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 + (3*a*Sqrt[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*(I*a + b)^(3/2)*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",14,10,25,0.4000,1,"{4241, 3570, 3655, 6725, 63, 217, 206, 93, 205, 208}"
852,1,286,0,1.3772189,"\int \frac{(a+b \tan (c+d x))^{3/2}}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(3/2)/Cot[c + d*x]^(3/2),x]","\frac{\left(3 a^2-8 b^2\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{(-b+i a)^{3/2} \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 \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}+\frac{3 a \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} \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{\left(3 a^2-8 b^2\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{(-b+i a)^{3/2} \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 \tan (c+d x))^{3/2}}{2 d \sqrt{\cot (c+d x)}}+\frac{3 a \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{3/2} \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}",1,"((I*a - b)^(3/2)*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 + ((3*a^2 - 8*b^2)*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)*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 + (3*a*Sqrt[a + b*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]]) + (a + b*Tan[c + d*x])^(3/2)/(2*d*Sqrt[Cot[c + d*x]])","A",15,11,25,0.4400,1,"{4241, 3570, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
853,1,358,0,1.6715018,"\int \cot ^{\frac{11}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(11/2)*(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 \left(21 a^2-25 b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 b \left(231 a^2-5 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a d}-\frac{2 \left(-483 a^2 b^2+315 a^4-10 b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 a^2 \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{9 d}-\frac{38 a b \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{63 d}+\frac{(-b+i a)^{5/2} \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} \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 \left(21 a^2-25 b^2\right) \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{105 d}+\frac{2 b \left(231 a^2-5 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{315 a d}-\frac{2 \left(-483 a^2 b^2+315 a^4-10 b^4\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{315 a^2 d}-\frac{2 a^2 \cot ^{\frac{9}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{9 d}-\frac{38 a b \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{63 d}+\frac{(-b+i a)^{5/2} \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} \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}",1,"((I*a - b)^(5/2)*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)*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 - 483*a^2*b^2 - 10*b^4)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(315*a^2*d) + (2*b*(231*a^2 - 5*b^2)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(315*a*d) + (2*(21*a^2 - 25*b^2)*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(105*d) - (38*a*b*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(63*d) - (2*a^2*Cot[c + d*x]^(9/2)*Sqrt[a + b*Tan[c + d*x]])/(9*d)","A",13,8,25,0.3200,1,"{4241, 3565, 3649, 3616, 3615, 93, 203, 206}"
854,1,310,0,1.3473645,"\int \cot ^{\frac{9}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(9/2)*(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 \left(7 a^2-9 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{21 d}+\frac{2 b \left(49 a^2-3 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{21 a d}-\frac{2 a^2 \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}-\frac{6 a b \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}+\frac{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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 \left(7 a^2-9 b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{21 d}+\frac{2 b \left(49 a^2-3 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{21 a d}-\frac{2 a^2 \cot ^{\frac{7}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}-\frac{6 a b \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{7 d}+\frac{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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}",1,"(I*(I*a - b)^(5/2)*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*(I*a + b)^(5/2)*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*b*(49*a^2 - 3*b^2)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(21*a*d) + (2*(7*a^2 - 9*b^2)*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(21*d) - (6*a*b*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(7*d) - (2*a^2*Cot[c + d*x]^(7/2)*Sqrt[a + b*Tan[c + d*x]])/(7*d)","A",12,8,25,0.3200,1,"{4241, 3565, 3649, 3616, 3615, 93, 203, 206}"
855,1,259,0,1.0408293,"\int \cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{5/2} \, dx","Int[Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(5/2),x]","\frac{2 \left(15 a^2-23 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{22 a b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{(-b+i a)^{5/2} \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} \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 \left(15 a^2-23 b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{2 a^2 \cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{5 d}-\frac{22 a b \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{15 d}-\frac{(-b+i a)^{5/2} \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} \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}",1,"-(((I*a - b)^(5/2)*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)*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 - 23*b^2)*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(15*d) - (22*a*b*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(15*d) - (2*a^2*Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]])/(5*d)","A",11,8,25,0.3200,1,"{4241, 3565, 3649, 3616, 3615, 93, 203, 206}"
856,1,222,0,0.803491,"\int \cot ^{\frac{5}{2}}(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])^(5/2),x]","-\frac{2 a^2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (-b+i a)^{5/2} \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{14 a b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (b+i a)^{5/2} \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^2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (-b+i a)^{5/2} \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{14 a b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 d}-\frac{i (b+i a)^{5/2} \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}",1,"((-I)*(I*a - b)^(5/2)*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*(I*a + b)^(5/2)*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*b*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*d) - (2*a^2*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*d)","A",10,8,25,0.3200,1,"{4241, 3565, 3649, 3616, 3615, 93, 203, 206}"
857,1,243,0,1.3931611,"\int \cot ^{\frac{3}{2}}(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])^(5/2),x]","-\frac{2 a^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b^{5/2} \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} \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} \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^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{d}+\frac{2 b^{5/2} \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} \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} \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}",1,"((I*a - b)^(5/2)*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)*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)*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*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/d","A",14,10,25,0.4000,1,"{4241, 3565, 3655, 6725, 63, 217, 206, 93, 205, 208}"
858,1,248,0,1.3842658,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{5/2} \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{5 a b^{3/2} \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{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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^2 \sqrt{a+b \tan (c+d x)}}{d \sqrt{\cot (c+d x)}}+\frac{5 a b^{3/2} \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{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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}",1,"(I*(I*a - b)^(5/2)*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 + (5*a*b^(3/2)*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*(I*a + b)^(5/2)*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*Sqrt[a + b*Tan[c + d*x]])/(d*Sqrt[Cot[c + d*x]])","A",14,10,25,0.4000,1,"{4241, 3566, 3655, 6725, 63, 217, 206, 93, 205, 208}"
859,1,291,0,1.9983034,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Sqrt[Cot[c + d*x]],x]","\frac{\sqrt{b} \left(15 a^2-8 b^2\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^2 \sqrt{a+b \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{(-b+i a)^{5/2} \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{9 a b \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} \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{\sqrt{b} \left(15 a^2-8 b^2\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^2 \sqrt{a+b \tan (c+d x)}}{2 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{(-b+i a)^{5/2} \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{9 a b \sqrt{a+b \tan (c+d x)}}{4 d \sqrt{\cot (c+d x)}}+\frac{(b+i a)^{5/2} \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}",1,"-(((I*a - b)^(5/2)*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]*(15*a^2 - 8*b^2)*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)*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*Sqrt[a + b*Tan[c + d*x]])/(2*d*Cot[c + d*x]^(3/2)) + (9*a*b*Sqrt[a + b*Tan[c + d*x]])/(4*d*Sqrt[Cot[c + d*x]])","A",15,11,25,0.4400,1,"{4241, 3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
860,1,337,0,2.1256358,"\int \frac{(a+b \tan (c+d x))^{5/2}}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^(5/2)/Cot[c + d*x]^(3/2),x]","\frac{\left(11 a^2-8 b^2\right) \sqrt{a+b \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}+\frac{5 a \left(a^2-8 b^2\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^2 \sqrt{a+b \tan (c+d x)}}{3 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{13 a b \sqrt{a+b \tan (c+d x)}}{12 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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{\left(11 a^2-8 b^2\right) \sqrt{a+b \tan (c+d x)}}{8 d \sqrt{\cot (c+d x)}}+\frac{5 a \left(a^2-8 b^2\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^2 \sqrt{a+b \tan (c+d x)}}{3 d \cot ^{\frac{5}{2}}(c+d x)}+\frac{13 a b \sqrt{a+b \tan (c+d x)}}{12 d \cot ^{\frac{3}{2}}(c+d x)}-\frac{i (-b+i a)^{5/2} \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{i (b+i a)^{5/2} \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}",1,"((-I)*(I*a - b)^(5/2)*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 + (5*a*(a^2 - 8*b^2)*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*(I*a + b)^(5/2)*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*Sqrt[a + b*Tan[c + d*x]])/(3*d*Cot[c + d*x]^(5/2)) + (13*a*b*Sqrt[a + b*Tan[c + d*x]])/(12*d*Cot[c + d*x]^(3/2)) + ((11*a^2 - 8*b^2)*Sqrt[a + b*Tan[c + d*x]])/(8*d*Sqrt[Cot[c + d*x]])","A",16,11,25,0.4400,1,"{4241, 3566, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
861,1,220,0,0.4391665,"\int \frac{\cot ^{\frac{5}{2}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^(5/2)/Sqrt[a + b*Tan[c + d*x]],x]","\frac{4 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a^2 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 a d}-\frac{\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{\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{4 b \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{3 a^2 d}-\frac{2 \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}{3 a d}-\frac{\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{\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,"-((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)) - (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) + (4*b*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(3*a^2*d) - (2*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]])/(3*a*d)","A",11,9,25,0.3600,1,"{4241, 3569, 3649, 12, 3575, 912, 93, 205, 208}"
862,1,187,0,0.2753597,"\int \frac{\cot ^{\frac{3}{2}}(c+d x)}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Cot[c + d*x]^(3/2)/Sqrt[a + b*Tan[c + d*x]],x]","-\frac{i \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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{a d}+\frac{i \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 \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 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}{a d}+\frac{i \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)*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*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*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])/(a*d)","A",10,8,25,0.3200,1,"{4241, 3569, 12, 3575, 910, 93, 205, 208}"
863,1,149,0,0.1944045,"\int \frac{\sqrt{\cot (c+d x)}}{\sqrt{a+b \tan (c+d x)}} \, dx","Int[Sqrt[Cot[c + d*x]]/Sqrt[a + b*Tan[c + d*x]],x]","\frac{\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{\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{\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{\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,"(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) + (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",8,6,25,0.2400,1,"{4241, 3575, 912, 93, 205, 208}"
864,1,155,0,0.1947747,"\int \frac{1}{\sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]),x]","\frac{i \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 \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 \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 \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*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*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",8,6,25,0.2400,1,"{4241, 3575, 910, 93, 205, 208}"
865,1,212,0,0.2362655,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]),x]","-\frac{\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 \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{\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{\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 \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{\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,"-((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*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) - (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",13,10,25,0.4000,1,"{4241, 3575, 910, 63, 217, 206, 912, 93, 205, 208}"
866,1,248,0,0.7275249,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*Sqrt[a + b*Tan[c + d*x]]),x]","-\frac{a \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{i \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{\sqrt{a+b \tan (c+d x)}}{b d \sqrt{\cot (c+d x)}}+\frac{i \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 \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{i \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{\sqrt{a+b \tan (c+d x)}}{b d \sqrt{\cot (c+d x)}}+\frac{i \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)*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*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*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) + Sqrt[a + b*Tan[c + d*x]]/(b*d*Sqrt[Cot[c + d*x]])","A",14,11,25,0.4400,1,"{4241, 3566, 3655, 6725, 63, 217, 206, 910, 93, 205, 208}"
867,1,281,0,0.929805,"\int \frac{\cot ^{\frac{5}{2}}(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])^(3/2),x]","\frac{2 b^2 \left(5 a^2+8 b^2\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{8 b \sqrt{\cot (c+d x)}}{3 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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^2 \left(5 a^2+8 b^2\right)}{3 a^3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{8 b \sqrt{\cot (c+d x)}}{3 a^2 d \sqrt{a+b \tan (c+d x)}}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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)*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*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^2*(5*a^2 + 8*b^2))/(3*a^3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) + (8*b*Sqrt[Cot[c + d*x]])/(3*a^2*d*Sqrt[a + b*Tan[c + d*x]]) - (2*Cot[c + d*x]^(3/2))/(3*a*d*Sqrt[a + b*Tan[c + d*x]])","A",11,9,25,0.3600,1,"{4241, 3569, 3649, 3650, 3616, 3615, 93, 203, 206}"
868,1,233,0,0.7214423,"\int \frac{\cot ^{\frac{3}{2}}(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])^(3/2),x]","-\frac{2 b \left(a^2+2 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{\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{2 \sqrt{\cot (c+d x)}}{a d \sqrt{a+b \tan (c+d x)}}-\frac{\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 \left(a^2+2 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{\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{2 \sqrt{\cot (c+d x)}}{a d \sqrt{a+b \tan (c+d x)}}-\frac{\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,"(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) - (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 + 2*b^2))/(a^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]]) - (2*Sqrt[Cot[c + d*x]])/(a*d*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{4241, 3569, 3649, 3616, 3615, 93, 203, 206}"
869,1,199,0,0.5382361,"\int \frac{\sqrt{\cot (c+d x)}}{(a+b \tan (c+d x))^{3/2}} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + b*Tan[c + d*x])^(3/2),x]","\frac{2 b^2}{a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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^2}{a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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*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*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^2)/(a*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{4241, 3569, 3616, 3615, 93, 203, 206}"
870,1,189,0,0.5041914,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 b}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{\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{\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}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{\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{\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,"-((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)) + (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 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{4241, 3568, 3616, 3615, 93, 203, 206}"
871,1,194,0,0.5081041,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(3/2)),x]","\frac{2 a}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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}{d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{i \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{i \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)*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*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^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",9,7,25,0.2800,1,"{4241, 3567, 3616, 3615, 93, 203, 206}"
872,1,255,0,1.2504617,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 a^2}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 \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{\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{\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^2}{b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{2 \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{\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{\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,"(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*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) - (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^2)/(b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",14,10,25,0.4000,1,"{4241, 3565, 3655, 6725, 63, 217, 206, 93, 205, 208}"
873,1,310,0,1.5704553,"\int \frac{1}{\cot ^{\frac{7}{2}}(c+d x) (a+b \tan (c+d x))^{3/2}} \, dx","Int[1/(Cot[c + d*x]^(7/2)*(a + b*Tan[c + d*x])^(3/2)),x]","-\frac{2 a^2}{b d \left(a^2+b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}+\frac{\left(3 a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}-\frac{3 a \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{i \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{i \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^2}{b d \left(a^2+b^2\right) \cot ^{\frac{3}{2}}(c+d x) \sqrt{a+b \tan (c+d x)}}+\frac{\left(3 a^2+b^2\right) \sqrt{a+b \tan (c+d x)}}{b^2 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)}}-\frac{3 a \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{i \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{i \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*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) - (3*a*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*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^2)/(b*(a^2 + b^2)*d*Cot[c + d*x]^(3/2)*Sqrt[a + b*Tan[c + d*x]]) + ((3*a^2 + b^2)*Sqrt[a + b*Tan[c + d*x]])/(b^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]])","A",15,11,25,0.4400,1,"{4241, 3565, 3647, 3655, 6725, 63, 217, 206, 93, 205, 208}"
874,1,338,0,1.2763961,"\int \frac{\cot ^{\frac{5}{2}}(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])^(5/2),x]","\frac{4 b^2 \left(15 a^2 b^2+4 a^4+8 b^4\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^2 \left(7 a^2+8 b^2\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{4 b \sqrt{\cot (c+d x)}}{a^2 d (a+b \tan (c+d x))^{3/2}}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d (a+b \tan (c+d x))^{3/2}}+\frac{\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{\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{4 b^2 \left(15 a^2 b^2+4 a^4+8 b^4\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^2 \left(7 a^2+8 b^2\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{4 b \sqrt{\cot (c+d x)}}{a^2 d (a+b \tan (c+d x))^{3/2}}-\frac{2 \cot ^{\frac{3}{2}}(c+d x)}{3 a d (a+b \tan (c+d x))^{3/2}}+\frac{\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{\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,"(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) + (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^2*(7*a^2 + 8*b^2))/(3*a^3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (4*b*Sqrt[Cot[c + d*x]])/(a^2*d*(a + b*Tan[c + d*x])^(3/2)) - (2*Cot[c + d*x]^(3/2))/(3*a*d*(a + b*Tan[c + d*x])^(3/2)) + (4*b^2*(4*a^4 + 15*a^2*b^2 + 8*b^4))/(3*a^4*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",12,9,25,0.3600,1,"{4241, 3569, 3649, 3650, 3616, 3615, 93, 203, 206}"
875,1,305,0,1.0331987,"\int \frac{\cot ^{\frac{3}{2}}(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])^(5/2),x]","-\frac{2 b \left(3 a^2+4 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{2 b \left(17 a^2 b^2+3 a^4+8 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{i \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{2 \sqrt{\cot (c+d x)}}{a d (a+b \tan (c+d x))^{3/2}}-\frac{i \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 \left(3 a^2+4 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{2 b \left(17 a^2 b^2+3 a^4+8 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{i \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{2 \sqrt{\cot (c+d x)}}{a d (a+b \tan (c+d x))^{3/2}}-\frac{i \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*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*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 + 4*b^2))/(3*a^2*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*Sqrt[Cot[c + d*x]])/(a*d*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(3*a^4 + 17*a^2*b^2 + 8*b^4))/(3*a^3*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",11,8,25,0.3200,1,"{4241, 3569, 3649, 3616, 3615, 93, 203, 206}"
876,1,252,0,0.7947134,"\int \frac{\sqrt{\cot (c+d x)}}{(a+b \tan (c+d x))^{5/2}} \, dx","Int[Sqrt[Cot[c + d*x]]/(a + b*Tan[c + d*x])^(5/2),x]","\frac{4 b^2 \left(4 a^2+b^2\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{2 b^2}{3 a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{\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{\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{4 b^2 \left(4 a^2+b^2\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{2 b^2}{3 a d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{\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{\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,"-((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)) - (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^2)/(3*a*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (4*b^2*(4*a^2 + b^2))/(3*a^2*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{4241, 3569, 3649, 3616, 3615, 93, 203, 206}"
877,1,251,0,0.755408,"\int \frac{1}{\sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(5/2)),x]","-\frac{2 b \left(5 a^2-b^2\right)}{3 a d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{2 b}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{i \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{i \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 \left(5 a^2-b^2\right)}{3 a d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}-\frac{2 b}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}-\frac{i \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{i \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)*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*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 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) - (2*b*(5*a^2 - b^2))/(3*a*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{4241, 3568, 3649, 3616, 3615, 93, 203, 206}"
878,1,239,0,0.7509345,"\int \frac{1}{\cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^(5/2)),x]","\frac{2 a}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{4 \left(a^2-2 b^2\right)}{3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{\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{\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}{3 d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{4 \left(a^2-2 b^2\right)}{3 d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{\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{\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,"(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) + (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)/(3*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (4*(a^2 - 2*b^2))/(3*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{4241, 3567, 3649, 3616, 3615, 93, 203, 206}"
879,1,254,0,0.8237191,"\int \frac{1}{\cot ^{\frac{5}{2}}(c+d x) (a+b \tan (c+d x))^{5/2}} \, dx","Int[1/(Cot[c + d*x]^(5/2)*(a + b*Tan[c + d*x])^(5/2)),x]","-\frac{2 a^2}{3 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(a^2+7 b^2\right)}{3 b d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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^2}{3 b d \left(a^2+b^2\right) \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^{3/2}}+\frac{2 a \left(a^2+7 b^2\right)}{3 b d \left(a^2+b^2\right)^2 \sqrt{\cot (c+d x)} \sqrt{a+b \tan (c+d x)}}+\frac{i \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{i \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*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*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^2)/(3*b*(a^2 + b^2)*d*Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^(3/2)) + (2*a*(a^2 + 7*b^2))/(3*b*(a^2 + b^2)^2*d*Sqrt[Cot[c + d*x]]*Sqrt[a + b*Tan[c + d*x]])","A",10,8,25,0.3200,1,"{4241, 3565, 3649, 3616, 3615, 93, 203, 206}"
880,1,206,0,0.4282318,"\int (d \cot (e+f x))^n (a+b \tan (e+f x))^3 \, dx","Int[(d*Cot[e + f*x])^n*(a + b*Tan[e + f*x])^3,x]","-\frac{b d^2 \left(3 a^2-b^2\right) (d \cot (e+f x))^{n-2} \, _2F_1\left(1,\frac{n-2}{2};\frac{n}{2};-\cot ^2(e+f x)\right)}{f (2-n)}-\frac{a d \left(a^2-3 b^2\right) (d \cot (e+f x))^{n-1} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};-\cot ^2(e+f x)\right)}{f (1-n)}+\frac{a^2 d^2 (a \cot (e+f x)+b) (d \cot (e+f x))^{n-2}}{f (1-n)}+\frac{a^2 b d^2 (1-2 n) (d \cot (e+f x))^{n-2}}{f (1-n) (2-n)}","-\frac{b d^2 \left(3 a^2-b^2\right) (d \cot (e+f x))^{n-2} \, _2F_1\left(1,\frac{n-2}{2};\frac{n}{2};-\cot ^2(e+f x)\right)}{f (2-n)}-\frac{a d \left(a^2-3 b^2\right) (d \cot (e+f x))^{n-1} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};-\cot ^2(e+f x)\right)}{f (1-n)}+\frac{a^2 d^2 (a \cot (e+f x)+b) (d \cot (e+f x))^{n-2}}{f (1-n)}+\frac{a^2 b d^2 (1-2 n) (d \cot (e+f x))^{n-2}}{f (1-n) (2-n)}",1,"(a^2*b*d^2*(1 - 2*n)*(d*Cot[e + f*x])^(-2 + n))/(f*(1 - n)*(2 - n)) + (a^2*d^2*(d*Cot[e + f*x])^(-2 + n)*(b + a*Cot[e + f*x]))/(f*(1 - n)) - (b*(3*a^2 - b^2)*d^2*(d*Cot[e + f*x])^(-2 + n)*Hypergeometric2F1[1, (-2 + n)/2, n/2, -Cot[e + f*x]^2])/(f*(2 - n)) - (a*(a^2 - 3*b^2)*d*(d*Cot[e + f*x])^(-1 + n)*Hypergeometric2F1[1, (-1 + n)/2, (1 + n)/2, -Cot[e + f*x]^2])/(f*(1 - n))","A",8,6,23,0.2609,1,"{3673, 3566, 3630, 3538, 3476, 364}"
881,1,132,0,0.2175627,"\int (d \cot (e+f x))^n (a+b \tan (e+f x))^2 \, dx","Int[(d*Cot[e + f*x])^n*(a + b*Tan[e + f*x])^2,x]","-\frac{d \left(a^2-b^2\right) (d \cot (e+f x))^{n-1} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};-\cot ^2(e+f x)\right)}{f (1-n)}+\frac{a^2 d (d \cot (e+f x))^{n-1}}{f (1-n)}-\frac{2 a b (d \cot (e+f x))^n \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};-\cot ^2(e+f x)\right)}{f n}","-\frac{d \left(a^2-b^2\right) (d \cot (e+f x))^{n-1} \, _2F_1\left(1,\frac{n-1}{2};\frac{n+1}{2};-\cot ^2(e+f x)\right)}{f (1-n)}+\frac{a^2 d (d \cot (e+f x))^{n-1}}{f (1-n)}-\frac{2 a b (d \cot (e+f x))^n \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};-\cot ^2(e+f x)\right)}{f n}",1,"(a^2*d*(d*Cot[e + f*x])^(-1 + n))/(f*(1 - n)) - ((a^2 - b^2)*d*(d*Cot[e + f*x])^(-1 + n)*Hypergeometric2F1[1, (-1 + n)/2, (1 + n)/2, -Cot[e + f*x]^2])/(f*(1 - n)) - (2*a*b*(d*Cot[e + f*x])^n*Hypergeometric2F1[1, n/2, (2 + n)/2, -Cot[e + f*x]^2])/(f*n)","A",7,5,23,0.2174,1,"{3673, 3543, 3538, 3476, 364}"
882,1,96,0,0.1203873,"\int (d \cot (e+f x))^n (a+b \tan (e+f x)) \, dx","Int[(d*Cot[e + f*x])^n*(a + b*Tan[e + f*x]),x]","-\frac{a (d \cot (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}-\frac{b (d \cot (e+f x))^n \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};-\cot ^2(e+f x)\right)}{f n}","-\frac{a (d \cot (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\cot ^2(e+f x)\right)}{d f (n+1)}-\frac{b (d \cot (e+f x))^n \, _2F_1\left(1,\frac{n}{2};\frac{n+2}{2};-\cot ^2(e+f x)\right)}{f n}",1,"-((b*(d*Cot[e + f*x])^n*Hypergeometric2F1[1, n/2, (2 + n)/2, -Cot[e + f*x]^2])/(f*n)) - (a*(d*Cot[e + f*x])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -Cot[e + f*x]^2])/(d*f*(1 + n))","A",6,4,21,0.1905,1,"{3673, 3538, 3476, 364}"
883,1,182,0,0.3896386,"\int \frac{(d \cot (e+f x))^n}{a+b \tan (e+f x)} \, dx","Int[(d*Cot[e + f*x])^n/(a + b*Tan[e + f*x]),x]","-\frac{b (d \cot (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\cot ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)}+\frac{a (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{d^3 f (n+3) \left(a^2+b^2\right)}-\frac{a^2 (d \cot (e+f x))^{n+2} \, _2F_1\left(1,n+2;n+3;-\frac{a \cot (e+f x)}{b}\right)}{b d^2 f (n+2) \left(a^2+b^2\right)}","-\frac{b (d \cot (e+f x))^{n+2} \, _2F_1\left(1,\frac{n+2}{2};\frac{n+4}{2};-\cot ^2(e+f x)\right)}{d^2 f (n+2) \left(a^2+b^2\right)}+\frac{a (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{d^3 f (n+3) \left(a^2+b^2\right)}-\frac{a^2 (d \cot (e+f x))^{n+2} \, _2F_1\left(1,n+2;n+3;-\frac{a \cot (e+f x)}{b}\right)}{b d^2 f (n+2) \left(a^2+b^2\right)}",1,"-((b*(d*Cot[e + f*x])^(2 + n)*Hypergeometric2F1[1, (2 + n)/2, (4 + n)/2, -Cot[e + f*x]^2])/((a^2 + b^2)*d^2*f*(2 + n))) - (a^2*(d*Cot[e + f*x])^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, -((a*Cot[e + f*x])/b)])/(b*(a^2 + b^2)*d^2*f*(2 + n)) + (a*(d*Cot[e + f*x])^(3 + n)*Hypergeometric2F1[1, (3 + n)/2, (5 + n)/2, -Cot[e + f*x]^2])/((a^2 + b^2)*d^3*f*(3 + n))","A",9,7,23,0.3043,1,"{3673, 3574, 3538, 3476, 364, 3634, 64}"
884,1,250,0,0.7770534,"\int \frac{(d \cot (e+f x))^n}{(a+b \tan (e+f x))^2} \, dx","Int[(d*Cot[e + f*x])^n/(a + b*Tan[e + f*x])^2,x]","\frac{\left(a^2-b^2\right) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{d^3 f (n+3) \left(a^2+b^2\right)^2}+\frac{2 a b (d \cot (e+f x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\cot ^2(e+f x)\right)}{d^4 f (n+4) \left(a^2+b^2\right)^2}+\frac{a^2 \left(a^2 (n+2)+b^2 n\right) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,n+3;n+4;-\frac{a \cot (e+f x)}{b}\right)}{b^2 d^3 f (n+3) \left(a^2+b^2\right)^2}-\frac{a^2 (d \cot (e+f x))^{n+3}}{b d^3 f \left(a^2+b^2\right) (a \cot (e+f x)+b)}","\frac{\left(a^2-b^2\right) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,\frac{n+3}{2};\frac{n+5}{2};-\cot ^2(e+f x)\right)}{d^3 f (n+3) \left(a^2+b^2\right)^2}+\frac{2 a b (d \cot (e+f x))^{n+4} \, _2F_1\left(1,\frac{n+4}{2};\frac{n+6}{2};-\cot ^2(e+f x)\right)}{d^4 f (n+4) \left(a^2+b^2\right)^2}+\frac{a^2 \left(a^2 (n+2)+b^2 n\right) (d \cot (e+f x))^{n+3} \, _2F_1\left(1,n+3;n+4;-\frac{a \cot (e+f x)}{b}\right)}{b^2 d^3 f (n+3) \left(a^2+b^2\right)^2}-\frac{a^2 (d \cot (e+f x))^{n+3}}{b d^3 f \left(a^2+b^2\right) (a \cot (e+f x)+b)}",1,"-((a^2*(d*Cot[e + f*x])^(3 + n))/(b*(a^2 + b^2)*d^3*f*(b + a*Cot[e + f*x]))) + ((a^2 - b^2)*(d*Cot[e + f*x])^(3 + n)*Hypergeometric2F1[1, (3 + n)/2, (5 + n)/2, -Cot[e + f*x]^2])/((a^2 + b^2)^2*d^3*f*(3 + n)) + (a^2*(b^2*n + a^2*(2 + n))*(d*Cot[e + f*x])^(3 + n)*Hypergeometric2F1[1, 3 + n, 4 + n, -((a*Cot[e + f*x])/b)])/(b^2*(a^2 + b^2)^2*d^3*f*(3 + n)) + (2*a*b*(d*Cot[e + f*x])^(4 + n)*Hypergeometric2F1[1, (4 + n)/2, (6 + n)/2, -Cot[e + f*x]^2])/((a^2 + b^2)^2*d^4*f*(4 + n))","A",10,8,23,0.3478,1,"{3673, 3569, 3653, 3538, 3476, 364, 3634, 64}"
885,1,193,0,0.2544853,"\int (d \cot (e+f x))^n (a+b \tan (e+f x))^m \, dx","Int[(d*Cot[e + f*x])^n*(a + b*Tan[e + f*x])^m,x]","\frac{\tan (e+f x) (d \cot (e+f x))^n (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(1-n;-m,1;2-n;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 f (1-n)}+\frac{\tan (e+f x) (d \cot (e+f x))^n (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(1-n;-m,1;2-n;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 f (1-n)}","\frac{\tan (e+f x) (d \cot (e+f x))^n (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(1-n;-m,1;2-n;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 f (1-n)}+\frac{\tan (e+f x) (d \cot (e+f x))^n (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} F_1\left(1-n;-m,1;2-n;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 f (1-n)}",1,"(AppellF1[1 - n, -m, 1, 2 - n, -((b*Tan[e + f*x])/a), (-I)*Tan[e + f*x]]*(d*Cot[e + f*x])^n*Tan[e + f*x]*(a + b*Tan[e + f*x])^m)/(2*f*(1 - n)*(1 + (b*Tan[e + f*x])/a)^m) + (AppellF1[1 - n, -m, 1, 2 - n, -((b*Tan[e + f*x])/a), I*Tan[e + f*x]]*(d*Cot[e + f*x])^n*Tan[e + f*x]*(a + b*Tan[e + f*x])^m)/(2*f*(1 - n)*(1 + (b*Tan[e + f*x])/a)^m)","A",8,5,23,0.2174,1,"{4241, 3575, 912, 135, 133}"
886,1,155,0,0.2774667,"\int \cot ^{\frac{3}{2}}(c+d x) (a+b \tan (c+d x))^n \, dx","Int[Cot[c + d*x]^(3/2)*(a + b*Tan[c + d*x])^n,x]","-\frac{\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{\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{\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{\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,"-((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)) - (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",10,6,23,0.2609,1,"{4241, 3575, 912, 130, 511, 510}"
887,1,153,0,0.2407472,"\int \sqrt{\cot (c+d x)} (a+b \tan (c+d x))^n \, dx","Int[Sqrt[Cot[c + d*x]]*(a + b*Tan[c + d*x])^n,x]","\frac{(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+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+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+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,"(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) + (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",10,6,23,0.2609,1,"{4241, 3575, 912, 130, 430, 429}"
888,1,159,0,0.2709866,"\int \frac{(a+b \tan (c+d x))^n}{\sqrt{\cot (c+d x)}} \, dx","Int[(a + b*Tan[c + d*x])^n/Sqrt[Cot[c + d*x]],x]","\frac{(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+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+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+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,"(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) + (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",10,6,23,0.2609,1,"{4241, 3575, 912, 130, 511, 510}"
889,1,159,0,0.2700009,"\int \frac{(a+b \tan (c+d x))^n}{\cot ^{\frac{3}{2}}(c+d x)} \, dx","Int[(a + b*Tan[c + d*x])^n/Cot[c + d*x]^(3/2),x]","\frac{(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+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+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+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,"(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) + (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",10,6,23,0.2609,1,"{4241, 3575, 912, 130, 511, 510}"
890,1,25,0,0.0698879,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x]),x]","-\frac{i c (a+i a \tan (e+f x))^3}{3 f}","-\frac{i c (a+i a \tan (e+f x))^3}{3 f}",1,"((-I/3)*c*(a + I*a*Tan[e + f*x])^3)/f","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
891,1,36,0,0.0641839,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x]),x]","\frac{a^2 c \tan (e+f x)}{f}+\frac{i a^2 c \sec ^2(e+f x)}{2 f}","-\frac{i c (a+i a \tan (e+f x))^2}{2 f}",1,"((I/2)*a^2*c*Sec[e + f*x]^2)/f + (a^2*c*Tan[e + f*x])/f","A",4,4,29,0.1379,1,"{3522, 3486, 3767, 8}"
892,1,12,0,0.0239701,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x]),x]","\frac{a c \tan (e+f x)}{f}","\frac{a c \tan (e+f x)}{f}",1,"(a*c*Tan[e + f*x])/f","A",3,3,27,0.1111,1,"{3522, 3767, 8}"
893,1,23,0,0.0771408,"\int \frac{c-i c \tan (e+f x)}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])/(a + I*a*Tan[e + f*x]),x]","\frac{i c}{f (a+i a \tan (e+f x))}","\frac{i c}{f (a+i a \tan (e+f x))}",1,"(I*c)/(f*(a + I*a*Tan[e + f*x]))","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
894,1,25,0,0.074293,"\int \frac{c-i c \tan (e+f x)}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^2,x]","\frac{i c}{2 f (a+i a \tan (e+f x))^2}","\frac{i c}{2 f (a+i a \tan (e+f x))^2}",1,"((I/2)*c)/(f*(a + I*a*Tan[e + f*x])^2)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
895,1,25,0,0.0708741,"\int \frac{c-i c \tan (e+f x)}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^3,x]","\frac{i c}{3 f (a+i a \tan (e+f x))^3}","\frac{i c}{3 f (a+i a \tan (e+f x))^3}",1,"((I/3)*c)/(f*(a + I*a*Tan[e + f*x])^3)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
896,1,58,0,0.1007477,"\int (a+i a \tan (e+f x))^4 (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^4*(c - I*c*Tan[e + f*x])^2,x]","\frac{i c^2 (a+i a \tan (e+f x))^5}{5 a f}-\frac{i c^2 (a+i a \tan (e+f x))^4}{2 f}","\frac{i c^2 (a+i a \tan (e+f x))^5}{5 a f}-\frac{i c^2 (a+i a \tan (e+f x))^4}{2 f}",1,"((-I/2)*c^2*(a + I*a*Tan[e + f*x])^4)/f + ((I/5)*c^2*(a + I*a*Tan[e + f*x])^5)/(a*f)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
897,1,61,0,0.0874086,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^2,x]","\frac{a^3 c^2 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^2 \tan (e+f x)}{f}+\frac{i a^3 c^2 \sec ^4(e+f x)}{4 f}","\frac{a^3 c^2 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^2 \tan (e+f x)}{f}+\frac{i a^3 c^2 \sec ^4(e+f x)}{4 f}",1,"((I/4)*a^3*c^2*Sec[e + f*x]^4)/f + (a^3*c^2*Tan[e + f*x])/f + (a^3*c^2*Tan[e + f*x]^3)/(3*f)","A",4,3,31,0.09677,1,"{3522, 3486, 3767}"
898,1,38,0,0.0623472,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^2,x]","\frac{a^2 c^2 \tan ^3(e+f x)}{3 f}+\frac{a^2 c^2 \tan (e+f x)}{f}","\frac{a^2 c^2 \tan ^3(e+f x)}{3 f}+\frac{a^2 c^2 \tan (e+f x)}{f}",1,"(a^2*c^2*Tan[e + f*x])/f + (a^2*c^2*Tan[e + f*x]^3)/(3*f)","A",3,2,31,0.06452,1,"{3522, 3767}"
899,1,36,0,0.059842,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2,x]","\frac{a c^2 \tan (e+f x)}{f}-\frac{i a c^2 \sec ^2(e+f x)}{2 f}","\frac{i a (c-i c \tan (e+f x))^2}{2 f}",1,"((-I/2)*a*c^2*Sec[e + f*x]^2)/f + (a*c^2*Tan[e + f*x])/f","A",4,4,29,0.1379,1,"{3522, 3486, 3767, 8}"
900,1,55,0,0.1147377,"\int \frac{(c-i c \tan (e+f x))^2}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x]),x]","\frac{2 i c^2}{f (a+i a \tan (e+f x))}-\frac{i c^2 \log (\cos (e+f x))}{a f}-\frac{c^2 x}{a}","\frac{2 i c^2}{f (a+i a \tan (e+f x))}-\frac{i c^2 \log (\cos (e+f x))}{a f}-\frac{c^2 x}{a}",1,"-((c^2*x)/a) - (I*c^2*Log[Cos[e + f*x]])/(a*f) + ((2*I)*c^2)/(f*(a + I*a*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
901,1,28,0,0.0997602,"\int \frac{(c-i c \tan (e+f x))^2}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x])^2,x]","\frac{c^2 \tan (e+f x)}{f (a+i a \tan (e+f x))^2}","\frac{c^2 \tan (e+f x)}{f (a+i a \tan (e+f x))^2}",1,"(c^2*Tan[e + f*x])/(f*(a + I*a*Tan[e + f*x])^2)","A",3,3,31,0.09677,1,"{3522, 3487, 34}"
902,1,58,0,0.1078718,"\int \frac{(c-i c \tan (e+f x))^2}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x])^3,x]","\frac{2 i c^2}{3 f (a+i a \tan (e+f x))^3}-\frac{i c^2}{2 a f (a+i a \tan (e+f x))^2}","\frac{2 i c^2}{3 f (a+i a \tan (e+f x))^3}-\frac{i c^2}{2 a f (a+i a \tan (e+f x))^2}",1,"(((2*I)/3)*c^2)/(f*(a + I*a*Tan[e + f*x])^3) - ((I/2)*c^2)/(a*f*(a + I*a*Tan[e + f*x])^2)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
903,1,62,0,0.1087417,"\int \frac{(c-i c \tan (e+f x))^2}{(a+i a \tan (e+f x))^4} \, dx","Int[(c - I*c*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x])^4,x]","\frac{i c^2}{2 f (a+i a \tan (e+f x))^4}-\frac{i a^2 c^2}{3 f \left(a^2+i a^2 \tan (e+f x)\right)^3}","\frac{i c^2}{2 f (a+i a \tan (e+f x))^4}-\frac{i a^2 c^2}{3 f \left(a^2+i a^2 \tan (e+f x)\right)^3}",1,"((I/2)*c^2)/(f*(a + I*a*Tan[e + f*x])^4) - ((I/3)*a^2*c^2)/(f*(a^2 + I*a^2*Tan[e + f*x])^3)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
904,1,88,0,0.1170987,"\int (a+i a \tan (e+f x))^5 (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^5*(c - I*c*Tan[e + f*x])^3,x]","-\frac{i c^3 (a+i a \tan (e+f x))^7}{7 a^2 f}+\frac{2 i c^3 (a+i a \tan (e+f x))^6}{3 a f}-\frac{4 i c^3 (a+i a \tan (e+f x))^5}{5 f}","-\frac{i c^3 (a+i a \tan (e+f x))^7}{7 a^2 f}+\frac{2 i c^3 (a+i a \tan (e+f x))^6}{3 a f}-\frac{4 i c^3 (a+i a \tan (e+f x))^5}{5 f}",1,"(((-4*I)/5)*c^3*(a + I*a*Tan[e + f*x])^5)/f + (((2*I)/3)*c^3*(a + I*a*Tan[e + f*x])^6)/(a*f) - ((I/7)*c^3*(a + I*a*Tan[e + f*x])^7)/(a^2*f)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
905,1,82,0,0.0963688,"\int (a+i a \tan (e+f x))^4 (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^4*(c - I*c*Tan[e + f*x])^3,x]","\frac{a^4 c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^4 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^4 c^3 \tan (e+f x)}{f}+\frac{i a^4 c^3 \sec ^6(e+f x)}{6 f}","\frac{a^4 c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^4 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^4 c^3 \tan (e+f x)}{f}+\frac{i a^4 c^3 \sec ^6(e+f x)}{6 f}",1,"((I/6)*a^4*c^3*Sec[e + f*x]^6)/f + (a^4*c^3*Tan[e + f*x])/f + (2*a^4*c^3*Tan[e + f*x]^3)/(3*f) + (a^4*c^3*Tan[e + f*x]^5)/(5*f)","A",4,3,31,0.09677,1,"{3522, 3486, 3767}"
906,1,59,0,0.0681824,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^3,x]","\frac{a^3 c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^3 \tan (e+f x)}{f}","\frac{a^3 c^3 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^3 \tan (e+f x)}{f}",1,"(a^3*c^3*Tan[e + f*x])/f + (2*a^3*c^3*Tan[e + f*x]^3)/(3*f) + (a^3*c^3*Tan[e + f*x]^5)/(5*f)","A",3,2,31,0.06452,1,"{3522, 3767}"
907,1,61,0,0.0880692,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^3,x]","\frac{a^2 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^2 c^3 \tan (e+f x)}{f}-\frac{i a^2 c^3 \sec ^4(e+f x)}{4 f}","\frac{a^2 c^3 \tan ^3(e+f x)}{3 f}+\frac{a^2 c^3 \tan (e+f x)}{f}-\frac{i a^2 c^3 \sec ^4(e+f x)}{4 f}",1,"((-I/4)*a^2*c^3*Sec[e + f*x]^4)/f + (a^2*c^3*Tan[e + f*x])/f + (a^2*c^3*Tan[e + f*x]^3)/(3*f)","A",4,3,31,0.09677,1,"{3522, 3486, 3767}"
908,1,25,0,0.0705975,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3,x]","\frac{i a (c-i c \tan (e+f x))^3}{3 f}","\frac{i a (c-i c \tan (e+f x))^3}{3 f}",1,"((I/3)*a*(c - I*c*Tan[e + f*x])^3)/f","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
909,1,71,0,0.1210273,"\int \frac{(c-i c \tan (e+f x))^3}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x]),x]","\frac{c^3 \tan (e+f x)}{a f}+\frac{4 i c^3}{f (a+i a \tan (e+f x))}-\frac{4 i c^3 \log (\cos (e+f x))}{a f}-\frac{4 c^3 x}{a}","\frac{c^3 \tan (e+f x)}{a f}+\frac{4 i c^3}{f (a+i a \tan (e+f x))}-\frac{4 i c^3 \log (\cos (e+f x))}{a f}-\frac{4 c^3 x}{a}",1,"(-4*c^3*x)/a - ((4*I)*c^3*Log[Cos[e + f*x]])/(a*f) + (c^3*Tan[e + f*x])/(a*f) + ((4*I)*c^3)/(f*(a + I*a*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
910,1,83,0,0.1219462,"\int \frac{(c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^2,x]","-\frac{4 i c^3}{f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{i c^3 \log (\cos (e+f x))}{a^2 f}+\frac{c^3 x}{a^2}+\frac{2 i c^3}{f (a+i a \tan (e+f x))^2}","-\frac{4 i c^3}{f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{i c^3 \log (\cos (e+f x))}{a^2 f}+\frac{c^3 x}{a^2}+\frac{2 i c^3}{f (a+i a \tan (e+f x))^2}",1,"(c^3*x)/a^2 + (I*c^3*Log[Cos[e + f*x]])/(a^2*f) + ((2*I)*c^3)/(f*(a + I*a*Tan[e + f*x])^2) - ((4*I)*c^3)/(f*(a^2 + I*a^2*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
911,1,50,0,0.1050042,"\int \frac{(c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^3,x]","\frac{i c^3 \left(a^2-i a^2 \tan (e+f x)\right)^3}{6 f \left(a^3+i a^3 \tan (e+f x)\right)^3}","\frac{i c^3 \left(a^2-i a^2 \tan (e+f x)\right)^3}{6 f \left(a^3+i a^3 \tan (e+f x)\right)^3}",1,"((I/6)*c^3*(a^2 - I*a^2*Tan[e + f*x])^3)/(f*(a^3 + I*a^3*Tan[e + f*x])^3)","A",3,3,31,0.09677,1,"{3522, 3487, 37}"
912,1,87,0,0.1190523,"\int \frac{(c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^4} \, dx","Int[(c - I*c*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^4,x]","\frac{i c^3}{2 f \left(a^2+i a^2 \tan (e+f x)\right)^2}-\frac{4 i c^3}{3 a f (a+i a \tan (e+f x))^3}+\frac{i c^3}{f (a+i a \tan (e+f x))^4}","\frac{i c^3}{2 f \left(a^2+i a^2 \tan (e+f x)\right)^2}-\frac{4 i c^3}{3 a f (a+i a \tan (e+f x))^3}+\frac{i c^3}{f (a+i a \tan (e+f x))^4}",1,"(I*c^3)/(f*(a + I*a*Tan[e + f*x])^4) - (((4*I)/3)*c^3)/(a*f*(a + I*a*Tan[e + f*x])^3) + ((I/2)*c^3)/(f*(a^2 + I*a^2*Tan[e + f*x])^2)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
913,1,90,0,0.117911,"\int \frac{(c-i c \tan (e+f x))^3}{(a+i a \tan (e+f x))^5} \, dx","Int[(c - I*c*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^5,x]","\frac{i c^3}{3 a^2 f (a+i a \tan (e+f x))^3}-\frac{i a^3 c^3}{f \left(a^2+i a^2 \tan (e+f x)\right)^4}+\frac{4 i c^3}{5 f (a+i a \tan (e+f x))^5}","\frac{i c^3}{3 a^2 f (a+i a \tan (e+f x))^3}-\frac{i a^3 c^3}{f \left(a^2+i a^2 \tan (e+f x)\right)^4}+\frac{4 i c^3}{5 f (a+i a \tan (e+f x))^5}",1,"(((4*I)/5)*c^3)/(f*(a + I*a*Tan[e + f*x])^5) + ((I/3)*c^3)/(a^2*f*(a + I*a*Tan[e + f*x])^3) - (I*a^3*c^3)/(f*(a^2 + I*a^2*Tan[e + f*x])^4)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
914,1,100,0,0.1000316,"\int (a+i a \tan (e+f x))^5 (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^5*(c - I*c*Tan[e + f*x])^4,x]","\frac{a^5 c^4 \tan ^7(e+f x)}{7 f}+\frac{3 a^5 c^4 \tan ^5(e+f x)}{5 f}+\frac{a^5 c^4 \tan ^3(e+f x)}{f}+\frac{a^5 c^4 \tan (e+f x)}{f}+\frac{i a^5 c^4 \sec ^8(e+f x)}{8 f}","\frac{a^5 c^4 \tan ^7(e+f x)}{7 f}+\frac{3 a^5 c^4 \tan ^5(e+f x)}{5 f}+\frac{a^5 c^4 \tan ^3(e+f x)}{f}+\frac{a^5 c^4 \tan (e+f x)}{f}+\frac{i a^5 c^4 \sec ^8(e+f x)}{8 f}",1,"((I/8)*a^5*c^4*Sec[e + f*x]^8)/f + (a^5*c^4*Tan[e + f*x])/f + (a^5*c^4*Tan[e + f*x]^3)/f + (3*a^5*c^4*Tan[e + f*x]^5)/(5*f) + (a^5*c^4*Tan[e + f*x]^7)/(7*f)","A",4,3,31,0.09677,1,"{3522, 3486, 3767}"
915,1,77,0,0.0707983,"\int (a+i a \tan (e+f x))^4 (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^4*(c - I*c*Tan[e + f*x])^4,x]","\frac{a^4 c^4 \tan ^7(e+f x)}{7 f}+\frac{3 a^4 c^4 \tan ^5(e+f x)}{5 f}+\frac{a^4 c^4 \tan ^3(e+f x)}{f}+\frac{a^4 c^4 \tan (e+f x)}{f}","\frac{a^4 c^4 \tan ^7(e+f x)}{7 f}+\frac{3 a^4 c^4 \tan ^5(e+f x)}{5 f}+\frac{a^4 c^4 \tan ^3(e+f x)}{f}+\frac{a^4 c^4 \tan (e+f x)}{f}",1,"(a^4*c^4*Tan[e + f*x])/f + (a^4*c^4*Tan[e + f*x]^3)/f + (3*a^4*c^4*Tan[e + f*x]^5)/(5*f) + (a^4*c^4*Tan[e + f*x]^7)/(7*f)","A",3,2,31,0.06452,1,"{3522, 3767}"
916,1,82,0,0.0993435,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^4,x]","\frac{a^3 c^4 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 c^4 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^4 \tan (e+f x)}{f}-\frac{i a^3 c^4 \sec ^6(e+f x)}{6 f}","\frac{a^3 c^4 \tan ^5(e+f x)}{5 f}+\frac{2 a^3 c^4 \tan ^3(e+f x)}{3 f}+\frac{a^3 c^4 \tan (e+f x)}{f}-\frac{i a^3 c^4 \sec ^6(e+f x)}{6 f}",1,"((-I/6)*a^3*c^4*Sec[e + f*x]^6)/f + (a^3*c^4*Tan[e + f*x])/f + (2*a^3*c^4*Tan[e + f*x]^3)/(3*f) + (a^3*c^4*Tan[e + f*x]^5)/(5*f)","A",4,3,31,0.09677,1,"{3522, 3486, 3767}"
917,1,58,0,0.1023702,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^4,x]","\frac{i a^2 (c-i c \tan (e+f x))^4}{2 f}-\frac{i a^2 (c-i c \tan (e+f x))^5}{5 c f}","\frac{i a^2 (c-i c \tan (e+f x))^4}{2 f}-\frac{i a^2 (c-i c \tan (e+f x))^5}{5 c f}",1,"((I/2)*a^2*(c - I*c*Tan[e + f*x])^4)/f - ((I/5)*a^2*(c - I*c*Tan[e + f*x])^5)/(c*f)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
918,1,25,0,0.0676489,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4,x]","\frac{i a (c-i c \tan (e+f x))^4}{4 f}","\frac{i a (c-i c \tan (e+f x))^4}{4 f}",1,"((I/4)*a*(c - I*c*Tan[e + f*x])^4)/f","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
919,1,95,0,0.129874,"\int \frac{(c-i c \tan (e+f x))^4}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^4/(a + I*a*Tan[e + f*x]),x]","-\frac{i c^4 \tan ^2(e+f x)}{2 a f}+\frac{5 c^4 \tan (e+f x)}{a f}+\frac{8 i c^4}{f (a+i a \tan (e+f x))}-\frac{12 i c^4 \log (\cos (e+f x))}{a f}-\frac{12 c^4 x}{a}","-\frac{i c^4 \tan ^2(e+f x)}{2 a f}+\frac{5 c^4 \tan (e+f x)}{a f}+\frac{8 i c^4}{f (a+i a \tan (e+f x))}-\frac{12 i c^4 \log (\cos (e+f x))}{a f}-\frac{12 c^4 x}{a}",1,"(-12*c^4*x)/a - ((12*I)*c^4*Log[Cos[e + f*x]])/(a*f) + (5*c^4*Tan[e + f*x])/(a*f) - ((I/2)*c^4*Tan[e + f*x]^2)/(a*f) + ((8*I)*c^4)/(f*(a + I*a*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
920,1,101,0,0.1327038,"\int \frac{(c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^4/(a + I*a*Tan[e + f*x])^2,x]","-\frac{c^4 \tan (e+f x)}{a^2 f}-\frac{12 i c^4}{f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{6 i c^4 \log (\cos (e+f x))}{a^2 f}+\frac{6 c^4 x}{a^2}+\frac{4 i c^4}{f (a+i a \tan (e+f x))^2}","-\frac{c^4 \tan (e+f x)}{a^2 f}-\frac{12 i c^4}{f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{6 i c^4 \log (\cos (e+f x))}{a^2 f}+\frac{6 c^4 x}{a^2}+\frac{4 i c^4}{f (a+i a \tan (e+f x))^2}",1,"(6*c^4*x)/a^2 + ((6*I)*c^4*Log[Cos[e + f*x]])/(a^2*f) - (c^4*Tan[e + f*x])/(a^2*f) + ((4*I)*c^4)/(f*(a + I*a*Tan[e + f*x])^2) - ((12*I)*c^4)/(f*(a^2 + I*a^2*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
921,1,114,0,0.1332076,"\int \frac{(c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^4/(a + I*a*Tan[e + f*x])^3,x]","\frac{6 i c^4}{f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{i c^4 \log (\cos (e+f x))}{a^3 f}-\frac{c^4 x}{a^3}-\frac{6 i c^4}{a f (a+i a \tan (e+f x))^2}+\frac{8 i c^4}{3 f (a+i a \tan (e+f x))^3}","\frac{6 i c^4}{f \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{i c^4 \log (\cos (e+f x))}{a^3 f}-\frac{c^4 x}{a^3}-\frac{6 i c^4}{a f (a+i a \tan (e+f x))^2}+\frac{8 i c^4}{3 f (a+i a \tan (e+f x))^3}",1,"-((c^4*x)/a^3) - (I*c^4*Log[Cos[e + f*x]])/(a^3*f) + (((8*I)/3)*c^4)/(f*(a + I*a*Tan[e + f*x])^3) - ((6*I)*c^4)/(a*f*(a + I*a*Tan[e + f*x])^2) + ((6*I)*c^4)/(f*(a^3 + I*a^3*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
922,1,50,0,0.1024171,"\int \frac{(c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^4} \, dx","Int[(c - I*c*Tan[e + f*x])^4/(a + I*a*Tan[e + f*x])^4,x]","\frac{i c^4 \left(a^2-i a^2 \tan (e+f x)\right)^4}{8 f \left(a^3+i a^3 \tan (e+f x)\right)^4}","\frac{i c^4 \left(a^2-i a^2 \tan (e+f x)\right)^4}{8 f \left(a^3+i a^3 \tan (e+f x)\right)^4}",1,"((I/8)*c^4*(a^2 - I*a^2*Tan[e + f*x])^4)/(f*(a^3 + I*a^3*Tan[e + f*x])^4)","A",3,3,31,0.09677,1,"{3522, 3487, 37}"
923,1,87,0,0.1185509,"\int \frac{(c-i c \tan (e+f x))^4}{(a+i a \tan (e+f x))^5} \, dx","Int[(c - I*c*Tan[e + f*x])^4/(a + I*a*Tan[e + f*x])^5,x]","\frac{i c^4 (a-i a \tan (e+f x))^4}{80 a^5 f (a+i a \tan (e+f x))^4}+\frac{i c^4 (1-i \tan (e+f x))^4}{10 f (a+i a \tan (e+f x))^5}","\frac{i c^4 (a-i a \tan (e+f x))^4}{80 a^5 f (a+i a \tan (e+f x))^4}+\frac{i c^4 (1-i \tan (e+f x))^4}{10 f (a+i a \tan (e+f x))^5}",1,"((I/10)*c^4*(1 - I*Tan[e + f*x])^4)/(f*(a + I*a*Tan[e + f*x])^5) + ((I/80)*c^4*(a - I*a*Tan[e + f*x])^4)/(a^5*f*(a + I*a*Tan[e + f*x])^4)","A",4,4,31,0.1290,1,"{3522, 3487, 45, 37}"
924,1,95,0,0.1338853,"\int \frac{(a+i a \tan (e+f x))^4}{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^4/(c - I*c*Tan[e + f*x]),x]","\frac{i a^4 \tan ^2(e+f x)}{2 c f}+\frac{5 a^4 \tan (e+f x)}{c f}-\frac{8 i a^4}{f (c-i c \tan (e+f x))}+\frac{12 i a^4 \log (\cos (e+f x))}{c f}-\frac{12 a^4 x}{c}","\frac{i a^4 \tan ^2(e+f x)}{2 c f}+\frac{5 a^4 \tan (e+f x)}{c f}-\frac{8 i a^4}{f (c-i c \tan (e+f x))}+\frac{12 i a^4 \log (\cos (e+f x))}{c f}-\frac{12 a^4 x}{c}",1,"(-12*a^4*x)/c + ((12*I)*a^4*Log[Cos[e + f*x]])/(c*f) + (5*a^4*Tan[e + f*x])/(c*f) + ((I/2)*a^4*Tan[e + f*x]^2)/(c*f) - ((8*I)*a^4)/(f*(c - I*c*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
925,1,71,0,0.1221433,"\int \frac{(a+i a \tan (e+f x))^3}{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x]),x]","\frac{a^3 \tan (e+f x)}{c f}-\frac{4 i a^3}{f (c-i c \tan (e+f x))}+\frac{4 i a^3 \log (\cos (e+f x))}{c f}-\frac{4 a^3 x}{c}","\frac{a^3 \tan (e+f x)}{c f}-\frac{4 i a^3}{f (c-i c \tan (e+f x))}+\frac{4 i a^3 \log (\cos (e+f x))}{c f}-\frac{4 a^3 x}{c}",1,"(-4*a^3*x)/c + ((4*I)*a^3*Log[Cos[e + f*x]])/(c*f) + (a^3*Tan[e + f*x])/(c*f) - ((4*I)*a^3)/(f*(c - I*c*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
926,1,55,0,0.1158637,"\int \frac{(a+i a \tan (e+f x))^2}{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x]),x]","-\frac{2 i a^2}{f (c-i c \tan (e+f x))}+\frac{i a^2 \log (\cos (e+f x))}{c f}-\frac{a^2 x}{c}","-\frac{2 i a^2}{f (c-i c \tan (e+f x))}+\frac{i a^2 \log (\cos (e+f x))}{c f}-\frac{a^2 x}{c}",1,"-((a^2*x)/c) + (I*a^2*Log[Cos[e + f*x]])/(c*f) - ((2*I)*a^2)/(f*(c - I*c*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
927,1,23,0,0.0773809,"\int \frac{a+i a \tan (e+f x)}{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x]),x]","-\frac{i a}{f (c-i c \tan (e+f x))}","-\frac{i a}{f (c-i c \tan (e+f x))}",1,"((-I)*a)/(f*(c - I*c*Tan[e + f*x]))","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
928,1,37,0,0.0725315,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])),x]","\frac{\sin (e+f x) \cos (e+f x)}{2 a c f}+\frac{x}{2 a c}","\frac{\sin (e+f x) \cos (e+f x)}{2 a c f}+\frac{x}{2 a c}",1,"x/(2*a*c) + (Cos[e + f*x]*Sin[e + f*x])/(2*a*c*f)","A",3,3,31,0.09677,1,"{3522, 2635, 8}"
929,1,87,0,0.1100063,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])),x]","\frac{i \cos ^4(e+f x)}{4 a^2 c f}+\frac{\sin (e+f x) \cos ^3(e+f x)}{4 a^2 c f}+\frac{3 \sin (e+f x) \cos (e+f x)}{8 a^2 c f}+\frac{3 x}{8 a^2 c}","\frac{i \cos ^4(e+f x)}{4 a^2 c f}+\frac{\sin (e+f x) \cos ^3(e+f x)}{4 a^2 c f}+\frac{3 \sin (e+f x) \cos (e+f x)}{8 a^2 c f}+\frac{3 x}{8 a^2 c}",1,"(3*x)/(8*a^2*c) + ((I/4)*Cos[e + f*x]^4)/(a^2*c*f) + (3*Cos[e + f*x]*Sin[e + f*x])/(8*a^2*c*f) + (Cos[e + f*x]^3*Sin[e + f*x])/(4*a^2*c*f)","A",5,4,31,0.1290,1,"{3522, 3486, 2635, 8}"
930,1,124,0,0.1598608,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])),x]","\frac{i c^2}{12 a^3 f (c+i c \tan (e+f x))^3}+\frac{i c}{8 a^3 f (c+i c \tan (e+f x))^2}-\frac{i}{16 a^3 f (c-i c \tan (e+f x))}+\frac{3 i}{16 a^3 f (c+i c \tan (e+f x))}+\frac{x}{4 a^3 c}","\frac{i c^2}{12 a^3 f (c+i c \tan (e+f x))^3}+\frac{i c}{8 a^3 f (c+i c \tan (e+f x))^2}-\frac{i}{16 a^3 f (c-i c \tan (e+f x))}+\frac{3 i}{16 a^3 f (c+i c \tan (e+f x))}+\frac{x}{4 a^3 c}",1,"x/(4*a^3*c) - (I/16)/(a^3*f*(c - I*c*Tan[e + f*x])) + ((I/12)*c^2)/(a^3*f*(c + I*c*Tan[e + f*x])^3) + ((I/8)*c)/(a^3*f*(c + I*c*Tan[e + f*x])^2) + ((3*I)/16)/(a^3*f*(c + I*c*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
931,1,101,0,0.1360188,"\int \frac{(a+i a \tan (e+f x))^4}{(c-i c \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^4/(c - I*c*Tan[e + f*x])^2,x]","-\frac{a^4 \tan (e+f x)}{c^2 f}+\frac{12 i a^4}{f \left(c^2-i c^2 \tan (e+f x)\right)}-\frac{6 i a^4 \log (\cos (e+f x))}{c^2 f}+\frac{6 a^4 x}{c^2}-\frac{4 i a^4}{f (c-i c \tan (e+f x))^2}","-\frac{a^4 \tan (e+f x)}{c^2 f}+\frac{12 i a^4}{f \left(c^2-i c^2 \tan (e+f x)\right)}-\frac{6 i a^4 \log (\cos (e+f x))}{c^2 f}+\frac{6 a^4 x}{c^2}-\frac{4 i a^4}{f (c-i c \tan (e+f x))^2}",1,"(6*a^4*x)/c^2 - ((6*I)*a^4*Log[Cos[e + f*x]])/(c^2*f) - (a^4*Tan[e + f*x])/(c^2*f) - ((4*I)*a^4)/(f*(c - I*c*Tan[e + f*x])^2) + ((12*I)*a^4)/(f*(c^2 - I*c^2*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
932,1,83,0,0.1229774,"\int \frac{(a+i a \tan (e+f x))^3}{(c-i c \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x])^2,x]","\frac{4 i a^3}{f \left(c^2-i c^2 \tan (e+f x)\right)}-\frac{i a^3 \log (\cos (e+f x))}{c^2 f}+\frac{a^3 x}{c^2}-\frac{2 i a^3}{f (c-i c \tan (e+f x))^2}","\frac{4 i a^3}{f \left(c^2-i c^2 \tan (e+f x)\right)}-\frac{i a^3 \log (\cos (e+f x))}{c^2 f}+\frac{a^3 x}{c^2}-\frac{2 i a^3}{f (c-i c \tan (e+f x))^2}",1,"(a^3*x)/c^2 - (I*a^3*Log[Cos[e + f*x]])/(c^2*f) - ((2*I)*a^3)/(f*(c - I*c*Tan[e + f*x])^2) + ((4*I)*a^3)/(f*(c^2 - I*c^2*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
933,1,28,0,0.1017184,"\int \frac{(a+i a \tan (e+f x))^2}{(c-i c \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x])^2,x]","\frac{a^2 \tan (e+f x)}{f (c-i c \tan (e+f x))^2}","\frac{a^2 \tan (e+f x)}{f (c-i c \tan (e+f x))^2}",1,"(a^2*Tan[e + f*x])/(f*(c - I*c*Tan[e + f*x])^2)","A",3,3,31,0.09677,1,"{3522, 3487, 34}"
934,1,25,0,0.0735024,"\int \frac{a+i a \tan (e+f x)}{(c-i c \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x])^2,x]","-\frac{i a}{2 f (c-i c \tan (e+f x))^2}","-\frac{i a}{2 f (c-i c \tan (e+f x))^2}",1,"((-I/2)*a)/(f*(c - I*c*Tan[e + f*x])^2)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
935,1,101,0,0.1440049,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^2),x]","-\frac{i}{4 a f \left(c^2-i c^2 \tan (e+f x)\right)}+\frac{i}{8 a f \left(c^2+i c^2 \tan (e+f x)\right)}+\frac{3 x}{8 a c^2}-\frac{i}{8 a f (c-i c \tan (e+f x))^2}","-\frac{i}{4 a f \left(c^2-i c^2 \tan (e+f x)\right)}+\frac{i}{8 a f \left(c^2+i c^2 \tan (e+f x)\right)}+\frac{3 x}{8 a c^2}-\frac{i}{8 a f (c-i c \tan (e+f x))^2}",1,"(3*x)/(8*a*c^2) - (I/8)/(a*f*(c - I*c*Tan[e + f*x])^2) - (I/4)/(a*f*(c^2 - I*c^2*Tan[e + f*x])) + (I/8)/(a*f*(c^2 + I*c^2*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
936,1,64,0,0.0814768,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^2),x]","\frac{\sin (e+f x) \cos ^3(e+f x)}{4 a^2 c^2 f}+\frac{3 \sin (e+f x) \cos (e+f x)}{8 a^2 c^2 f}+\frac{3 x}{8 a^2 c^2}","\frac{\sin (e+f x) \cos ^3(e+f x)}{4 a^2 c^2 f}+\frac{3 \sin (e+f x) \cos (e+f x)}{8 a^2 c^2 f}+\frac{3 x}{8 a^2 c^2}",1,"(3*x)/(8*a^2*c^2) + (3*Cos[e + f*x]*Sin[e + f*x])/(8*a^2*c^2*f) + (Cos[e + f*x]^3*Sin[e + f*x])/(4*a^2*c^2*f)","A",4,3,31,0.09677,1,"{3522, 2635, 8}"
937,1,114,0,0.1256459,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^2),x]","\frac{i \cos ^6(e+f x)}{6 a^3 c^2 f}+\frac{\sin (e+f x) \cos ^5(e+f x)}{6 a^3 c^2 f}+\frac{5 \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^2 f}+\frac{5 \sin (e+f x) \cos (e+f x)}{16 a^3 c^2 f}+\frac{5 x}{16 a^3 c^2}","\frac{i \cos ^6(e+f x)}{6 a^3 c^2 f}+\frac{\sin (e+f x) \cos ^5(e+f x)}{6 a^3 c^2 f}+\frac{5 \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^2 f}+\frac{5 \sin (e+f x) \cos (e+f x)}{16 a^3 c^2 f}+\frac{5 x}{16 a^3 c^2}",1,"(5*x)/(16*a^3*c^2) + ((I/6)*Cos[e + f*x]^6)/(a^3*c^2*f) + (5*Cos[e + f*x]*Sin[e + f*x])/(16*a^3*c^2*f) + (5*Cos[e + f*x]^3*Sin[e + f*x])/(24*a^3*c^2*f) + (Cos[e + f*x]^5*Sin[e + f*x])/(6*a^3*c^2*f)","A",6,4,31,0.1290,1,"{3522, 3486, 2635, 8}"
938,1,154,0,0.1619129,"\int \frac{(a+i a \tan (e+f x))^6}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^6/(c - I*c*Tan[e + f*x])^3,x]","\frac{i a^6 \tan ^2(e+f x)}{2 c^3 f}+\frac{9 a^6 \tan (e+f x)}{c^3 f}-\frac{80 i a^6}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{40 i a^6 \log (\cos (e+f x))}{c^3 f}-\frac{40 a^6 x}{c^3}+\frac{40 i a^6}{c f (c-i c \tan (e+f x))^2}-\frac{32 i a^6}{3 f (c-i c \tan (e+f x))^3}","\frac{i a^6 \tan ^2(e+f x)}{2 c^3 f}+\frac{9 a^6 \tan (e+f x)}{c^3 f}-\frac{80 i a^6}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{40 i a^6 \log (\cos (e+f x))}{c^3 f}-\frac{40 a^6 x}{c^3}+\frac{40 i a^6}{c f (c-i c \tan (e+f x))^2}-\frac{32 i a^6}{3 f (c-i c \tan (e+f x))^3}",1,"(-40*a^6*x)/c^3 + ((40*I)*a^6*Log[Cos[e + f*x]])/(c^3*f) + (9*a^6*Tan[e + f*x])/(c^3*f) + ((I/2)*a^6*Tan[e + f*x]^2)/(c^3*f) - (((32*I)/3)*a^6)/(f*(c - I*c*Tan[e + f*x])^3) + ((40*I)*a^6)/(c*f*(c - I*c*Tan[e + f*x])^2) - ((80*I)*a^6)/(f*(c^3 - I*c^3*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
939,1,134,0,0.1459384,"\int \frac{(a+i a \tan (e+f x))^5}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^5/(c - I*c*Tan[e + f*x])^3,x]","\frac{a^5 \tan (e+f x)}{c^3 f}-\frac{24 i a^5}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{16 i a^5 c^5}{f \left(c^4-i c^4 \tan (e+f x)\right)^2}+\frac{8 i a^5 \log (\cos (e+f x))}{c^3 f}-\frac{8 a^5 x}{c^3}-\frac{16 i a^5}{3 f (c-i c \tan (e+f x))^3}","\frac{a^5 \tan (e+f x)}{c^3 f}-\frac{24 i a^5}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{16 i a^5 c^5}{f \left(c^4-i c^4 \tan (e+f x)\right)^2}+\frac{8 i a^5 \log (\cos (e+f x))}{c^3 f}-\frac{8 a^5 x}{c^3}-\frac{16 i a^5}{3 f (c-i c \tan (e+f x))^3}",1,"(-8*a^5*x)/c^3 + ((8*I)*a^5*Log[Cos[e + f*x]])/(c^3*f) + (a^5*Tan[e + f*x])/(c^3*f) - (((16*I)/3)*a^5)/(f*(c - I*c*Tan[e + f*x])^3) - ((24*I)*a^5)/(f*(c^3 - I*c^3*Tan[e + f*x])) + ((16*I)*a^5*c^5)/(f*(c^4 - I*c^4*Tan[e + f*x])^2)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
940,1,114,0,0.1363891,"\int \frac{(a+i a \tan (e+f x))^4}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^4/(c - I*c*Tan[e + f*x])^3,x]","-\frac{6 i a^4}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i a^4 \log (\cos (e+f x))}{c^3 f}-\frac{a^4 x}{c^3}+\frac{6 i a^4}{c f (c-i c \tan (e+f x))^2}-\frac{8 i a^4}{3 f (c-i c \tan (e+f x))^3}","-\frac{6 i a^4}{f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i a^4 \log (\cos (e+f x))}{c^3 f}-\frac{a^4 x}{c^3}+\frac{6 i a^4}{c f (c-i c \tan (e+f x))^2}-\frac{8 i a^4}{3 f (c-i c \tan (e+f x))^3}",1,"-((a^4*x)/c^3) + (I*a^4*Log[Cos[e + f*x]])/(c^3*f) - (((8*I)/3)*a^4)/(f*(c - I*c*Tan[e + f*x])^3) + ((6*I)*a^4)/(c*f*(c - I*c*Tan[e + f*x])^2) - ((6*I)*a^4)/(f*(c^3 - I*c^3*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
941,1,50,0,0.1073049,"\int \frac{(a+i a \tan (e+f x))^3}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x])^3,x]","-\frac{i a^3 \left(c^2+i c^2 \tan (e+f x)\right)^3}{6 f \left(c^3-i c^3 \tan (e+f x)\right)^3}","-\frac{i a^3 \left(c^2+i c^2 \tan (e+f x)\right)^3}{6 f \left(c^3-i c^3 \tan (e+f x)\right)^3}",1,"((-I/6)*a^3*(c^2 + I*c^2*Tan[e + f*x])^3)/(f*(c^3 - I*c^3*Tan[e + f*x])^3)","A",3,3,31,0.09677,1,"{3522, 3487, 37}"
942,1,58,0,0.113296,"\int \frac{(a+i a \tan (e+f x))^2}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x])^3,x]","\frac{i a^2}{2 c f (c-i c \tan (e+f x))^2}-\frac{2 i a^2}{3 f (c-i c \tan (e+f x))^3}","\frac{i a^2}{2 c f (c-i c \tan (e+f x))^2}-\frac{2 i a^2}{3 f (c-i c \tan (e+f x))^3}",1,"(((-2*I)/3)*a^2)/(f*(c - I*c*Tan[e + f*x])^3) + ((I/2)*a^2)/(c*f*(c - I*c*Tan[e + f*x])^2)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
943,1,25,0,0.0738695,"\int \frac{a+i a \tan (e+f x)}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x])^3,x]","-\frac{i a}{3 f (c-i c \tan (e+f x))^3}","-\frac{i a}{3 f (c-i c \tan (e+f x))^3}",1,"((-I/3)*a)/(f*(c - I*c*Tan[e + f*x])^3)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
944,1,131,0,0.1559457,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^3),x]","-\frac{3 i}{16 a f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i}{16 a f \left(c^3+i c^3 \tan (e+f x)\right)}+\frac{x}{4 a c^3}-\frac{i}{8 a c f (c-i c \tan (e+f x))^2}-\frac{i}{12 a f (c-i c \tan (e+f x))^3}","-\frac{3 i}{16 a f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i}{16 a f \left(c^3+i c^3 \tan (e+f x)\right)}+\frac{x}{4 a c^3}-\frac{i}{8 a c f (c-i c \tan (e+f x))^2}-\frac{i}{12 a f (c-i c \tan (e+f x))^3}",1,"x/(4*a*c^3) - (I/12)/(a*f*(c - I*c*Tan[e + f*x])^3) - (I/8)/(a*c*f*(c - I*c*Tan[e + f*x])^2) - ((3*I)/16)/(a*f*(c^3 - I*c^3*Tan[e + f*x])) + (I/16)/(a*f*(c^3 + I*c^3*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
945,1,161,0,0.176972,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^3),x]","-\frac{3 i}{16 a^2 f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i}{8 a^2 f \left(c^3+i c^3 \tan (e+f x)\right)}+\frac{5 x}{16 a^2 c^3}-\frac{3 i}{32 a^2 c f (c-i c \tan (e+f x))^2}+\frac{i}{32 a^2 c f (c+i c \tan (e+f x))^2}-\frac{i}{24 a^2 f (c-i c \tan (e+f x))^3}","-\frac{3 i}{16 a^2 f \left(c^3-i c^3 \tan (e+f x)\right)}+\frac{i}{8 a^2 f \left(c^3+i c^3 \tan (e+f x)\right)}+\frac{5 x}{16 a^2 c^3}-\frac{3 i}{32 a^2 c f (c-i c \tan (e+f x))^2}+\frac{i}{32 a^2 c f (c+i c \tan (e+f x))^2}-\frac{i}{24 a^2 f (c-i c \tan (e+f x))^3}",1,"(5*x)/(16*a^2*c^3) - (I/24)/(a^2*f*(c - I*c*Tan[e + f*x])^3) - ((3*I)/32)/(a^2*c*f*(c - I*c*Tan[e + f*x])^2) + (I/32)/(a^2*c*f*(c + I*c*Tan[e + f*x])^2) - ((3*I)/16)/(a^2*f*(c^3 - I*c^3*Tan[e + f*x])) + (I/8)/(a^2*f*(c^3 + I*c^3*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
946,1,91,0,0.0926657,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^3),x]","\frac{\sin (e+f x) \cos ^5(e+f x)}{6 a^3 c^3 f}+\frac{5 \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^3 f}+\frac{5 \sin (e+f x) \cos (e+f x)}{16 a^3 c^3 f}+\frac{5 x}{16 a^3 c^3}","\frac{\sin (e+f x) \cos ^5(e+f x)}{6 a^3 c^3 f}+\frac{5 \sin (e+f x) \cos ^3(e+f x)}{24 a^3 c^3 f}+\frac{5 \sin (e+f x) \cos (e+f x)}{16 a^3 c^3 f}+\frac{5 x}{16 a^3 c^3}",1,"(5*x)/(16*a^3*c^3) + (5*Cos[e + f*x]*Sin[e + f*x])/(16*a^3*c^3*f) + (5*Cos[e + f*x]^3*Sin[e + f*x])/(24*a^3*c^3*f) + (Cos[e + f*x]^5*Sin[e + f*x])/(6*a^3*c^3*f)","A",5,3,31,0.09677,1,"{3522, 2635, 8}"
947,1,160,0,0.1601877,"\int \frac{(a+i a \tan (e+f x))^6}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^6/(c - I*c*Tan[e + f*x])^4,x]","-\frac{a^6 \tan (e+f x)}{c^4 f}+\frac{40 i a^6}{f \left(c^4-i c^4 \tan (e+f x)\right)}-\frac{40 i a^6}{f \left(c^2-i c^2 \tan (e+f x)\right)^2}-\frac{10 i a^6 \log (\cos (e+f x))}{c^4 f}+\frac{10 a^6 x}{c^4}+\frac{80 i a^6}{3 c f (c-i c \tan (e+f x))^3}-\frac{8 i a^6}{f (c-i c \tan (e+f x))^4}","-\frac{a^6 \tan (e+f x)}{c^4 f}+\frac{40 i a^6}{f \left(c^4-i c^4 \tan (e+f x)\right)}-\frac{40 i a^6}{f \left(c^2-i c^2 \tan (e+f x)\right)^2}-\frac{10 i a^6 \log (\cos (e+f x))}{c^4 f}+\frac{10 a^6 x}{c^4}+\frac{80 i a^6}{3 c f (c-i c \tan (e+f x))^3}-\frac{8 i a^6}{f (c-i c \tan (e+f x))^4}",1,"(10*a^6*x)/c^4 - ((10*I)*a^6*Log[Cos[e + f*x]])/(c^4*f) - (a^6*Tan[e + f*x])/(c^4*f) - ((8*I)*a^6)/(f*(c - I*c*Tan[e + f*x])^4) + (((80*I)/3)*a^6)/(c*f*(c - I*c*Tan[e + f*x])^3) - ((40*I)*a^6)/(f*(c^2 - I*c^2*Tan[e + f*x])^2) + ((40*I)*a^6)/(f*(c^4 - I*c^4*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
948,1,146,0,0.1456904,"\int \frac{(a+i a \tan (e+f x))^5}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^5/(c - I*c*Tan[e + f*x])^4,x]","\frac{8 i a^5}{f \left(c^4-i c^4 \tan (e+f x)\right)}-\frac{12 i a^5}{f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{32 i a^5 c^5}{3 f \left(c^3-i c^3 \tan (e+f x)\right)^3}-\frac{i a^5 \log (\cos (e+f x))}{c^4 f}+\frac{a^5 x}{c^4}-\frac{4 i a^5}{f (c-i c \tan (e+f x))^4}","\frac{8 i a^5}{f \left(c^4-i c^4 \tan (e+f x)\right)}-\frac{12 i a^5}{f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{32 i a^5 c^5}{3 f \left(c^3-i c^3 \tan (e+f x)\right)^3}-\frac{i a^5 \log (\cos (e+f x))}{c^4 f}+\frac{a^5 x}{c^4}-\frac{4 i a^5}{f (c-i c \tan (e+f x))^4}",1,"(a^5*x)/c^4 - (I*a^5*Log[Cos[e + f*x]])/(c^4*f) - ((4*I)*a^5)/(f*(c - I*c*Tan[e + f*x])^4) - ((12*I)*a^5)/(f*(c^2 - I*c^2*Tan[e + f*x])^2) + (((32*I)/3)*a^5*c^5)/(f*(c^3 - I*c^3*Tan[e + f*x])^3) + ((8*I)*a^5)/(f*(c^4 - I*c^4*Tan[e + f*x]))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
949,1,50,0,0.1042936,"\int \frac{(a+i a \tan (e+f x))^4}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^4/(c - I*c*Tan[e + f*x])^4,x]","-\frac{i a^4 \left(c^2+i c^2 \tan (e+f x)\right)^4}{8 f \left(c^3-i c^3 \tan (e+f x)\right)^4}","-\frac{i a^4 \left(c^2+i c^2 \tan (e+f x)\right)^4}{8 f \left(c^3-i c^3 \tan (e+f x)\right)^4}",1,"((-I/8)*a^4*(c^2 + I*c^2*Tan[e + f*x])^4)/(f*(c^3 - I*c^3*Tan[e + f*x])^4)","A",3,3,31,0.09677,1,"{3522, 3487, 37}"
950,1,87,0,0.1203982,"\int \frac{(a+i a \tan (e+f x))^3}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x])^4,x]","-\frac{i a^3}{2 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{4 i a^3}{3 c f (c-i c \tan (e+f x))^3}-\frac{i a^3}{f (c-i c \tan (e+f x))^4}","-\frac{i a^3}{2 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{4 i a^3}{3 c f (c-i c \tan (e+f x))^3}-\frac{i a^3}{f (c-i c \tan (e+f x))^4}",1,"((-I)*a^3)/(f*(c - I*c*Tan[e + f*x])^4) + (((4*I)/3)*a^3)/(c*f*(c - I*c*Tan[e + f*x])^3) - ((I/2)*a^3)/(f*(c^2 - I*c^2*Tan[e + f*x])^2)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
951,1,62,0,0.1120793,"\int \frac{(a+i a \tan (e+f x))^2}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x])^4,x]","\frac{i a^2 c^2}{3 f \left(c^2-i c^2 \tan (e+f x)\right)^3}-\frac{i a^2}{2 f (c-i c \tan (e+f x))^4}","\frac{i a^2 c^2}{3 f \left(c^2-i c^2 \tan (e+f x)\right)^3}-\frac{i a^2}{2 f (c-i c \tan (e+f x))^4}",1,"((-I/2)*a^2)/(f*(c - I*c*Tan[e + f*x])^4) + ((I/3)*a^2*c^2)/(f*(c^2 - I*c^2*Tan[e + f*x])^3)","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
952,1,25,0,0.0725323,"\int \frac{a+i a \tan (e+f x)}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x])^4,x]","-\frac{i a}{4 f (c-i c \tan (e+f x))^4}","-\frac{i a}{4 f (c-i c \tan (e+f x))^4}",1,"((-I/4)*a)/(f*(c - I*c*Tan[e + f*x])^4)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
953,1,162,0,0.1685799,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^4} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^4),x]","-\frac{i}{8 a f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{i}{32 a f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{3 i}{32 a f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{5 x}{32 a c^4}-\frac{i}{12 a c f (c-i c \tan (e+f x))^3}-\frac{i}{16 a f (c-i c \tan (e+f x))^4}","-\frac{i}{8 a f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{i}{32 a f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{3 i}{32 a f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{5 x}{32 a c^4}-\frac{i}{12 a c f (c-i c \tan (e+f x))^3}-\frac{i}{16 a f (c-i c \tan (e+f x))^4}",1,"(5*x)/(32*a*c^4) - (I/16)/(a*f*(c - I*c*Tan[e + f*x])^4) - (I/12)/(a*c*f*(c - I*c*Tan[e + f*x])^3) - ((3*I)/32)/(a*f*(c^2 - I*c^2*Tan[e + f*x])^2) - (I/8)/(a*f*(c^4 - I*c^4*Tan[e + f*x])) + (I/32)/(a*f*(c^4 + I*c^4*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
954,1,193,0,0.1905318,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^4} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^4),x]","-\frac{5 i}{32 a^2 f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{5 i}{64 a^2 f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{3 i}{32 a^2 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{i}{64 a^2 f \left(c^2+i c^2 \tan (e+f x)\right)^2}+\frac{15 x}{64 a^2 c^4}-\frac{i}{16 a^2 c f (c-i c \tan (e+f x))^3}-\frac{i}{32 a^2 f (c-i c \tan (e+f x))^4}","-\frac{5 i}{32 a^2 f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{5 i}{64 a^2 f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{3 i}{32 a^2 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{i}{64 a^2 f \left(c^2+i c^2 \tan (e+f x)\right)^2}+\frac{15 x}{64 a^2 c^4}-\frac{i}{16 a^2 c f (c-i c \tan (e+f x))^3}-\frac{i}{32 a^2 f (c-i c \tan (e+f x))^4}",1,"(15*x)/(64*a^2*c^4) - (I/32)/(a^2*f*(c - I*c*Tan[e + f*x])^4) - (I/16)/(a^2*c*f*(c - I*c*Tan[e + f*x])^3) - ((3*I)/32)/(a^2*f*(c^2 - I*c^2*Tan[e + f*x])^2) + (I/64)/(a^2*f*(c^2 + I*c^2*Tan[e + f*x])^2) - ((5*I)/32)/(a^2*f*(c^4 - I*c^4*Tan[e + f*x])) + ((5*I)/64)/(a^2*f*(c^4 + I*c^4*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
955,1,223,0,0.2083412,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^4} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^4),x]","-\frac{5 i}{32 a^3 f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{15 i}{128 a^3 f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{5 i}{64 a^3 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{5 i}{128 a^3 f \left(c^2+i c^2 \tan (e+f x)\right)^2}+\frac{35 x}{128 a^3 c^4}-\frac{i}{24 a^3 c f (c-i c \tan (e+f x))^3}+\frac{i}{96 a^3 c f (c+i c \tan (e+f x))^3}-\frac{i}{64 a^3 f (c-i c \tan (e+f x))^4}","-\frac{5 i}{32 a^3 f \left(c^4-i c^4 \tan (e+f x)\right)}+\frac{15 i}{128 a^3 f \left(c^4+i c^4 \tan (e+f x)\right)}-\frac{5 i}{64 a^3 f \left(c^2-i c^2 \tan (e+f x)\right)^2}+\frac{5 i}{128 a^3 f \left(c^2+i c^2 \tan (e+f x)\right)^2}+\frac{35 x}{128 a^3 c^4}-\frac{i}{24 a^3 c f (c-i c \tan (e+f x))^3}+\frac{i}{96 a^3 c f (c+i c \tan (e+f x))^3}-\frac{i}{64 a^3 f (c-i c \tan (e+f x))^4}",1,"(35*x)/(128*a^3*c^4) - (I/64)/(a^3*f*(c - I*c*Tan[e + f*x])^4) - (I/24)/(a^3*c*f*(c - I*c*Tan[e + f*x])^3) + (I/96)/(a^3*c*f*(c + I*c*Tan[e + f*x])^3) - ((5*I)/64)/(a^3*f*(c^2 - I*c^2*Tan[e + f*x])^2) + ((5*I)/128)/(a^3*f*(c^2 + I*c^2*Tan[e + f*x])^2) - ((5*I)/32)/(a^3*f*(c^4 - I*c^4*Tan[e + f*x])) + ((15*I)/128)/(a^3*f*(c^4 + I*c^4*Tan[e + f*x]))","A",5,4,31,0.1290,1,"{3522, 3487, 44, 206}"
956,1,92,0,0.1627483,"\int (a+i a \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^3*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{8 i a^3 \sqrt{c-i c \tan (e+f x)}}{f}","\frac{2 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 c f}+\frac{8 i a^3 \sqrt{c-i c \tan (e+f x)}}{f}",1,"((8*I)*a^3*Sqrt[c - I*c*Tan[e + f*x]])/f - (((8*I)/3)*a^3*(c - I*c*Tan[e + f*x])^(3/2))/(c*f) + (((2*I)/5)*a^3*(c - I*c*Tan[e + f*x])^(5/2))/(c^2*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
957,1,60,0,0.1519256,"\int (a+i a \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{4 i a^2 \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{3/2}}{3 c f}","\frac{4 i a^2 \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{3/2}}{3 c f}",1,"((4*I)*a^2*Sqrt[c - I*c*Tan[e + f*x]])/f - (((2*I)/3)*a^2*(c - I*c*Tan[e + f*x])^(3/2))/(c*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
958,1,25,0,0.1006926,"\int (a+i a \tan (e+f x)) \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 i a \sqrt{c-i c \tan (e+f x)}}{f}","\frac{2 i a \sqrt{c-i c \tan (e+f x)}}{f}",1,"((2*I)*a*Sqrt[c - I*c*Tan[e + f*x]])/f","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
959,1,95,0,0.1798227,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{a+i a \tan (e+f x)} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x]),x]","\frac{i \sqrt{c-i c \tan (e+f x)}}{2 a f (1+i \tan (e+f x))}+\frac{i \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a f}","\frac{i \sqrt{c-i c \tan (e+f x)}}{2 a f (1+i \tan (e+f x))}+\frac{i \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{2 \sqrt{2} a f}",1,"((I/2)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*f) + ((I/2)*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*(1 + I*Tan[e + f*x]))","A",5,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
960,1,138,0,0.1934815,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^2} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^2,x]","\frac{3 i \sqrt{c-i c \tan (e+f x)}}{16 a^2 f (1+i \tan (e+f x))}+\frac{i \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (1+i \tan (e+f x))^2}+\frac{3 i \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^2 f}","\frac{3 i \sqrt{c-i c \tan (e+f x)}}{16 a^2 f (1+i \tan (e+f x))}+\frac{i \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (1+i \tan (e+f x))^2}+\frac{3 i \sqrt{c} \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)/16)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*f) + ((I/4)*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(1 + I*Tan[e + f*x])^2) + (((3*I)/16)*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(1 + I*Tan[e + f*x]))","A",6,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
961,1,181,0,0.2085871,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^3} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^3,x]","\frac{5 i \sqrt{c-i c \tan (e+f x)}}{64 a^3 f (1+i \tan (e+f x))}+\frac{5 i \sqrt{c-i c \tan (e+f x)}}{48 a^3 f (1+i \tan (e+f x))^2}+\frac{i \sqrt{c-i c \tan (e+f x)}}{6 a^3 f (1+i \tan (e+f x))^3}+\frac{5 i \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{64 \sqrt{2} a^3 f}","\frac{5 i \sqrt{c-i c \tan (e+f x)}}{64 a^3 f (1+i \tan (e+f x))}+\frac{5 i \sqrt{c-i c \tan (e+f x)}}{48 a^3 f (1+i \tan (e+f x))^2}+\frac{i \sqrt{c-i c \tan (e+f x)}}{6 a^3 f (1+i \tan (e+f x))^3}+\frac{5 i \sqrt{c} \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)/64)*Sqrt[c]*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*f) + ((I/6)*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(1 + I*Tan[e + f*x])^3) + (((5*I)/48)*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(1 + I*Tan[e + f*x])^2) + (((5*I)/64)*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(1 + I*Tan[e + f*x]))","A",7,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
962,1,94,0,0.169365,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 i a^3 (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{8 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 f}","\frac{2 i a^3 (c-i c \tan (e+f x))^{7/2}}{7 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 c f}+\frac{8 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 f}",1,"(((8*I)/3)*a^3*(c - I*c*Tan[e + f*x])^(3/2))/f - (((8*I)/5)*a^3*(c - I*c*Tan[e + f*x])^(5/2))/(c*f) + (((2*I)/7)*a^3*(c - I*c*Tan[e + f*x])^(7/2))/(c^2*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
963,1,62,0,0.1501551,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{4 i a^2 (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{5/2}}{5 c f}","\frac{4 i a^2 (c-i c \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{5/2}}{5 c f}",1,"(((4*I)/3)*a^2*(c - I*c*Tan[e + f*x])^(3/2))/f - (((2*I)/5)*a^2*(c - I*c*Tan[e + f*x])^(5/2))/(c*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
964,1,27,0,0.0987998,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 i a (c-i c \tan (e+f x))^{3/2}}{3 f}","\frac{2 i a (c-i c \tan (e+f x))^{3/2}}{3 f}",1,"(((2*I)/3)*a*(c - I*c*Tan[e + f*x])^(3/2))/f","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
965,1,95,0,0.1794563,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x]),x]","\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{a f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a f}","\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{a f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{\sqrt{2} a f}",1,"((-I)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*f) + (I*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*(c + I*c*Tan[e + f*x]))","A",5,5,33,0.1515,1,"{3522, 3487, 47, 63, 206}"
966,1,146,0,0.191614,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{2 a^2 f (c+i c \tan (e+f x))^2}-\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{8 a^2 f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^2 f}","\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{2 a^2 f (c+i c \tan (e+f x))^2}-\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{8 a^2 f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{2} a^2 f}",1,"((-I/8)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*f) + ((I/2)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(c + I*c*Tan[e + f*x])^2) - ((I/8)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(c + I*c*Tan[e + f*x]))","A",6,6,33,0.1818,1,"{3522, 3487, 47, 51, 63, 206}"
967,1,193,0,0.2069326,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{i c^4 \sqrt{c-i c \tan (e+f x)}}{3 a^3 f (c+i c \tan (e+f x))^3}-\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{24 a^3 f (c+i c \tan (e+f x))^2}-\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{32 a^3 f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^3 f}","\frac{i c^4 \sqrt{c-i c \tan (e+f x)}}{3 a^3 f (c+i c \tan (e+f x))^3}-\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{24 a^3 f (c+i c \tan (e+f x))^2}-\frac{i c^2 \sqrt{c-i c \tan (e+f x)}}{32 a^3 f (c+i c \tan (e+f x))}-\frac{i c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{32 \sqrt{2} a^3 f}",1,"((-I/32)*c^(3/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*f) + ((I/3)*c^4*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(c + I*c*Tan[e + f*x])^3) - ((I/24)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(c + I*c*Tan[e + f*x])^2) - ((I/32)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(c + I*c*Tan[e + f*x]))","A",7,6,33,0.1818,1,"{3522, 3487, 47, 51, 63, 206}"
968,1,94,0,0.1576652,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 i a^3 (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{8 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 f}","\frac{2 i a^3 (c-i c \tan (e+f x))^{9/2}}{9 c^2 f}-\frac{8 i a^3 (c-i c \tan (e+f x))^{7/2}}{7 c f}+\frac{8 i a^3 (c-i c \tan (e+f x))^{5/2}}{5 f}",1,"(((8*I)/5)*a^3*(c - I*c*Tan[e + f*x])^(5/2))/f - (((8*I)/7)*a^3*(c - I*c*Tan[e + f*x])^(7/2))/(c*f) + (((2*I)/9)*a^3*(c - I*c*Tan[e + f*x])^(9/2))/(c^2*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
969,1,62,0,0.1447949,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{4 i a^2 (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{7/2}}{7 c f}","\frac{4 i a^2 (c-i c \tan (e+f x))^{5/2}}{5 f}-\frac{2 i a^2 (c-i c \tan (e+f x))^{7/2}}{7 c f}",1,"(((4*I)/5)*a^2*(c - I*c*Tan[e + f*x])^(5/2))/f - (((2*I)/7)*a^2*(c - I*c*Tan[e + f*x])^(7/2))/(c*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
970,1,27,0,0.1008227,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 i a (c-i c \tan (e+f x))^{5/2}}{5 f}","\frac{2 i a (c-i c \tan (e+f x))^{5/2}}{5 f}",1,"(((2*I)/5)*a*(c - I*c*Tan[e + f*x])^(5/2))/f","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
971,1,125,0,0.1849495,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x]),x]","\frac{3 i c^2 \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{i c^2 (c-i c \tan (e+f x))^{3/2}}{a f (c+i c \tan (e+f x))}-\frac{3 i \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}","\frac{3 i c^2 \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{i c^2 (c-i c \tan (e+f x))^{3/2}}{a f (c+i c \tan (e+f x))}-\frac{3 i \sqrt{2} c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{a f}",1,"((-3*I)*Sqrt[2]*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(a*f) + ((3*I)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a*f) + (I*c^2*(c - I*c*Tan[e + f*x])^(3/2))/(a*f*(c + I*c*Tan[e + f*x]))","A",6,6,33,0.1818,1,"{3522, 3487, 47, 50, 63, 206}"
972,1,146,0,0.1876672,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^2,x]","-\frac{3 i c^3 \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (c+i c \tan (e+f x))}+\frac{i c^3 (c-i c \tan (e+f x))^{3/2}}{2 a^2 f (c+i c \tan (e+f x))^2}+\frac{3 i c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^2 f}","-\frac{3 i c^3 \sqrt{c-i c \tan (e+f x)}}{4 a^2 f (c+i c \tan (e+f x))}+\frac{i c^3 (c-i c \tan (e+f x))^{3/2}}{2 a^2 f (c+i c \tan (e+f x))^2}+\frac{3 i c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{4 \sqrt{2} a^2 f}",1,"(((3*I)/4)*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*f) + ((I/2)*c^3*(c - I*c*Tan[e + f*x])^(3/2))/(a^2*f*(c + I*c*Tan[e + f*x])^2) - (((3*I)/4)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(c + I*c*Tan[e + f*x]))","A",6,5,33,0.1515,1,"{3522, 3487, 47, 63, 206}"
973,1,193,0,0.2046206,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^3,x]","-\frac{i c^4 \sqrt{c-i c \tan (e+f x)}}{4 a^3 f (c+i c \tan (e+f x))^2}+\frac{i c^4 (c-i c \tan (e+f x))^{3/2}}{3 a^3 f (c+i c \tan (e+f x))^3}+\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{16 a^3 f (c+i c \tan (e+f x))}+\frac{i c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^3 f}","-\frac{i c^4 \sqrt{c-i c \tan (e+f x)}}{4 a^3 f (c+i c \tan (e+f x))^2}+\frac{i c^4 (c-i c \tan (e+f x))^{3/2}}{3 a^3 f (c+i c \tan (e+f x))^3}+\frac{i c^3 \sqrt{c-i c \tan (e+f x)}}{16 a^3 f (c+i c \tan (e+f x))}+\frac{i c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{2} \sqrt{c}}\right)}{16 \sqrt{2} a^3 f}",1,"((I/16)*c^(5/2)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*f) + ((I/3)*c^4*(c - I*c*Tan[e + f*x])^(3/2))/(a^3*f*(c + I*c*Tan[e + f*x])^3) - ((I/4)*c^4*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(c + I*c*Tan[e + f*x])^2) + ((I/16)*c^3*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*(c + I*c*Tan[e + f*x]))","A",7,6,33,0.1818,1,"{3522, 3487, 47, 51, 63, 206}"
974,1,90,0,0.1609962,"\int \frac{(a+i a \tan (e+f x))^3}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}-\frac{8 i a^3 \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{8 i a^3}{f \sqrt{c-i c \tan (e+f x)}}","\frac{2 i a^3 (c-i c \tan (e+f x))^{3/2}}{3 c^2 f}-\frac{8 i a^3 \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{8 i a^3}{f \sqrt{c-i c \tan (e+f x)}}",1,"((-8*I)*a^3)/(f*Sqrt[c - I*c*Tan[e + f*x]]) - ((8*I)*a^3*Sqrt[c - I*c*Tan[e + f*x]])/(c*f) + (((2*I)/3)*a^3*(c - I*c*Tan[e + f*x])^(3/2))/(c^2*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
975,1,58,0,0.1478387,"\int \frac{(a+i a \tan (e+f x))^2}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 i a^2 \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{4 i a^2}{f \sqrt{c-i c \tan (e+f x)}}","-\frac{2 i a^2 \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{4 i a^2}{f \sqrt{c-i c \tan (e+f x)}}",1,"((-4*I)*a^2)/(f*Sqrt[c - I*c*Tan[e + f*x]]) - ((2*I)*a^2*Sqrt[c - I*c*Tan[e + f*x]])/(c*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
976,1,25,0,0.1030653,"\int \frac{a+i a \tan (e+f x)}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 i a}{f \sqrt{c-i c \tan (e+f x)}}","-\frac{2 i a}{f \sqrt{c-i c \tan (e+f x)}}",1,"((-2*I)*a)/(f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
977,1,124,0,0.1756647,"\int \frac{1}{(a+i a \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]]),x]","-\frac{3 i}{4 a f \sqrt{c-i c \tan (e+f x)}}+\frac{i}{2 a f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{3 i \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{3 i}{4 a f \sqrt{c-i c \tan (e+f x)}}+\frac{i}{2 a f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{3 i \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)/4)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*Sqrt[c]*f) - ((3*I)/4)/(a*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I/2)/(a*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",6,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
978,1,167,0,0.1980741,"\int \frac{1}{(a+i a \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]),x]","-\frac{15 i}{32 a^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{5 i}{16 a^2 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{15 i \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{15 i}{32 a^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{5 i}{16 a^2 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{15 i \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,"(((15*I)/32)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*Sqrt[c]*f) - ((15*I)/32)/(a^2*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I/4)/(a^2*f*(1 + I*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]) + ((5*I)/16)/(a^2*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
979,1,210,0,0.2151943,"\int \frac{1}{(a+i a \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*Sqrt[c - I*c*Tan[e + f*x]]),x]","-\frac{35 i}{128 a^3 f \sqrt{c-i c \tan (e+f x)}}+\frac{35 i}{192 a^3 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{7 i}{48 a^3 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}}+\frac{35 i \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{35 i}{128 a^3 f \sqrt{c-i c \tan (e+f x)}}+\frac{35 i}{192 a^3 f (1+i \tan (e+f x)) \sqrt{c-i c \tan (e+f x)}}+\frac{7 i}{48 a^3 f (1+i \tan (e+f x))^2 \sqrt{c-i c \tan (e+f x)}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 \sqrt{c-i c \tan (e+f x)}}+\frac{35 i \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,"(((35*I)/128)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*Sqrt[c]*f) - ((35*I)/128)/(a^3*f*Sqrt[c - I*c*Tan[e + f*x]]) + (I/6)/(a^3*f*(1 + I*Tan[e + f*x])^3*Sqrt[c - I*c*Tan[e + f*x]]) + ((7*I)/48)/(a^3*f*(1 + I*Tan[e + f*x])^2*Sqrt[c - I*c*Tan[e + f*x]]) + ((35*I)/192)/(a^3*f*(1 + I*Tan[e + f*x])*Sqrt[c - I*c*Tan[e + f*x]])","A",8,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
980,1,90,0,0.1631471,"\int \frac{(a+i a \tan (e+f x))^3}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 i a^3 \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{8 i a^3}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{8 i a^3}{3 f (c-i c \tan (e+f x))^{3/2}}","\frac{2 i a^3 \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{8 i a^3}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{8 i a^3}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(((-8*I)/3)*a^3)/(f*(c - I*c*Tan[e + f*x])^(3/2)) + ((8*I)*a^3)/(c*f*Sqrt[c - I*c*Tan[e + f*x]]) + ((2*I)*a^3*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f)","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
981,1,60,0,0.154045,"\int \frac{(a+i a \tan (e+f x))^2}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{2 i a^2}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{4 i a^2}{3 f (c-i c \tan (e+f x))^{3/2}}","\frac{2 i a^2}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{4 i a^2}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(((-4*I)/3)*a^2)/(f*(c - I*c*Tan[e + f*x])^(3/2)) + ((2*I)*a^2)/(c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
982,1,27,0,0.1065961,"\int \frac{a+i a \tan (e+f x)}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 i a}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{2 i a}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"(((-2*I)/3)*a)/(f*(c - I*c*Tan[e + f*x])^(3/2))","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
983,1,156,0,0.1996663,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{5 i \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{5 i}{8 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{5 i}{12 a f (c-i c \tan (e+f x))^{3/2}}+\frac{i}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}","\frac{5 i \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{5 i}{8 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{5 i}{12 a f (c-i c \tan (e+f x))^{3/2}}+\frac{i}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}",1,"(((5*I)/8)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*c^(3/2)*f) - ((5*I)/12)/(a*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I/2)/(a*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - ((5*I)/8)/(a*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
984,1,199,0,0.2115712,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{35 i \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{35 i}{64 a^2 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 i}{96 a^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{7 i}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}","\frac{35 i \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{35 i}{64 a^2 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 i}{96 a^2 f (c-i c \tan (e+f x))^{3/2}}+\frac{7 i}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}",1,"(((35*I)/64)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*c^(3/2)*f) - ((35*I)/96)/(a^2*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I/4)/(a^2*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)) + ((7*I)/16)/(a^2*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - ((35*I)/64)/(a^2*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",8,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
985,1,242,0,0.2445916,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{105 i \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{105 i}{256 a^3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 i}{128 a^3 f (c-i c \tan (e+f x))^{3/2}}+\frac{21 i}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{3 i}{16 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}}","\frac{105 i \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{105 i}{256 a^3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{35 i}{128 a^3 f (c-i c \tan (e+f x))^{3/2}}+\frac{21 i}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{3/2}}+\frac{3 i}{16 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{3/2}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{3/2}}",1,"(((105*I)/256)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*c^(3/2)*f) - ((35*I)/128)/(a^3*f*(c - I*c*Tan[e + f*x])^(3/2)) + (I/6)/(a^3*f*(1 + I*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(3/2)) + ((3*I)/16)/(a^3*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(3/2)) + ((21*I)/64)/(a^3*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(3/2)) - ((105*I)/256)/(a^3*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",9,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
986,1,92,0,0.1637776,"\int \frac{(a+i a \tan (e+f x))^3}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{2 i a^3}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{8 i a^3}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{8 i a^3}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{2 i a^3}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{8 i a^3}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{8 i a^3}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"(((-8*I)/5)*a^3)/(f*(c - I*c*Tan[e + f*x])^(5/2)) + (((8*I)/3)*a^3)/(c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((2*I)*a^3)/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
987,1,62,0,0.1532128,"\int \frac{(a+i a \tan (e+f x))^2}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 i a^2}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 i a^2}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{2 i a^2}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 i a^2}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"(((-4*I)/5)*a^2)/(f*(c - I*c*Tan[e + f*x])^(5/2)) + (((2*I)/3)*a^2)/(c*f*(c - I*c*Tan[e + f*x])^(3/2))","A",4,3,33,0.09091,1,"{3522, 3487, 43}"
988,1,27,0,0.1046541,"\int \frac{a+i a \tan (e+f x)}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{2 i a}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{2 i a}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"(((-2*I)/5)*a)/(f*(c - I*c*Tan[e + f*x])^(5/2))","A",3,3,31,0.09677,1,"{3522, 3487, 32}"
989,1,188,0,0.2236939,"\int \frac{1}{(a+i a \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{7 i}{16 a c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{7 i \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{7 i}{24 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{7 i}{20 a f (c-i c \tan (e+f x))^{5/2}}+\frac{i}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}","-\frac{7 i}{16 a c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{7 i \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{7 i}{24 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{7 i}{20 a f (c-i c \tan (e+f x))^{5/2}}+\frac{i}{2 a f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}",1,"(((7*I)/16)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a*c^(5/2)*f) - ((7*I)/20)/(a*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I/2)/(a*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - ((7*I)/24)/(a*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((7*I)/16)/(a*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",8,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
990,1,231,0,0.2358621,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{63 i}{128 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{63 i \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{21 i}{64 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{63 i}{160 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{9 i}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}","-\frac{63 i}{128 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{63 i \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{21 i}{64 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{63 i}{160 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{9 i}{16 a^2 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{i}{4 a^2 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}",1,"(((63*I)/128)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^2*c^(5/2)*f) - ((63*I)/160)/(a^2*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I/4)/(a^2*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)) + ((9*I)/16)/(a^2*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - ((21*I)/64)/(a^2*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((63*I)/128)/(a^2*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",9,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
991,1,274,0,0.2503885,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{231 i}{512 a^3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{231 i \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{77 i}{256 a^3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{231 i}{640 a^3 f (c-i c \tan (e+f x))^{5/2}}+\frac{33 i}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{11 i}{48 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}}","-\frac{231 i}{512 a^3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{231 i \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{77 i}{256 a^3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{231 i}{640 a^3 f (c-i c \tan (e+f x))^{5/2}}+\frac{33 i}{64 a^3 f (1+i \tan (e+f x)) (c-i c \tan (e+f x))^{5/2}}+\frac{11 i}{48 a^3 f (1+i \tan (e+f x))^2 (c-i c \tan (e+f x))^{5/2}}+\frac{i}{6 a^3 f (1+i \tan (e+f x))^3 (c-i c \tan (e+f x))^{5/2}}",1,"(((231*I)/512)*ArcTanh[Sqrt[c - I*c*Tan[e + f*x]]/(Sqrt[2]*Sqrt[c])])/(Sqrt[2]*a^3*c^(5/2)*f) - ((231*I)/640)/(a^3*f*(c - I*c*Tan[e + f*x])^(5/2)) + (I/6)/(a^3*f*(1 + I*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^(5/2)) + ((11*I)/48)/(a^3*f*(1 + I*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^(5/2)) + ((33*I)/64)/(a^3*f*(1 + I*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^(5/2)) - ((77*I)/256)/(a^3*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((231*I)/512)/(a^3*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",10,5,33,0.1515,1,"{3522, 3487, 51, 63, 206}"
992,1,154,0,0.1596508,"\int (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{3 i a^{5/2} \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{3 i a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{i a (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 f}","-\frac{3 i a^{5/2} \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{3 i a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{i a (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 f}",1,"((-3*I)*a^(5/2)*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (((3*I)/2)*a^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/f + ((I/2)*a*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/f","A",6,5,35,0.1429,1,"{3523, 50, 63, 217, 203}"
993,1,106,0,0.1409295,"\int (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{i a \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i a^{3/2} \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{i a \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}-\frac{2 i a^{3/2} \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)*a^(3/2)*Sqrt[c]*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/f + (I*a*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/f","A",5,5,35,0.1429,1,"{3523, 50, 63, 217, 203}"
994,1,63,0,0.1171065,"\int \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{2 i \sqrt{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{2 i \sqrt{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]*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",4,4,35,0.1143,1,"{3523, 63, 217, 203}"
995,1,41,0,0.0955962,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{i \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}","\frac{i \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}",1,"(I*Sqrt[c - I*c*Tan[e + f*x]])/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",2,2,35,0.05714,1,"{3523, 37}"
996,1,90,0,0.1189389,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{i \sqrt{c-i c \tan (e+f x)}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{3 f (a+i a \tan (e+f x))^{3/2}}","\frac{i \sqrt{c-i c \tan (e+f x)}}{3 a f \sqrt{a+i a \tan (e+f x)}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{3 f (a+i a \tan (e+f x))^{3/2}}",1,"((I/3)*Sqrt[c - I*c*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I/3)*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,35,0.08571,1,"{3523, 45, 37}"
997,1,136,0,0.1369504,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{2 i \sqrt{c-i c \tan (e+f x)}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i \sqrt{c-i c \tan (e+f x)}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{2 i \sqrt{c-i c \tan (e+f x)}}{15 a^2 f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i \sqrt{c-i c \tan (e+f x)}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"((I/5)*Sqrt[c - I*c*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^(5/2)) + (((2*I)/15)*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*(a + I*a*Tan[e + f*x])^(3/2)) + (((2*I)/15)*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*Sqrt[a + I*a*Tan[e + f*x]])","A",4,3,35,0.08571,1,"{3523, 45, 37}"
998,1,182,0,0.1553751,"\int \frac{\sqrt{c-i c \tan (e+f x)}}{(a+i a \tan (e+f x))^{7/2}} \, dx","Int[Sqrt[c - I*c*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^(7/2),x]","\frac{2 i \sqrt{c-i c \tan (e+f x)}}{35 a^3 f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i \sqrt{c-i c \tan (e+f x)}}{35 a^2 f (a+i a \tan (e+f x))^{3/2}}+\frac{3 i \sqrt{c-i c \tan (e+f x)}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{7 f (a+i a \tan (e+f x))^{7/2}}","\frac{2 i \sqrt{c-i c \tan (e+f x)}}{35 a^3 f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i \sqrt{c-i c \tan (e+f x)}}{35 a^2 f (a+i a \tan (e+f x))^{3/2}}+\frac{3 i \sqrt{c-i c \tan (e+f x)}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i \sqrt{c-i c \tan (e+f x)}}{7 f (a+i a \tan (e+f x))^{7/2}}",1,"((I/7)*Sqrt[c - I*c*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^(7/2)) + (((3*I)/35)*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*(a + I*a*Tan[e + f*x])^(5/2)) + (((2*I)/35)*Sqrt[c - I*c*Tan[e + f*x]])/(a^2*f*(a + I*a*Tan[e + f*x])^(3/2)) + (((2*I)/35)*Sqrt[c - I*c*Tan[e + f*x]])/(a^3*f*Sqrt[a + I*a*Tan[e + f*x]])","A",5,3,35,0.08571,1,"{3523, 45, 37}"
999,1,159,0,0.1624642,"\int (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{i a^{5/2} 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^2 c \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{i a (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{3 f}","-\frac{i a^{5/2} 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^2 c \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}+\frac{i a (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}{3 f}",1,"((-I)*a^(5/2)*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^2*c*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) + ((I/3)*a*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/f","A",6,6,35,0.1714,1,"{3523, 49, 38, 63, 217, 203}"
1000,1,113,0,0.1435734,"\int (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{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{i a^{3/2} 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 c \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{i a^{3/2} 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}",1,"((-I)*a^(3/2)*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*c*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f)","A",5,5,35,0.1429,1,"{3523, 38, 63, 217, 203}"
1001,1,106,0,0.1359494,"\int \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 i \sqrt{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{i c \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}","-\frac{2 i \sqrt{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{i c \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{f}",1,"((-2*I)*Sqrt[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 - (I*c*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/f","A",5,5,35,0.1429,1,"{3523, 50, 63, 217, 203}"
1002,1,106,0,0.1423391,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{2 i 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)}{\sqrt{a} f}+\frac{2 i c \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}","\frac{2 i 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)}{\sqrt{a} f}+\frac{2 i c \sqrt{c-i c \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}",1,"((2*I)*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) + ((2*I)*c*Sqrt[c - I*c*Tan[e + f*x]])/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",5,5,35,0.1429,1,"{3523, 47, 63, 217, 203}"
1003,1,43,0,0.1092015,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{i (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}","\frac{i (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}",1,"((I/3)*(c - I*c*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(3/2))","A",2,2,35,0.05714,1,"{3523, 37}"
1004,1,90,0,0.1263058,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{i (c-i c \tan (e+f x))^{3/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{i (c-i c \tan (e+f x))^{3/2}}{15 a f (a+i a \tan (e+f x))^{3/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"((I/5)*(c - I*c*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(5/2)) + ((I/15)*(c - I*c*Tan[e + f*x])^(3/2))/(a*f*(a + I*a*Tan[e + f*x])^(3/2))","A",3,3,35,0.08571,1,"{3523, 45, 37}"
1005,1,136,0,0.1442825,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{7/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(7/2),x]","\frac{2 i (c-i c \tan (e+f x))^{3/2}}{105 a^2 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 i (c-i c \tan (e+f x))^{3/2}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{7 f (a+i a \tan (e+f x))^{7/2}}","\frac{2 i (c-i c \tan (e+f x))^{3/2}}{105 a^2 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 i (c-i c \tan (e+f x))^{3/2}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{7 f (a+i a \tan (e+f x))^{7/2}}",1,"((I/7)*(c - I*c*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(7/2)) + (((2*I)/35)*(c - I*c*Tan[e + f*x])^(3/2))/(a*f*(a + I*a*Tan[e + f*x])^(5/2)) + (((2*I)/105)*(c - I*c*Tan[e + f*x])^(3/2))/(a^2*f*(a + I*a*Tan[e + f*x])^(3/2))","A",4,3,35,0.08571,1,"{3523, 45, 37}"
1006,1,182,0,0.1658401,"\int \frac{(c-i c \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{9/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(9/2),x]","\frac{2 i (c-i c \tan (e+f x))^{3/2}}{315 a^3 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 i (c-i c \tan (e+f x))^{3/2}}{105 a^2 f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{21 a f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{9 f (a+i a \tan (e+f x))^{9/2}}","\frac{2 i (c-i c \tan (e+f x))^{3/2}}{315 a^3 f (a+i a \tan (e+f x))^{3/2}}+\frac{2 i (c-i c \tan (e+f x))^{3/2}}{105 a^2 f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{21 a f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{3/2}}{9 f (a+i a \tan (e+f x))^{9/2}}",1,"((I/9)*(c - I*c*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(9/2)) + ((I/21)*(c - I*c*Tan[e + f*x])^(3/2))/(a*f*(a + I*a*Tan[e + f*x])^(7/2)) + (((2*I)/105)*(c - I*c*Tan[e + f*x])^(3/2))/(a^2*f*(a + I*a*Tan[e + f*x])^(5/2)) + (((2*I)/315)*(c - I*c*Tan[e + f*x])^(3/2))/(a^3*f*(a + I*a*Tan[e + f*x])^(3/2))","A",5,3,35,0.08571,1,"{3523, 45, 37}"
1007,1,168,0,0.1597874,"\int (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{3 i a^{5/2} 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 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 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{3 i a^{5/2} 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 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 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}",1,"(((-3*I)/4)*a^(5/2)*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*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*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)","A",6,5,35,0.1429,1,"{3523, 38, 63, 217, 203}"
1008,1,159,0,0.1611518,"\int (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{i a^{3/2} 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)}{f}+\frac{a c^2 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{i c (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} 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)}{f}+\frac{a c^2 \tan (e+f x) \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{i c (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)*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 + (a*c^2*Tan[e + f*x]*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(2*f) - ((I/3)*c*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2))/f","A",6,6,35,0.1714,1,"{3523, 49, 38, 63, 217, 203}"
1009,1,154,0,0.1542247,"\int \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{3 i \sqrt{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)}{f}-\frac{3 i c^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{i c \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 f}","-\frac{3 i \sqrt{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)}{f}-\frac{3 i c^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 f}-\frac{i c \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}{2 f}",1,"((-3*I)*Sqrt[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*I)/2)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/f - ((I/2)*c*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2))/f","A",6,5,35,0.1429,1,"{3523, 50, 63, 217, 203}"
1010,1,153,0,0.1591908,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{6 i 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)}{\sqrt{a} f}+\frac{3 i c^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{2 i c (c-i c \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}","\frac{6 i 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)}{\sqrt{a} f}+\frac{3 i c^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{a f}+\frac{2 i c (c-i c \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}",1,"((6*I)*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*I)*c^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(a*f) + ((2*I)*c*(c - I*c*Tan[e + f*x])^(3/2))/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",6,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1011,1,155,0,0.1697911,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{2 i 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^{3/2} f}-\frac{2 i c^2 \sqrt{c-i c \tan (e+f x)}}{a f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i c (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}","-\frac{2 i 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^{3/2} f}-\frac{2 i c^2 \sqrt{c-i c \tan (e+f x)}}{a f \sqrt{a+i a \tan (e+f x)}}+\frac{2 i c (c-i c \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}",1,"((-2*I)*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) - ((2*I)*c^2*Sqrt[c - I*c*Tan[e + f*x]])/(a*f*Sqrt[a + I*a*Tan[e + f*x]]) + (((2*I)/3)*c*(c - I*c*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(3/2))","A",6,5,35,0.1429,1,"{3523, 47, 63, 217, 203}"
1012,1,43,0,0.1097892,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{i (c-i c \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}","\frac{i (c-i c \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"((I/5)*(c - I*c*Tan[e + f*x])^(5/2))/(f*(a + I*a*Tan[e + f*x])^(5/2))","A",2,2,35,0.05714,1,"{3523, 37}"
1013,1,90,0,0.1259009,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{7/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(7/2),x]","\frac{i (c-i c \tan (e+f x))^{5/2}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{7 f (a+i a \tan (e+f x))^{7/2}}","\frac{i (c-i c \tan (e+f x))^{5/2}}{35 a f (a+i a \tan (e+f x))^{5/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{7 f (a+i a \tan (e+f x))^{7/2}}",1,"((I/7)*(c - I*c*Tan[e + f*x])^(5/2))/(f*(a + I*a*Tan[e + f*x])^(7/2)) + ((I/35)*(c - I*c*Tan[e + f*x])^(5/2))/(a*f*(a + I*a*Tan[e + f*x])^(5/2))","A",3,3,35,0.08571,1,"{3523, 45, 37}"
1014,1,136,0,0.1423658,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{9/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(9/2),x]","\frac{2 i (c-i c \tan (e+f x))^{5/2}}{315 a^2 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 i (c-i c \tan (e+f x))^{5/2}}{63 a f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{9 f (a+i a \tan (e+f x))^{9/2}}","\frac{2 i (c-i c \tan (e+f x))^{5/2}}{315 a^2 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 i (c-i c \tan (e+f x))^{5/2}}{63 a f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{9 f (a+i a \tan (e+f x))^{9/2}}",1,"((I/9)*(c - I*c*Tan[e + f*x])^(5/2))/(f*(a + I*a*Tan[e + f*x])^(9/2)) + (((2*I)/63)*(c - I*c*Tan[e + f*x])^(5/2))/(a*f*(a + I*a*Tan[e + f*x])^(7/2)) + (((2*I)/315)*(c - I*c*Tan[e + f*x])^(5/2))/(a^2*f*(a + I*a*Tan[e + f*x])^(5/2))","A",4,3,35,0.08571,1,"{3523, 45, 37}"
1015,1,182,0,0.1644107,"\int \frac{(c-i c \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{11/2}} \, dx","Int[(c - I*c*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(11/2),x]","\frac{2 i (c-i c \tan (e+f x))^{5/2}}{1155 a^3 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 i (c-i c \tan (e+f x))^{5/2}}{231 a^2 f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{33 a f (a+i a \tan (e+f x))^{9/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{11 f (a+i a \tan (e+f x))^{11/2}}","\frac{2 i (c-i c \tan (e+f x))^{5/2}}{1155 a^3 f (a+i a \tan (e+f x))^{5/2}}+\frac{2 i (c-i c \tan (e+f x))^{5/2}}{231 a^2 f (a+i a \tan (e+f x))^{7/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{33 a f (a+i a \tan (e+f x))^{9/2}}+\frac{i (c-i c \tan (e+f x))^{5/2}}{11 f (a+i a \tan (e+f x))^{11/2}}",1,"((I/11)*(c - I*c*Tan[e + f*x])^(5/2))/(f*(a + I*a*Tan[e + f*x])^(11/2)) + ((I/33)*(c - I*c*Tan[e + f*x])^(5/2))/(a*f*(a + I*a*Tan[e + f*x])^(9/2)) + (((2*I)/231)*(c - I*c*Tan[e + f*x])^(5/2))/(a^2*f*(a + I*a*Tan[e + f*x])^(7/2)) + (((2*I)/1155)*(c - I*c*Tan[e + f*x])^(5/2))/(a^3*f*(a + I*a*Tan[e + f*x])^(5/2))","A",5,3,35,0.08571,1,"{3523, 45, 37}"
1016,1,204,0,0.1814729,"\int \frac{(a+i a \tan (e+f x))^{7/2}}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{15 i a^{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)}{\sqrt{c} f}-\frac{15 i a^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{5 i a^2 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{15 i a^{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)}{\sqrt{c} f}-\frac{15 i a^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{5 i a^2 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c f}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{f \sqrt{c-i c \tan (e+f x)}}",1,"((15*I)*a^(7/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((2*I)*a*(a + I*a*Tan[e + f*x])^(5/2))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - (((15*I)/2)*a^3*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c*f) - (((5*I)/2)*a^2*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(c*f)","A",7,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1017,1,153,0,0.1592527,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{6 i a^{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)}{\sqrt{c} f}-\frac{3 i a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{2 i a (a+i a \tan (e+f x))^{3/2}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{6 i a^{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)}{\sqrt{c} f}-\frac{3 i a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c f}-\frac{2 i a (a+i a \tan (e+f x))^{3/2}}{f \sqrt{c-i c \tan (e+f x)}}",1,"((6*I)*a^(5/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((2*I)*a*(a + I*a*Tan[e + f*x])^(3/2))/(f*Sqrt[c - I*c*Tan[e + f*x]]) - ((3*I)*a^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c*f)","A",6,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1018,1,106,0,0.1418215,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{2 i a^{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)}{\sqrt{c} f}-\frac{2 i a \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}","\frac{2 i a^{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)}{\sqrt{c} f}-\frac{2 i a \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}",1,"((2*I)*a^(3/2)*ArcTan[(Sqrt[c]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c - I*c*Tan[e + f*x]])])/(Sqrt[c]*f) - ((2*I)*a*Sqrt[a + I*a*Tan[e + f*x]])/(f*Sqrt[c - I*c*Tan[e + f*x]])","A",5,5,35,0.1429,1,"{3523, 47, 63, 217, 203}"
1019,1,41,0,0.0942072,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{i \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}","-\frac{i \sqrt{a+i a \tan (e+f x)}}{f \sqrt{c-i c \tan (e+f x)}}",1,"((-I)*Sqrt[a + I*a*Tan[e + f*x]])/(f*Sqrt[c - I*c*Tan[e + f*x]])","A",2,2,35,0.05714,1,"{3523, 37}"
1020,1,44,0,0.0998342,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{\tan (e+f x)}{f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}","\frac{\tan (e+f x)}{f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}",1,"Tan[e + f*x]/(f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",2,2,35,0.05714,1,"{3523, 39}"
1021,1,94,0,0.1208599,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{2 \tan (e+f x)}{3 a f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{3 f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}","\frac{2 \tan (e+f x)}{3 a f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{3 f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}",1,"(I/3)/(f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (2*Tan[e + f*x])/(3*a*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",3,3,35,0.08571,1,"{3523, 45, 39}"
1022,1,140,0,0.1392437,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{2 \tan (e+f x)}{5 a^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{5 a f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{5 f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}","\frac{2 \tan (e+f x)}{5 a^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{5 a f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{5 f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}",1,"(I/5)/(f*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (I/5)/(a*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (2*Tan[e + f*x])/(5*a^2*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",4,3,35,0.08571,1,"{3523, 45, 39}"
1023,1,186,0,0.1630035,"\int \frac{1}{(a+i a \tan (e+f x))^{7/2} \sqrt{c-i c \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(7/2)*Sqrt[c - I*c*Tan[e + f*x]]),x]","\frac{8 \tan (e+f x)}{35 a^3 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{4 i}{35 a^2 f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{4 i}{35 a f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} \sqrt{c-i c \tan (e+f x)}}","\frac{8 \tan (e+f x)}{35 a^3 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{4 i}{35 a^2 f (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}+\frac{4 i}{35 a f (a+i a \tan (e+f x))^{5/2} \sqrt{c-i c \tan (e+f x)}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} \sqrt{c-i c \tan (e+f x)}}",1,"(I/7)/(f*(a + I*a*Tan[e + f*x])^(7/2)*Sqrt[c - I*c*Tan[e + f*x]]) + ((4*I)/35)/(a*f*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c - I*c*Tan[e + f*x]]) + ((4*I)/35)/(a^2*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]]) + (8*Tan[e + f*x])/(35*a^3*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",5,3,35,0.08571,1,"{3523, 45, 39}"
1024,1,255,0,0.2145653,"\int \frac{(a+i a \tan (e+f x))^{9/2}}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(9/2)/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{35 i a^{9/2} \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)}{c^{3/2} f}+\frac{35 i a^4 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^2 f}+\frac{35 i a^3 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c^2 f}+\frac{14 i a^2 (a+i a \tan (e+f x))^{5/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{7/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{35 i a^{9/2} \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)}{c^{3/2} f}+\frac{35 i a^4 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^2 f}+\frac{35 i a^3 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{6 c^2 f}+\frac{14 i a^2 (a+i a \tan (e+f x))^{5/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{7/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-35*I)*a^(9/2)*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) - (((2*I)/3)*a*(a + I*a*Tan[e + f*x])^(7/2))/(f*(c - I*c*Tan[e + f*x])^(3/2)) + (((14*I)/3)*a^2*(a + I*a*Tan[e + f*x])^(5/2))/(c*f*Sqrt[c - I*c*Tan[e + f*x]]) + (((35*I)/2)*a^4*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f) + (((35*I)/6)*a^3*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f)","A",8,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1025,1,204,0,0.1901544,"\int \frac{(a+i a \tan (e+f x))^{7/2}}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{10 i a^{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)}{c^{3/2} f}+\frac{5 i a^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{10 i a^2 (a+i a \tan (e+f x))^{3/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{10 i a^{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)}{c^{3/2} f}+\frac{5 i a^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^2 f}+\frac{10 i a^2 (a+i a \tan (e+f x))^{3/2}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-10*I)*a^(7/2)*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) - (((2*I)/3)*a*(a + I*a*Tan[e + f*x])^(5/2))/(f*(c - I*c*Tan[e + f*x])^(3/2)) + (((10*I)/3)*a^2*(a + I*a*Tan[e + f*x])^(3/2))/(c*f*Sqrt[c - I*c*Tan[e + f*x]]) + ((5*I)*a^3*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^2*f)","A",7,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1026,1,155,0,0.1658586,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{2 i a^{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)}{c^{3/2} f}+\frac{2 i a^2 \sqrt{a+i a \tan (e+f x)}}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{2 i a^{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)}{c^{3/2} f}+\frac{2 i a^2 \sqrt{a+i a \tan (e+f x)}}{c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i a (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-2*I)*a^(5/2)*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) - (((2*I)/3)*a*(a + I*a*Tan[e + f*x])^(3/2))/(f*(c - I*c*Tan[e + f*x])^(3/2)) + ((2*I)*a^2*Sqrt[a + I*a*Tan[e + f*x]])/(c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",6,5,35,0.1429,1,"{3523, 47, 63, 217, 203}"
1027,1,43,0,0.1083837,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{i (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{i (a+i a \tan (e+f x))^{3/2}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-I/3)*(a + I*a*Tan[e + f*x])^(3/2))/(f*(c - I*c*Tan[e + f*x])^(3/2))","A",2,2,35,0.05714,1,"{3523, 37}"
1028,1,90,0,0.1173791,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{i \sqrt{a+i a \tan (e+f x)}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{i \sqrt{a+i a \tan (e+f x)}}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{i \sqrt{a+i a \tan (e+f x)}}{3 c f \sqrt{c-i c \tan (e+f x)}}-\frac{i \sqrt{a+i a \tan (e+f x)}}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-I/3)*Sqrt[a + I*a*Tan[e + f*x]])/(f*(c - I*c*Tan[e + f*x])^(3/2)) - ((I/3)*Sqrt[a + I*a*Tan[e + f*x]])/(c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",3,3,35,0.08571,1,"{3523, 45, 37}"
1029,1,137,0,0.1372222,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2)),x]","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{3 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i c \tan (e+f x))^{3/2}}+\frac{i}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{3 a c f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i c \tan (e+f x))^{3/2}}+\frac{i}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{3/2}}",1,"I/(f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)/3)*Sqrt[a + I*a*Tan[e + f*x]])/(a*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)/3)*Sqrt[a + I*a*Tan[e + f*x]])/(a*c*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,3,35,0.08571,1,"{3523, 45, 37}"
1030,1,101,0,0.1295227,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{2 \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{\tan (e+f x)}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}","\frac{2 \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{\tan (e+f x)}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}",1,"Tan[e + f*x]/(3*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (2*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",3,3,35,0.08571,1,"{3523, 40, 39}"
1031,1,147,0,0.1478595,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{8 \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{4 \tan (e+f x)}{15 a f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}","\frac{8 \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{4 \tan (e+f x)}{15 a f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}",1,"(I/5)/(f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (4*Tan[e + f*x])/(15*a*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (8*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",4,4,35,0.1143,1,"{3523, 45, 40, 39}"
1032,1,193,0,0.1699569,"\int \frac{1}{(a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(3/2)),x]","\frac{8 \tan (e+f x)}{21 a^3 c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{4 \tan (e+f x)}{21 a^2 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{7 a f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{3/2}}","\frac{8 \tan (e+f x)}{21 a^3 c f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{4 \tan (e+f x)}{21 a^2 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{7 a f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{3/2}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{3/2}}",1,"(I/7)/(f*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (I/7)/(a*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (4*Tan[e + f*x])/(21*a^2*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (8*Tan[e + f*x])/(21*a^3*c*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",5,4,35,0.1143,1,"{3523, 45, 40, 39}"
1033,1,304,0,0.2406935,"\int \frac{(a+i a \tan (e+f x))^{11/2}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(11/2)/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{63 i a^{11/2} \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)}{c^{5/2} f}-\frac{63 i a^5 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^3 f}-\frac{21 i a^4 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c^3 f}-\frac{42 i a^3 (a+i a \tan (e+f x))^{5/2}}{5 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{6 i a^2 (a+i a \tan (e+f x))^{7/2}}{5 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{9/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{63 i a^{11/2} \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)}{c^{5/2} f}-\frac{63 i a^5 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{2 c^3 f}-\frac{21 i a^4 (a+i a \tan (e+f x))^{3/2} \sqrt{c-i c \tan (e+f x)}}{2 c^3 f}-\frac{42 i a^3 (a+i a \tan (e+f x))^{5/2}}{5 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{6 i a^2 (a+i a \tan (e+f x))^{7/2}}{5 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{9/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((63*I)*a^(11/2)*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) - (((2*I)/5)*a*(a + I*a*Tan[e + f*x])^(9/2))/(f*(c - I*c*Tan[e + f*x])^(5/2)) + (((6*I)/5)*a^2*(a + I*a*Tan[e + f*x])^(7/2))/(c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((42*I)/5)*a^3*(a + I*a*Tan[e + f*x])^(5/2))/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]]) - (((63*I)/2)*a^5*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^3*f) - (((21*I)/2)*a^4*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c - I*c*Tan[e + f*x]])/(c^3*f)","A",9,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1034,1,253,0,0.2156716,"\int \frac{(a+i a \tan (e+f x))^{9/2}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(9/2)/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{14 i a^{9/2} \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)}{c^{5/2} f}-\frac{7 i a^4 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^3 f}-\frac{14 i a^3 (a+i a \tan (e+f x))^{3/2}}{3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{14 i a^2 (a+i a \tan (e+f x))^{5/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{7/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{14 i a^{9/2} \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)}{c^{5/2} f}-\frac{7 i a^4 \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}{c^3 f}-\frac{14 i a^3 (a+i a \tan (e+f x))^{3/2}}{3 c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{14 i a^2 (a+i a \tan (e+f x))^{5/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{7/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((14*I)*a^(9/2)*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) - (((2*I)/5)*a*(a + I*a*Tan[e + f*x])^(7/2))/(f*(c - I*c*Tan[e + f*x])^(5/2)) + (((14*I)/15)*a^2*(a + I*a*Tan[e + f*x])^(5/2))/(c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((14*I)/3)*a^3*(a + I*a*Tan[e + f*x])^(3/2))/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]]) - ((7*I)*a^4*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])/(c^3*f)","A",8,6,35,0.1714,1,"{3523, 47, 50, 63, 217, 203}"
1035,1,204,0,0.1894743,"\int \frac{(a+i a \tan (e+f x))^{7/2}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(7/2)/(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{2 i a^{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)}{c^{5/2} f}-\frac{2 i a^3 \sqrt{a+i a \tan (e+f x)}}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{2 i a^2 (a+i a \tan (e+f x))^{3/2}}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","\frac{2 i a^{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)}{c^{5/2} f}-\frac{2 i a^3 \sqrt{a+i a \tan (e+f x)}}{c^2 f \sqrt{c-i c \tan (e+f x)}}+\frac{2 i a^2 (a+i a \tan (e+f x))^{3/2}}{3 c f (c-i c \tan (e+f x))^{3/2}}-\frac{2 i a (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((2*I)*a^(7/2)*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) - (((2*I)/5)*a*(a + I*a*Tan[e + f*x])^(5/2))/(f*(c - I*c*Tan[e + f*x])^(5/2)) + (((2*I)/3)*a^2*(a + I*a*Tan[e + f*x])^(3/2))/(c*f*(c - I*c*Tan[e + f*x])^(3/2)) - ((2*I)*a^3*Sqrt[a + I*a*Tan[e + f*x]])/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",7,5,35,0.1429,1,"{3523, 47, 63, 217, 203}"
1036,1,43,0,0.1080644,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{i (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{i (a+i a \tan (e+f x))^{5/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((-I/5)*(a + I*a*Tan[e + f*x])^(5/2))/(f*(c - I*c*Tan[e + f*x])^(5/2))","A",2,2,35,0.05714,1,"{3523, 37}"
1037,1,90,0,0.1275522,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{i (a+i a \tan (e+f x))^{3/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{i (a+i a \tan (e+f x))^{3/2}}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{i (a+i a \tan (e+f x))^{3/2}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{i (a+i a \tan (e+f x))^{3/2}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((-I/5)*(a + I*a*Tan[e + f*x])^(3/2))/(f*(c - I*c*Tan[e + f*x])^(5/2)) - ((I/15)*(a + I*a*Tan[e + f*x])^(3/2))/(c*f*(c - I*c*Tan[e + f*x])^(3/2))","A",3,3,35,0.08571,1,"{3523, 45, 37}"
1038,1,136,0,0.133025,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{15 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{i \sqrt{a+i a \tan (e+f x)}}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{15 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{15 c f (c-i c \tan (e+f x))^{3/2}}-\frac{i \sqrt{a+i a \tan (e+f x)}}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((-I/5)*Sqrt[a + I*a*Tan[e + f*x]])/(f*(c - I*c*Tan[e + f*x])^(5/2)) - (((2*I)/15)*Sqrt[a + I*a*Tan[e + f*x]])/(c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)/15)*Sqrt[a + I*a*Tan[e + f*x]])/(c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",4,3,35,0.08571,1,"{3523, 45, 37}"
1039,1,186,0,0.1611747,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{5 a c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{5 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{3 i \sqrt{a+i a \tan (e+f x)}}{5 a f (c-i c \tan (e+f x))^{5/2}}+\frac{i}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}","-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{5 a c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{2 i \sqrt{a+i a \tan (e+f x)}}{5 a c f (c-i c \tan (e+f x))^{3/2}}-\frac{3 i \sqrt{a+i a \tan (e+f x)}}{5 a f (c-i c \tan (e+f x))^{5/2}}+\frac{i}{f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}",1,"I/(f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)) - (((3*I)/5)*Sqrt[a + I*a*Tan[e + f*x]])/(a*f*(c - I*c*Tan[e + f*x])^(5/2)) - (((2*I)/5)*Sqrt[a + I*a*Tan[e + f*x]])/(a*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((2*I)/5)*Sqrt[a + I*a*Tan[e + f*x]])/(a*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",5,3,35,0.08571,1,"{3523, 45, 37}"
1040,1,234,0,0.1909288,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2)),x]","-\frac{8 i \sqrt{a+i a \tan (e+f x)}}{15 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{8 i \sqrt{a+i a \tan (e+f x)}}{15 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 i \sqrt{a+i a \tan (e+f x)}}{5 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{4 i}{3 a f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}+\frac{i}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}","-\frac{8 i \sqrt{a+i a \tan (e+f x)}}{15 a^2 c^2 f \sqrt{c-i c \tan (e+f x)}}-\frac{8 i \sqrt{a+i a \tan (e+f x)}}{15 a^2 c f (c-i c \tan (e+f x))^{3/2}}-\frac{4 i \sqrt{a+i a \tan (e+f x)}}{5 a^2 f (c-i c \tan (e+f x))^{5/2}}+\frac{4 i}{3 a f \sqrt{a+i a \tan (e+f x)} (c-i c \tan (e+f x))^{5/2}}+\frac{i}{3 f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{5/2}}",1,"(I/3)/(f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(5/2)) + ((4*I)/3)/(a*f*Sqrt[a + I*a*Tan[e + f*x]]*(c - I*c*Tan[e + f*x])^(5/2)) - (((4*I)/5)*Sqrt[a + I*a*Tan[e + f*x]])/(a^2*f*(c - I*c*Tan[e + f*x])^(5/2)) - (((8*I)/15)*Sqrt[a + I*a*Tan[e + f*x]])/(a^2*c*f*(c - I*c*Tan[e + f*x])^(3/2)) - (((8*I)/15)*Sqrt[a + I*a*Tan[e + f*x]])/(a^2*c^2*f*Sqrt[c - I*c*Tan[e + f*x]])","A",6,3,35,0.08571,1,"{3523, 45, 37}"
1041,1,154,0,0.1482453,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2)),x]","\frac{8 \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{4 \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{\tan (e+f x)}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}","\frac{8 \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{4 \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{\tan (e+f x)}{5 f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}",1,"Tan[e + f*x]/(5*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2)) + (4*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*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",4,3,35,0.08571,1,"{3523, 40, 39}"
1042,1,200,0,0.1689202,"\int \frac{1}{(a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(5/2)),x]","\frac{16 \tan (e+f x)}{35 a^3 c^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{8 \tan (e+f x)}{35 a^2 c f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{6 \tan (e+f x)}{35 a f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{5/2}}","\frac{16 \tan (e+f x)}{35 a^3 c^2 f \sqrt{a+i a \tan (e+f x)} \sqrt{c-i c \tan (e+f x)}}+\frac{8 \tan (e+f x)}{35 a^2 c f (a+i a \tan (e+f x))^{3/2} (c-i c \tan (e+f x))^{3/2}}+\frac{6 \tan (e+f x)}{35 a f (a+i a \tan (e+f x))^{5/2} (c-i c \tan (e+f x))^{5/2}}+\frac{i}{7 f (a+i a \tan (e+f x))^{7/2} (c-i c \tan (e+f x))^{5/2}}",1,"(I/7)/(f*(a + I*a*Tan[e + f*x])^(7/2)*(c - I*c*Tan[e + f*x])^(5/2)) + (6*Tan[e + f*x])/(35*a*f*(a + I*a*Tan[e + f*x])^(5/2)*(c - I*c*Tan[e + f*x])^(5/2)) + (8*Tan[e + f*x])/(35*a^2*c*f*(a + I*a*Tan[e + f*x])^(3/2)*(c - I*c*Tan[e + f*x])^(3/2)) + (16*Tan[e + f*x])/(35*a^3*c^2*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c - I*c*Tan[e + f*x]])","A",5,4,35,0.1143,1,"{3523, 45, 40, 39}"
1043,1,134,0,0.1532866,"\int (a+i a \tan (e+f x))^4 (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^4*(c - I*c*Tan[e + f*x])^n,x]","\frac{6 i a^4 (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}-\frac{i a^4 (c-i c \tan (e+f x))^{n+3}}{c^3 f (n+3)}+\frac{8 i a^4 (c-i c \tan (e+f x))^n}{f n}-\frac{12 i a^4 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}","\frac{6 i a^4 (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}-\frac{i a^4 (c-i c \tan (e+f x))^{n+3}}{c^3 f (n+3)}+\frac{8 i a^4 (c-i c \tan (e+f x))^n}{f n}-\frac{12 i a^4 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}",1,"((8*I)*a^4*(c - I*c*Tan[e + f*x])^n)/(f*n) - ((12*I)*a^4*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n)) + ((6*I)*a^4*(c - I*c*Tan[e + f*x])^(2 + n))/(c^2*f*(2 + n)) - (I*a^4*(c - I*c*Tan[e + f*x])^(3 + n))/(c^3*f*(3 + n))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1044,1,99,0,0.1408801,"\int (a+i a \tan (e+f x))^3 (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c - I*c*Tan[e + f*x])^n,x]","\frac{i a^3 (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}+\frac{4 i a^3 (c-i c \tan (e+f x))^n}{f n}-\frac{4 i a^3 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}","\frac{i a^3 (c-i c \tan (e+f x))^{n+2}}{c^2 f (n+2)}+\frac{4 i a^3 (c-i c \tan (e+f x))^n}{f n}-\frac{4 i a^3 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}",1,"((4*I)*a^3*(c - I*c*Tan[e + f*x])^n)/(f*n) - ((4*I)*a^3*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n)) + (I*a^3*(c - I*c*Tan[e + f*x])^(2 + n))/(c^2*f*(2 + n))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1045,1,64,0,0.127287,"\int (a+i a \tan (e+f x))^2 (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c - I*c*Tan[e + f*x])^n,x]","\frac{2 i a^2 (c-i c \tan (e+f x))^n}{f n}-\frac{i a^2 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}","\frac{2 i a^2 (c-i c \tan (e+f x))^n}{f n}-\frac{i a^2 (c-i c \tan (e+f x))^{n+1}}{c f (n+1)}",1,"((2*I)*a^2*(c - I*c*Tan[e + f*x])^n)/(f*n) - (I*a^2*(c - I*c*Tan[e + f*x])^(1 + n))/(c*f*(1 + n))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1046,1,26,0,0.082872,"\int (a+i a \tan (e+f x)) (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])*(c - I*c*Tan[e + f*x])^n,x]","\frac{i a (c-i c \tan (e+f x))^n}{f n}","\frac{i a (c-i c \tan (e+f x))^n}{f n}",1,"(I*a*(c - I*c*Tan[e + f*x])^n)/(f*n)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
1047,1,52,0,0.1242929,"\int \frac{(c-i c \tan (e+f x))^n}{a+i a \tan (e+f x)} \, dx","Int[(c - I*c*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x]),x]","\frac{i (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)}{4 a f n}","\frac{i (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)}{4 a f n}",1,"((I/4)*Hypergeometric2F1[2, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(a*f*n)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1048,1,52,0,0.1218653,"\int \frac{(c-i c \tan (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx","Int[(c - I*c*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^2,x]","\frac{i (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)}{8 a^2 f n}","\frac{i (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)}{8 a^2 f n}",1,"((I/8)*Hypergeometric2F1[3, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(a^2*f*n)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1049,1,52,0,0.1195008,"\int \frac{(c-i c \tan (e+f x))^n}{(a+i a \tan (e+f x))^3} \, dx","Int[(c - I*c*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^3,x]","\frac{i (c-i c \tan (e+f x))^n \, _2F_1\left(4,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{16 a^3 f n}","\frac{i (c-i c \tan (e+f x))^n \, _2F_1\left(4,n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{16 a^3 f n}",1,"((I/16)*Hypergeometric2F1[4, n, 1 + n, (1 - I*Tan[e + f*x])/2]*(c - I*c*Tan[e + f*x])^n)/(a^3*f*n)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1050,1,87,0,0.0940459,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^n,x]","-\frac{i 2^{n-1} (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,1-n;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{f m}","\frac{i (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^n \, _2F_1\left(1,m+n;n+1;\frac{1}{2} (1-i \tan (e+f x))\right)}{2 f n}",1,"((-I)*2^(-1 + n)*Hypergeometric2F1[m, 1 - 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*(1 - I*Tan[e + f*x])^n)","A",3,3,31,0.09677,1,"{3523, 70, 69}"
1051,1,134,0,0.1700843,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^4 \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^4,x]","-\frac{6 i c^4 (a+i a \tan (e+f x))^{m+2}}{a^2 f (m+2)}+\frac{i c^4 (a+i a \tan (e+f x))^{m+3}}{a^3 f (m+3)}-\frac{8 i c^4 (a+i a \tan (e+f x))^m}{f m}+\frac{12 i c^4 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}","-\frac{6 i c^4 (a+i a \tan (e+f x))^{m+2}}{a^2 f (m+2)}+\frac{i c^4 (a+i a \tan (e+f x))^{m+3}}{a^3 f (m+3)}-\frac{8 i c^4 (a+i a \tan (e+f x))^m}{f m}+\frac{12 i c^4 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}",1,"((-8*I)*c^4*(a + I*a*Tan[e + f*x])^m)/(f*m) + ((12*I)*c^4*(a + I*a*Tan[e + f*x])^(1 + m))/(a*f*(1 + m)) - ((6*I)*c^4*(a + I*a*Tan[e + f*x])^(2 + m))/(a^2*f*(2 + m)) + (I*c^4*(a + I*a*Tan[e + f*x])^(3 + m))/(a^3*f*(3 + m))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1052,1,99,0,0.1457729,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^3,x]","-\frac{i c^3 (a+i a \tan (e+f x))^{m+2}}{a^2 f (m+2)}-\frac{4 i c^3 (a+i a \tan (e+f x))^m}{f m}+\frac{4 i c^3 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}","-\frac{i c^3 (a+i a \tan (e+f x))^{m+2}}{a^2 f (m+2)}-\frac{4 i c^3 (a+i a \tan (e+f x))^m}{f m}+\frac{4 i c^3 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}",1,"((-4*I)*c^3*(a + I*a*Tan[e + f*x])^m)/(f*m) + ((4*I)*c^3*(a + I*a*Tan[e + f*x])^(1 + m))/(a*f*(1 + m)) - (I*c^3*(a + I*a*Tan[e + f*x])^(2 + m))/(a^2*f*(2 + m))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1053,1,64,0,0.1312897,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^2,x]","\frac{i c^2 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}-\frac{2 i c^2 (a+i a \tan (e+f x))^m}{f m}","\frac{i c^2 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}-\frac{2 i c^2 (a+i a \tan (e+f x))^m}{f m}",1,"((-2*I)*c^2*(a + I*a*Tan[e + f*x])^m)/(f*m) + (I*c^2*(a + I*a*Tan[e + f*x])^(1 + m))/(a*f*(1 + m))","A",4,3,31,0.09677,1,"{3522, 3487, 43}"
1054,1,26,0,0.0857937,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x]),x]","-\frac{i c (a+i a \tan (e+f x))^m}{f m}","-\frac{i c (a+i a \tan (e+f x))^m}{f m}",1,"((-I)*c*(a + I*a*Tan[e + f*x])^m)/(f*m)","A",3,3,29,0.1034,1,"{3522, 3487, 32}"
1055,1,52,0,0.1278377,"\int \frac{(a+i a \tan (e+f x))^m}{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x]),x]","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(2,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{4 c f m}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(2,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{4 c f m}",1,"((-I/4)*Hypergeometric2F1[2, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(c*f*m)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1056,1,52,0,0.1272242,"\int \frac{(a+i a \tan (e+f x))^m}{(c-i c \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x])^2,x]","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(3,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{8 c^2 f m}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(3,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{8 c^2 f m}",1,"((-I/8)*Hypergeometric2F1[3, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(c^2*f*m)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1057,1,52,0,0.1208016,"\int \frac{(a+i a \tan (e+f x))^m}{(c-i c \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x])^3,x]","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(4,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{16 c^3 f m}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(4,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{16 c^3 f m}",1,"((-I/16)*Hypergeometric2F1[4, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(c^3*f*m)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1058,1,52,0,0.1216623,"\int \frac{(a+i a \tan (e+f x))^m}{(c-i c \tan (e+f x))^4} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x])^4,x]","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(5,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{32 c^4 f m}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(5,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{32 c^4 f m}",1,"((-I/32)*Hypergeometric2F1[5, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(c^4*f*m)","A",3,3,31,0.09677,1,"{3522, 3487, 68}"
1059,1,88,0,0.1129483,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(5/2),x]","\frac{i 2^m (c-i c \tan (e+f x))^{5/2} (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(\frac{5}{2},1-m;\frac{7}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f}","\frac{i (c-i c \tan (e+f x))^{5/2} (a+i a \tan (e+f x))^m \, _2F_1\left(1,m+\frac{5}{2};\frac{7}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f}",1,"((I/5)*2^m*Hypergeometric2F1[5/2, 1 - m, 7/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(5/2))/(f*(1 + I*Tan[e + f*x])^m)","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1060,1,88,0,0.110022,"\int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(3/2),x]","\frac{i 2^m (c-i c \tan (e+f x))^{3/2} (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(\frac{3}{2},1-m;\frac{5}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{3 f}","\frac{i (c-i c \tan (e+f x))^{3/2} (a+i a \tan (e+f x))^m \, _2F_1\left(1,m+\frac{3}{2};\frac{5}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{3 f}",1,"((I/3)*2^m*Hypergeometric2F1[3/2, 1 - m, 5/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(3/2))/(f*(1 + I*Tan[e + f*x])^m)","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1061,1,86,0,0.1021814,"\int (a+i a \tan (e+f x))^m \sqrt{c-i c \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^m*Sqrt[c - I*c*Tan[e + f*x]],x]","\frac{i 2^m \sqrt{c-i c \tan (e+f x)} (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(\frac{1}{2},1-m;\frac{3}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{f}","\frac{i \sqrt{c-i c \tan (e+f x)} (a+i a \tan (e+f x))^m \, _2F_1\left(1,m+\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{f}",1,"(I*2^m*Hypergeometric2F1[1/2, 1 - m, 3/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[c - I*c*Tan[e + f*x]])/(f*(1 + I*Tan[e + f*x])^m)","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1062,1,86,0,0.1082802,"\int \frac{(a+i a \tan (e+f x))^m}{\sqrt{c-i c \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/Sqrt[c - I*c*Tan[e + f*x]],x]","-\frac{i 2^m (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(-\frac{1}{2},1-m;\frac{1}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt{c-i c \tan (e+f x)}}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(1,m-\frac{1}{2};\frac{1}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{f \sqrt{c-i c \tan (e+f x)}}",1,"((-I)*2^m*Hypergeometric2F1[-1/2, 1 - m, 1/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(f*(1 + I*Tan[e + f*x])^m*Sqrt[c - I*c*Tan[e + f*x]])","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1063,1,88,0,0.112425,"\int \frac{(a+i a \tan (e+f x))^m}{(c-i c \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x])^(3/2),x]","-\frac{i 2^m (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(-\frac{3}{2},1-m;-\frac{1}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{3 f (c-i c \tan (e+f x))^{3/2}}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(1,m-\frac{3}{2};-\frac{1}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{3 f (c-i c \tan (e+f x))^{3/2}}",1,"((-I/3)*2^m*Hypergeometric2F1[-3/2, 1 - m, -1/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(f*(1 + I*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(3/2))","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1064,1,88,0,0.1143033,"\int \frac{(a+i a \tan (e+f x))^m}{(c-i c \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c - I*c*Tan[e + f*x])^(5/2),x]","-\frac{i 2^m (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m \, _2F_1\left(-\frac{5}{2},1-m;-\frac{3}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (c-i c \tan (e+f x))^{5/2}}","-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(1,m-\frac{5}{2};-\frac{3}{2};\frac{1}{2} (1-i \tan (e+f x))\right)}{5 f (c-i c \tan (e+f x))^{5/2}}",1,"((-I/5)*2^m*Hypergeometric2F1[-5/2, 1 - m, -3/2, (1 - I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(f*(1 + I*Tan[e + f*x])^m*(c - I*c*Tan[e + f*x])^(5/2))","A",3,3,33,0.09091,1,"{3523, 70, 69}"
1065,1,110,0,0.0952098,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x]),x]","-\frac{2 a^3 (c-i d) \tan (e+f x)}{f}-\frac{4 a^3 (d+i c) \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)+\frac{a (d+i c) (a+i a \tan (e+f x))^2}{2 f}+\frac{d (a+i a \tan (e+f x))^3}{3 f}","-\frac{2 a^3 (c-i d) \tan (e+f x)}{f}-\frac{4 a^3 (d+i c) \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)+\frac{a (d+i c) (a+i a \tan (e+f x))^2}{2 f}+\frac{d (a+i a \tan (e+f x))^3}{3 f}",1,"4*a^3*(c - I*d)*x - (4*a^3*(I*c + d)*Log[Cos[e + f*x]])/f - (2*a^3*(c - I*d)*Tan[e + f*x])/f + (a*(I*c + d)*(a + I*a*Tan[e + f*x])^2)/(2*f) + (d*(a + I*a*Tan[e + f*x])^3)/(3*f)","A",4,4,26,0.1538,1,"{3527, 3478, 3477, 3475}"
1066,1,80,0,0.0682502,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x]),x]","-\frac{a^2 (c-i d) \tan (e+f x)}{f}-\frac{2 a^2 (d+i c) \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)+\frac{d (a+i a \tan (e+f x))^2}{2 f}","-\frac{a^2 (c-i d) \tan (e+f x)}{f}-\frac{2 a^2 (d+i c) \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)+\frac{d (a+i a \tan (e+f x))^2}{2 f}",1,"2*a^2*(c - I*d)*x - (2*a^2*(I*c + d)*Log[Cos[e + f*x]])/f - (a^2*(c - I*d)*Tan[e + f*x])/f + (d*(a + I*a*Tan[e + f*x])^2)/(2*f)","A",3,3,26,0.1154,1,"{3527, 3477, 3475}"
1067,1,46,0,0.0296109,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x]),x]","-\frac{a (d+i c) \log (\cos (e+f x))}{f}+a x (c-i d)+\frac{i a d \tan (e+f x)}{f}","-\frac{a (d+i c) \log (\cos (e+f x))}{f}+a x (c-i d)+\frac{i a d \tan (e+f x)}{f}",1,"a*(c - I*d)*x - (a*(I*c + d)*Log[Cos[e + f*x]])/f + (I*a*d*Tan[e + f*x])/f","A",2,2,24,0.08333,1,"{3525, 3475}"
1068,1,47,0,0.042418,"\int \frac{c+d \tan (e+f x)}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])/(a + I*a*Tan[e + f*x]),x]","\frac{-d+i c}{2 f (a+i a \tan (e+f x))}+\frac{x (c-i d)}{2 a}","\frac{-d+i c}{2 f (a+i a \tan (e+f x))}+\frac{x (c-i d)}{2 a}",1,"((c - I*d)*x)/(2*a) + (I*c - d)/(2*f*(a + I*a*Tan[e + f*x]))","A",2,2,26,0.07692,1,"{3526, 8}"
1069,1,80,0,0.0625688,"\int \frac{c+d \tan (e+f x)}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^2,x]","\frac{d+i c}{4 f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{x (c-i d)}{4 a^2}+\frac{-d+i c}{4 f (a+i a \tan (e+f x))^2}","\frac{d+i c}{4 f \left(a^2+i a^2 \tan (e+f x)\right)}+\frac{x (c-i d)}{4 a^2}+\frac{-d+i c}{4 f (a+i a \tan (e+f x))^2}",1,"((c - I*d)*x)/(4*a^2) + (I*c - d)/(4*f*(a + I*a*Tan[e + f*x])^2) + (I*c + d)/(4*f*(a^2 + I*a^2*Tan[e + f*x]))","A",3,3,26,0.1154,1,"{3526, 3479, 8}"
1070,1,112,0,0.0832925,"\int \frac{c+d \tan (e+f x)}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])/(a + I*a*Tan[e + f*x])^3,x]","\frac{d+i c}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (c-i d)}{8 a^3}+\frac{-d+i c}{6 f (a+i a \tan (e+f x))^3}+\frac{d+i c}{8 a f (a+i a \tan (e+f x))^2}","\frac{d+i c}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (c-i d)}{8 a^3}+\frac{-d+i c}{6 f (a+i a \tan (e+f x))^3}+\frac{d+i c}{8 a f (a+i a \tan (e+f x))^2}",1,"((c - I*d)*x)/(8*a^3) + (I*c - d)/(6*f*(a + I*a*Tan[e + f*x])^3) + (I*c + d)/(8*a*f*(a + I*a*Tan[e + f*x])^2) + (I*c + d)/(8*f*(a^3 + I*a^3*Tan[e + f*x]))","A",4,3,26,0.1154,1,"{3526, 3479, 8}"
1071,1,153,0,0.1960238,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2,x]","-\frac{2 a^3 (c-i d)^2 \tan (e+f x)}{f}-\frac{4 i a^3 (c-i d)^2 \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)^2+\frac{2 c d (a+i a \tan (e+f x))^3}{3 f}+\frac{i a (c-i d)^2 (a+i a \tan (e+f x))^2}{2 f}-\frac{i d^2 (a+i a \tan (e+f x))^4}{4 a f}","-\frac{2 a^3 (c-i d)^2 \tan (e+f x)}{f}-\frac{4 i a^3 (c-i d)^2 \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)^2+\frac{2 c d (a+i a \tan (e+f x))^3}{3 f}+\frac{i a (c-i d)^2 (a+i a \tan (e+f x))^2}{2 f}-\frac{i d^2 (a+i a \tan (e+f x))^4}{4 a f}",1,"4*a^3*(c - I*d)^2*x - ((4*I)*a^3*(c - I*d)^2*Log[Cos[e + f*x]])/f - (2*a^3*(c - I*d)^2*Tan[e + f*x])/f + ((I/2)*a*(c - I*d)^2*(a + I*a*Tan[e + f*x])^2)/f + (2*c*d*(a + I*a*Tan[e + f*x])^3)/(3*f) - ((I/4)*d^2*(a + I*a*Tan[e + f*x])^4)/(a*f)","A",5,5,28,0.1786,1,"{3543, 3527, 3478, 3477, 3475}"
1072,1,116,0,0.1654809,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2,x]","-\frac{a^2 (c-i d)^2 \tan (e+f x)}{f}-\frac{2 i a^2 (c-i d)^2 \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)^2+\frac{c d (a+i a \tan (e+f x))^2}{f}-\frac{i d^2 (a+i a \tan (e+f x))^3}{3 a f}","-\frac{a^2 (c-i d)^2 \tan (e+f x)}{f}-\frac{2 i a^2 (c-i d)^2 \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)^2+\frac{c d (a+i a \tan (e+f x))^2}{f}-\frac{i d^2 (a+i a \tan (e+f x))^3}{3 a f}",1,"2*a^2*(c - I*d)^2*x - ((2*I)*a^2*(c - I*d)^2*Log[Cos[e + f*x]])/f - (a^2*(c - I*d)^2*Tan[e + f*x])/f + (c*d*(a + I*a*Tan[e + f*x])^2)/f - ((I/3)*d^2*(a + I*a*Tan[e + f*x])^3)/(a*f)","A",4,4,28,0.1429,1,"{3543, 3527, 3477, 3475}"
1073,1,78,0,0.0921949,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^2,x]","\frac{i a (c+d \tan (e+f x))^2}{2 f}+\frac{a d (d+i c) \tan (e+f x)}{f}-\frac{i a (c-i d)^2 \log (\cos (e+f x))}{f}+a x (c-i d)^2","\frac{i a (c+d \tan (e+f x))^2}{2 f}+\frac{a d (d+i c) \tan (e+f x)}{f}-\frac{i a (c-i d)^2 \log (\cos (e+f x))}{f}+a x (c-i d)^2",1,"a*(c - I*d)^2*x - (I*a*(c - I*d)^2*Log[Cos[e + f*x]])/f + (a*d*(I*c + d)*Tan[e + f*x])/f + ((I/2)*a*(c + d*Tan[e + f*x])^2)/f","A",3,3,26,0.1154,1,"{3528, 3525, 3475}"
1074,1,75,0,0.0825378,"\int \frac{(c+d \tan (e+f x))^2}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x]),x]","\frac{x \left(c^2-2 i c d+d^2\right)}{2 a}+\frac{i (c+i d)^2}{2 f (a+i a \tan (e+f x))}+\frac{i d^2 \log (\cos (e+f x))}{a f}","\frac{x \left(c^2-2 i c d+d^2\right)}{2 a}+\frac{i (c+i d)^2}{2 f (a+i a \tan (e+f x))}+\frac{i d^2 \log (\cos (e+f x))}{a f}",1,"((c^2 - (2*I)*c*d + d^2)*x)/(2*a) + (I*d^2*Log[Cos[e + f*x]])/(a*f) + ((I/2)*(c + I*d)^2)/(f*(a + I*a*Tan[e + f*x]))","A",3,2,28,0.07143,1,"{3540, 3475}"
1075,1,91,0,0.1465132,"\int \frac{(c+d \tan (e+f x))^2}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x])^2,x]","\frac{(c+i d) (3 d+i c)}{4 a^2 f (1+i \tan (e+f x))}+\frac{x (c-i d)^2}{4 a^2}+\frac{i (c+i d)^2}{4 f (a+i a \tan (e+f x))^2}","\frac{(c+i d) (3 d+i c)}{4 a^2 f (1+i \tan (e+f x))}+\frac{x (c-i d)^2}{4 a^2}+\frac{i (c+i d)^2}{4 f (a+i a \tan (e+f x))^2}",1,"((c - I*d)^2*x)/(4*a^2) + ((c + I*d)*(I*c + 3*d))/(4*a^2*f*(1 + I*Tan[e + f*x])) + ((I/4)*(c + I*d)^2)/(f*(a + I*a*Tan[e + f*x])^2)","A",3,3,28,0.1071,1,"{3540, 3526, 8}"
1076,1,129,0,0.1678246,"\int \frac{(c+d \tan (e+f x))^2}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + I*a*Tan[e + f*x])^3,x]","\frac{i (c-i d)^2}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (c-i d)^2}{8 a^3}+\frac{(c+i d) (3 d+i c)}{8 a f (a+i a \tan (e+f x))^2}+\frac{i (c+i d)^2}{6 f (a+i a \tan (e+f x))^3}","\frac{i (c-i d)^2}{8 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x (c-i d)^2}{8 a^3}+\frac{(c+i d) (3 d+i c)}{8 a f (a+i a \tan (e+f x))^2}+\frac{i (c+i d)^2}{6 f (a+i a \tan (e+f x))^3}",1,"((c - I*d)^2*x)/(8*a^3) + ((I/6)*(c + I*d)^2)/(f*(a + I*a*Tan[e + f*x])^3) + ((c + I*d)*(I*c + 3*d))/(8*a*f*(a + I*a*Tan[e + f*x])^2) + ((I/8)*(c - I*d)^2)/(f*(a^3 + I*a^3*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3540, 3526, 3479, 8}"
1077,1,190,0,0.3366719,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^3,x]","\frac{a^3 (-11 d+i c) (c+d \tan (e+f x))^4}{20 d^2 f}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^4}{5 d f}+\frac{4 i a^3 (c+d \tan (e+f x))^3}{3 f}+\frac{2 a^3 (d+i c) (c+d \tan (e+f x))^2}{f}+\frac{4 i a^3 d (c-i d)^2 \tan (e+f x)}{f}+\frac{4 a^3 (d+i c)^3 \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)^3","\frac{a^3 (-11 d+i c) (c+d \tan (e+f x))^4}{20 d^2 f}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^4}{5 d f}+\frac{4 i a^3 (c+d \tan (e+f x))^3}{3 f}+\frac{2 a^3 (d+i c) (c+d \tan (e+f x))^2}{f}+\frac{4 i a^3 d (c-i d)^2 \tan (e+f x)}{f}+\frac{4 a^3 (d+i c)^3 \log (\cos (e+f x))}{f}+4 a^3 x (c-i d)^3",1,"4*a^3*(c - I*d)^3*x + (4*a^3*(I*c + d)^3*Log[Cos[e + f*x]])/f + ((4*I)*a^3*(c - I*d)^2*d*Tan[e + f*x])/f + (2*a^3*(I*c + d)*(c + d*Tan[e + f*x])^2)/f + (((4*I)/3)*a^3*(c + d*Tan[e + f*x])^3)/f + (a^3*(I*c - 11*d)*(c + d*Tan[e + f*x])^4)/(20*d^2*f) - ((a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^4)/(5*d*f)","A",6,5,28,0.1786,1,"{3556, 3592, 3528, 3525, 3475}"
1078,1,141,0,0.199663,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3,x]","-\frac{a^2 (c+d \tan (e+f x))^4}{4 d f}+\frac{2 i a^2 (c+d \tan (e+f x))^3}{3 f}+\frac{a^2 (d+i c) (c+d \tan (e+f x))^2}{f}+\frac{2 i a^2 d (c-i d)^2 \tan (e+f x)}{f}+\frac{2 a^2 (d+i c)^3 \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)^3","-\frac{a^2 (c+d \tan (e+f x))^4}{4 d f}+\frac{2 i a^2 (c+d \tan (e+f x))^3}{3 f}+\frac{a^2 (d+i c) (c+d \tan (e+f x))^2}{f}+\frac{2 i a^2 d (c-i d)^2 \tan (e+f x)}{f}+\frac{2 a^2 (d+i c)^3 \log (\cos (e+f x))}{f}+2 a^2 x (c-i d)^3",1,"2*a^2*(c - I*d)^3*x + (2*a^2*(I*c + d)^3*Log[Cos[e + f*x]])/f + ((2*I)*a^2*(c - I*d)^2*d*Tan[e + f*x])/f + (a^2*(I*c + d)*(c + d*Tan[e + f*x])^2)/f + (((2*I)/3)*a^2*(c + d*Tan[e + f*x])^3)/f - (a^2*(c + d*Tan[e + f*x])^4)/(4*d*f)","A",5,4,28,0.1429,1,"{3543, 3528, 3525, 3475}"
1079,1,107,0,0.1309398,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^3,x]","\frac{i a d (c-i d)^2 \tan (e+f x)}{f}+\frac{i a (c+d \tan (e+f x))^3}{3 f}+\frac{a (d+i c) (c+d \tan (e+f x))^2}{2 f}+\frac{a (d+i c)^3 \log (\cos (e+f x))}{f}+a x (c-i d)^3","\frac{i a d (c-i d)^2 \tan (e+f x)}{f}+\frac{i a (c+d \tan (e+f x))^3}{3 f}+\frac{a (d+i c) (c+d \tan (e+f x))^2}{2 f}+\frac{a (d+i c)^3 \log (\cos (e+f x))}{f}+a x (c-i d)^3",1,"a*(c - I*d)^3*x + (a*(I*c + d)^3*Log[Cos[e + f*x]])/f + (I*a*(c - I*d)^2*d*Tan[e + f*x])/f + (a*(I*c + d)*(c + d*Tan[e + f*x])^2)/(2*f) + ((I/3)*a*(c + d*Tan[e + f*x])^3)/f","A",4,3,26,0.1154,1,"{3528, 3525, 3475}"
1080,1,129,0,0.1557027,"\int \frac{(c+d \tan (e+f x))^3}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x]),x]","\frac{x \left(-3 i c^2 d+c^3+3 c d^2+3 i d^3\right)}{2 a}-\frac{d^2 (c+3 i d) \tan (e+f x)}{2 a f}+\frac{d^2 (-d+3 i c) \log (\cos (e+f x))}{a f}+\frac{(-d+i c) (c+d \tan (e+f x))^2}{2 f (a+i a \tan (e+f x))}","\frac{x \left(-3 i c^2 d+c^3+3 c d^2+3 i d^3\right)}{2 a}-\frac{d^2 (c+3 i d) \tan (e+f x)}{2 a f}+\frac{d^2 (-d+3 i c) \log (\cos (e+f x))}{a f}+\frac{(-d+i c) (c+d \tan (e+f x))^2}{2 f (a+i a \tan (e+f x))}",1,"((c^3 - (3*I)*c^2*d + 3*c*d^2 + (3*I)*d^3)*x)/(2*a) + (((3*I)*c - d)*d^2*Log[Cos[e + f*x]])/(a*f) - ((c + (3*I)*d)*d^2*Tan[e + f*x])/(2*a*f) + ((I*c - d)*(c + d*Tan[e + f*x])^2)/(2*f*(a + I*a*Tan[e + f*x]))","A",3,3,28,0.1071,1,"{3550, 3525, 3475}"
1081,1,136,0,0.3026015,"\int \frac{(c+d \tan (e+f x))^3}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^2,x]","\frac{x \left(-3 i c^2 d+c^3-3 c d^2-3 i d^3\right)}{4 a^2}+\frac{(c+i d)^2 (3 d+i c)}{4 a^2 f (1+i \tan (e+f x))}+\frac{d^3 \log (\cos (e+f x))}{a^2 f}+\frac{(-d+i c) (c+d \tan (e+f x))^2}{4 f (a+i a \tan (e+f x))^2}","\frac{x \left(-3 i c^2 d+c^3-3 c d^2-3 i d^3\right)}{4 a^2}+\frac{(c+i d)^2 (3 d+i c)}{4 a^2 f (1+i \tan (e+f x))}+\frac{d^3 \log (\cos (e+f x))}{a^2 f}+\frac{(-d+i c) (c+d \tan (e+f x))^2}{4 f (a+i a \tan (e+f x))^2}",1,"((c^3 - (3*I)*c^2*d - 3*c*d^2 - (3*I)*d^3)*x)/(4*a^2) + (d^3*Log[Cos[e + f*x]])/(a^2*f) + ((c + I*d)^2*(I*c + 3*d))/(4*a^2*f*(1 + I*Tan[e + f*x])) + ((I*c - d)*(c + d*Tan[e + f*x])^2)/(4*f*(a + I*a*Tan[e + f*x])^2)","A",5,5,28,0.1786,1,"{3558, 3589, 3475, 3526, 8}"
1082,1,140,0,0.2191591,"\int \frac{(c+d \tan (e+f x))^3}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + I*a*Tan[e + f*x])^3,x]","\frac{(c+i d) (c-3 i d) (d+i c)}{8 a^3 f (1+i \tan (e+f x))}+\frac{x (c-i d)^3}{8 a^3}+\frac{i (c+d \tan (e+f x))^3}{6 f (a+i a \tan (e+f x))^3}+\frac{(c+i d)^2 (d+i c)}{8 a f (a+i a \tan (e+f x))^2}","\frac{(c+i d) (c-3 i d) (d+i c)}{8 a^3 f (1+i \tan (e+f x))}+\frac{x (c-i d)^3}{8 a^3}+\frac{i (c+d \tan (e+f x))^3}{6 f (a+i a \tan (e+f x))^3}+\frac{(c+i d)^2 (d+i c)}{8 a f (a+i a \tan (e+f x))^2}",1,"((c - I*d)^3*x)/(8*a^3) + ((c + I*d)*(c - (3*I)*d)*(I*c + d))/(8*a^3*f*(1 + I*Tan[e + f*x])) + ((c + I*d)^2*(I*c + d))/(8*a*f*(a + I*a*Tan[e + f*x])^2) + ((I/6)*(c + d*Tan[e + f*x])^3)/(f*(a + I*a*Tan[e + f*x])^3)","A",4,4,28,0.1429,1,"{3546, 3540, 3526, 8}"
1083,1,115,0,0.3601458,"\int \frac{(a+i a \tan (e+f x))^3}{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c + d*Tan[e + f*x]),x]","-\frac{a^3 (-3 d+i c) \log (\cos (e+f x))}{d^2 f}-\frac{a^3 (c+i d)^2 \log (c \cos (e+f x)+d \sin (e+f x))}{d^2 f (d+i c)}+\frac{4 a^3 x}{c-i d}-\frac{a^3+i a^3 \tan (e+f x)}{d f}","-\frac{a^3 (-3 d+i c) \log (\cos (e+f x))}{d^2 f}-\frac{a^3 (c+i d)^2 \log (c \cos (e+f x)+d \sin (e+f x))}{d^2 f (d+i c)}+\frac{4 a^3 x}{c-i d}-\frac{a^3+i a^3 \tan (e+f x)}{d f}",1,"(4*a^3*x)/(c - I*d) - (a^3*(I*c - 3*d)*Log[Cos[e + f*x]])/(d^2*f) - (a^3*(c + I*d)^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(d^2*(I*c + d)*f) - (a^3 + I*a^3*Tan[e + f*x])/(d*f)","A",5,5,28,0.1786,1,"{3556, 3589, 3475, 3531, 3530}"
1084,1,106,0,0.1234869,"\int \frac{(a+i a \tan (e+f x))^2}{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c + d*Tan[e + f*x]),x]","-\frac{a^2 c x (c+i d)}{d^2 (c-i d)}+\frac{a^2 x (c+2 i d)}{d^2}-\frac{a^2 (-d+i c) \log (c \cos (e+f x)+d \sin (e+f x))}{d f (d+i c)}+\frac{a^2 \log (\cos (e+f x))}{d f}","-\frac{a^2 c x (c+i d)}{d^2 (c-i d)}+\frac{a^2 x (c+2 i d)}{d^2}-\frac{a^2 (-d+i c) \log (c \cos (e+f x)+d \sin (e+f x))}{d f (d+i c)}+\frac{a^2 \log (\cos (e+f x))}{d f}",1,"-((a^2*c*(c + I*d)*x)/((c - I*d)*d^2)) + (a^2*(c + (2*I)*d)*x)/d^2 + (a^2*Log[Cos[e + f*x]])/(d*f) - (a^2*(I*c - d)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(d*(I*c + d)*f)","A",4,4,28,0.1429,1,"{3541, 3475, 3484, 3530}"
1085,1,45,0,0.0716694,"\int \frac{a+i a \tan (e+f x)}{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])/(c + d*Tan[e + f*x]),x]","\frac{a \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)}+\frac{a x}{c-i d}","\frac{a \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)}+\frac{a x}{c-i d}",1,"(a*x)/(c - I*d) + (a*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((I*c + d)*f)","A",2,2,26,0.07692,1,"{3531, 3530}"
1086,1,128,0,0.1445014,"\int \frac{1}{(a+i a \tan (e+f x)) (c+d \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])),x]","-\frac{d^2 \log (c \cos (e+f x)+d \sin (e+f x))}{a f (-d+i c) \left(c^2+d^2\right)}-\frac{c d x}{a (-d+i c) \left(c^2+d^2\right)}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x))}+\frac{x}{2 a (c+i d)}","-\frac{d^2 \log (c \cos (e+f x)+d \sin (e+f x))}{a f (-d+i c) \left(c^2+d^2\right)}-\frac{c d x}{a (-d+i c) \left(c^2+d^2\right)}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x))}+\frac{x}{2 a (c+i d)}",1,"x/(2*a*(c + I*d)) - (c*d*x)/(a*(I*c - d)*(c^2 + d^2)) - (d^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a*(I*c - d)*(c^2 + d^2)*f) - 1/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x]))","A",5,5,28,0.1786,1,"{3551, 3479, 8, 3484, 3530}"
1087,1,174,0,0.4112057,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c+d \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])),x]","\frac{x \left(3 i c^2 d+c^3-3 c d^2+3 i d^3\right)}{4 a^2 (c-i d) (c+i d)^3}-\frac{d^3 \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (c-i d) (c+i d)^3}+\frac{-3 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2}","\frac{x \left(3 i c^2 d+c^3-3 c d^2+3 i d^3\right)}{4 a^2 (c-i d) (c+i d)^3}-\frac{d^3 \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (c-i d) (c+i d)^3}+\frac{-3 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2}",1,"((c^3 + (3*I)*c^2*d - 3*c*d^2 + (3*I)*d^3)*x)/(4*a^2*(c - I*d)*(c + I*d)^3) - (d^3*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^2*(c - I*d)*(c + I*d)^3*f) + (I*c - 3*d)/(4*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])) - 1/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2)","A",4,4,28,0.1429,1,"{3559, 3596, 3531, 3530}"
1088,1,234,0,0.672629,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])),x]","\frac{c^2+4 i c d-7 d^2}{8 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x \left(-6 c^2 d^2+4 i c^3 d+c^4-4 i c d^3-7 d^4\right)}{8 a^3 (c-i d) (c+i d)^4}+\frac{d^4 \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (c+i d)^4 (d+i c)}+\frac{-3 d+i c}{8 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3}","\frac{c^2+4 i c d-7 d^2}{8 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{x \left(-6 c^2 d^2+4 i c^3 d+c^4-4 i c d^3-7 d^4\right)}{8 a^3 (c-i d) (c+i d)^4}+\frac{d^4 \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (c+i d)^4 (d+i c)}+\frac{-3 d+i c}{8 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3}",1,"((c^4 + (4*I)*c^3*d - 6*c^2*d^2 - (4*I)*c*d^3 - 7*d^4)*x)/(8*a^3*(c - I*d)*(c + I*d)^4) + (d^4*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^3*(c + I*d)^4*(I*c + d)*f) - 1/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3) + (I*c - 3*d)/(8*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2) + (c^2 + (4*I)*c*d - 7*d^2)/(8*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x]))","A",5,4,28,0.1429,1,"{3559, 3596, 3531, 3530}"
1089,1,142,0,0.3690059,"\int \frac{(a+i a \tan (e+f x))^3}{(c+d \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^2,x]","-\frac{a^3 (-d+i c) (c-3 i d) \log (c \cos (e+f x)+d \sin (e+f x))}{d^2 f (c-i d)^2}+\frac{(c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{d f (c-i d) (c+d \tan (e+f x))}+\frac{4 a^3 x}{(c-i d)^2}+\frac{i a^3 \log (\cos (e+f x))}{d^2 f}","-\frac{a^3 (-d+i c) (c-3 i d) \log (c \cos (e+f x)+d \sin (e+f x))}{d^2 f (c-i d)^2}+\frac{(c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{d f (c-i d) (c+d \tan (e+f x))}+\frac{4 a^3 x}{(c-i d)^2}+\frac{i a^3 \log (\cos (e+f x))}{d^2 f}",1,"(4*a^3*x)/(c - I*d)^2 + (I*a^3*Log[Cos[e + f*x]])/(d^2*f) - (a^3*(I*c - d)*(c - (3*I)*d)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c - I*d)^2*d^2*f) + ((c + I*d)*(a^3 + I*a^3*Tan[e + f*x]))/((c - I*d)*d*f*(c + d*Tan[e + f*x]))","A",5,5,28,0.1786,1,"{3553, 3589, 3475, 3531, 3530}"
1090,1,93,0,0.1925236,"\int \frac{(a+i a \tan (e+f x))^2}{(c+d \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^2,x]","\frac{a^2 (-d+i c)}{d f (d+i c) (c+d \tan (e+f x))}-\frac{2 i a^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f (c-i d)^2}+\frac{2 a^2 x}{(c-i d)^2}","\frac{a^2 (-d+i c)}{d f (d+i c) (c+d \tan (e+f x))}-\frac{2 i a^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f (c-i d)^2}+\frac{2 a^2 x}{(c-i d)^2}",1,"(2*a^2*x)/(c - I*d)^2 - ((2*I)*a^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c - I*d)^2*f) + (a^2*(I*c - d))/(d*(I*c + d)*f*(c + d*Tan[e + f*x]))","A",3,3,28,0.1071,1,"{3542, 3531, 3530}"
1091,1,75,0,0.1535045,"\int \frac{a+i a \tan (e+f x)}{(c+d \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])/(c + d*Tan[e + f*x])^2,x]","-\frac{a}{f (d+i c) (c+d \tan (e+f x))}-\frac{i a \log (c \cos (e+f x)+d \sin (e+f x))}{f (c-i d)^2}+\frac{a x}{(c-i d)^2}","-\frac{a}{f (d+i c) (c+d \tan (e+f x))}-\frac{i a \log (c \cos (e+f x)+d \sin (e+f x))}{f (c-i d)^2}+\frac{a x}{(c-i d)^2}",1,"(a*x)/(c - I*d)^2 - (I*a*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c - I*d)^2*f) - a/((I*c + d)*f*(c + d*Tan[e + f*x]))","A",3,3,26,0.1154,1,"{3529, 3531, 3530}"
1092,1,202,0,0.32224,"\int \frac{1}{(a+i a \tan (e+f x)) (c+d \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^2),x]","\frac{x \left(3 i c^2 d+c^3+3 c d^2-3 i d^3\right)}{2 a (c-i d)^2 (c+i d)^3}+\frac{d^2 (3 c-i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a f (-d+i c)^3 (c-i d)^2}+\frac{d (c-3 i d)}{2 a f (c-i d) (c+i d)^2 (c+d \tan (e+f x))}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))}","\frac{x \left(3 i c^2 d+c^3+3 c d^2-3 i d^3\right)}{2 a (c-i d)^2 (c+i d)^3}+\frac{d^2 (3 c-i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a f (-d+i c)^3 (c-i d)^2}+\frac{d (c-3 i d)}{2 a f (c-i d) (c+i d)^2 (c+d \tan (e+f x))}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))}",1,"((c^3 + (3*I)*c^2*d + 3*c*d^2 - (3*I)*d^3)*x)/(2*a*(c - I*d)^2*(c + I*d)^3) + ((3*c - I*d)*d^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a*(I*c - d)^3*(c - I*d)^2*f) + ((c - (3*I)*d)*d)/(2*a*(c - I*d)*(c + I*d)^2*f*(c + d*Tan[e + f*x])) - 1/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3552, 3529, 3531, 3530}"
1093,1,271,0,0.5412692,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2),x]","\frac{d \left(c^2+4 i c d+9 d^2\right)}{4 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))}+\frac{x \left(-6 c^2 d^2+4 i c^3 d+c^4+12 i c d^3+9 d^4\right)}{4 a^2 (c-i d)^2 (c+i d)^4}-\frac{2 d^3 (2 c-i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (c-i d)^2 (c+i d)^4}+\frac{-4 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))}","\frac{d \left(c^2+4 i c d+9 d^2\right)}{4 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))}+\frac{x \left(-6 c^2 d^2+4 i c^3 d+c^4+12 i c d^3+9 d^4\right)}{4 a^2 (c-i d)^2 (c+i d)^4}-\frac{2 d^3 (2 c-i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (c-i d)^2 (c+i d)^4}+\frac{-4 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))}",1,"((c^4 + (4*I)*c^3*d - 6*c^2*d^2 + (12*I)*c*d^3 + 9*d^4)*x)/(4*a^2*(c - I*d)^2*(c + I*d)^4) - (2*(2*c - I*d)*d^3*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^2*(c - I*d)^2*(c + I*d)^4*f) + (d*(c^2 + (4*I)*c*d + 9*d^2))/(4*a^2*(c - I*d)*(c + I*d)^3*f*(c + d*Tan[e + f*x])) + (I*c - 4*d)/(4*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])*(c + d*Tan[e + f*x])) - 1/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x]))","A",5,5,28,0.1786,1,"{3559, 3596, 3529, 3531, 3530}"
1094,1,357,0,0.9147413,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^2} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2),x]","\frac{d \left(5 i c^2 d+c^3-11 c d^2+25 i d^3\right)}{8 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))}+\frac{c^2+5 i c d-12 d^2}{8 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))}+\frac{x \left(-10 c^3 d^2-10 i c^2 d^3+5 i c^4 d+c^5-35 c d^4+25 i d^5\right)}{8 a^3 (c-i d)^2 (c+i d)^5}+\frac{d^4 (5 c-3 i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (-d+i c)^5 (c-i d)^2}+\frac{-11 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))}","\frac{d \left(5 i c^2 d+c^3-11 c d^2+25 i d^3\right)}{8 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))}+\frac{c^2+5 i c d-12 d^2}{8 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))}+\frac{x \left(-10 c^3 d^2-10 i c^2 d^3+5 i c^4 d+c^5-35 c d^4+25 i d^5\right)}{8 a^3 (c-i d)^2 (c+i d)^5}+\frac{d^4 (5 c-3 i d) \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (-d+i c)^5 (c-i d)^2}+\frac{-11 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))}",1,"((c^5 + (5*I)*c^4*d - 10*c^3*d^2 - (10*I)*c^2*d^3 - 35*c*d^4 + (25*I)*d^5)*x)/(8*a^3*(c - I*d)^2*(c + I*d)^5) + ((5*c - (3*I)*d)*d^4*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^3*(I*c - d)^5*(c - I*d)^2*f) + (d*(c^3 + (5*I)*c^2*d - 11*c*d^2 + (25*I)*d^3))/(8*a^3*(c - I*d)*(c + I*d)^4*f*(c + d*Tan[e + f*x])) - 1/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])) + ((3*I)*c - 11*d)/(24*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])) + (c^2 + (5*I)*c*d - 12*d^2)/(8*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",6,5,28,0.1786,1,"{3559, 3596, 3529, 3531, 3530}"
1095,1,134,0,0.2618812,"\int \frac{(a+i a \tan (e+f x))^3}{(c+d \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^3,x]","\frac{2 a^3 (c+i d)}{d f (c-i d)^2 (c+d \tan (e+f x))}-\frac{4 a^3 \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{4 a^3 x}{(c-i d)^3}-\frac{a (a+i a \tan (e+f x))^2}{2 f (d+i c) (c+d \tan (e+f x))^2}","\frac{2 a^3 (c+i d)}{d f (c-i d)^2 (c+d \tan (e+f x))}-\frac{4 a^3 \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{4 a^3 x}{(c-i d)^3}-\frac{a (a+i a \tan (e+f x))^2}{2 f (d+i c) (c+d \tan (e+f x))^2}",1,"(4*a^3*x)/(c - I*d)^3 - (4*a^3*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((I*c + d)^3*f) - (a*(a + I*a*Tan[e + f*x])^2)/(2*(I*c + d)*f*(c + d*Tan[e + f*x])^2) + (2*a^3*(c + I*d))/((c - I*d)^2*d*f*(c + d*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3545, 3542, 3531, 3530}"
1096,1,125,0,0.2731929,"\int \frac{(a+i a \tan (e+f x))^2}{(c+d \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^3,x]","\frac{2 i a^2}{f (c-i d)^2 (c+d \tan (e+f x))}+\frac{a^2 (-d+i c)}{2 d f (d+i c) (c+d \tan (e+f x))^2}-\frac{2 a^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{2 a^2 x}{(c-i d)^3}","\frac{2 i a^2}{f (c-i d)^2 (c+d \tan (e+f x))}+\frac{a^2 (-d+i c)}{2 d f (d+i c) (c+d \tan (e+f x))^2}-\frac{2 a^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{2 a^2 x}{(c-i d)^3}",1,"(2*a^2*x)/(c - I*d)^3 - (2*a^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((I*c + d)^3*f) + (a^2*(I*c - d))/(2*d*(I*c + d)*f*(c + d*Tan[e + f*x])^2) + ((2*I)*a^2)/((c - I*d)^2*f*(c + d*Tan[e + f*x]))","A",4,4,28,0.1429,1,"{3542, 3529, 3531, 3530}"
1097,1,104,0,0.2498515,"\int \frac{a+i a \tan (e+f x)}{(c+d \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])/(c + d*Tan[e + f*x])^3,x]","\frac{i a}{f (c-i d)^2 (c+d \tan (e+f x))}-\frac{a}{2 f (d+i c) (c+d \tan (e+f x))^2}-\frac{a \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{a x}{(c-i d)^3}","\frac{i a}{f (c-i d)^2 (c+d \tan (e+f x))}-\frac{a}{2 f (d+i c) (c+d \tan (e+f x))^2}-\frac{a \log (c \cos (e+f x)+d \sin (e+f x))}{f (d+i c)^3}+\frac{a x}{(c-i d)^3}",1,"(a*x)/(c - I*d)^3 - (a*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((I*c + d)^3*f) - a/(2*(I*c + d)*f*(c + d*Tan[e + f*x])^2) + (I*a)/((c - I*d)^2*f*(c + d*Tan[e + f*x]))","A",4,3,26,0.1154,1,"{3529, 3531, 3530}"
1098,1,273,0,0.4940644,"\int \frac{1}{(a+i a \tan (e+f x)) (c+d \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^3),x]","\frac{d \left(c^2-8 i c d-3 d^2\right)}{2 a f (c-i d)^2 (c+i d)^3 (c+d \tan (e+f x))}+\frac{2 d^2 \left(3 c^2-2 i c d-d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a f (c+i d)^4 (d+i c)^3}+\frac{x \left(6 c^2 d^2+4 i c^3 d+c^4-12 i c d^3-3 d^4\right)}{2 a (c-i d)^3 (c+i d)^4}+\frac{d (c-2 i d)}{2 a f (c-i d) (c+i d)^2 (c+d \tan (e+f x))^2}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))^2}","\frac{d \left(c^2-8 i c d-3 d^2\right)}{2 a f (c-i d)^2 (c+i d)^3 (c+d \tan (e+f x))}+\frac{2 d^2 \left(3 c^2-2 i c d-d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a f (c+i d)^4 (d+i c)^3}+\frac{x \left(6 c^2 d^2+4 i c^3 d+c^4-12 i c d^3-3 d^4\right)}{2 a (c-i d)^3 (c+i d)^4}+\frac{d (c-2 i d)}{2 a f (c-i d) (c+i d)^2 (c+d \tan (e+f x))^2}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))^2}",1,"((c^4 + (4*I)*c^3*d + 6*c^2*d^2 - (12*I)*c*d^3 - 3*d^4)*x)/(2*a*(c - I*d)^3*(c + I*d)^4) + (2*d^2*(3*c^2 - (2*I)*c*d - d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a*(c + I*d)^4*(I*c + d)^3*f) + ((c - (2*I)*d)*d)/(2*a*(c - I*d)*(c + I*d)^2*f*(c + d*Tan[e + f*x])^2) - 1/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) + (d*(c^2 - (8*I)*c*d - 3*d^2))/(2*a*(c - I*d)^2*(c + I*d)^3*f*(c + d*Tan[e + f*x]))","A",5,4,28,0.1429,1,"{3552, 3529, 3531, 3530}"
1099,1,354,0,0.7378809,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3),x]","\frac{d (c-3 i d) \left(c^2+8 i c d+5 d^2\right)}{4 a^2 f (c-i d)^2 (c+i d)^4 (c+d \tan (e+f x))}+\frac{d \left(c^2+5 i c d+8 d^2\right)}{4 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^2}-\frac{2 d^3 \left(5 c^2-5 i c d-2 d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (-d+i c)^5 (d+i c)^3}+\frac{x \left(-10 c^3 d^2+30 i c^2 d^3+5 i c^4 d+c^5+45 c d^4-15 i d^5\right)}{4 a^2 (c-i d)^3 (c+i d)^5}+\frac{-5 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2}","\frac{d (c-3 i d) \left(c^2+8 i c d+5 d^2\right)}{4 a^2 f (c-i d)^2 (c+i d)^4 (c+d \tan (e+f x))}+\frac{d \left(c^2+5 i c d+8 d^2\right)}{4 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^2}-\frac{2 d^3 \left(5 c^2-5 i c d-2 d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a^2 f (-d+i c)^5 (d+i c)^3}+\frac{x \left(-10 c^3 d^2+30 i c^2 d^3+5 i c^4 d+c^5+45 c d^4-15 i d^5\right)}{4 a^2 (c-i d)^3 (c+i d)^5}+\frac{-5 d+i c}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))^2}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2}",1,"((c^5 + (5*I)*c^4*d - 10*c^3*d^2 + (30*I)*c^2*d^3 + 45*c*d^4 - (15*I)*d^5)*x)/(4*a^2*(c - I*d)^3*(c + I*d)^5) - (2*d^3*(5*c^2 - (5*I)*c*d - 2*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^2*(I*c - d)^5*(I*c + d)^3*f) + (d*(c^2 + (5*I)*c*d + 8*d^2))/(4*a^2*(c - I*d)*(c + I*d)^3*f*(c + d*Tan[e + f*x])^2) + (I*c - 5*d)/(4*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) - 1/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2) + ((c - (3*I)*d)*d*(c^2 + (8*I)*c*d + 5*d^2))/(4*a^2*(c - I*d)^2*(c + I*d)^4*f*(c + d*Tan[e + f*x]))","A",6,5,28,0.1786,1,"{3559, 3596, 3529, 3531, 3530}"
1100,1,448,0,1.1456767,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^3} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^3),x]","\frac{d \left(-16 c^2 d^2+6 i c^3 d+c^4+94 i c d^3+55 d^4\right)}{8 a^3 f (c-i d)^2 (c+i d)^5 (c+d \tan (e+f x))}+\frac{d \left(6 i c^2 d+c^3-17 c d^2+28 i d^3\right)}{8 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^2}+\frac{3 c^2+18 i c d-55 d^2}{24 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^2}-\frac{d^4 \left(15 c^2-18 i c d-7 d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (c+i d)^6 (d+i c)^3}+\frac{x \left(-15 c^4 d^2-20 i c^3 d^3-105 c^2 d^4+6 i c^5 d+c^6+150 i c d^5+55 d^6\right)}{8 a^3 (c-i d)^3 (c+i d)^6}+\frac{-13 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^2}","\frac{d \left(-16 c^2 d^2+6 i c^3 d+c^4+94 i c d^3+55 d^4\right)}{8 a^3 f (c-i d)^2 (c+i d)^5 (c+d \tan (e+f x))}+\frac{d \left(6 i c^2 d+c^3-17 c d^2+28 i d^3\right)}{8 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^2}+\frac{3 c^2+18 i c d-55 d^2}{24 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^2}-\frac{d^4 \left(15 c^2-18 i c d-7 d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{a^3 f (c+i d)^6 (d+i c)^3}+\frac{x \left(-15 c^4 d^2-20 i c^3 d^3-105 c^2 d^4+6 i c^5 d+c^6+150 i c d^5+55 d^6\right)}{8 a^3 (c-i d)^3 (c+i d)^6}+\frac{-13 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^2}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^2}",1,"((c^6 + (6*I)*c^5*d - 15*c^4*d^2 - (20*I)*c^3*d^3 - 105*c^2*d^4 + (150*I)*c*d^5 + 55*d^6)*x)/(8*a^3*(c - I*d)^3*(c + I*d)^6) - (d^4*(15*c^2 - (18*I)*c*d - 7*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(a^3*(c + I*d)^6*(I*c + d)^3*f) + (d*(c^3 + (6*I)*c^2*d - 17*c*d^2 + (28*I)*d^3))/(8*a^3*(c - I*d)*(c + I*d)^4*f*(c + d*Tan[e + f*x])^2) - 1/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2) + ((3*I)*c - 13*d)/(24*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2) + (3*c^2 + (18*I)*c*d - 55*d^2)/(24*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) + (d*(c^4 + (6*I)*c^3*d - 16*c^2*d^2 + (94*I)*c*d^3 + 55*d^4))/(8*a^3*(c - I*d)^2*(c + I*d)^5*f*(c + d*Tan[e + f*x]))","A",7,5,28,0.1786,1,"{3559, 3596, 3529, 3531, 3530}"
1101,1,150,0,0.4231018,"\int (a+i a \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]],x]","\frac{4 a^3 (-6 d+i c) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{8 i a^3 \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{3/2}}{5 d f}-\frac{8 i a^3 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{4 a^3 (-6 d+i c) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{8 i a^3 \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{3/2}}{5 d f}-\frac{8 i a^3 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-8*I)*a^3*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((8*I)*a^3*Sqrt[c + d*Tan[e + f*x]])/f + (4*a^3*(I*c - 6*d)*(c + d*Tan[e + f*x])^(3/2))/(15*d^2*f) - (2*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2))/(5*d*f)","A",6,6,30,0.2000,1,"{3556, 3592, 3528, 3537, 63, 208}"
1102,1,100,0,0.2389065,"\int (a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 a^2 (c+d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 i a^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","-\frac{2 a^2 (c+d \tan (e+f x))^{3/2}}{3 d f}+\frac{4 i a^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-4*I)*a^2*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((4*I)*a^2*Sqrt[c + d*Tan[e + f*x]])/f - (2*a^2*(c + d*Tan[e + f*x])^(3/2))/(3*d*f)","A",5,5,30,0.1667,1,"{3543, 3528, 3537, 63, 208}"
1103,1,69,0,0.1436936,"\int (a+i a \tan (e+f x)) \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]],x]","\frac{2 i a \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 i a \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{2 i a \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 i a \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-2*I)*a*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((2*I)*a*Sqrt[c + d*Tan[e + f*x]])/f","A",4,4,28,0.1429,1,"{3528, 3537, 63, 208}"
1104,1,140,0,0.3599236,"\int \frac{\sqrt{c+d \tan (e+f x)}}{a+i a \tan (e+f x)} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x]),x]","\frac{i \sqrt{c+d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{i c \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f \sqrt{c+i d}}","\frac{i \sqrt{c+d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{i c \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f \sqrt{c+i d}}",1,"((-I/2)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*f) + ((I/2)*c*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(a*Sqrt[c + I*d]*f) + ((I/2)*Sqrt[c + d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x]))","A",8,5,30,0.1667,1,"{3549, 3539, 3537, 63, 208}"
1105,1,211,0,0.5960159,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+i a \tan (e+f x))^2} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^2,x]","-\frac{\left(2 c d-i \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{3/2}}+\frac{(-d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (c+i d) (1+i \tan (e+f x))}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{i \sqrt{c+d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}","-\frac{\left(2 c d-i \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{3/2}}+\frac{(-d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (c+i d) (1+i \tan (e+f x))}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{i \sqrt{c+d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}",1,"((-I/4)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*f) - ((2*c*d - I*(2*c^2 + d^2))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*(c + I*d)^(3/2)*f) + (((2*I)*c - d)*Sqrt[c + d*Tan[e + f*x]])/(8*a^2*(c + I*d)*f*(1 + I*Tan[e + f*x])) + ((I/4)*Sqrt[c + d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^2)","A",9,6,30,0.2000,1,"{3557, 3596, 3539, 3537, 63, 208}"
1106,1,280,0,0.9818637,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+i a \tan (e+f x))^3} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^3,x]","\frac{\left(-4 c^2 d+2 i c^3-i c d^2-2 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{5/2}}+\frac{c (-3 d+2 i c) \sqrt{c+d \tan (e+f x)}}{16 f (c+i d)^2 \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(-2 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (c+i d) (a+i a \tan (e+f x))^2}+\frac{i \sqrt{c+d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}","\frac{\left(-4 c^2 d+2 i c^3-i c d^2-2 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{5/2}}+\frac{c (-3 d+2 i c) \sqrt{c+d \tan (e+f x)}}{16 f (c+i d)^2 \left(a^3+i a^3 \tan (e+f x)\right)}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(-2 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (c+i d) (a+i a \tan (e+f x))^2}+\frac{i \sqrt{c+d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}",1,"((-I/8)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*f) + (((2*I)*c^3 - 4*c^2*d - I*c*d^2 - 2*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*(c + I*d)^(5/2)*f) + ((I/6)*Sqrt[c + d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^3) + (((3*I)*c - 2*d)*Sqrt[c + d*Tan[e + f*x]])/(24*a*(c + I*d)*f*(a + I*a*Tan[e + f*x])^2) + (c*((2*I)*c - 3*d)*Sqrt[c + d*Tan[e + f*x]])/(16*(c + I*d)^2*f*(a^3 + I*a^3*Tan[e + f*x]))","A",10,6,30,0.2000,1,"{3557, 3596, 3539, 3537, 63, 208}"
1107,1,181,0,0.5165019,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2),x]","\frac{4 a^3 (-8 d+i c) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{8 i a^3 (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{8 a^3 (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{5/2}}{7 d f}-\frac{8 i a^3 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{4 a^3 (-8 d+i c) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{8 i a^3 (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{8 a^3 (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{5/2}}{7 d f}-\frac{8 i a^3 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-8*I)*a^3*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (8*a^3*(I*c + d)*Sqrt[c + d*Tan[e + f*x]])/f + (((8*I)/3)*a^3*(c + d*Tan[e + f*x])^(3/2))/f + (4*a^3*(I*c - 8*d)*(c + d*Tan[e + f*x])^(5/2))/(35*d^2*f) - (2*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2))/(7*d*f)","A",7,6,30,0.2000,1,"{3556, 3592, 3528, 3537, 63, 208}"
1108,1,131,0,0.3209628,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 a^2 (c+d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 i a^2 (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^2 (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","-\frac{2 a^2 (c+d \tan (e+f x))^{5/2}}{5 d f}+\frac{4 i a^2 (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a^2 (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-4*I)*a^2*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (4*a^2*(I*c + d)*Sqrt[c + d*Tan[e + f*x]])/f + (((4*I)/3)*a^2*(c + d*Tan[e + f*x])^(3/2))/f - (2*a^2*(c + d*Tan[e + f*x])^(5/2))/(5*d*f)","A",6,5,30,0.1667,1,"{3543, 3528, 3537, 63, 208}"
1109,1,98,0,0.2253107,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 i a (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 a (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 i a (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{2 i a (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 a (d+i c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{2 i a (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-2*I)*a*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (2*a*(I*c + d)*Sqrt[c + d*Tan[e + f*x]])/f + (((2*I)/3)*a*(c + d*Tan[e + f*x])^(3/2))/f","A",5,4,28,0.1429,1,"{3528, 3537, 63, 208}"
1110,1,153,0,0.334361,"\int \frac{(c+d \tan (e+f x))^{3/2}}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x]),x]","\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{\sqrt{c+i d} (2 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f}","\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{2 f (a+i a \tan (e+f x))}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{\sqrt{c+i d} (2 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f}",1,"((-I/2)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*f) + (Sqrt[c + I*d]*(I*c + 2*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(2*a*f) + ((I*c - d)*Sqrt[c + d*Tan[e + f*x]])/(2*f*(a + I*a*Tan[e + f*x]))","A",8,5,30,0.1667,1,"{3550, 3539, 3537, 63, 208}"
1111,1,209,0,0.6502505,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{\left(2 c d+i \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f \sqrt{c+i d}}+\frac{(3 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}","\frac{\left(2 c d+i \left(2 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f \sqrt{c+i d}}+\frac{(3 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{4 f (a+i a \tan (e+f x))^2}",1,"((-I/4)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*f) + ((2*c*d + I*(2*c^2 + d^2))*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*Sqrt[c + I*d]*f) + (((2*I)*c + 3*d)*Sqrt[c + d*Tan[e + f*x]])/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*c - d)*Sqrt[c + d*Tan[e + f*x]])/(4*f*(a + I*a*Tan[e + f*x])^2)","A",9,6,30,0.2000,1,"{3558, 3596, 3539, 3537, 63, 208}"
1112,1,274,0,1.0578112,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^3,x]","-\frac{\left(2 c^2-i c d+2 d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f (-d+i c) \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{i c \left(2 c^2+3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{3/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(4 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (a+i a \tan (e+f x))^2}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}","-\frac{\left(2 c^2-i c d+2 d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f (-d+i c) \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{i c \left(2 c^2+3 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{3/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(4 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (a+i a \tan (e+f x))^2}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{6 f (a+i a \tan (e+f x))^3}",1,"((-I/8)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*f) + ((I/16)*c*(2*c^2 + 3*d^2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(a^3*(c + I*d)^(3/2)*f) + ((I*c - d)*Sqrt[c + d*Tan[e + f*x]])/(6*f*(a + I*a*Tan[e + f*x])^3) + (((3*I)*c + 4*d)*Sqrt[c + d*Tan[e + f*x]])/(24*a*f*(a + I*a*Tan[e + f*x])^2) - ((2*c^2 - I*c*d + 2*d^2)*Sqrt[c + d*Tan[e + f*x]])/(16*(I*c - d)*f*(a^3 + I*a^3*Tan[e + f*x]))","A",10,6,30,0.2000,1,"{3558, 3596, 3539, 3537, 63, 208}"
1113,1,216,0,0.6339283,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 a^3 (-10 d+i c) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{7/2}}{9 d f}+\frac{8 i a^3 (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{8 a^3 (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{8 i a^3 (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{8 i a^3 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{4 a^3 (-10 d+i c) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{7/2}}{9 d f}+\frac{8 i a^3 (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{8 a^3 (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{8 i a^3 (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{8 i a^3 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-8*I)*a^3*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((8*I)*a^3*(c - I*d)^2*Sqrt[c + d*Tan[e + f*x]])/f + (8*a^3*(I*c + d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (((8*I)/5)*a^3*(c + d*Tan[e + f*x])^(5/2))/f + (4*a^3*(I*c - 10*d)*(c + d*Tan[e + f*x])^(7/2))/(63*d^2*f) - (2*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^(7/2))/(9*d*f)","A",8,6,30,0.2000,1,"{3556, 3592, 3528, 3537, 63, 208}"
1114,1,166,0,0.4411336,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 a^2 (c+d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 i a^2 (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{4 a^2 (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 i a^2 (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","-\frac{2 a^2 (c+d \tan (e+f x))^{7/2}}{7 d f}+\frac{4 i a^2 (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{4 a^2 (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 i a^2 (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 i a^2 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-4*I)*a^2*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((4*I)*a^2*(c - I*d)^2*Sqrt[c + d*Tan[e + f*x]])/f + (4*a^2*(I*c + d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (((4*I)/5)*a^2*(c + d*Tan[e + f*x])^(5/2))/f - (2*a^2*(c + d*Tan[e + f*x])^(7/2))/(7*d*f)","A",7,5,30,0.1667,1,"{3543, 3528, 3537, 63, 208}"
1115,1,131,0,0.2935565,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 i a (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 i a (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 a (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{2 i a (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 i a (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 a (d+i c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{2 i a (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((-2*I)*a*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + ((2*I)*a*(c - I*d)^2*Sqrt[c + d*Tan[e + f*x]])/f + (2*a*(I*c + d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (((2*I)/5)*a*(c + d*Tan[e + f*x])^(5/2))/f","A",6,4,28,0.1429,1,"{3528, 3537, 63, 208}"
1116,1,185,0,0.4252631,"\int \frac{(c+d \tan (e+f x))^{5/2}}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x]),x]","\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{2 f (a+i a \tan (e+f x))}-\frac{d (c+5 i d) \sqrt{c+d \tan (e+f x)}}{2 a f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{(c+i d)^{3/2} (4 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f}","\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{2 f (a+i a \tan (e+f x))}-\frac{d (c+5 i d) \sqrt{c+d \tan (e+f x)}}{2 a f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f}+\frac{(c+i d)^{3/2} (4 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f}",1,"((-I/2)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*f) + ((c + I*d)^(3/2)*(I*c + 4*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(2*a*f) - ((c + (5*I)*d)*d*Sqrt[c + d*Tan[e + f*x]])/(2*a*f) + ((I*c - d)*(c + d*Tan[e + f*x])^(3/2))/(2*f*(a + I*a*Tan[e + f*x]))","A",9,6,30,0.2000,1,"{3550, 3528, 3539, 3537, 63, 208}"
1117,1,217,0,0.6377236,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^2,x]","\frac{\sqrt{c+i d} \left(2 i c^2+6 c d-7 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f}+\frac{(c+i d) (5 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{4 f (a+i a \tan (e+f x))^2}","\frac{\sqrt{c+i d} \left(2 i c^2+6 c d-7 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f}+\frac{(c+i d) (5 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (1+i \tan (e+f x))}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{4 f (a+i a \tan (e+f x))^2}",1,"((-I/4)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*f) + (Sqrt[c + I*d]*((2*I)*c^2 + 6*c*d - (7*I)*d^2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*f) + ((c + I*d)*((2*I)*c + 5*d)*Sqrt[c + d*Tan[e + f*x]])/(8*a^2*f*(1 + I*Tan[e + f*x])) + ((I*c - d)*(c + d*Tan[e + f*x])^(3/2))/(4*f*(a + I*a*Tan[e + f*x])^2)","A",9,6,30,0.2000,1,"{3558, 3595, 3539, 3537, 63, 208}"
1118,1,285,0,1.028186,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^3,x]","\frac{\left(2 i c^2+5 c d-4 i d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(4 c^2 d+2 i c^3-i c d^2+2 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f \sqrt{c+i d}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{6 f (a+i a \tan (e+f x))^3}+\frac{(c+i d) (2 d+i c) \sqrt{c+d \tan (e+f x)}}{8 a f (a+i a \tan (e+f x))^2}","\frac{\left(2 i c^2+5 c d-4 i d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(4 c^2 d+2 i c^3-i c d^2+2 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f \sqrt{c+i d}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{6 f (a+i a \tan (e+f x))^3}+\frac{(c+i d) (2 d+i c) \sqrt{c+d \tan (e+f x)}}{8 a f (a+i a \tan (e+f x))^2}",1,"((-I/8)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*f) + (((2*I)*c^3 + 4*c^2*d - I*c*d^2 + 2*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*Sqrt[c + I*d]*f) + ((c + I*d)*(I*c + 2*d)*Sqrt[c + d*Tan[e + f*x]])/(8*a*f*(a + I*a*Tan[e + f*x])^2) + (((2*I)*c^2 + 5*c*d - (4*I)*d^2)*Sqrt[c + d*Tan[e + f*x]])/(16*f*(a^3 + I*a^3*Tan[e + f*x])) + ((I*c - d)*(c + d*Tan[e + f*x])^(3/2))/(6*f*(a + I*a*Tan[e + f*x])^3)","A",10,7,30,0.2333,1,"{3558, 3595, 3596, 3539, 3537, 63, 208}"
1119,1,126,0,0.2995719,"\int \frac{(a+i a \tan (e+f x))^3}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/Sqrt[c + d*Tan[e + f*x]],x]","\frac{4 a^3 (-4 d+i c) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{c+d \tan (e+f x)}}{3 d f}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}","\frac{4 a^3 (-4 d+i c) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}-\frac{2 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{c+d \tan (e+f x)}}{3 d f}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}",1,"((-8*I)*a^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) + (4*a^3*(I*c - 4*d)*Sqrt[c + d*Tan[e + f*x]])/(3*d^2*f) - (2*(a^3 + I*a^3*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])/(3*d*f)","A",5,5,30,0.1667,1,"{3556, 3592, 3537, 63, 208}"
1120,1,74,0,0.1514479,"\int \frac{(a+i a \tan (e+f x))^2}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 a^2 \sqrt{c+d \tan (e+f x)}}{d f}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}","-\frac{2 a^2 \sqrt{c+d \tan (e+f x)}}{d f}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}",1,"((-4*I)*a^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) - (2*a^2*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",4,4,30,0.1333,1,"{3543, 3537, 63, 208}"
1121,1,46,0,0.0724957,"\int \frac{a+i a \tan (e+f x)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}","-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}",1,"((-2*I)*a*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f)","A",3,3,28,0.1071,1,"{3537, 63, 208}"
1122,1,155,0,0.3034449,"\int \frac{1}{(a+i a \tan (e+f x)) \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{\sqrt{c+d \tan (e+f x)}}{2 f (-d+i c) (a+i a \tan (e+f x))}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f \sqrt{c-i d}}+\frac{(-2 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{3/2}}","-\frac{\sqrt{c+d \tan (e+f x)}}{2 f (-d+i c) (a+i a \tan (e+f x))}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f \sqrt{c-i d}}+\frac{(-2 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{3/2}}",1,"((-I/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*Sqrt[c - I*d]*f) + ((I*c - 2*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(2*a*(c + I*d)^(3/2)*f) - Sqrt[c + d*Tan[e + f*x]]/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x]))","A",8,5,30,0.1667,1,"{3552, 3539, 3537, 63, 208}"
1123,1,221,0,0.6062993,"\int \frac{1}{(a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]]),x]","\frac{\left(2 i c^2-6 c d-7 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{5/2}}+\frac{(-5 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f \sqrt{c-i d}}-\frac{\sqrt{c+d \tan (e+f x)}}{4 f (-d+i c) (a+i a \tan (e+f x))^2}","\frac{\left(2 i c^2-6 c d-7 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{5/2}}+\frac{(-5 d+2 i c) \sqrt{c+d \tan (e+f x)}}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f \sqrt{c-i d}}-\frac{\sqrt{c+d \tan (e+f x)}}{4 f (-d+i c) (a+i a \tan (e+f x))^2}",1,"((-I/4)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*Sqrt[c - I*d]*f) + (((2*I)*c^2 - 6*c*d - (7*I)*d^2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*(c + I*d)^(5/2)*f) + (((2*I)*c - 5*d)*Sqrt[c + d*Tan[e + f*x]])/(8*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])) - Sqrt[c + d*Tan[e + f*x]]/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2)","A",9,6,30,0.2000,1,"{3559, 3596, 3539, 3537, 63, 208}"
1124,1,298,0,0.9568893,"\int \frac{1}{(a+i a \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]]),x]","\frac{\left(2 c^2+7 i c d-10 d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(-8 c^2 d+2 i c^3-13 i c d^2+12 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{7/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f \sqrt{c-i d}}+\frac{(-8 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)}}{6 f (-d+i c) (a+i a \tan (e+f x))^3}","\frac{\left(2 c^2+7 i c d-10 d^2\right) \sqrt{c+d \tan (e+f x)}}{16 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{\left(-8 c^2 d+2 i c^3-13 i c d^2+12 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{7/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f \sqrt{c-i d}}+\frac{(-8 d+3 i c) \sqrt{c+d \tan (e+f x)}}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{\sqrt{c+d \tan (e+f x)}}{6 f (-d+i c) (a+i a \tan (e+f x))^3}",1,"((-I/8)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*Sqrt[c - I*d]*f) + (((2*I)*c^3 - 8*c^2*d - (13*I)*c*d^2 + 12*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*(c + I*d)^(7/2)*f) - Sqrt[c + d*Tan[e + f*x]]/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3) + (((3*I)*c - 8*d)*Sqrt[c + d*Tan[e + f*x]])/(24*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2) + ((2*c^2 + (7*I)*c*d - 10*d^2)*Sqrt[c + d*Tan[e + f*x]])/(16*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x]))","A",10,6,30,0.2000,1,"{3559, 3596, 3539, 3537, 63, 208}"
1125,1,139,0,0.3149427,"\int \frac{(a+i a \tan (e+f x))^3}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^(3/2),x]","\frac{4 a^3 c \sqrt{c+d \tan (e+f x)}}{d^2 f (d+i c)}+\frac{2 (c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{d f (c-i d) \sqrt{c+d \tan (e+f x)}}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}","\frac{4 a^3 c \sqrt{c+d \tan (e+f x)}}{d^2 f (d+i c)}+\frac{2 (c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{d f (c-i d) \sqrt{c+d \tan (e+f x)}}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}",1,"((-8*I)*a^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) + (2*(c + I*d)*(a^3 + I*a^3*Tan[e + f*x]))/((c - I*d)*d*f*Sqrt[c + d*Tan[e + f*x]]) + (4*a^3*c*Sqrt[c + d*Tan[e + f*x]])/(d^2*(I*c + d)*f)","A",5,5,30,0.1667,1,"{3553, 3592, 3537, 63, 208}"
1126,1,92,0,0.2226347,"\int \frac{(a+i a \tan (e+f x))^2}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 a^2 (-d+i c)}{d f (d+i c) \sqrt{c+d \tan (e+f x)}}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}","\frac{2 a^2 (-d+i c)}{d f (d+i c) \sqrt{c+d \tan (e+f x)}}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}",1,"((-4*I)*a^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) + (2*a^2*(I*c - d))/(d*(I*c + d)*f*Sqrt[c + d*Tan[e + f*x]])","A",4,4,30,0.1333,1,"{3542, 3537, 63, 208}"
1127,1,76,0,0.1611948,"\int \frac{a+i a \tan (e+f x)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 a}{f (d+i c) \sqrt{c+d \tan (e+f x)}}-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}","-\frac{2 a}{f (d+i c) \sqrt{c+d \tan (e+f x)}}-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}",1,"((-2*I)*a*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) - (2*a)/((I*c + d)*f*Sqrt[c + d*Tan[e + f*x]])","A",4,4,28,0.1429,1,"{3529, 3537, 63, 208}"
1128,1,205,0,0.4684869,"\int \frac{1}{(a+i a \tan (e+f x)) (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d (c-5 i d)}{2 a f (c-i d) (c+i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f (c-i d)^{3/2}}+\frac{(-4 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{5/2}}","\frac{d (c-5 i d)}{2 a f (c-i d) (c+i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f (c-i d)^{3/2}}+\frac{(-4 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{5/2}}",1,"((-I/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*(c - I*d)^(3/2)*f) + ((I*c - 4*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(2*a*(c + I*d)^(5/2)*f) + ((c - (5*I)*d)*d)/(2*a*(c - I*d)*(c + I*d)^2*f*Sqrt[c + d*Tan[e + f*x]]) - 1/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])","A",9,6,30,0.2000,1,"{3552, 3529, 3539, 3537, 63, 208}"
1129,1,281,0,0.7638496,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d \left(2 c^2+7 i c d+25 d^2\right)}{8 a^2 f (c-i d) (c+i d)^3 \sqrt{c+d \tan (e+f x)}}+\frac{\left(2 i c^2-10 c d-23 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{7/2}}+\frac{-7 d+2 i c}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f (c-i d)^{3/2}}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}","\frac{d \left(2 c^2+7 i c d+25 d^2\right)}{8 a^2 f (c-i d) (c+i d)^3 \sqrt{c+d \tan (e+f x)}}+\frac{\left(2 i c^2-10 c d-23 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{7/2}}+\frac{-7 d+2 i c}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f (c-i d)^{3/2}}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}",1,"((-I/4)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*(c - I*d)^(3/2)*f) + (((2*I)*c^2 - 10*c*d - (23*I)*d^2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*(c + I*d)^(7/2)*f) + (d*(2*c^2 + (7*I)*c*d + 25*d^2))/(8*a^2*(c - I*d)*(c + I*d)^3*f*Sqrt[c + d*Tan[e + f*x]]) + ((2*I)*c - 7*d)/(8*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]]) - 1/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]])","A",10,7,30,0.2333,1,"{3559, 3596, 3529, 3539, 3537, 63, 208}"
1130,1,368,0,1.2008069,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d \left(9 i c^2 d+2 c^3-17 c d^2+60 i d^3\right)}{16 a^3 f (c-i d) (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{6 c^2+27 i c d-56 d^2}{48 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{c+d \tan (e+f x)}}+\frac{\left(-12 c^2 d+2 i c^3-33 i c d^2+58 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{9/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f (c-i d)^{3/2}}+\frac{-10 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)}}","\frac{d \left(9 i c^2 d+2 c^3-17 c d^2+60 i d^3\right)}{16 a^3 f (c-i d) (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{6 c^2+27 i c d-56 d^2}{48 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) \sqrt{c+d \tan (e+f x)}}+\frac{\left(-12 c^2 d+2 i c^3-33 i c d^2+58 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{9/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f (c-i d)^{3/2}}+\frac{-10 d+3 i c}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)}}",1,"((-I/8)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*(c - I*d)^(3/2)*f) + (((2*I)*c^3 - 12*c^2*d - (33*I)*c*d^2 + 58*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*(c + I*d)^(9/2)*f) + (d*(2*c^3 + (9*I)*c^2*d - 17*c*d^2 + (60*I)*d^3))/(16*a^3*(c - I*d)*(c + I*d)^4*f*Sqrt[c + d*Tan[e + f*x]]) - 1/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]]) + ((3*I)*c - 10*d)/(24*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]]) + (6*c^2 + (27*I)*c*d - 56*d^2)/(48*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])","A",11,7,30,0.2333,1,"{3559, 3596, 3529, 3539, 3537, 63, 208}"
1131,1,158,0,0.4208892,"\int \frac{(a+i a \tan (e+f x))^3}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 a^3 (-d+i c) (c-4 i d)}{3 d^2 f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 (c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{3 d f (c-i d) (c+d \tan (e+f x))^{3/2}}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}","\frac{4 a^3 (-d+i c) (c-4 i d)}{3 d^2 f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 (c+i d) \left(a^3+i a^3 \tan (e+f x)\right)}{3 d f (c-i d) (c+d \tan (e+f x))^{3/2}}-\frac{8 i a^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}",1,"((-8*I)*a^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) + (2*(c + I*d)*(a^3 + I*a^3*Tan[e + f*x]))/(3*(c - I*d)*d*f*(c + d*Tan[e + f*x])^(3/2)) + (4*a^3*(I*c - d)*(c - (4*I)*d))/(3*(c - I*d)^2*d^2*f*Sqrt[c + d*Tan[e + f*x]])","A",5,5,30,0.1667,1,"{3553, 3591, 3537, 63, 208}"
1132,1,127,0,0.3288274,"\int \frac{(a+i a \tan (e+f x))^2}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 i a^2}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 a^2 (-d+i c)}{3 d f (d+i c) (c+d \tan (e+f x))^{3/2}}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}","\frac{4 i a^2}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 a^2 (-d+i c)}{3 d f (d+i c) (c+d \tan (e+f x))^{3/2}}-\frac{4 i a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}",1,"((-4*I)*a^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) + (2*a^2*(I*c - d))/(3*d*(I*c + d)*f*(c + d*Tan[e + f*x])^(3/2)) + ((4*I)*a^2)/((c - I*d)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",5,5,30,0.1667,1,"{3542, 3529, 3537, 63, 208}"
1133,1,109,0,0.264716,"\int \frac{a+i a \tan (e+f x)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 i a}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 a}{3 f (d+i c) (c+d \tan (e+f x))^{3/2}}-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}","\frac{2 i a}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 a}{3 f (d+i c) (c+d \tan (e+f x))^{3/2}}-\frac{2 i a \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}",1,"((-2*I)*a*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) - (2*a)/(3*(I*c + d)*f*(c + d*Tan[e + f*x])^(3/2)) + ((2*I)*a)/((c - I*d)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",5,4,28,0.1429,1,"{3529, 3537, 63, 208}"
1134,1,267,0,0.6139684,"\int \frac{1}{(a+i a \tan (e+f x)) (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d (7 d+3 i c)}{6 a f (-d+i c) \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{d \left(c^2-14 i c d-5 d^2\right)}{2 a f (c-i d)^2 (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f (c-i d)^{5/2}}+\frac{(-6 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{7/2}}","\frac{d (7 d+3 i c)}{6 a f (-d+i c) \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{d \left(c^2-14 i c d-5 d^2\right)}{2 a f (c-i d)^2 (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{1}{2 f (-d+i c) (a+i a \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{2 a f (c-i d)^{5/2}}+\frac{(-6 d+i c) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{2 a f (c+i d)^{7/2}}",1,"((-I/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a*(c - I*d)^(5/2)*f) + ((I*c - 6*d)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(2*a*(c + I*d)^(7/2)*f) + (d*((3*I)*c + 7*d))/(6*a*(I*c - d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - 1/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)) + (d*(c^2 - (14*I)*c*d - 5*d^2))/(2*a*(c - I*d)^2*(c + I*d)^3*f*Sqrt[c + d*Tan[e + f*x]])","A",10,6,30,0.2000,1,"{3552, 3529, 3539, 3537, 63, 208}"
1135,1,351,0,0.9683846,"\int \frac{1}{(a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d \left(9 i c^2 d+2 c^3+88 c d^2-45 i d^3\right)}{8 a^2 f (c-i d)^2 (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(6 c^2+27 i c d+49 d^2\right)}{24 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^{3/2}}+\frac{\left(2 i c^2-14 c d-47 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{9/2}}+\frac{-9 d+2 i c}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f (c-i d)^{5/2}}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}","\frac{d \left(9 i c^2 d+2 c^3+88 c d^2-45 i d^3\right)}{8 a^2 f (c-i d)^2 (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(6 c^2+27 i c d+49 d^2\right)}{24 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^{3/2}}+\frac{\left(2 i c^2-14 c d-47 i d^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{8 a^2 f (c+i d)^{9/2}}+\frac{-9 d+2 i c}{8 a^2 f (c+i d)^2 (1+i \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{4 a^2 f (c-i d)^{5/2}}-\frac{1}{4 f (-d+i c) (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}",1,"((-I/4)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^2*(c - I*d)^(5/2)*f) + (((2*I)*c^2 - 14*c*d - (47*I)*d^2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(8*a^2*(c + I*d)^(9/2)*f) + (d*(6*c^2 + (27*I)*c*d + 49*d^2))/(24*a^2*(c - I*d)*(c + I*d)^3*f*(c + d*Tan[e + f*x])^(3/2)) + ((2*I)*c - 9*d)/(8*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)) - 1/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)) + (d*(2*c^3 + (9*I)*c^2*d + 88*c*d^2 - (45*I)*d^3))/(8*a^2*(c - I*d)^2*(c + I*d)^4*f*Sqrt[c + d*Tan[e + f*x]])","A",11,7,30,0.2333,1,"{3559, 3596, 3529, 3539, 3537, 63, 208}"
1136,1,446,0,1.4819371,"\int \frac{1}{(a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d \left(-26 c^2 d^2+11 i c^3 d+2 c^4+253 i c d^3+150 d^4\right)}{16 a^3 f (c-i d)^2 (c+i d)^5 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(33 i c^2 d+6 c^3-83 c d^2+154 i d^3\right)}{48 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^{3/2}}+\frac{2 c^2+11 i c d-30 d^2}{16 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{3/2}}+\frac{\left(-16 c^2 d+2 i c^3-61 i c d^2+152 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{11/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f (c-i d)^{5/2}}+\frac{-4 d+i c}{8 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2}}","\frac{d \left(-26 c^2 d^2+11 i c^3 d+2 c^4+253 i c d^3+150 d^4\right)}{16 a^3 f (c-i d)^2 (c+i d)^5 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(33 i c^2 d+6 c^3-83 c d^2+154 i d^3\right)}{48 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^{3/2}}+\frac{2 c^2+11 i c d-30 d^2}{16 f (-d+i c)^3 \left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{3/2}}+\frac{\left(-16 c^2 d+2 i c^3-61 i c d^2+152 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{16 a^3 f (c+i d)^{11/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{8 a^3 f (c-i d)^{5/2}}+\frac{-4 d+i c}{8 a f (c+i d)^2 (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}}-\frac{1}{6 f (-d+i c) (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2}}",1,"((-I/8)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(a^3*(c - I*d)^(5/2)*f) + (((2*I)*c^3 - 16*c^2*d - (61*I)*c*d^2 + 152*d^3)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(16*a^3*(c + I*d)^(11/2)*f) + (d*(6*c^3 + (33*I)*c^2*d - 83*c*d^2 + (154*I)*d^3))/(48*a^3*(c - I*d)*(c + I*d)^4*f*(c + d*Tan[e + f*x])^(3/2)) - 1/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2)) + (I*c - 4*d)/(8*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)) + (2*c^2 + (11*I)*c*d - 30*d^2)/(16*(I*c - d)^3*f*(a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)) + (d*(2*c^4 + (11*I)*c^3*d - 26*c^2*d^2 + (253*I)*c*d^3 + 150*d^4))/(16*a^3*(c - I*d)^2*(c + I*d)^5*f*Sqrt[c + d*Tan[e + f*x]])","A",12,7,30,0.2333,1,"{3559, 3596, 3529, 3539, 3537, 63, 208}"
1137,1,263,0,1.0044016,"\int (a+i a \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{\sqrt[4]{-1} a^{5/2} \left(c^2+10 i c d+23 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}+\frac{a^2 (c+9 i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d f}-\frac{4 i \sqrt{2} a^{5/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","-\frac{\sqrt[4]{-1} a^{5/2} \left(c^2+10 i c d+23 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}+\frac{a^2 (c+9 i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d f}-\frac{4 i \sqrt{2} a^{5/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"-((-1)^(1/4)*a^(5/2)*(c^2 + (10*I)*c*d + 23*d^2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(4*d^(3/2)*f) - ((4*I)*Sqrt[2]*a^(5/2)*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a^2*(c + (9*I)*d)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*d*f) - (a^2*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*d*f)","A",9,9,32,0.2812,1,"{3556, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1138,1,250,0,0.960962,"\int (a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{a^2 (c+d \tan (e+f x))^{3/2}}{d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) \sqrt{c+d \tan (e+f x)}}{d f \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt[4]{-1} a^{3/2} (3 d+i c) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{2 i \sqrt{2} a^{3/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","-\frac{a^2 (c+d \tan (e+f x))^{3/2}}{d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) \sqrt{c+d \tan (e+f x)}}{d f \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt[4]{-1} a^{3/2} (3 d+i c) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{2 i \sqrt{2} a^{3/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"-(((-1)^(1/4)*a^(3/2)*(I*c + 3*d)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[d]*f)) - ((2*I)*Sqrt[2]*a^(3/2)*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a^2*(c + I*d)*Sqrt[c + d*Tan[e + f*x]])/(d*f*Sqrt[a + I*a*Tan[e + f*x]]) - (a^2*(c + d*Tan[e + f*x])^(3/2))/(d*f*Sqrt[a + I*a*Tan[e + f*x]])","A",9,9,32,0.2812,1,"{3556, 3595, 3601, 3544, 208, 3599, 63, 217, 206}"
1139,1,151,0,0.4173964,"\int \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 \sqrt[4]{-1} \sqrt{a} \sqrt{d} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{i \sqrt{2} \sqrt{a} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","-\frac{2 \sqrt[4]{-1} \sqrt{a} \sqrt{d} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{f}-\frac{i \sqrt{2} \sqrt{a} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"(-2*(-1)^(1/4)*Sqrt[a]*Sqrt[d]*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/f - (I*Sqrt[2]*Sqrt[a]*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f","A",7,7,32,0.2188,1,"{3563, 3544, 208, 3599, 63, 217, 206}"
1140,1,121,0,0.2149198,"\int \frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{i \sqrt{c+d \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}","\frac{i \sqrt{c+d \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}",1,"((-I)*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*f) + (I*Sqrt[c + d*Tan[e + f*x]])/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",3,3,32,0.09375,1,"{3546, 3544, 208}"
1141,1,177,0,0.315414,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(c+d \tan (e+f x))^{3/2}}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}","-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(c+d \tan (e+f x))^{3/2}}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}",1,"((-I/2)*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*f) + ((I/2)*Sqrt[c + d*Tan[e + f*x]])/(a*f*Sqrt[a + I*a*Tan[e + f*x]]) - (c + d*Tan[e + f*x])^(3/2)/(3*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(3/2))","A",4,4,32,0.1250,1,"{3547, 3546, 3544, 208}"
1142,1,254,0,0.7898024,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + I*a*Tan[e + f*x])^(5/2),x]","-\frac{\left(20 c d-i \left(15 c^2+3 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{60 a^2 f (c+i d)^2 \sqrt{a+i a \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}+\frac{(-3 d+5 i c) \sqrt{c+d \tan (e+f x)}}{30 a f (c+i d) (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c+d \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}","-\frac{\left(20 c d-i \left(15 c^2+3 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{60 a^2 f (c+i d)^2 \sqrt{a+i a \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}+\frac{(-3 d+5 i c) \sqrt{c+d \tan (e+f x)}}{30 a f (c+i d) (a+i a \tan (e+f x))^{3/2}}+\frac{i \sqrt{c+d \tan (e+f x)}}{5 f (a+i a \tan (e+f x))^{5/2}}",1,"((-I/4)*Sqrt[c - I*d]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*f) + ((I/5)*Sqrt[c + d*Tan[e + f*x]])/(f*(a + I*a*Tan[e + f*x])^(5/2)) + (((5*I)*c - 3*d)*Sqrt[c + d*Tan[e + f*x]])/(30*a*(c + I*d)*f*(a + I*a*Tan[e + f*x])^(3/2)) - ((20*c*d - I*(15*c^2 + 3*d^2))*Sqrt[c + d*Tan[e + f*x]])/(60*a^2*(c + I*d)^2*f*Sqrt[a + I*a*Tan[e + f*x]])","A",6,5,32,0.1562,1,"{3557, 3596, 12, 3544, 208}"
1143,1,329,0,1.3590579,"\int (a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2),x]","\frac{a^2 \left(c^2+14 i c d+19 d^2\right) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 d f}-\frac{\sqrt[4]{-1} a^{5/2} (c-3 i d) \left(c^2+18 i c d+15 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{8 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 d f}+\frac{a^2 (c+13 i d) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 d f}-\frac{4 i \sqrt{2} a^{5/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","\frac{a^2 \left(c^2+14 i c d+19 d^2\right) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 d f}-\frac{\sqrt[4]{-1} a^{5/2} (c-3 i d) \left(c^2+18 i c d+15 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{8 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{3 d f}+\frac{a^2 (c+13 i d) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 d f}-\frac{4 i \sqrt{2} a^{5/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"-((-1)^(1/4)*a^(5/2)*(c - (3*I)*d)*(c^2 + (18*I)*c*d + 15*d^2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(8*d^(3/2)*f) - ((4*I)*Sqrt[2]*a^(5/2)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a^2*(c^2 + (14*I)*c*d + 19*d^2)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*d*f) + (a^2*(c + (13*I)*d)*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(12*d*f) - (a^2*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(3*d*f)","A",10,9,32,0.2812,1,"{3556, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1144,1,315,0,1.3333755,"\int (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2),x]","-\frac{\sqrt[4]{-1} a^{3/2} \left(3 i c^2+18 c d-11 i d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{d} f}-\frac{a^2 (c+d \tan (e+f x))^{5/2}}{2 d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) (c+d \tan (e+f x))^{3/2}}{2 d f \sqrt{a+i a \tan (e+f x)}}-\frac{2 i \sqrt{2} a^{3/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}+\frac{a (5 d+3 i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}","-\frac{\sqrt[4]{-1} a^{3/2} \left(3 i c^2+18 c d-11 i d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{d} f}-\frac{a^2 (c+d \tan (e+f x))^{5/2}}{2 d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) (c+d \tan (e+f x))^{3/2}}{2 d f \sqrt{a+i a \tan (e+f x)}}-\frac{2 i \sqrt{2} a^{3/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}+\frac{a (5 d+3 i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}",1,"-((-1)^(1/4)*a^(3/2)*((3*I)*c^2 + 18*c*d - (11*I)*d^2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(4*Sqrt[d]*f) - ((2*I)*Sqrt[2]*a^(3/2)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a*((3*I)*c + 5*d)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*f) + (a^2*(c + I*d)*(c + d*Tan[e + f*x])^(3/2))/(2*d*f*Sqrt[a + I*a*Tan[e + f*x]]) - (a^2*(c + d*Tan[e + f*x])^(5/2))/(2*d*f*Sqrt[a + I*a*Tan[e + f*x]])","A",10,10,32,0.3125,1,"{3556, 3595, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1145,1,196,0,0.7362661,"\int \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2),x]","\frac{d \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i \sqrt{2} \sqrt{a} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}-\frac{\sqrt[4]{-1} \sqrt{a} \sqrt{d} (3 c-i d) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{f}","\frac{d \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i \sqrt{2} \sqrt{a} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}-\frac{\sqrt[4]{-1} \sqrt{a} \sqrt{d} (3 c-i d) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"-(((-1)^(1/4)*Sqrt[a]*(3*c - I*d)*Sqrt[d]*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/f) - (I*Sqrt[2]*Sqrt[a]*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (d*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/f","A",8,8,32,0.2500,1,"{3560, 3601, 3544, 208, 3599, 63, 217, 206}"
1146,1,195,0,0.6996197,"\int \frac{(c+d \tan (e+f x))^{3/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{2 (-1)^{3/4} d^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}","\frac{2 (-1)^{3/4} d^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{(-d+i c) \sqrt{c+d \tan (e+f x)}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}",1,"(2*(-1)^(3/4)*d^(3/2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a]*f) - (I*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*f) + ((I*c - d)*Sqrt[c + d*Tan[e + f*x]])/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",8,8,32,0.2500,1,"{3558, 3601, 3544, 208, 3599, 63, 217, 206}"
1147,1,173,0,0.3404897,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(3/2),x]","-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{i (c+d \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(d+i c) \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}","-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{i (c+d \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(d+i c) \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}",1,"((-I/2)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*f) + ((I*c + d)*Sqrt[c + d*Tan[e + f*x]])/(2*a*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I/3)*(c + d*Tan[e + f*x])^(3/2))/(f*(a + I*a*Tan[e + f*x])^(3/2))","A",4,3,32,0.09375,1,"{3546, 3544, 208}"
1148,1,225,0,0.4586629,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{(d+i c) \sqrt{c+d \tan (e+f x)}}{4 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}-\frac{(c+d \tan (e+f x))^{5/2}}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2}}+\frac{i (c+d \tan (e+f x))^{3/2}}{6 a f (a+i a \tan (e+f x))^{3/2}}","\frac{(d+i c) \sqrt{c+d \tan (e+f x)}}{4 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}-\frac{(c+d \tan (e+f x))^{5/2}}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2}}+\frac{i (c+d \tan (e+f x))^{3/2}}{6 a f (a+i a \tan (e+f x))^{3/2}}",1,"((-I/4)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*f) + ((I*c + d)*Sqrt[c + d*Tan[e + f*x]])/(4*a^2*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I/6)*(c + d*Tan[e + f*x])^(3/2))/(a*f*(a + I*a*Tan[e + f*x])^(3/2)) - (c + d*Tan[e + f*x])^(5/2)/(5*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(5/2))","A",5,4,32,0.1250,1,"{3547, 3546, 3544, 208}"
1149,1,415,0,1.723068,"\int (a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(5/2),x]","\frac{a^2 \left(5 c^2+90 i c d+107 d^2\right) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{96 d f}+\frac{a^2 \left(95 i c^2 d+5 c^3+273 c d^2-149 i d^3\right) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{64 d f}-\frac{\sqrt[4]{-1} a^{5/2} \left(690 c^2 d^2+100 i c^3 d+5 c^4-900 i c d^3-363 d^4\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{64 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{7/2}}{4 d f}+\frac{a^2 (c+17 i d) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 d f}-\frac{4 i \sqrt{2} a^{5/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","\frac{a^2 \left(5 c^2+90 i c d+107 d^2\right) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{96 d f}+\frac{a^2 \left(95 i c^2 d+5 c^3+273 c d^2-149 i d^3\right) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{64 d f}-\frac{\sqrt[4]{-1} a^{5/2} \left(690 c^2 d^2+100 i c^3 d+5 c^4-900 i c d^3-363 d^4\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{64 d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{7/2}}{4 d f}+\frac{a^2 (c+17 i d) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2}}{24 d f}-\frac{4 i \sqrt{2} a^{5/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"-((-1)^(1/4)*a^(5/2)*(5*c^4 + (100*I)*c^3*d + 690*c^2*d^2 - (900*I)*c*d^3 - 363*d^4)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(64*d^(3/2)*f) - ((4*I)*Sqrt[2]*a^(5/2)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a^2*(5*c^3 + (95*I)*c^2*d + 273*c*d^2 - (149*I)*d^3)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(64*d*f) + (a^2*(5*c^2 + (90*I)*c*d + 107*d^2)*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(96*d*f) + (a^2*(c + (17*I)*d)*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2))/(24*d*f) - (a^2*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(7/2))/(4*d*f)","A",11,9,32,0.2812,1,"{3556, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1150,1,378,0,1.755666,"\int (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2),x]","-\frac{\sqrt[4]{-1} a^{3/2} \left(45 c^2 d+5 i c^3-55 i c d^2-23 d^3\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{8 \sqrt{d} f}-\frac{a^2 (c+d \tan (e+f x))^{7/2}}{3 d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) (c+d \tan (e+f x))^{5/2}}{3 d f \sqrt{a+i a \tan (e+f x)}}-\frac{2 i \sqrt{2} a^{3/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}+\frac{a (7 d+5 i c) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 f}+\frac{a (c-3 i d) (3 d+5 i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 f}","-\frac{\sqrt[4]{-1} a^{3/2} \left(45 c^2 d+5 i c^3-55 i c d^2-23 d^3\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{8 \sqrt{d} f}-\frac{a^2 (c+d \tan (e+f x))^{7/2}}{3 d f \sqrt{a+i a \tan (e+f x)}}+\frac{a^2 (c+i d) (c+d \tan (e+f x))^{5/2}}{3 d f \sqrt{a+i a \tan (e+f x)}}-\frac{2 i \sqrt{2} a^{3/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}+\frac{a (7 d+5 i c) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{12 f}+\frac{a (c-3 i d) (3 d+5 i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 f}",1,"-((-1)^(1/4)*a^(3/2)*((5*I)*c^3 + 45*c^2*d - (55*I)*c*d^2 - 23*d^3)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(8*Sqrt[d]*f) - ((2*I)*Sqrt[2]*a^(3/2)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + (a*(c - (3*I)*d)*((5*I)*c + 3*d)*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*f) + (a*((5*I)*c + 7*d)*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(12*f) + (a^2*(c + I*d)*(c + d*Tan[e + f*x])^(5/2))/(3*d*f*Sqrt[a + I*a*Tan[e + f*x]]) - (a^2*(c + d*Tan[e + f*x])^(7/2))/(3*d*f*Sqrt[a + I*a*Tan[e + f*x]])","A",11,10,32,0.3125,1,"{3556, 3595, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1151,1,257,0,1.0450669,"\int \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2),x]","-\frac{\sqrt[4]{-1} \sqrt{a} \sqrt{d} \left(15 c^2-10 i c d-7 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 f}+\frac{d \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 f}+\frac{d (7 c-i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}-\frac{i \sqrt{2} \sqrt{a} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}","-\frac{\sqrt[4]{-1} \sqrt{a} \sqrt{d} \left(15 c^2-10 i c d-7 d^2\right) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{4 f}+\frac{d \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 f}+\frac{d (7 c-i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}-\frac{i \sqrt{2} \sqrt{a} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f}",1,"-((-1)^(1/4)*Sqrt[a]*Sqrt[d]*(15*c^2 - (10*I)*c*d - 7*d^2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(4*f) - (I*Sqrt[2]*Sqrt[a]*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/f + ((7*c - I*d)*d*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*f) + (d*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*f)","A",9,9,32,0.2812,1,"{3560, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1152,1,250,0,1.0250747,"\int \frac{(c+d \tan (e+f x))^{5/2}}{\sqrt{a+i a \tan (e+f x)}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/Sqrt[a + I*a*Tan[e + f*x]],x]","\frac{\sqrt[4]{-1} d^{3/2} (-d+5 i c) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{d (c+2 i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{a f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}","\frac{\sqrt[4]{-1} d^{3/2} (-d+5 i c) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{a} f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{f \sqrt{a+i a \tan (e+f x)}}-\frac{d (c+2 i d) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{a f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f}",1,"((-1)^(1/4)*((5*I)*c - d)*d^(3/2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a]*f) - (I*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*f) - ((c + (2*I)*d)*d*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(a*f) + ((I*c - d)*(c + d*Tan[e + f*x])^(3/2))/(f*Sqrt[a + I*a*Tan[e + f*x]])","A",9,9,32,0.2812,1,"{3558, 3597, 3601, 3544, 208, 3599, 63, 217, 206}"
1153,1,257,0,0.9956153,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{3/2}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(3/2),x]","\frac{2 \sqrt[4]{-1} d^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(c+i d) (3 d+i c) \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}","\frac{2 \sqrt[4]{-1} d^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{a^{3/2} f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{(-d+i c) (c+d \tan (e+f x))^{3/2}}{3 f (a+i a \tan (e+f x))^{3/2}}+\frac{(c+i d) (3 d+i c) \sqrt{c+d \tan (e+f x)}}{2 a f \sqrt{a+i a \tan (e+f x)}}",1,"(2*(-1)^(1/4)*d^(5/2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(a^(3/2)*f) - ((I/2)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*f) + ((c + I*d)*(I*c + 3*d)*Sqrt[c + d*Tan[e + f*x]])/(2*a*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I*c - d)*(c + d*Tan[e + f*x])^(3/2))/(3*f*(a + I*a*Tan[e + f*x])^(3/2))","A",9,9,32,0.2812,1,"{3558, 3595, 3601, 3544, 208, 3599, 63, 217, 206}"
1154,1,225,0,0.477117,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+i a \tan (e+f x))^{5/2}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + I*a*Tan[e + f*x])^(5/2),x]","\frac{i (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{4 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}+\frac{i (c+d \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{(d+i c) (c+d \tan (e+f x))^{3/2}}{6 a f (a+i a \tan (e+f x))^{3/2}}","\frac{i (c-i d)^2 \sqrt{c+d \tan (e+f x)}}{4 a^2 f \sqrt{a+i a \tan (e+f x)}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f}+\frac{i (c+d \tan (e+f x))^{5/2}}{5 f (a+i a \tan (e+f x))^{5/2}}+\frac{(d+i c) (c+d \tan (e+f x))^{3/2}}{6 a f (a+i a \tan (e+f x))^{3/2}}",1,"((-I/4)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*f) + ((I/4)*(c - I*d)^2*Sqrt[c + d*Tan[e + f*x]])/(a^2*f*Sqrt[a + I*a*Tan[e + f*x]]) + ((I*c + d)*(c + d*Tan[e + f*x])^(3/2))/(6*a*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((I/5)*(c + d*Tan[e + f*x])^(5/2))/(f*(a + I*a*Tan[e + f*x])^(5/2))","A",5,3,32,0.09375,1,"{3546, 3544, 208}"
1155,1,200,0,0.6670433,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{\sqrt[4]{-1} a^{5/2} (c+5 i d) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}","-\frac{\sqrt[4]{-1} a^{5/2} (c+5 i d) \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{a^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}",1,"-(((-1)^(1/4)*a^(5/2)*(c + (5*I)*d)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(d^(3/2)*f)) - ((4*I)*Sqrt[2]*a^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[c - I*d]*f) - (a^2*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",8,8,32,0.2500,1,"{3556, 3601, 3544, 208, 3599, 63, 217, 206}"
1156,1,151,0,0.4347757,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 (-1)^{3/4} a^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}","-\frac{2 (-1)^{3/4} a^{3/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}",1,"(-2*(-1)^(3/4)*a^(3/2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[d]*f) - ((2*I)*Sqrt[2]*a^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[c - I*d]*f)","A",7,7,32,0.2188,1,"{3555, 3544, 208, 3599, 63, 217, 206}"
1157,1,82,0,0.1116008,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}","-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f \sqrt{c-i d}}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[c - I*d]*f)","A",2,2,32,0.06250,1,"{3544, 208}"
1158,1,174,0,0.3184336,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]),x]","\frac{2 d \sqrt{c+d \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt{c+d \tan (e+f x)}}{f (d+i c) \sqrt{a+i a \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f \sqrt{c-i d}}","\frac{2 d \sqrt{c+d \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt{c+d \tan (e+f x)}}{f (d+i c) \sqrt{a+i a \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f \sqrt{c-i d}}",1,"((-I)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*Sqrt[c - I*d]*f) - Sqrt[c + d*Tan[e + f*x]]/((I*c + d)*f*Sqrt[a + I*a*Tan[e + f*x]]) + (2*d*Sqrt[c + d*Tan[e + f*x]])/((c^2 + d^2)*f*Sqrt[a + I*a*Tan[e + f*x]])","A",4,4,32,0.1250,1,"{3548, 3546, 3544, 208}"
1159,1,193,0,0.4676142,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f \sqrt{c-i d}}+\frac{(-7 d+3 i c) \sqrt{c+d \tan (e+f x)}}{6 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt{c+d \tan (e+f x)}}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2}}","-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f \sqrt{c-i d}}+\frac{(-7 d+3 i c) \sqrt{c+d \tan (e+f x)}}{6 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)}}-\frac{\sqrt{c+d \tan (e+f x)}}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2}}",1,"((-I/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*Sqrt[c - I*d]*f) - Sqrt[c + d*Tan[e + f*x]]/(3*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(3/2)) + (((3*I)*c - 7*d)*Sqrt[c + d*Tan[e + f*x]])/(6*a*(c + I*d)^2*f*Sqrt[a + I*a*Tan[e + f*x]])","A",5,5,32,0.1562,1,"{3559, 3596, 12, 3544, 208}"
1160,1,262,0,0.8178197,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]]),x]","\frac{\left(15 c^2+50 i c d-67 d^2\right) \sqrt{c+d \tan (e+f x)}}{60 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f \sqrt{c-i d}}+\frac{(-13 d+5 i c) \sqrt{c+d \tan (e+f x)}}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2}}-\frac{\sqrt{c+d \tan (e+f x)}}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2}}","\frac{\left(15 c^2+50 i c d-67 d^2\right) \sqrt{c+d \tan (e+f x)}}{60 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f \sqrt{c-i d}}+\frac{(-13 d+5 i c) \sqrt{c+d \tan (e+f x)}}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2}}-\frac{\sqrt{c+d \tan (e+f x)}}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2}}",1,"((-I/4)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*Sqrt[c - I*d]*f) - Sqrt[c + d*Tan[e + f*x]]/(5*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(5/2)) + (((5*I)*c - 13*d)*Sqrt[c + d*Tan[e + f*x]])/(30*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^(3/2)) + ((15*c^2 + (50*I)*c*d - 67*d^2)*Sqrt[c + d*Tan[e + f*x]])/(60*a^2*(I*c - d)^3*f*Sqrt[a + I*a*Tan[e + f*x]])","A",6,5,32,0.1562,1,"{3559, 3596, 12, 3544, 208}"
1161,1,209,0,0.6998553,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 \sqrt[4]{-1} a^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{2 a^2 (c+i d) \sqrt{a+i a \tan (e+f x)}}{d f (c-i d) \sqrt{c+d \tan (e+f x)}}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}","\frac{2 \sqrt[4]{-1} a^{5/2} \tanh ^{-1}\left(\frac{(-1)^{3/4} \sqrt{d} \sqrt{a+i a \tan (e+f x)}}{\sqrt{a} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{2 a^2 (c+i d) \sqrt{a+i a \tan (e+f x)}}{d f (c-i d) \sqrt{c+d \tan (e+f x)}}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}",1,"(2*(-1)^(1/4)*a^(5/2)*ArcTanh[((-1)^(3/4)*Sqrt[d]*Sqrt[a + I*a*Tan[e + f*x]])/(Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])])/(d^(3/2)*f) - ((4*I)*Sqrt[2]*a^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) + (2*a^2*(c + I*d)*Sqrt[a + I*a*Tan[e + f*x]])/((c - I*d)*d*f*Sqrt[c + d*Tan[e + f*x]])","A",8,8,32,0.2500,1,"{3553, 3601, 3544, 208, 3599, 63, 217, 206}"
1162,1,129,0,0.2208577,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{2 a \sqrt{a+i a \tan (e+f x)}}{f (d+i c) \sqrt{c+d \tan (e+f x)}}","-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}-\frac{2 a \sqrt{a+i a \tan (e+f x)}}{f (d+i c) \sqrt{c+d \tan (e+f x)}}",1,"((-2*I)*Sqrt[2]*a^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) - (2*a*Sqrt[a + I*a*Tan[e + f*x]])/((I*c + d)*f*Sqrt[c + d*Tan[e + f*x]])","A",3,3,32,0.09375,1,"{3545, 3544, 208}"
1163,1,129,0,0.2120673,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 d \sqrt{a+i a \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}","-\frac{2 d \sqrt{a+i a \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) - (2*d*Sqrt[a + I*a*Tan[e + f*x]])/((c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",3,3,32,0.09375,1,"{3548, 3544, 208}"
1164,1,194,0,0.4733273,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d (c-3 i d) \sqrt{a+i a \tan (e+f x)}}{a f (c-i d) (c+i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{f (-d+i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f (c-i d)^{3/2}}","\frac{d (c-3 i d) \sqrt{a+i a \tan (e+f x)}}{a f (c-i d) (c+i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{1}{f (-d+i c) \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f (c-i d)^{3/2}}",1,"((-I)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*(c - I*d)^(3/2)*f) - 1/((I*c - d)*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) + ((c - (3*I)*d)*d*Sqrt[a + I*a*Tan[e + f*x]])/(a*(c - I*d)*(c + I*d)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",5,5,32,0.1562,1,"{3559, 3598, 12, 3544, 208}"
1165,1,269,0,0.8449488,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d (3 c-5 i d) (c+5 i d) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d) (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f (c-i d)^{3/2}}+\frac{-11 d+3 i c}{6 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{1}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}","\frac{d (3 c-5 i d) (c+5 i d) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d) (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f (c-i d)^{3/2}}+\frac{-11 d+3 i c}{6 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{1}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}",1,"((-I/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*(c - I*d)^(3/2)*f) - 1/(3*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]) + ((3*I)*c - 11*d)/(6*a*(c + I*d)^2*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) + ((3*c - (5*I)*d)*(c + (5*I)*d)*d*Sqrt[a + I*a*Tan[e + f*x]])/(6*a^2*(c - I*d)*(c + I*d)^3*f*Sqrt[c + d*Tan[e + f*x]])","A",6,6,32,0.1875,1,"{3559, 3596, 3598, 12, 3544, 208}"
1166,1,349,0,1.2401493,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{d \left(65 i c^2 d+15 c^3-117 c d^2+317 i d^3\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d) (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{15 c^2+70 i c d-151 d^2}{60 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f (c-i d)^{3/2}}+\frac{-17 d+5 i c}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{1}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}","\frac{d \left(65 i c^2 d+15 c^3-117 c d^2+317 i d^3\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d) (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{15 c^2+70 i c d-151 d^2}{60 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f (c-i d)^{3/2}}+\frac{-17 d+5 i c}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{1}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}",1,"((-I/4)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*(c - I*d)^(3/2)*f) - 1/(5*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]]) + ((5*I)*c - 17*d)/(30*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]) + (15*c^2 + (70*I)*c*d - 151*d^2)/(60*a^2*(I*c - d)^3*f*Sqrt[a + I*a*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) + (d*(15*c^3 + (65*I)*c^2*d - 117*c*d^2 + (317*I)*d^3)*Sqrt[a + I*a*Tan[e + f*x]])/(60*a^3*(c - I*d)*(c + I*d)^4*f*Sqrt[c + d*Tan[e + f*x]])","A",7,6,32,0.1875,1,"{3559, 3596, 3598, 12, 3544, 208}"
1167,1,181,0,0.3465422,"\int \frac{(a+i a \tan (e+f x))^{5/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(5/2)/(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 i a^2 \sqrt{a+i a \tan (e+f x)}}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{2 a (a+i a \tan (e+f x))^{3/2}}{3 f (d+i c) (c+d \tan (e+f x))^{3/2}}","\frac{4 i a^2 \sqrt{a+i a \tan (e+f x)}}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{4 i \sqrt{2} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{2 a (a+i a \tan (e+f x))^{3/2}}{3 f (d+i c) (c+d \tan (e+f x))^{3/2}}",1,"((-4*I)*Sqrt[2]*a^(5/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) - (2*a*(a + I*a*Tan[e + f*x])^(3/2))/(3*(I*c + d)*f*(c + d*Tan[e + f*x])^(3/2)) + ((4*I)*a^2*Sqrt[a + I*a*Tan[e + f*x]])/((c - I*d)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",4,3,32,0.09375,1,"{3545, 3544, 208}"
1168,1,179,0,0.3412623,"\int \frac{(a+i a \tan (e+f x))^{3/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^(3/2)/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{2 d (a+i a \tan (e+f x))^{3/2}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{2 i a \sqrt{a+i a \tan (e+f x)}}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}","-\frac{2 i \sqrt{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}-\frac{2 d (a+i a \tan (e+f x))^{3/2}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{2 i a \sqrt{a+i a \tan (e+f x)}}{f (c-i d)^2 \sqrt{c+d \tan (e+f x)}}",1,"((-2*I)*Sqrt[2]*a^(3/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) - (2*d*(a + I*a*Tan[e + f*x])^(3/2))/(3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + ((2*I)*a*Sqrt[a + I*a*Tan[e + f*x]])/((c - I*d)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",4,4,32,0.1250,1,"{3548, 3545, 3544, 208}"
1169,1,188,0,0.471206,"\int \frac{\sqrt{a+i a \tan (e+f x)}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[a + I*a*Tan[e + f*x]]/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 d (5 c+i d) \sqrt{a+i a \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+i a \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}","-\frac{2 d (5 c+i d) \sqrt{a+i a \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+i a \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i \sqrt{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}",1,"((-I)*Sqrt[2]*Sqrt[a]*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) - (2*d*Sqrt[a + I*a*Tan[e + f*x]])/(3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(5*c + I*d)*d*Sqrt[a + I*a*Tan[e + f*x]])/(3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",5,5,32,0.1562,1,"{3561, 3598, 12, 3544, 208}"
1170,1,277,0,0.8591027,"\int \frac{1}{\sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/(Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d (5 d+3 i c) \sqrt{a+i a \tan (e+f x)}}{3 a f (-d+i c) \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{d (3 c-i d) (c-7 i d) \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i d)^2 (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{1}{f (-d+i c) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f (c-i d)^{5/2}}","\frac{d (5 d+3 i c) \sqrt{a+i a \tan (e+f x)}}{3 a f (-d+i c) \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}+\frac{d (3 c-i d) (c-7 i d) \sqrt{a+i a \tan (e+f x)}}{3 a f (c-i d)^2 (c+i d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{1}{f (-d+i c) \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{\sqrt{2} \sqrt{a} f (c-i d)^{5/2}}",1,"((-I)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*Sqrt[a]*(c - I*d)^(5/2)*f) - 1/((I*c - d)*f*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) + (d*((3*I)*c + 5*d)*Sqrt[a + I*a*Tan[e + f*x]])/(3*a*(I*c - d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + ((3*c - I*d)*(c - (7*I)*d)*d*Sqrt[a + I*a*Tan[e + f*x]])/(3*a*(c - I*d)^2*(c + I*d)^3*f*Sqrt[c + d*Tan[e + f*x]])","A",6,5,32,0.1562,1,"{3559, 3598, 12, 3544, 208}"
1171,1,354,0,1.2382724,"\int \frac{1}{(a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d (c-3 i d) \left(3 c^2+22 i c d+13 d^2\right) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d)^2 (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(3 c^2+14 i c d+21 d^2\right) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f (c-i d)^{5/2}}+\frac{-5 d+i c}{2 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{1}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}","\frac{d (c-3 i d) \left(3 c^2+22 i c d+13 d^2\right) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d)^2 (c+i d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(3 c^2+14 i c d+21 d^2\right) \sqrt{a+i a \tan (e+f x)}}{6 a^2 f (c-i d) (c+i d)^3 (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{2 \sqrt{2} a^{3/2} f (c-i d)^{5/2}}+\frac{-5 d+i c}{2 a f (c+i d)^2 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{1}{3 f (-d+i c) (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}",1,"((-I/2)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(3/2)*(c - I*d)^(5/2)*f) - 1/(3*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)) + (I*c - 5*d)/(2*a*(c + I*d)^2*f*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) + (d*(3*c^2 + (14*I)*c*d + 21*d^2)*Sqrt[a + I*a*Tan[e + f*x]])/(6*a^2*(c - I*d)*(c + I*d)^3*f*(c + d*Tan[e + f*x])^(3/2)) + ((c - (3*I)*d)*d*(3*c^2 + (22*I)*c*d + 13*d^2)*Sqrt[a + I*a*Tan[e + f*x]])/(6*a^2*(c - I*d)^2*(c + I*d)^4*f*Sqrt[c + d*Tan[e + f*x]])","A",7,6,32,0.1875,1,"{3559, 3596, 3598, 12, 3544, 208}"
1172,1,444,0,1.7886811,"\int \frac{1}{(a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + I*a*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d \left(-182 c^2 d^2+80 i c^3 d+15 c^4+1224 i c d^3+707 d^4\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d)^2 (c+i d)^5 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(85 i c^2 d+15 c^3-221 c d^2+361 i d^3\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^{3/2}}+\frac{5 c^2+30 i c d-89 d^2}{20 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f (c-i d)^{5/2}}+\frac{-21 d+5 i c}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}-\frac{1}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}}","\frac{d \left(-182 c^2 d^2+80 i c^3 d+15 c^4+1224 i c d^3+707 d^4\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d)^2 (c+i d)^5 \sqrt{c+d \tan (e+f x)}}+\frac{d \left(85 i c^2 d+15 c^3-221 c d^2+361 i d^3\right) \sqrt{a+i a \tan (e+f x)}}{60 a^3 f (c-i d) (c+i d)^4 (c+d \tan (e+f x))^{3/2}}+\frac{5 c^2+30 i c d-89 d^2}{20 a^2 f (-d+i c)^3 \sqrt{a+i a \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{a} \sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d} \sqrt{a+i a \tan (e+f x)}}\right)}{4 \sqrt{2} a^{5/2} f (c-i d)^{5/2}}+\frac{-21 d+5 i c}{30 a f (c+i d)^2 (a+i a \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}-\frac{1}{5 f (-d+i c) (a+i a \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}}",1,"((-I/4)*ArcTanh[(Sqrt[2]*Sqrt[a]*Sqrt[c + d*Tan[e + f*x]])/(Sqrt[c - I*d]*Sqrt[a + I*a*Tan[e + f*x]])])/(Sqrt[2]*a^(5/2)*(c - I*d)^(5/2)*f) - 1/(5*(I*c - d)*f*(a + I*a*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2)) + ((5*I)*c - 21*d)/(30*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)) + (5*c^2 + (30*I)*c*d - 89*d^2)/(20*a^2*(I*c - d)^3*f*Sqrt[a + I*a*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) + (d*(15*c^3 + (85*I)*c^2*d - 221*c*d^2 + (361*I)*d^3)*Sqrt[a + I*a*Tan[e + f*x]])/(60*a^3*(c - I*d)*(c + I*d)^4*f*(c + d*Tan[e + f*x])^(3/2)) + (d*(15*c^4 + (80*I)*c^3*d - 182*c^2*d^2 + (1224*I)*c*d^3 + 707*d^4)*Sqrt[a + I*a*Tan[e + f*x]])/(60*a^3*(c - I*d)^2*(c + I*d)^5*f*Sqrt[c + d*Tan[e + f*x]])","A",8,6,32,0.1875,1,"{3559, 3596, 3598, 12, 3544, 208}"
1173,1,114,0,0.1691039,"\int (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n,x]","-\frac{i (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^n \left(\frac{c+d \tan (e+f x)}{c+i d}\right)^{-n} F_1\left(m;-n,1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}","-\frac{i (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^n \left(\frac{c+d \tan (e+f x)}{c+i d}\right)^{-n} F_1\left(m;-n,1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}",1,"((-I/2)*AppellF1[m, -n, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n)/(f*m*((c + d*Tan[e + f*x])/(c + I*d))^n)","A",3,3,28,0.1071,1,"{3564, 137, 136}"
1174,1,157,0,0.3371427,"\int (a+i a \tan (e+f x))^3 (c+d \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^n,x]","\frac{a^3 (-d (2 n+5)+i c) (c+d \tan (e+f x))^{n+1}}{d^2 f (n+1) (n+2)}+\frac{4 a^3 (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{n+1}}{d f (n+2)}","\frac{a^3 (-d (2 n+5)+i c) (c+d \tan (e+f x))^{n+1}}{d^2 f (n+1) (n+2)}+\frac{4 a^3 (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}-\frac{\left(a^3+i a^3 \tan (e+f x)\right) (c+d \tan (e+f x))^{n+1}}{d f (n+2)}",1,"(a^3*(I*c - d*(5 + 2*n))*(c + d*Tan[e + f*x])^(1 + n))/(d^2*f*(1 + n)*(2 + n)) + (4*a^3*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/((I*c + d)*f*(1 + n)) - ((a^3 + I*a^3*Tan[e + f*x])*(c + d*Tan[e + f*x])^(1 + n))/(d*f*(2 + n))","A",4,4,28,0.1429,1,"{3556, 3592, 3537, 68}"
1175,1,95,0,0.1273511,"\int (a+i a \tan (e+f x))^2 (c+d \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^n,x]","-\frac{a^2 (c+d \tan (e+f x))^{n+1}}{d f (n+1)}+\frac{2 a^2 (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}","-\frac{a^2 (c+d \tan (e+f x))^{n+1}}{d f (n+1)}+\frac{2 a^2 (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}",1,"-((a^2*(c + d*Tan[e + f*x])^(1 + n))/(d*f*(1 + n))) + (2*a^2*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/((I*c + d)*f*(1 + n))","A",3,3,28,0.1071,1,"{3543, 3537, 68}"
1176,1,61,0,0.0728441,"\int (a+i a \tan (e+f x)) (c+d \tan (e+f x))^n \, dx","Int[(a + I*a*Tan[e + f*x])*(c + d*Tan[e + f*x])^n,x]","\frac{a (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}","\frac{a (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{f (n+1) (d+i c)}",1,"(a*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/((I*c + d)*f*(1 + n))","A",2,2,26,0.07692,1,"{3537, 68}"
1177,1,193,0,0.2790092,"\int \frac{(c+d \tan (e+f x))^n}{a+i a \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x]),x]","\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{4 a f (n+1) (d+i c)}+\frac{(i c+2 d n-d) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{4 a f (n+1) (c+i d)^2}-\frac{(c+d \tan (e+f x))^{n+1}}{2 f (-d+i c) (a+i a \tan (e+f x))}","\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{4 a f (n+1) (d+i c)}+\frac{(i c+2 d n-d) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{4 a f (n+1) (c+i d)^2}-\frac{(c+d \tan (e+f x))^{n+1}}{2 f (-d+i c) (a+i a \tan (e+f x))}",1,"(Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(4*a*(I*c + d)*f*(1 + n)) + ((I*c - d + 2*d*n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c + I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(4*a*(c + I*d)^2*f*(1 + n)) - (c + d*Tan[e + f*x])^(1 + n)/(2*(I*c - d)*f*(a + I*a*Tan[e + f*x]))","A",6,4,28,0.1429,1,"{3552, 3539, 3537, 68}"
1178,1,273,0,0.5565232,"\int \frac{(c+d \tan (e+f x))^n}{(a+i a \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^2,x]","\frac{\left(c^2+2 i c d (1-n)-d^2 \left(2 n^2-4 n+1\right)\right) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{8 a^2 f (n+1) (-d+i c)^3}+\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{8 a^2 f (n+1) (d+i c)}+\frac{(-d (2-n)+i c) (c+d \tan (e+f x))^{n+1}}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{(c+d \tan (e+f x))^{n+1}}{4 f (-d+i c) (a+i a \tan (e+f x))^2}","\frac{\left(c^2+2 i c d (1-n)-d^2 \left(2 n^2-4 n+1\right)\right) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{8 a^2 f (n+1) (-d+i c)^3}+\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{8 a^2 f (n+1) (d+i c)}+\frac{(-d (2-n)+i c) (c+d \tan (e+f x))^{n+1}}{4 a^2 f (c+i d)^2 (1+i \tan (e+f x))}-\frac{(c+d \tan (e+f x))^{n+1}}{4 f (-d+i c) (a+i a \tan (e+f x))^2}",1,"(Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(8*a^2*(I*c + d)*f*(1 + n)) + ((c^2 + (2*I)*c*d*(1 - n) - d^2*(1 - 4*n + 2*n^2))*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c + I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(8*a^2*(I*c - d)^3*f*(1 + n)) + ((I*c - d*(2 - n))*(c + d*Tan[e + f*x])^(1 + n))/(4*a^2*(c + I*d)^2*f*(1 + I*Tan[e + f*x])) - (c + d*Tan[e + f*x])^(1 + n)/(4*(I*c - d)*f*(a + I*a*Tan[e + f*x])^2)","A",7,5,28,0.1786,1,"{3559, 3596, 3539, 3537, 68}"
1179,1,381,0,1.0603323,"\int \frac{(c+d \tan (e+f x))^n}{(a+i a \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^n/(a + I*a*Tan[e + f*x])^3,x]","\frac{\left(-c^2 d (9-6 n)+3 i c^3-3 i c d^2 \left(2 n^2-6 n+3\right)+d^3 \left(-4 n^3+18 n^2-20 n+3\right)\right) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{48 a^3 f (n+1) (c+i d)^4}+\frac{\left(3 i c^2-3 c d (3-n)-i d^2 \left(2 n^2-9 n+10\right)\right) (c+d \tan (e+f x))^{n+1}}{24 f (c+i d)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{16 a^3 f (n+1) (d+i c)}+\frac{(-d (7-2 n)+3 i c) (c+d \tan (e+f x))^{n+1}}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{(c+d \tan (e+f x))^{n+1}}{6 f (-d+i c) (a+i a \tan (e+f x))^3}","\frac{\left(-c^2 d (9-6 n)+3 i c^3-3 i c d^2 \left(2 n^2-6 n+3\right)+d^3 \left(-4 n^3+18 n^2-20 n+3\right)\right) (c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c+i d}\right)}{48 a^3 f (n+1) (c+i d)^4}+\frac{\left(3 i c^2-3 c d (3-n)-i d^2 \left(2 n^2-9 n+10\right)\right) (c+d \tan (e+f x))^{n+1}}{24 f (c+i d)^3 \left(a^3+i a^3 \tan (e+f x)\right)}+\frac{(c+d \tan (e+f x))^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c+d \tan (e+f x)}{c-i d}\right)}{16 a^3 f (n+1) (d+i c)}+\frac{(-d (7-2 n)+3 i c) (c+d \tan (e+f x))^{n+1}}{24 a f (c+i d)^2 (a+i a \tan (e+f x))^2}-\frac{(c+d \tan (e+f x))^{n+1}}{6 f (-d+i c) (a+i a \tan (e+f x))^3}",1,"(Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c - I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(16*a^3*(I*c + d)*f*(1 + n)) + (((3*I)*c^3 - c^2*d*(9 - 6*n) - (3*I)*c*d^2*(3 - 6*n + 2*n^2) + d^3*(3 - 20*n + 18*n^2 - 4*n^3))*Hypergeometric2F1[1, 1 + n, 2 + n, (c + d*Tan[e + f*x])/(c + I*d)]*(c + d*Tan[e + f*x])^(1 + n))/(48*a^3*(c + I*d)^4*f*(1 + n)) - (c + d*Tan[e + f*x])^(1 + n)/(6*(I*c - d)*f*(a + I*a*Tan[e + f*x])^3) + (((3*I)*c - d*(7 - 2*n))*(c + d*Tan[e + f*x])^(1 + n))/(24*a*(c + I*d)^2*f*(a + I*a*Tan[e + f*x])^2) + (((3*I)*c^2 - 3*c*d*(3 - n) - I*d^2*(10 - 9*n + 2*n^2))*(c + d*Tan[e + f*x])^(1 + n))/(24*(c + I*d)^3*f*(a^3 + I*a^3*Tan[e + f*x]))","A",8,5,28,0.1786,1,"{3559, 3596, 3539, 3537, 68}"
1180,1,192,0,0.4621474,"\int (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^3 \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^3,x]","-\frac{2 d \left(c^2 (-(m+3))+i c d m+d^2\right) (a+i a \tan (e+f x))^m}{f m (m+2)}-\frac{d^2 (d m+i c (m+4)) (a+i a \tan (e+f x))^{m+1}}{a f (m+1) (m+2)}+\frac{(d+i c)^3 (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}+\frac{d (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^2}{f (m+2)}","-\frac{2 d \left(c^2 (-(m+3))+i c d m+d^2\right) (a+i a \tan (e+f x))^m}{f m (m+2)}-\frac{d^2 (d m+i c (m+4)) (a+i a \tan (e+f x))^{m+1}}{a f (m+1) (m+2)}+\frac{(d+i c)^3 (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}+\frac{d (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^2}{f (m+2)}",1,"(-2*d*(d^2 + I*c*d*m - c^2*(3 + m))*(a + I*a*Tan[e + f*x])^m)/(f*m*(2 + m)) + ((I*c + d)^3*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(2*f*m) - (d^2*(d*m + I*c*(4 + m))*(a + I*a*Tan[e + f*x])^(1 + m))/(a*f*(1 + m)*(2 + m)) + (d*(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^2)/(f*(2 + m))","A",5,5,28,0.1786,1,"{3560, 3592, 3527, 3481, 68}"
1181,1,119,0,0.1667364,"\int (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^2 \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^2,x]","-\frac{i (c-i d)^2 (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}+\frac{2 c d (a+i a \tan (e+f x))^m}{f m}-\frac{i d^2 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}","-\frac{i (c-i d)^2 (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}+\frac{2 c d (a+i a \tan (e+f x))^m}{f m}-\frac{i d^2 (a+i a \tan (e+f x))^{m+1}}{a f (m+1)}",1,"(2*c*d*(a + I*a*Tan[e + f*x])^m)/(f*m) - ((I/2)*(c - I*d)^2*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(f*m) - (I*d^2*(a + I*a*Tan[e + f*x])^(1 + m))/(a*f*(1 + m))","A",4,4,28,0.1429,1,"{3543, 3527, 3481, 68}"
1182,1,78,0,0.0697399,"\int (a+i a \tan (e+f x))^m (c+d \tan (e+f x)) \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x]),x]","\frac{d (a+i a \tan (e+f x))^m}{f m}-\frac{(d+i c) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}","\frac{d (a+i a \tan (e+f x))^m}{f m}-\frac{(d+i c) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m}",1,"(d*(a + I*a*Tan[e + f*x])^m)/(f*m) - ((I*c + d)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(2*f*m)","A",3,3,26,0.1154,1,"{3527, 3481, 68}"
1183,1,122,0,0.2596037,"\int \frac{(a+i a \tan (e+f x))^m}{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c + d*Tan[e + f*x]),x]","\frac{(a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (d+i c)}-\frac{d (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{f m \left(c^2+d^2\right)}","\frac{(a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (d+i c)}-\frac{d (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{f m \left(c^2+d^2\right)}",1,"(Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(2*(I*c + d)*f*m) - (d*Hypergeometric2F1[1, m, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d))]*(a + I*a*Tan[e + f*x])^m)/((c^2 + d^2)*f*m)","A",5,4,28,0.1429,1,"{3562, 3481, 68, 3599}"
1184,1,180,0,0.4716456,"\int \frac{(a+i a \tan (e+f x))^m}{(c+d \tan (e+f x))^2} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^2,x]","-\frac{d (c (2-m)+i d m) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{f m \left(c^2+d^2\right)^2}-\frac{d (a+i a \tan (e+f x))^m}{f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (c-i d)^2}","-\frac{d (c (2-m)+i d m) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{f m \left(c^2+d^2\right)^2}-\frac{d (a+i a \tan (e+f x))^m}{f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{i (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (c-i d)^2}",1,"((-I/2)*Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/((c - I*d)^2*f*m) - (d*(c*(2 - m) + I*d*m)*Hypergeometric2F1[1, m, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d))]*(a + I*a*Tan[e + f*x])^m)/((c^2 + d^2)^2*f*m) - (d*(a + I*a*Tan[e + f*x])^m)/((c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",6,5,28,0.1786,1,"{3561, 3600, 3481, 68, 3599}"
1185,1,264,0,0.8832344,"\int \frac{(a+i a \tan (e+f x))^m}{(c+d \tan (e+f x))^3} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^3,x]","-\frac{d \left(c^2 \left(m^2-5 m+6\right)+2 i c d (3-m) m-d^2 \left(m^2-m+2\right)\right) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{2 f m \left(c^2+d^2\right)^3}-\frac{d (c (4-m)+i d m) (a+i a \tan (e+f x))^m}{2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{d (a+i a \tan (e+f x))^m}{2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{(a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (d+i c)^3}","-\frac{d \left(c^2 \left(m^2-5 m+6\right)+2 i c d (3-m) m-d^2 \left(m^2-m+2\right)\right) (a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d}\right)}{2 f m \left(c^2+d^2\right)^3}-\frac{d (c (4-m)+i d m) (a+i a \tan (e+f x))^m}{2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{d (a+i a \tan (e+f x))^m}{2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{(a+i a \tan (e+f x))^m \, _2F_1\left(1,m;m+1;\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (d+i c)^3}",1,"-(Hypergeometric2F1[1, m, 1 + m, (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m)/(2*(I*c + d)^3*f*m) - (d*((2*I)*c*d*(3 - m)*m + c^2*(6 - 5*m + m^2) - d^2*(2 - m + m^2))*Hypergeometric2F1[1, m, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d))]*(a + I*a*Tan[e + f*x])^m)/(2*(c^2 + d^2)^3*f*m) - (d*(a + I*a*Tan[e + f*x])^m)/(2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (d*(c*(4 - m) + I*d*m)*(a + I*a*Tan[e + f*x])^m)/(2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",7,6,28,0.2143,1,"{3561, 3598, 3600, 3481, 68, 3599}"
1186,1,123,0,0.1792192,"\int (a+i a \tan (e+f x))^m (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + I*a*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^(3/2),x]","-\frac{(-d+i c) (a+i a \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} F_1\left(m;-\frac{3}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}}}","-\frac{(-d+i c) (a+i a \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} F_1\left(m;-\frac{3}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}}}",1,"-((I*c - d)*AppellF1[m, -3/2, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[c + d*Tan[e + f*x]])/(2*f*m*Sqrt[(c + d*Tan[e + f*x])/(c + I*d)])","A",3,3,30,0.1000,1,"{3564, 137, 136}"
1187,1,116,0,0.1415863,"\int (a+i a \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + I*a*Tan[e + f*x])^m*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{i (a+i a \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} F_1\left(m;-\frac{1}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}}}","-\frac{i (a+i a \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} F_1\left(m;-\frac{1}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}}}",1,"((-I/2)*AppellF1[m, -1/2, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[c + d*Tan[e + f*x]])/(f*m*Sqrt[(c + d*Tan[e + f*x])/(c + I*d)])","A",3,3,30,0.1000,1,"{3564, 137, 136}"
1188,1,116,0,0.1473857,"\int \frac{(a+i a \tan (e+f x))^m}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{i (a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{1}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{c+d \tan (e+f x)}}","-\frac{i (a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{1}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m \sqrt{c+d \tan (e+f x)}}",1,"((-I/2)*AppellF1[m, 1/2, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[(c + d*Tan[e + f*x])/(c + I*d)])/(f*m*Sqrt[c + d*Tan[e + f*x]])","A",3,3,30,0.1000,1,"{3564, 137, 136}"
1189,1,125,0,0.1563083,"\int \frac{(a+i a \tan (e+f x))^m}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^(3/2),x]","\frac{(a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{3}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (-d+i c) \sqrt{c+d \tan (e+f x)}}","\frac{(a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{3}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (-d+i c) \sqrt{c+d \tan (e+f x)}}",1,"(AppellF1[m, 3/2, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[(c + d*Tan[e + f*x])/(c + I*d)])/(2*(I*c - d)*f*m*Sqrt[c + d*Tan[e + f*x]])","A",3,3,30,0.1000,1,"{3564, 137, 136}"
1190,1,125,0,0.1575463,"\int \frac{(a+i a \tan (e+f x))^m}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + I*a*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{i (a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{5}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (c+i d)^2 \sqrt{c+d \tan (e+f x)}}","-\frac{i (a+i a \tan (e+f x))^m \sqrt{\frac{c+d \tan (e+f x)}{c+i d}} F_1\left(m;\frac{5}{2},1;m+1;-\frac{d (i \tan (e+f x)+1)}{i c-d},\frac{1}{2} (i \tan (e+f x)+1)\right)}{2 f m (c+i d)^2 \sqrt{c+d \tan (e+f x)}}",1,"((-I/2)*AppellF1[m, 5/2, 1, 1 + m, -((d*(1 + I*Tan[e + f*x]))/(I*c - d)), (1 + I*Tan[e + f*x])/2]*(a + I*a*Tan[e + f*x])^m*Sqrt[(c + d*Tan[e + f*x])/(c + I*d)])/((c + I*d)^2*f*m*Sqrt[c + d*Tan[e + f*x]])","A",3,3,30,0.1000,1,"{3564, 137, 136}"
1191,1,140,0,0.1620004,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x)) \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x]),x]","\frac{b \left(a^2 d+2 a b c-b^2 d\right) \tan (e+f x)}{f}-\frac{\left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) \log (\cos (e+f x))}{f}+x \left(-3 a^2 b d+a^3 c-3 a b^2 c+b^3 d\right)+\frac{(a d+b c) (a+b \tan (e+f x))^2}{2 f}+\frac{d (a+b \tan (e+f x))^3}{3 f}","\frac{b \left(a^2 d+2 a b c-b^2 d\right) \tan (e+f x)}{f}-\frac{\left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) \log (\cos (e+f x))}{f}+x \left(-3 a^2 b d+a^3 c-3 a b^2 c+b^3 d\right)+\frac{(a d+b c) (a+b \tan (e+f x))^2}{2 f}+\frac{d (a+b \tan (e+f x))^3}{3 f}",1,"(a^3*c - 3*a*b^2*c - 3*a^2*b*d + b^3*d)*x - ((3*a^2*b*c - b^3*c + a^3*d - 3*a*b^2*d)*Log[Cos[e + f*x]])/f + (b*(2*a*b*c + a^2*d - b^2*d)*Tan[e + f*x])/f + ((b*c + a*d)*(a + b*Tan[e + f*x])^2)/(2*f) + (d*(a + b*Tan[e + f*x])^3)/(3*f)","A",4,3,23,0.1304,1,"{3528, 3525, 3475}"
1192,1,87,0,0.0798564,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x)) \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x]),x]","-\frac{\left(a^2 d+2 a b c-b^2 d\right) \log (\cos (e+f x))}{f}+x \left(a^2 c-2 a b d-b^2 c\right)+\frac{b (a d+b c) \tan (e+f x)}{f}+\frac{d (a+b \tan (e+f x))^2}{2 f}","-\frac{\left(a^2 d+2 a b c-b^2 d\right) \log (\cos (e+f x))}{f}+x \left(a^2 c-2 a b d-b^2 c\right)+\frac{b (a d+b c) \tan (e+f x)}{f}+\frac{d (a+b \tan (e+f x))^2}{2 f}",1,"(a^2*c - b^2*c - 2*a*b*d)*x - ((2*a*b*c + a^2*d - b^2*d)*Log[Cos[e + f*x]])/f + (b*(b*c + a*d)*Tan[e + f*x])/f + (d*(a + b*Tan[e + f*x])^2)/(2*f)","A",3,3,23,0.1304,1,"{3528, 3525, 3475}"
1193,1,42,0,0.0253722,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x)) \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x]),x]","-\frac{(a d+b c) \log (\cos (e+f x))}{f}+x (a c-b d)+\frac{b d \tan (e+f x)}{f}","-\frac{(a d+b c) \log (\cos (e+f x))}{f}+x (a c-b d)+\frac{b d \tan (e+f x)}{f}",1,"(a*c - b*d)*x - ((b*c + a*d)*Log[Cos[e + f*x]])/f + (b*d*Tan[e + f*x])/f","A",2,2,21,0.09524,1,"{3525, 3475}"
1194,1,58,0,0.0725751,"\int \frac{c+d \tan (e+f x)}{a+b \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])/(a + b*Tan[e + f*x]),x]","\frac{(b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)}+\frac{x (a c+b d)}{a^2+b^2}","\frac{(b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)}+\frac{x (a c+b d)}{a^2+b^2}",1,"((a*c + b*d)*x)/(a^2 + b^2) + ((b*c - a*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*f)","A",2,2,23,0.08696,1,"{3531, 3530}"
1195,1,111,0,0.1472372,"\int \frac{c+d \tan (e+f x)}{(a+b \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])/(a + b*Tan[e + f*x])^2,x]","-\frac{b c-a d}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(a^2 (-d)+2 a b c+b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2}+\frac{x \left(a^2 c+2 a b d-b^2 c\right)}{\left(a^2+b^2\right)^2}","-\frac{b c-a d}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(a^2 (-d)+2 a b c+b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2}+\frac{x \left(a^2 c+2 a b d-b^2 c\right)}{\left(a^2+b^2\right)^2}",1,"((a^2*c - b^2*c + 2*a*b*d)*x)/(a^2 + b^2)^2 + ((2*a*b*c - a^2*d + b^2*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*f) - (b*c - a*d)/((a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",3,3,23,0.1304,1,"{3529, 3531, 3530}"
1196,1,175,0,0.2700962,"\int \frac{c+d \tan (e+f x)}{(a+b \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])/(a + b*Tan[e + f*x])^3,x]","-\frac{b c-a d}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{a^2 (-d)+2 a b c+b^2 d}{f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}+\frac{\left(3 a^2 b c+a^3 (-d)+3 a b^2 d-b^3 c\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b d+a^3 c-3 a b^2 c-b^3 d\right)}{\left(a^2+b^2\right)^3}","-\frac{b c-a d}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{a^2 (-d)+2 a b c+b^2 d}{f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}+\frac{\left(3 a^2 b c+a^3 (-d)+3 a b^2 d-b^3 c\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(3 a^2 b d+a^3 c-3 a b^2 c-b^3 d\right)}{\left(a^2+b^2\right)^3}",1,"((a^3*c - 3*a*b^2*c + 3*a^2*b*d - b^3*d)*x)/(a^2 + b^2)^3 + ((3*a^2*b*c - b^3*c - a^3*d + 3*a*b^2*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*f) - (b*c - a*d)/(2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (2*a*b*c - a^2*d + b^2*d)/((a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",4,3,23,0.1304,1,"{3529, 3531, 3530}"
1197,1,215,0,0.2657927,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^2 \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2,x]","-\frac{\left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(6 a^2 b c d+a^3 \left(-\left(c^2-d^2\right)\right)+3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)+\frac{\left(2 a c d+b \left(c^2-d^2\right)\right) (a+b \tan (e+f x))^2}{2 f}+\frac{2 c d (a+b \tan (e+f x))^3}{3 f}+\frac{2 b (a d+b c) (a c-b d) \tan (e+f x)}{f}+\frac{d^2 (a+b \tan (e+f x))^4}{4 b f}","-\frac{\left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(6 a^2 b c d+a^3 \left(-\left(c^2-d^2\right)\right)+3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)+\frac{\left(2 a c d+b \left(c^2-d^2\right)\right) (a+b \tan (e+f x))^2}{2 f}+\frac{2 c d (a+b \tan (e+f x))^3}{3 f}+\frac{2 b (a d+b c) (a c-b d) \tan (e+f x)}{f}+\frac{d^2 (a+b \tan (e+f x))^4}{4 b f}",1,"-((6*a^2*b*c*d - 2*b^3*c*d - a^3*(c^2 - d^2) + 3*a*b^2*(c^2 - d^2))*x) - ((2*a^3*c*d - 6*a*b^2*c*d + 3*a^2*b*(c^2 - d^2) - b^3*(c^2 - d^2))*Log[Cos[e + f*x]])/f + (2*b*(b*c + a*d)*(a*c - b*d)*Tan[e + f*x])/f + ((2*a*c*d + b*(c^2 - d^2))*(a + b*Tan[e + f*x])^2)/(2*f) + (2*c*d*(a + b*Tan[e + f*x])^3)/(3*f) + (d^2*(a + b*Tan[e + f*x])^4)/(4*b*f)","A",5,4,25,0.1600,1,"{3543, 3528, 3525, 3475}"
1198,1,131,0,0.1865995,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2 \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2,x]","\frac{b \left(2 a c d+b \left(c^2-d^2\right)\right) \tan (e+f x)}{f}+\frac{c d (a+b \tan (e+f x))^2}{f}-\frac{2 (a d+b c) (a c-b d) \log (\cos (e+f x))}{f}+x (a c-a d-b c-b d) (a c+a d+b c-b d)+\frac{d^2 (a+b \tan (e+f x))^3}{3 b f}","\frac{b \left(2 a c d+b \left(c^2-d^2\right)\right) \tan (e+f x)}{f}+\frac{c d (a+b \tan (e+f x))^2}{f}-\frac{2 (a d+b c) (a c-b d) \log (\cos (e+f x))}{f}+x (a c-a d-b c-b d) (a c+a d+b c-b d)+\frac{d^2 (a+b \tan (e+f x))^3}{3 b f}",1,"(a*c - b*c - a*d - b*d)*(a*c + b*c + a*d - b*d)*x - (2*(b*c + a*d)*(a*c - b*d)*Log[Cos[e + f*x]])/f + (b*(2*a*c*d + b*(c^2 - d^2))*Tan[e + f*x])/f + (c*d*(a + b*Tan[e + f*x])^2)/f + (d^2*(a + b*Tan[e + f*x])^3)/(3*b*f)","A",4,4,25,0.1600,1,"{3543, 3528, 3525, 3475}"
1199,1,89,0,0.0844995,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^2 \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2,x]","-\frac{\left(2 a c d+b \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(2 b c d-a \left(c^2-d^2\right)\right)+\frac{d (a d+b c) \tan (e+f x)}{f}+\frac{b (c+d \tan (e+f x))^2}{2 f}","-\frac{\left(2 a c d+b \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(2 b c d-a \left(c^2-d^2\right)\right)+\frac{d (a d+b c) \tan (e+f x)}{f}+\frac{b (c+d \tan (e+f x))^2}{2 f}",1,"-((2*b*c*d - a*(c^2 - d^2))*x) - ((2*a*c*d + b*(c^2 - d^2))*Log[Cos[e + f*x]])/f + (d*(b*c + a*d)*Tan[e + f*x])/f + (b*(c + d*Tan[e + f*x])^2)/(2*f)","A",3,3,23,0.1304,1,"{3528, 3525, 3475}"
1200,1,103,0,0.1238442,"\int \frac{(c+d \tan (e+f x))^2}{a+b \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + b*Tan[e + f*x]),x]","\frac{(b c-a d)^2 \log (a \cos (e+f x)+b \sin (e+f x))}{b f \left(a^2+b^2\right)}+\frac{a x (b c-a d)^2}{b^2 \left(a^2+b^2\right)}+\frac{d x (2 b c-a d)}{b^2}-\frac{d^2 \log (\cos (e+f x))}{b f}","\frac{(b c-a d)^2 \log (a \cos (e+f x)+b \sin (e+f x))}{b f \left(a^2+b^2\right)}+\frac{a x (b c-a d)^2}{b^2 \left(a^2+b^2\right)}+\frac{d x (2 b c-a d)}{b^2}-\frac{d^2 \log (\cos (e+f x))}{b f}",1,"(a*(b*c - a*d)^2*x)/(b^2*(a^2 + b^2)) + (d*(2*b*c - a*d)*x)/b^2 - (d^2*Log[Cos[e + f*x]])/(b*f) + ((b*c - a*d)^2*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/(b*(a^2 + b^2)*f)","A",4,4,25,0.1600,1,"{3541, 3475, 3484, 3530}"
1201,1,126,0,0.2315619,"\int \frac{(c+d \tan (e+f x))^2}{(a+b \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + b*Tan[e + f*x])^2,x]","-\frac{(b c-a d)^2}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{2 (a c+b d) (b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2}-\frac{x (b (c-d)-a (c+d)) (a (c-d)+b (c+d))}{\left(a^2+b^2\right)^2}","-\frac{(b c-a d)^2}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{2 (a c+b d) (b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2}-\frac{x (b (c-d)-a (c+d)) (a (c-d)+b (c+d))}{\left(a^2+b^2\right)^2}",1,"-(((b*(c - d) - a*(c + d))*(a*(c - d) + b*(c + d))*x)/(a^2 + b^2)^2) + (2*(b*c - a*d)*(a*c + b*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*f) - (b*c - a*d)^2/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",3,3,25,0.1200,1,"{3542, 3531, 3530}"
1202,1,214,0,0.3572694,"\int \frac{(c+d \tan (e+f x))^2}{(a+b \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^2/(a + b*Tan[e + f*x])^3,x]","-\frac{\left(-3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d+b^3 \left(c^2-d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(6 a^2 b c d+a^3 \left(c^2-d^2\right)-3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(a^2+b^2\right)^3}-\frac{(b c-a d)^2}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{2 (a c+b d) (b c-a d)}{f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}","-\frac{\left(-3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d+b^3 \left(c^2-d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x \left(6 a^2 b c d+a^3 \left(c^2-d^2\right)-3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(a^2+b^2\right)^3}-\frac{(b c-a d)^2}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{2 (a c+b d) (b c-a d)}{f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}",1,"((6*a^2*b*c*d - 2*b^3*c*d + a^3*(c^2 - d^2) - 3*a*b^2*(c^2 - d^2))*x)/(a^2 + b^2)^3 - ((2*a^3*c*d - 6*a*b^2*c*d - 3*a^2*b*(c^2 - d^2) + b^3*(c^2 - d^2))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*f) - (b*c - a*d)^2/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (2*(b*c - a*d)*(a*c + b*d))/((a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",4,4,25,0.1600,1,"{3542, 3529, 3531, 3530}"
1203,1,302,0,0.5124077,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^3 \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^3,x]","\frac{d \left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \tan (e+f x)}{f}+\frac{(a d+b c) \left(a^2 \left(-\left(3 c^2-d^2\right)\right)+8 a b c d+b^2 \left(c^2-3 d^2\right)\right) \log (\cos (e+f x))}{f}-x (a c-b d) \left(a^2 \left(-\left(c^2-3 d^2\right)\right)+8 a b c d+b^2 \left(3 c^2-d^2\right)\right)+\frac{b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^3}{3 f}+\frac{\left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) (c+d \tan (e+f x))^2}{2 f}-\frac{b^2 (b c-11 a d) (c+d \tan (e+f x))^4}{20 d^2 f}+\frac{b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^4}{5 d f}","\frac{d \left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \tan (e+f x)}{f}+\frac{(a d+b c) \left(a^2 \left(-\left(3 c^2-d^2\right)\right)+8 a b c d+b^2 \left(c^2-3 d^2\right)\right) \log (\cos (e+f x))}{f}-x (a c-b d) \left(a^2 \left(-\left(c^2-3 d^2\right)\right)+8 a b c d+b^2 \left(3 c^2-d^2\right)\right)+\frac{b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^3}{3 f}+\frac{\left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) (c+d \tan (e+f x))^2}{2 f}-\frac{b^2 (b c-11 a d) (c+d \tan (e+f x))^4}{20 d^2 f}+\frac{b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^4}{5 d f}",1,"-((a*c - b*d)*(8*a*b*c*d - a^2*(c^2 - 3*d^2) + b^2*(3*c^2 - d^2))*x) + ((b*c + a*d)*(8*a*b*c*d + b^2*(c^2 - 3*d^2) - a^2*(3*c^2 - d^2))*Log[Cos[e + f*x]])/f + (d*(2*a^3*c*d - 6*a*b^2*c*d + 3*a^2*b*(c^2 - d^2) - b^3*(c^2 - d^2))*Tan[e + f*x])/f + ((3*a^2*b*c - b^3*c + a^3*d - 3*a*b^2*d)*(c + d*Tan[e + f*x])^2)/(2*f) + (b*(3*a^2 - b^2)*(c + d*Tan[e + f*x])^3)/(3*f) - (b^2*(b*c - 11*a*d)*(c + d*Tan[e + f*x])^4)/(20*d^2*f) + (b^2*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^4)/(5*d*f)","A",6,5,25,0.2000,1,"{3566, 3630, 3528, 3525, 3475}"
1204,1,219,0,0.2676869,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3 \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3,x]","-\frac{\left(a^2 \left(3 c^2 d-d^3\right)+2 a b c \left(c^2-3 d^2\right)-b^2 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)+2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)+\frac{\left(a^2 d+2 a b c-b^2 d\right) (c+d \tan (e+f x))^2}{2 f}+\frac{2 a b (c+d \tan (e+f x))^3}{3 f}+\frac{2 d (a d+b c) (a c-b d) \tan (e+f x)}{f}+\frac{b^2 (c+d \tan (e+f x))^4}{4 d f}","-\frac{\left(a^2 \left(3 c^2 d-d^3\right)+2 a b c \left(c^2-3 d^2\right)-b^2 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f}-x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)+2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)+\frac{\left(a^2 d+2 a b c-b^2 d\right) (c+d \tan (e+f x))^2}{2 f}+\frac{2 a b (c+d \tan (e+f x))^3}{3 f}+\frac{2 d (a d+b c) (a c-b d) \tan (e+f x)}{f}+\frac{b^2 (c+d \tan (e+f x))^4}{4 d f}",1,"-((b^2*c*(c^2 - 3*d^2) + 2*a*b*d*(3*c^2 - d^2) - a^2*(c^3 - 3*c*d^2))*x) - ((2*a*b*c*(c^2 - 3*d^2) - b^2*d*(3*c^2 - d^2) + a^2*(3*c^2*d - d^3))*Log[Cos[e + f*x]])/f + (2*d*(b*c + a*d)*(a*c - b*d)*Tan[e + f*x])/f + ((2*a*b*c + a^2*d - b^2*d)*(c + d*Tan[e + f*x])^2)/(2*f) + (2*a*b*(c + d*Tan[e + f*x])^3)/(3*f) + (b^2*(c + d*Tan[e + f*x])^4)/(4*d*f)","A",5,4,25,0.1600,1,"{3543, 3528, 3525, 3475}"
1205,1,144,0,0.1714339,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^3 \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^3,x]","\frac{d \left(2 a c d+b \left(c^2-d^2\right)\right) \tan (e+f x)}{f}-\frac{\left(3 a c^2 d-a d^3+b c^3-3 b c d^2\right) \log (\cos (e+f x))}{f}-x \left(b d \left(3 c^2-d^2\right)-a \left(c^3-3 c d^2\right)\right)+\frac{(a d+b c) (c+d \tan (e+f x))^2}{2 f}+\frac{b (c+d \tan (e+f x))^3}{3 f}","\frac{d \left(2 a c d+b \left(c^2-d^2\right)\right) \tan (e+f x)}{f}-\frac{\left(3 a c^2 d-a d^3+b c^3-3 b c d^2\right) \log (\cos (e+f x))}{f}-x \left(b d \left(3 c^2-d^2\right)-a \left(c^3-3 c d^2\right)\right)+\frac{(a d+b c) (c+d \tan (e+f x))^2}{2 f}+\frac{b (c+d \tan (e+f x))^3}{3 f}",1,"-((b*d*(3*c^2 - d^2) - a*(c^3 - 3*c*d^2))*x) - ((b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3)*Log[Cos[e + f*x]])/f + (d*(2*a*c*d + b*(c^2 - d^2))*Tan[e + f*x])/f + ((b*c + a*d)*(c + d*Tan[e + f*x])^2)/(2*f) + (b*(c + d*Tan[e + f*x])^3)/(3*f)","A",4,3,23,0.1304,1,"{3528, 3525, 3475}"
1206,1,140,0,0.2817578,"\int \frac{(c+d \tan (e+f x))^3}{a+b \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + b*Tan[e + f*x]),x]","\frac{\left(-3 a c^2 d+a d^3+b c^3-3 b c d^2\right) \log (\cos (e+f x))}{f \left(a^2+b^2\right)}+\frac{x \left(a c^3-3 a c d^2+3 b c^2 d-b d^3\right)}{a^2+b^2}+\frac{(b c-a d)^3 \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)}+\frac{d^2 (c+d \tan (e+f x))}{b f}","\frac{\left(-3 a c^2 d+a d^3+b c^3-3 b c d^2\right) \log (\cos (e+f x))}{f \left(a^2+b^2\right)}+\frac{x \left(a c^3-3 a c d^2+3 b c^2 d-b d^3\right)}{a^2+b^2}+\frac{(b c-a d)^3 \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)}+\frac{d^2 (c+d \tan (e+f x))}{b f}",1,"((a*c^3 + 3*b*c^2*d - 3*a*c*d^2 - b*d^3)*x)/(a^2 + b^2) + ((b*c^3 - 3*a*c^2*d - 3*b*c*d^2 + a*d^3)*Log[Cos[e + f*x]])/((a^2 + b^2)*f) + ((b*c - a*d)^3*Log[a + b*Tan[e + f*x]])/(b^2*(a^2 + b^2)*f) + (d^2*(c + d*Tan[e + f*x]))/(b*f)","A",5,5,25,0.2000,1,"{3566, 3626, 3617, 31, 3475}"
1207,1,230,0,0.3416539,"\int \frac{(c+d \tan (e+f x))^3}{(a+b \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + b*Tan[e + f*x])^2,x]","\frac{\left(a^2 \left(-\left(3 c^2 d-d^3\right)\right)+2 a b c \left(c^2-3 d^2\right)+b^2 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)-2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{(b c-a d)^2 (c+d \tan (e+f x))}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(a^2 d+2 a b c+3 b^2 d\right) (b c-a d)^2 \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)^2}","\frac{\left(a^2 \left(-\left(3 c^2 d-d^3\right)\right)+2 a b c \left(c^2-3 d^2\right)+b^2 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(a^2+b^2\right)^2}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)-2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(a^2+b^2\right)^2}-\frac{(b c-a d)^2 (c+d \tan (e+f x))}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}+\frac{\left(a^2 d+2 a b c+3 b^2 d\right) (b c-a d)^2 \log (a+b \tan (e+f x))}{b^2 f \left(a^2+b^2\right)^2}",1,"-(((b^2*c*(c^2 - 3*d^2) - 2*a*b*d*(3*c^2 - d^2) - a^2*(c^3 - 3*c*d^2))*x)/(a^2 + b^2)^2) + ((2*a*b*c*(c^2 - 3*d^2) + b^2*d*(3*c^2 - d^2) - a^2*(3*c^2*d - d^3))*Log[Cos[e + f*x]])/((a^2 + b^2)^2*f) + ((b*c - a*d)^2*(2*a*b*c + a^2*d + 3*b^2*d)*Log[a + b*Tan[e + f*x]])/(b^2*(a^2 + b^2)^2*f) - ((b*c - a*d)^2*(c + d*Tan[e + f*x]))/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",5,5,25,0.2000,1,"{3565, 3626, 3617, 31, 3475}"
1208,1,239,0,0.5115002,"\int \frac{(c+d \tan (e+f x))^3}{(a+b \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^3/(a + b*Tan[e + f*x])^3,x]","\frac{\left(a^2 \left(3 c^2-d^2\right)+8 a b c d-b^2 \left(c^2-3 d^2\right)\right) (b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x (a c+b d) \left(a^2 \left(c^2-3 d^2\right)+8 a b c d-b^2 \left(3 c^2-d^2\right)\right)}{\left(a^2+b^2\right)^3}-\frac{(b c-a d)^2 (c+d \tan (e+f x))}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\left(a^2 d+4 a b c+5 b^2 d\right) (b c-a d)^2}{2 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}","\frac{\left(a^2 \left(3 c^2-d^2\right)+8 a b c d-b^2 \left(c^2-3 d^2\right)\right) (b c-a d) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3}+\frac{x (a c+b d) \left(a^2 \left(c^2-3 d^2\right)+8 a b c d-b^2 \left(3 c^2-d^2\right)\right)}{\left(a^2+b^2\right)^3}-\frac{(b c-a d)^2 (c+d \tan (e+f x))}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\left(a^2 d+4 a b c+5 b^2 d\right) (b c-a d)^2}{2 b^2 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}",1,"((a*c + b*d)*(8*a*b*c*d + a^2*(c^2 - 3*d^2) - b^2*(3*c^2 - d^2))*x)/(a^2 + b^2)^3 + ((b*c - a*d)*(8*a*b*c*d - b^2*(c^2 - 3*d^2) + a^2*(3*c^2 - d^2))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*f) - ((b*c - a*d)^2*(4*a*b*c + a^2*d + 5*b^2*d))/(2*b^2*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])) - ((b*c - a*d)^2*(c + d*Tan[e + f*x]))/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2)","A",4,4,25,0.1600,1,"{3565, 3628, 3531, 3530}"
1209,1,190,0,0.4911243,"\int \frac{(a+b \tan (e+f x))^4}{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x]),x]","-\frac{\left(6 a^2 b^2 d+4 a^3 b c+a^4 (-d)-4 a b^3 c-b^4 d\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x \left(-6 a^2 b^2 c+4 a^3 b d+a^4 c-4 a b^3 d+b^4 c\right)}{c^2+d^2}-\frac{b^3 (b c-3 a d) \tan (e+f x)}{d^2 f}+\frac{b^2 (a+b \tan (e+f x))^2}{2 d f}+\frac{(b c-a d)^4 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)}","-\frac{\left(6 a^2 b^2 d+4 a^3 b c+a^4 (-d)-4 a b^3 c-b^4 d\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x \left(-6 a^2 b^2 c+4 a^3 b d+a^4 c-4 a b^3 d+b^4 c\right)}{c^2+d^2}-\frac{b^3 (b c-3 a d) \tan (e+f x)}{d^2 f}+\frac{b^2 (a+b \tan (e+f x))^2}{2 d f}+\frac{(b c-a d)^4 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)}",1,"((a^4*c - 6*a^2*b^2*c + b^4*c + 4*a^3*b*d - 4*a*b^3*d)*x)/(c^2 + d^2) - ((4*a^3*b*c - 4*a*b^3*c - a^4*d + 6*a^2*b^2*d - b^4*d)*Log[Cos[e + f*x]])/((c^2 + d^2)*f) + ((b*c - a*d)^4*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)*f) - (b^3*(b*c - 3*a*d)*Tan[e + f*x])/(d^2*f) + (b^2*(a + b*Tan[e + f*x])^2)/(2*d*f)","A",6,6,25,0.2400,1,"{3566, 3637, 3626, 3617, 31, 3475}"
1210,1,144,0,0.2681875,"\int \frac{(a+b \tan (e+f x))^3}{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^3/(c + d*Tan[e + f*x]),x]","-\frac{\left(3 a^2 b c+a^3 (-d)+3 a b^2 d-b^3 c\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x \left(3 a^2 b d+a^3 c-3 a b^2 c-b^3 d\right)}{c^2+d^2}+\frac{b^2 (a+b \tan (e+f x))}{d f}-\frac{(b c-a d)^3 \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)}","-\frac{\left(3 a^2 b c+a^3 (-d)+3 a b^2 d-b^3 c\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)}+\frac{x \left(3 a^2 b d+a^3 c-3 a b^2 c-b^3 d\right)}{c^2+d^2}+\frac{b^2 (a+b \tan (e+f x))}{d f}-\frac{(b c-a d)^3 \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)}",1,"((a^3*c - 3*a*b^2*c + 3*a^2*b*d - b^3*d)*x)/(c^2 + d^2) - ((3*a^2*b*c - b^3*c - a^3*d + 3*a*b^2*d)*Log[Cos[e + f*x]])/((c^2 + d^2)*f) - ((b*c - a*d)^3*Log[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)*f) + (b^2*(a + b*Tan[e + f*x]))/(d*f)","A",5,5,25,0.2000,1,"{3566, 3626, 3617, 31, 3475}"
1211,1,103,0,0.1178469,"\int \frac{(a+b \tan (e+f x))^2}{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^2/(c + d*Tan[e + f*x]),x]","\frac{(b c-a d)^2 \log (c \cos (e+f x)+d \sin (e+f x))}{d f \left(c^2+d^2\right)}+\frac{c x (b c-a d)^2}{d^2 \left(c^2+d^2\right)}-\frac{b x (b c-2 a d)}{d^2}-\frac{b^2 \log (\cos (e+f x))}{d f}","\frac{(b c-a d)^2 \log (c \cos (e+f x)+d \sin (e+f x))}{d f \left(c^2+d^2\right)}+\frac{c x (b c-a d)^2}{d^2 \left(c^2+d^2\right)}-\frac{b x (b c-2 a d)}{d^2}-\frac{b^2 \log (\cos (e+f x))}{d f}",1,"-((b*(b*c - 2*a*d)*x)/d^2) + (c*(b*c - a*d)^2*x)/(d^2*(c^2 + d^2)) - (b^2*Log[Cos[e + f*x]])/(d*f) + ((b*c - a*d)^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/(d*(c^2 + d^2)*f)","A",4,4,25,0.1600,1,"{3541, 3475, 3484, 3530}"
1212,1,59,0,0.0716156,"\int \frac{a+b \tan (e+f x)}{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])/(c + d*Tan[e + f*x]),x]","\frac{x (a c+b d)}{c^2+d^2}-\frac{(b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)}","\frac{x (a c+b d)}{c^2+d^2}-\frac{(b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)}",1,"((a*c + b*d)*x)/(c^2 + d^2) - ((b*c - a*d)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)*f)","A",2,2,23,0.08696,1,"{3531, 3530}"
1213,1,118,0,0.1452145,"\int \frac{1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))} \, dx","Int[1/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])),x]","\frac{x (a c-b d)}{\left(a^2+b^2\right) \left(c^2+d^2\right)}+\frac{b^2 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)}-\frac{d^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)}","\frac{x (a c-b d)}{\left(a^2+b^2\right) \left(c^2+d^2\right)}+\frac{b^2 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)}-\frac{d^2 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)}",1,"((a*c - b*d)*x)/((a^2 + b^2)*(c^2 + d^2)) + (b^2*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f) - (d^2*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)*(c^2 + d^2)*f)","A",3,2,25,0.08000,1,"{3571, 3530}"
1214,1,183,0,0.4632192,"\int \frac{1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))} \, dx","Int[1/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])),x]","\frac{x \left(a^2 c-2 a b d-b^2 c\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}+\frac{b^2 \left(-3 a^2 d+2 a b c-b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^2}+\frac{d^3 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^2}","\frac{x \left(a^2 c-2 a b d-b^2 c\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}+\frac{b^2 \left(-3 a^2 d+2 a b c-b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^2}+\frac{d^3 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^2}",1,"((a^2*c - b^2*c - 2*a*b*d)*x)/((a^2 + b^2)^2*(c^2 + d^2)) + (b^2*(2*a*b*c - 3*a^2*d - b^2*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^2*f) + (d^3*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^2*(c^2 + d^2)*f) - b^2/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",4,3,25,0.1200,1,"{3569, 3651, 3530}"
1215,1,279,0,0.9258309,"\int \frac{1}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))} \, dx","Int[1/((a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])),x]","-\frac{b^2 \left(-3 a^2 b^2 \left(c^2+d^2\right)+8 a^3 b c d-6 a^4 d^2+b^4 \left(c^2-d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^3}+\frac{x \left(-3 a^2 b d+a^3 c-3 a b^2 c+b^3 d\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)}-\frac{b^2 \left(-3 a^2 d+2 a b c-b^2 d\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x))}-\frac{b^2}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2}-\frac{d^4 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^3}","-\frac{b^2 \left(-3 a^2 b^2 \left(c^2+d^2\right)+8 a^3 b c d-6 a^4 d^2+b^4 \left(c^2-d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^3}+\frac{x \left(-3 a^2 b d+a^3 c-3 a b^2 c+b^3 d\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)}-\frac{b^2 \left(-3 a^2 d+2 a b c-b^2 d\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x))}-\frac{b^2}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2}-\frac{d^4 \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right) (b c-a d)^3}",1,"((a^3*c - 3*a*b^2*c - 3*a^2*b*d + b^3*d)*x)/((a^2 + b^2)^3*(c^2 + d^2)) - (b^2*(8*a^3*b*c*d - 6*a^4*d^2 + b^4*(c^2 - d^2) - 3*a^2*b^2*(c^2 + d^2))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*(b*c - a*d)^3*f) - (d^4*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)*f) - b^2/(2*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2) - (b^2*(2*a*b*c - 3*a^2*d - b^2*d))/((a^2 + b^2)^2*(b*c - a*d)^2*f*(a + b*Tan[e + f*x]))","A",5,4,25,0.1600,1,"{3569, 3649, 3651, 3530}"
1216,1,285,0,0.8042431,"\int \frac{(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^2} \, dx","Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^2,x]","-\frac{2 \left(a^2 c+2 a b d-b^2 c\right) \left(a^2 (-d)+2 a b c+b^2 d\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(-6 a^2 b^2 \left(c^2-d^2\right)+8 a^3 b c d+a^4 \left(c^2-d^2\right)-8 a b^3 c d+b^4 \left(c^2-d^2\right)\right)}{\left(c^2+d^2\right)^2}-\frac{b^2 \left(a d (2 b c-a d)-b^2 \left(2 c^2+d^2\right)\right) \tan (e+f x)}{d^2 f \left(c^2+d^2\right)}-\frac{(b c-a d)^2 (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{2 \left(a c d+b \left(c^2+2 d^2\right)\right) (b c-a d)^3 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^2}","-\frac{2 \left(a^2 c+2 a b d-b^2 c\right) \left(a^2 (-d)+2 a b c+b^2 d\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(-6 a^2 b^2 \left(c^2-d^2\right)+8 a^3 b c d+a^4 \left(c^2-d^2\right)-8 a b^3 c d+b^4 \left(c^2-d^2\right)\right)}{\left(c^2+d^2\right)^2}-\frac{b^2 \left(a d (2 b c-a d)-b^2 \left(2 c^2+d^2\right)\right) \tan (e+f x)}{d^2 f \left(c^2+d^2\right)}-\frac{(b c-a d)^2 (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{2 \left(a c d+b \left(c^2+2 d^2\right)\right) (b c-a d)^3 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^2}",1,"((8*a^3*b*c*d - 8*a*b^3*c*d + a^4*(c^2 - d^2) - 6*a^2*b^2*(c^2 - d^2) + b^4*(c^2 - d^2))*x)/(c^2 + d^2)^2 - (2*(a^2*c - b^2*c + 2*a*b*d)*(2*a*b*c - a^2*d + b^2*d)*Log[Cos[e + f*x]])/((c^2 + d^2)^2*f) - (2*(b*c - a*d)^3*(a*c*d + b*(c^2 + 2*d^2))*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^2*f) - (b^2*(a*d*(2*b*c - a*d) - b^2*(2*c^2 + d^2))*Tan[e + f*x])/(d^2*(c^2 + d^2)*f) - ((b*c - a*d)^2*(a + b*Tan[e + f*x])^2)/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",6,6,25,0.2400,1,"{3565, 3637, 3626, 3617, 31, 3475}"
1217,1,223,0,0.3638165,"\int \frac{(a+b \tan (e+f x))^3}{(c+d \tan (e+f x))^2} \, dx","Int[(a + b*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^2,x]","\frac{\left(-3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d+b^3 \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(6 a^2 b c d+a^3 \left(c^2-d^2\right)-3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(c^2+d^2\right)^2}-\frac{(b c-a d)^2 (a+b \tan (e+f x))}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 a c d+b \left(c^2+3 d^2\right)\right) (b c-a d)^2 \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)^2}","\frac{\left(-3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d+b^3 \left(c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(6 a^2 b c d+a^3 \left(c^2-d^2\right)-3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(c^2+d^2\right)^2}-\frac{(b c-a d)^2 (a+b \tan (e+f x))}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 a c d+b \left(c^2+3 d^2\right)\right) (b c-a d)^2 \log (c+d \tan (e+f x))}{d^2 f \left(c^2+d^2\right)^2}",1,"((6*a^2*b*c*d - 2*b^3*c*d + a^3*(c^2 - d^2) - 3*a*b^2*(c^2 - d^2))*x)/(c^2 + d^2)^2 + ((2*a^3*c*d - 6*a*b^2*c*d - 3*a^2*b*(c^2 - d^2) + b^3*(c^2 - d^2))*Log[Cos[e + f*x]])/((c^2 + d^2)^2*f) + ((b*c - a*d)^2*(2*a*c*d + b*(c^2 + 3*d^2))*Log[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)^2*f) - ((b*c - a*d)^2*(a + b*Tan[e + f*x]))/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",5,5,25,0.2000,1,"{3565, 3626, 3617, 31, 3475}"
1218,1,126,0,0.2227067,"\int \frac{(a+b \tan (e+f x))^2}{(c+d \tan (e+f x))^2} \, dx","Int[(a + b*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^2,x]","-\frac{(b c-a d)^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{2 (a c+b d) (b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}-\frac{x (b (c-d)-a (c+d)) (a (c-d)+b (c+d))}{\left(c^2+d^2\right)^2}","-\frac{(b c-a d)^2}{d f \left(c^2+d^2\right) (c+d \tan (e+f x))}-\frac{2 (a c+b d) (b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}-\frac{x (b (c-d)-a (c+d)) (a (c-d)+b (c+d))}{\left(c^2+d^2\right)^2}",1,"-(((b*(c - d) - a*(c + d))*(a*(c - d) + b*(c + d))*x)/(c^2 + d^2)^2) - (2*(b*c - a*d)*(a*c + b*d)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^2*f) - (b*c - a*d)^2/(d*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",3,3,25,0.1200,1,"{3542, 3531, 3530}"
1219,1,111,0,0.1533368,"\int \frac{a+b \tan (e+f x)}{(c+d \tan (e+f x))^2} \, dx","Int[(a + b*Tan[e + f*x])/(c + d*Tan[e + f*x])^2,x]","\frac{b c-a d}{f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 a c d-b \left(c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(a \left(c^2-d^2\right)+2 b c d\right)}{\left(c^2+d^2\right)^2}","\frac{b c-a d}{f \left(c^2+d^2\right) (c+d \tan (e+f x))}+\frac{\left(2 a c d-b \left(c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2}+\frac{x \left(a \left(c^2-d^2\right)+2 b c d\right)}{\left(c^2+d^2\right)^2}",1,"((2*b*c*d + a*(c^2 - d^2))*x)/(c^2 + d^2)^2 + ((2*a*c*d - b*(c^2 - d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^2*f) + (b*c - a*d)/((c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",3,3,23,0.1304,1,"{3529, 3531, 3530}"
1220,1,184,0,0.5079707,"\int \frac{1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^2} \, dx","Int[1/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2),x]","-\frac{x \left(2 b c d-a \left(c^2-d^2\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^2}+\frac{b^3 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^2}+\frac{d^2}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^2}","-\frac{x \left(2 b c d-a \left(c^2-d^2\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^2}+\frac{b^3 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^2}+\frac{d^2}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^2}",1,"-(((2*b*c*d - a*(c^2 - d^2))*x)/((a^2 + b^2)*(c^2 + d^2)^2)) + (b^3*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^2*f) + (d^2*(2*a*c*d - b*(3*c^2 + d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^2*(c^2 + d^2)^2*f) + d^2/((b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",4,3,25,0.1200,1,"{3569, 3651, 3530}"
1221,1,290,0,1.0309354,"\int \frac{1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^2} \, dx","Int[1/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^2),x]","-\frac{d \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))}+\frac{x (a (c+d)+b (c-d)) (a (c-d)-b (c+d))}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))}+\frac{2 b^3 \left(-2 a^2 d+a b c-b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^3}-\frac{2 d^3 \left(a c d-b \left(2 c^2+d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^3}","-\frac{d \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))}+\frac{x (a (c+d)+b (c-d)) (a (c-d)-b (c+d))}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))}+\frac{2 b^3 \left(-2 a^2 d+a b c-b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^3}-\frac{2 d^3 \left(a c d-b \left(2 c^2+d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^3}",1,"((b*(c - d) + a*(c + d))*(a*(c - d) - b*(c + d))*x)/((a^2 + b^2)^2*(c^2 + d^2)^2) + (2*b^3*(a*b*c - 2*a^2*d - b^2*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^3*f) - (2*d^3*(a*c*d - b*(2*c^2 + d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)^2*f) - (d*(a^2*d^2 + b^2*(c^2 + 2*d^2)))/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])) - b^2/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",5,4,25,0.1600,1,"{3569, 3649, 3651, 3530}"
1222,1,457,0,1.8046853,"\int \frac{1}{(a+b \tan (e+f x))^3 (c+d \tan (e+f x))^2} \, dx","Int[1/((a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^2),x]","\frac{d \left(2 a^2 b^2 d \left(2 c^2+3 d^2\right)+a^4 d^3-2 a b^3 c \left(c^2+d^2\right)+b^4 d \left(2 c^2+3 d^2\right)\right)}{f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 (c+d \tan (e+f x))}-\frac{b^3 \left(-3 a^2 b^2 \left(c^2+3 d^2\right)+10 a^3 b c d-10 a^4 d^2+2 a b^3 c d+b^4 \left(c^2-3 d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^4}-\frac{x \left(6 a^2 b c d+a^3 \left(-\left(c^2-d^2\right)\right)+3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)^2}-\frac{b^2 \left(-7 a^2 d+4 a b c-3 b^2 d\right)}{2 f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))}-\frac{b^2}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))}-\frac{d^4 \left(-2 a c d+5 b c^2+3 b d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^4}","\frac{d \left(2 a^2 b^2 d \left(2 c^2+3 d^2\right)+a^4 d^3-2 a b^3 c \left(c^2+d^2\right)+b^4 d \left(2 c^2+3 d^2\right)\right)}{f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 (c+d \tan (e+f x))}-\frac{b^3 \left(-3 a^2 b^2 \left(c^2+3 d^2\right)+10 a^3 b c d-10 a^4 d^2+2 a b^3 c d+b^4 \left(c^2-3 d^2\right)\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^3 (b c-a d)^4}-\frac{x \left(6 a^2 b c d+a^3 \left(-\left(c^2-d^2\right)\right)+3 a b^2 \left(c^2-d^2\right)-2 b^3 c d\right)}{\left(a^2+b^2\right)^3 \left(c^2+d^2\right)^2}-\frac{b^2 \left(-7 a^2 d+4 a b c-3 b^2 d\right)}{2 f \left(a^2+b^2\right)^2 (b c-a d)^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))}-\frac{b^2}{2 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^2 (c+d \tan (e+f x))}-\frac{d^4 \left(-2 a c d+5 b c^2+3 b d^2\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^2 (b c-a d)^4}",1,"-(((6*a^2*b*c*d - 2*b^3*c*d - a^3*(c^2 - d^2) + 3*a*b^2*(c^2 - d^2))*x)/((a^2 + b^2)^3*(c^2 + d^2)^2)) - (b^3*(10*a^3*b*c*d + 2*a*b^3*c*d - 10*a^4*d^2 + b^4*(c^2 - 3*d^2) - 3*a^2*b^2*(c^2 + 3*d^2))*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^3*(b*c - a*d)^4*f) - (d^4*(5*b*c^2 - 2*a*c*d + 3*b*d^2)*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^4*(c^2 + d^2)^2*f) + (d*(a^4*d^3 - 2*a*b^3*c*(c^2 + d^2) + 2*a^2*b^2*d*(2*c^2 + 3*d^2) + b^4*d*(2*c^2 + 3*d^2)))/((a^2 + b^2)^2*(b*c - a*d)^3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])) - b^2/(2*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])) - (b^2*(4*a*b*c - 7*a^2*d - 3*b^2*d))/(2*(a^2 + b^2)^2*(b*c - a*d)^2*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x]))","A",6,4,25,0.1600,1,"{3569, 3649, 3651, 3530}"
1223,1,406,0,0.775519,"\int \frac{(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^3} \, dx","Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^3,x]","\frac{\left(a^2 d^2 \left(3 c^2-d^2\right)+2 a b c d \left(c^2+5 d^2\right)+b^2 \left(3 c^2 d^2+c^4+6 d^4\right)\right) (b c-a d)^2 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^3}-\frac{\left(6 a^2 b^2 d \left(3 c^2-d^2\right)+4 a^3 b c \left(c^2-3 d^2\right)+a^4 \left(-\left(3 c^2 d-d^3\right)\right)-4 a b^3 c \left(c^2-3 d^2\right)-b^4 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(6 a^2 b^2 c \left(c^2-3 d^2\right)-4 a^3 b d \left(3 c^2-d^2\right)+a^4 \left(-\left(c^3-3 c d^2\right)\right)+4 a b^3 d \left(3 c^2-d^2\right)-b^4 c \left(c^2-3 d^2\right)\right)}{\left(c^2+d^2\right)^3}+\frac{\left(2 a c d+b \left(c^2+3 d^2\right)\right) (b c-a d)^3}{d^3 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{(b c-a d)^2 (a+b \tan (e+f x))^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}","\frac{\left(a^2 d^2 \left(3 c^2-d^2\right)+2 a b c d \left(c^2+5 d^2\right)+b^2 \left(3 c^2 d^2+c^4+6 d^4\right)\right) (b c-a d)^2 \log (c+d \tan (e+f x))}{d^3 f \left(c^2+d^2\right)^3}-\frac{\left(6 a^2 b^2 d \left(3 c^2-d^2\right)+4 a^3 b c \left(c^2-3 d^2\right)+a^4 \left(-\left(3 c^2 d-d^3\right)\right)-4 a b^3 c \left(c^2-3 d^2\right)-b^4 d \left(3 c^2-d^2\right)\right) \log (\cos (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(6 a^2 b^2 c \left(c^2-3 d^2\right)-4 a^3 b d \left(3 c^2-d^2\right)+a^4 \left(-\left(c^3-3 c d^2\right)\right)+4 a b^3 d \left(3 c^2-d^2\right)-b^4 c \left(c^2-3 d^2\right)\right)}{\left(c^2+d^2\right)^3}+\frac{\left(2 a c d+b \left(c^2+3 d^2\right)\right) (b c-a d)^3}{d^3 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{(b c-a d)^2 (a+b \tan (e+f x))^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}",1,"-(((6*a^2*b^2*c*(c^2 - 3*d^2) - b^4*c*(c^2 - 3*d^2) - 4*a^3*b*d*(3*c^2 - d^2) + 4*a*b^3*d*(3*c^2 - d^2) - a^4*(c^3 - 3*c*d^2))*x)/(c^2 + d^2)^3) - ((4*a^3*b*c*(c^2 - 3*d^2) - 4*a*b^3*c*(c^2 - 3*d^2) + 6*a^2*b^2*d*(3*c^2 - d^2) - b^4*d*(3*c^2 - d^2) - a^4*(3*c^2*d - d^3))*Log[Cos[e + f*x]])/((c^2 + d^2)^3*f) + ((b*c - a*d)^2*(a^2*d^2*(3*c^2 - d^2) + 2*a*b*c*d*(c^2 + 5*d^2) + b^2*(c^4 + 3*c^2*d^2 + 6*d^4))*Log[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^3*f) - ((b*c - a*d)^2*(a + b*Tan[e + f*x])^2)/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) + ((b*c - a*d)^3*(2*a*c*d + b*(c^2 + 3*d^2)))/(d^3*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",6,6,25,0.2400,1,"{3565, 3635, 3626, 3617, 31, 3475}"
1224,1,240,0,0.5173567,"\int \frac{(a+b \tan (e+f x))^3}{(c+d \tan (e+f x))^3} \, dx","Int[(a + b*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^3,x]","-\frac{\left(a^2 \left(3 c^2-d^2\right)+8 a b c d-b^2 \left(c^2-3 d^2\right)\right) (b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}+\frac{x (a c+b d) \left(a^2 \left(c^2-3 d^2\right)+8 a b c d-b^2 \left(3 c^2-d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{\left(4 a c d+b \left(c^2+5 d^2\right)\right) (b c-a d)^2}{2 d^2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{(b c-a d)^2 (a+b \tan (e+f x))}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}","-\frac{\left(a^2 \left(3 c^2-d^2\right)+8 a b c d-b^2 \left(c^2-3 d^2\right)\right) (b c-a d) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}+\frac{x (a c+b d) \left(a^2 \left(c^2-3 d^2\right)+8 a b c d-b^2 \left(3 c^2-d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{\left(4 a c d+b \left(c^2+5 d^2\right)\right) (b c-a d)^2}{2 d^2 f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}-\frac{(b c-a d)^2 (a+b \tan (e+f x))}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}",1,"((a*c + b*d)*(8*a*b*c*d + a^2*(c^2 - 3*d^2) - b^2*(3*c^2 - d^2))*x)/(c^2 + d^2)^3 - ((b*c - a*d)*(8*a*b*c*d - b^2*(c^2 - 3*d^2) + a^2*(3*c^2 - d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^3*f) - ((b*c - a*d)^2*(a + b*Tan[e + f*x]))/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - ((b*c - a*d)^2*(4*a*c*d + b*(c^2 + 5*d^2)))/(2*d^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",4,4,25,0.1600,1,"{3565, 3628, 3531, 3530}"
1225,1,221,0,0.4068763,"\int \frac{(a+b \tan (e+f x))^2}{(c+d \tan (e+f x))^3} \, dx","Int[(a + b*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^3,x]","-\frac{\left(a^2 \left(-\left(3 c^2 d-d^3\right)\right)+2 a b c \left(c^2-3 d^2\right)+b^2 d \left(3 c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)-2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{(b c-a d)^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}+\frac{2 (a c+b d) (b c-a d)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}","-\frac{\left(a^2 \left(-\left(3 c^2 d-d^3\right)\right)+2 a b c \left(c^2-3 d^2\right)+b^2 d \left(3 c^2-d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)-2 a b d \left(3 c^2-d^2\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(c^2+d^2\right)^3}-\frac{(b c-a d)^2}{2 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}+\frac{2 (a c+b d) (b c-a d)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}",1,"-(((b^2*c*(c^2 - 3*d^2) - 2*a*b*d*(3*c^2 - d^2) - a^2*(c^3 - 3*c*d^2))*x)/(c^2 + d^2)^3) - ((2*a*b*c*(c^2 - 3*d^2) + b^2*d*(3*c^2 - d^2) - a^2*(3*c^2*d - d^3))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^3*f) - (b*c - a*d)^2/(2*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) + (2*(b*c - a*d)*(a*c + b*d))/((c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",4,4,25,0.1600,1,"{3542, 3529, 3531, 3530}"
1226,1,177,0,0.2908422,"\int \frac{a+b \tan (e+f x)}{(c+d \tan (e+f x))^3} \, dx","Int[(a + b*Tan[e + f*x])/(c + d*Tan[e + f*x])^3,x]","\frac{b c-a d}{2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{2 a c d-b \left(c^2-d^2\right)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(a d \left(3 c^2-d^2\right)-b \left(c^3-3 c d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}+\frac{x \left(a c^3-3 a c d^2+3 b c^2 d-b d^3\right)}{\left(c^2+d^2\right)^3}","\frac{b c-a d}{2 f \left(c^2+d^2\right) (c+d \tan (e+f x))^2}-\frac{2 a c d-b \left(c^2-d^2\right)}{f \left(c^2+d^2\right)^2 (c+d \tan (e+f x))}+\frac{\left(a d \left(3 c^2-d^2\right)-b \left(c^3-3 c d^2\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3}+\frac{x \left(a c^3-3 a c d^2+3 b c^2 d-b d^3\right)}{\left(c^2+d^2\right)^3}",1,"((a*c^3 + 3*b*c^2*d - 3*a*c*d^2 - b*d^3)*x)/(c^2 + d^2)^3 + ((a*d*(3*c^2 - d^2) - b*(c^3 - 3*c*d^2))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((c^2 + d^2)^3*f) + (b*c - a*d)/(2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (2*a*c*d - b*(c^2 - d^2))/((c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",4,3,23,0.1304,1,"{3529, 3531, 3530}"
1227,1,286,0,0.9676968,"\int \frac{1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^3} \, dx","Int[1/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^3),x]","\frac{d^2 \left(-a^2 d^2 \left(3 c^2-d^2\right)+8 a b c^3 d-b^2 \left(3 c^2 d^2+6 c^4+d^4\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{x \left(b d \left(3 c^2-d^2\right)-a \left(c^3-3 c d^2\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^3}+\frac{b^4 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^3}-\frac{d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{d^2}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}","\frac{d^2 \left(-a^2 d^2 \left(3 c^2-d^2\right)+8 a b c^3 d-b^2 \left(3 c^2 d^2+6 c^4+d^4\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{x \left(b d \left(3 c^2-d^2\right)-a \left(c^3-3 c d^2\right)\right)}{\left(a^2+b^2\right) \left(c^2+d^2\right)^3}+\frac{b^4 \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right) (b c-a d)^3}-\frac{d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{d^2}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}",1,"-(((b*d*(3*c^2 - d^2) - a*(c^3 - 3*c*d^2))*x)/((a^2 + b^2)*(c^2 + d^2)^3)) + (b^4*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^3*f) + (d^2*(8*a*b*c^3*d - a^2*d^2*(3*c^2 - d^2) - b^2*(6*c^4 + 3*c^2*d^2 + d^4))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^3*(c^2 + d^2)^3*f) + d^2/(2*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (d^2*(2*a*c*d - b*(3*c^2 + d^2)))/((b*c - a*d)^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",5,4,25,0.1600,1,"{3569, 3649, 3651, 3530}"
1228,1,457,0,1.8749879,"\int \frac{1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^3} \, dx","Int[1/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^3),x]","\frac{d \left(-2 a^2 b d^2 \left(2 c^2+d^2\right)+2 a^3 c d^3+2 a b^2 c d^3+b^3 \left(-\left(6 c^2 d^2+c^4+3 d^4\right)\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 (c+d \tan (e+f x))}-\frac{d \left(a^2 d^2+b^2 \left(2 c^2+3 d^2\right)\right)}{2 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^2}+\frac{d^3 \left(a^2 d^2 \left(3 c^2-d^2\right)-2 a b c d \left(5 c^2+d^2\right)+b^2 \left(9 c^2 d^2+10 c^4+3 d^4\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^4}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)+a b \left(6 c^2 d-2 d^3\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^3}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}+\frac{b^4 \left(-5 a^2 d+2 a b c-3 b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^4}","\frac{d \left(-2 a^2 b d^2 \left(2 c^2+d^2\right)+2 a^3 c d^3+2 a b^2 c d^3+b^3 \left(-\left(6 c^2 d^2+c^4+3 d^4\right)\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 (c+d \tan (e+f x))}-\frac{d \left(a^2 d^2+b^2 \left(2 c^2+3 d^2\right)\right)}{2 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^2}+\frac{d^3 \left(a^2 d^2 \left(3 c^2-d^2\right)-2 a b c d \left(5 c^2+d^2\right)+b^2 \left(9 c^2 d^2+10 c^4+3 d^4\right)\right) \log (c \cos (e+f x)+d \sin (e+f x))}{f \left(c^2+d^2\right)^3 (b c-a d)^4}-\frac{x \left(a^2 \left(-\left(c^3-3 c d^2\right)\right)+a b \left(6 c^2 d-2 d^3\right)+b^2 c \left(c^2-3 d^2\right)\right)}{\left(a^2+b^2\right)^2 \left(c^2+d^2\right)^3}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^2}+\frac{b^4 \left(-5 a^2 d+2 a b c-3 b^2 d\right) \log (a \cos (e+f x)+b \sin (e+f x))}{f \left(a^2+b^2\right)^2 (b c-a d)^4}",1,"-(((b^2*c*(c^2 - 3*d^2) - a^2*(c^3 - 3*c*d^2) + a*b*(6*c^2*d - 2*d^3))*x)/((a^2 + b^2)^2*(c^2 + d^2)^3)) + (b^4*(2*a*b*c - 5*a^2*d - 3*b^2*d)*Log[a*Cos[e + f*x] + b*Sin[e + f*x]])/((a^2 + b^2)^2*(b*c - a*d)^4*f) + (d^3*(a^2*d^2*(3*c^2 - d^2) - 2*a*b*c*d*(5*c^2 + d^2) + b^2*(10*c^4 + 9*c^2*d^2 + 3*d^4))*Log[c*Cos[e + f*x] + d*Sin[e + f*x]])/((b*c - a*d)^4*(c^2 + d^2)^3*f) - (d*(a^2*d^2 + b^2*(2*c^2 + 3*d^2)))/(2*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - b^2/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^2) + (d*(2*a^3*c*d^3 + 2*a*b^2*c*d^3 - 2*a^2*b*d^2*(2*c^2 + d^2) - b^3*(c^4 + 6*c^2*d^2 + 3*d^4)))/((a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",6,4,25,0.1600,1,"{3569, 3649, 3651, 3530}"
1229,1,209,0,0.5611255,"\int (a+b \tan (e+f x))^3 \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^3*Sqrt[c + d*Tan[e + f*x]],x]","\frac{2 b \left(3 a^2-b^2\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 b^2 (b c-6 a d) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}{5 d f}-\frac{(-b+i a)^3 \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{2 b \left(3 a^2-b^2\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 b^2 (b c-6 a d) (c+d \tan (e+f x))^{3/2}}{15 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}{5 d f}-\frac{(-b+i a)^3 \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((I*a + b)^3*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f - ((I*a - b)^3*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*b*(3*a^2 - b^2)*Sqrt[c + d*Tan[e + f*x]])/f - (4*b^2*(b*c - 6*a*d)*(c + d*Tan[e + f*x])^(3/2))/(15*d^2*f) + (2*b^2*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2))/(5*d*f)","A",10,7,27,0.2593,1,"{3566, 3630, 3528, 3539, 3537, 63, 208}"
1230,1,157,0,0.349869,"\int (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]],x]","\frac{4 a b \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^2 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{3/2}}{3 d f}","\frac{4 a b \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^2 \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{3/2}}{3 d f}",1,"((-I)*(a - I*b)^2*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (I*(a + I*b)^2*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (4*a*b*Sqrt[c + d*Tan[e + f*x]])/f + (2*b^2*(c + d*Tan[e + f*x])^(3/2))/(3*d*f)","A",9,6,27,0.2222,1,"{3543, 3528, 3539, 3537, 63, 208}"
1231,1,122,0,0.2182086,"\int (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{(b+i a) \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b \sqrt{c+d \tan (e+f x)}}{f}","-\frac{(b+i a) \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b \sqrt{c+d \tan (e+f x)}}{f}",1,"-(((I*a + b)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*b*Sqrt[c + d*Tan[e + f*x]])/f","A",8,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
1232,1,170,0,0.4902428,"\int \frac{\sqrt{c+d \tan (e+f x)}}{a+b \tan (e+f x)} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + b*Tan[e + f*x]),x]","-\frac{2 \sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)}+\frac{\sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{\sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}","-\frac{2 \sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)}+\frac{\sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{\sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}",1,"(Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)*f) - (Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)*f) - (2*Sqrt[b]*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*f)","A",11,6,27,0.2222,1,"{3572, 3539, 3537, 63, 208, 3634}"
1233,1,231,0,0.7751301,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+b \tan (e+f x))^2} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + b*Tan[e + f*x])^2,x]","-\frac{b \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{b} \left(-3 a^2 d+4 a b c+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 \sqrt{b c-a d}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{b \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{b} \left(-3 a^2 d+4 a b c+b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 \sqrt{b c-a d}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"((-I)*Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f) + (I*Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) - (Sqrt[b]*(4*a*b*c - 3*a^2*d + b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*Sqrt[b*c - a*d]*f) - (b*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",12,7,27,0.2593,1,"{3568, 3653, 3539, 3537, 63, 208, 3634}"
1234,1,342,0,1.5172899,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+b \tan (e+f x))^3} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + b*Tan[e + f*x])^3,x]","\frac{\sqrt{b} \left(-6 a^2 b^2 \left(4 c^2-3 d^2\right)+40 a^3 b c d-15 a^4 d^2-24 a b^3 c d+b^4 \left(8 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 f \left(a^2+b^2\right)^3 (b c-a d)^{3/2}}-\frac{b \left(-7 a^2 d+8 a b c+b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))}-\frac{b \sqrt{c+d \tan (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{\sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","\frac{\sqrt{b} \left(-6 a^2 b^2 \left(4 c^2-3 d^2\right)+40 a^3 b c d-15 a^4 d^2-24 a b^3 c d+b^4 \left(8 c^2+d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 f \left(a^2+b^2\right)^3 (b c-a d)^{3/2}}-\frac{b \left(-7 a^2 d+8 a b c+b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 f \left(a^2+b^2\right)^2 (b c-a d) (a+b \tan (e+f x))}-\frac{b \sqrt{c+d \tan (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{\sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{\sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-((Sqrt[c - I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + (Sqrt[c + I*d]*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) + (Sqrt[b]*(40*a^3*b*c*d - 24*a*b^3*c*d - 15*a^4*d^2 - 6*a^2*b^2*(4*c^2 - 3*d^2) + b^4*(8*c^2 + d^2))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*(a^2 + b^2)^3*(b*c - a*d)^(3/2)*f) - (b*Sqrt[c + d*Tan[e + f*x]])/(2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - (b*(8*a*b*c - 7*a^2*d + b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(4*(a^2 + b^2)^2*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",13,8,27,0.2963,1,"{3568, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1235,1,256,0,0.7288805,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 b^2 (b c-8 a d) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}}{7 d f}-\frac{(-b+i a)^3 (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}","\frac{2 b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{2 \left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) \sqrt{c+d \tan (e+f x)}}{f}-\frac{4 b^2 (b c-8 a d) (c+d \tan (e+f x))^{5/2}}{35 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}}{7 d f}-\frac{(-b+i a)^3 (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{(b+i a)^3 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}",1,"((I*a + b)^3*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f - ((I*a - b)^3*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(3*a^2*b*c - b^3*c + a^3*d - 3*a*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/f + (2*b*(3*a^2 - b^2)*(c + d*Tan[e + f*x])^(3/2))/(3*f) - (4*b^2*(b*c - 8*a*d)*(c + d*Tan[e + f*x])^(5/2))/(35*d^2*f) + (2*b^2*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2))/(7*d*f)","A",11,7,27,0.2593,1,"{3566, 3630, 3528, 3539, 3537, 63, 208}"
1236,1,195,0,0.4484032,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 \left(a^2 d+2 a b c-b^2 d\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{4 a b (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{i (a-i b)^2 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{5/2}}{5 d f}","\frac{2 \left(a^2 d+2 a b c-b^2 d\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{4 a b (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{i (a-i b)^2 (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{5/2}}{5 d f}",1,"((-I)*(a - I*b)^2*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (I*(a + I*b)^2*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*a*b*c + a^2*d - b^2*d)*Sqrt[c + d*Tan[e + f*x]])/f + (4*a*b*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*b^2*(c + d*Tan[e + f*x])^(5/2))/(5*d*f)","A",10,6,27,0.2222,1,"{3543, 3528, 3539, 3537, 63, 208}"
1237,1,150,0,0.3207017,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 (a d+b c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(b+i a) (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b (c+d \tan (e+f x))^{3/2}}{3 f}","\frac{2 (a d+b c) \sqrt{c+d \tan (e+f x)}}{f}-\frac{(b+i a) (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b (c+d \tan (e+f x))^{3/2}}{3 f}",1,"-(((I*a + b)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(b*c + a*d)*Sqrt[c + d*Tan[e + f*x]])/f + (2*b*(c + d*Tan[e + f*x])^(3/2))/(3*f)","A",9,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
1238,1,170,0,0.5156822,"\int \frac{(c+d \tan (e+f x))^{3/2}}{a+b \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x]),x]","-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)}+\frac{(c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{(c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}","-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)}+\frac{(c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{(c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}",1,"((c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)*f) - ((c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)*f) - (2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(Sqrt[b]*(a^2 + b^2)*f)","A",11,6,27,0.2222,1,"{3573, 3539, 3537, 63, 208, 3634}"
1239,1,239,0,0.922341,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+b \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^2,x]","-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{b c-a d} \left(a^2 (-d)+4 a b c+3 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)^2}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{\sqrt{b c-a d} \left(a^2 (-d)+4 a b c+3 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{\sqrt{b} f \left(a^2+b^2\right)^2}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"((-I)*(c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f) + (I*(c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) - (Sqrt[b*c - a*d]*(4*a*b*c - a^2*d + 3*b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(Sqrt[b]*(a^2 + b^2)^2*f) - ((b*c - a*d)*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",12,7,27,0.2593,1,"{3567, 3653, 3539, 3537, 63, 208, 3634}"
1240,1,341,0,1.8686661,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+b \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^3,x]","\frac{\left(-2 a^2 b^2 \left(12 c^2-13 d^2\right)+24 a^3 b c d-3 a^4 d^2-40 a b^3 c d+b^4 \left(8 c^2-3 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} f \left(a^2+b^2\right)^3 \sqrt{b c-a d}}-\frac{\left(-3 a^2 d+8 a b c+5 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","\frac{\left(-2 a^2 b^2 \left(12 c^2-13 d^2\right)+24 a^3 b c d-3 a^4 d^2-40 a b^3 c d+b^4 \left(8 c^2-3 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} f \left(a^2+b^2\right)^3 \sqrt{b c-a d}}-\frac{\left(-3 a^2 d+8 a b c+5 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)}}{2 f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-(((c - I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + ((c + I*d)^(3/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) + ((24*a^3*b*c*d - 40*a*b^3*c*d - 3*a^4*d^2 - 2*a^2*b^2*(12*c^2 - 13*d^2) + b^4*(8*c^2 - 3*d^2))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*Sqrt[b]*(a^2 + b^2)^3*Sqrt[b*c - a*d]*f) - ((b*c - a*d)*Sqrt[c + d*Tan[e + f*x]])/(2*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - ((8*a*b*c - 3*a^2*d + 5*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(4*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",13,8,27,0.2963,1,"{3567, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1241,1,322,0,0.9070817,"\int (a+b \tan (e+f x))^3 (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + b*Tan[e + f*x])^3*(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 \left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 \left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{4 b^2 (b c-10 a d) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{7/2}}{9 d f}+\frac{(b+i a)^3 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(-b+i a)^3 (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}","\frac{2 \left(3 a^2 b \left(c^2-d^2\right)+2 a^3 c d-6 a b^2 c d-b^3 \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 b \left(3 a^2-b^2\right) (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{2 \left(3 a^2 b c+a^3 d-3 a b^2 d-b^3 c\right) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{4 b^2 (b c-10 a d) (c+d \tan (e+f x))^{7/2}}{63 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) (c+d \tan (e+f x))^{7/2}}{9 d f}+\frac{(b+i a)^3 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}-\frac{(-b+i a)^3 (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}",1,"((I*a + b)^3*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f - ((I*a - b)^3*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*a^3*c*d - 6*a*b^2*c*d + 3*a^2*b*(c^2 - d^2) - b^3*(c^2 - d^2))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(3*a^2*b*c - b^3*c + a^3*d - 3*a*b^2*d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*b*(3*a^2 - b^2)*(c + d*Tan[e + f*x])^(5/2))/(5*f) - (4*b^2*(b*c - 10*a*d)*(c + d*Tan[e + f*x])^(7/2))/(63*d^2*f) + (2*b^2*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(7/2))/(9*d*f)","A",12,7,27,0.2593,1,"{3566, 3630, 3528, 3539, 3537, 63, 208}"
1242,1,231,0,0.6166893,"\int (a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 \left(a^2 d+2 a b c-b^2 d\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a b (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{4 (a d+b c) (a c-b d) \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^2 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{7/2}}{7 d f}","\frac{2 \left(a^2 d+2 a b c-b^2 d\right) (c+d \tan (e+f x))^{3/2}}{3 f}+\frac{4 a b (c+d \tan (e+f x))^{5/2}}{5 f}+\frac{4 (a d+b c) (a c-b d) \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^2 (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{i (a+i b)^2 (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b^2 (c+d \tan (e+f x))^{7/2}}{7 d f}",1,"((-I)*(a - I*b)^2*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f + (I*(a + I*b)^2*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (4*(b*c + a*d)*(a*c - b*d)*Sqrt[c + d*Tan[e + f*x]])/f + (2*(2*a*b*c + a^2*d - b^2*d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (4*a*b*(c + d*Tan[e + f*x])^(5/2))/(5*f) + (2*b^2*(c + d*Tan[e + f*x])^(7/2))/(7*d*f)","A",11,6,27,0.2222,1,"{3543, 3528, 3539, 3537, 63, 208}"
1243,1,188,0,0.4273777,"\int (a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 \left(2 a c d+b \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 (a d+b c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{(b+i a) (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b (c+d \tan (e+f x))^{5/2}}{5 f}","\frac{2 \left(2 a c d+b \left(c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{f}+\frac{2 (a d+b c) (c+d \tan (e+f x))^{3/2}}{3 f}-\frac{(b+i a) (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f}+\frac{(-b+i a) (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f}+\frac{2 b (c+d \tan (e+f x))^{5/2}}{5 f}",1,"-(((I*a + b)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/f) + ((I*a - b)*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/f + (2*(2*a*c*d + b*(c^2 - d^2))*Sqrt[c + d*Tan[e + f*x]])/f + (2*(b*c + a*d)*(c + d*Tan[e + f*x])^(3/2))/(3*f) + (2*b*(c + d*Tan[e + f*x])^(5/2))/(5*f)","A",10,5,25,0.2000,1,"{3528, 3539, 3537, 63, 208}"
1244,1,195,0,0.9151931,"\int \frac{(c+d \tan (e+f x))^{5/2}}{a+b \tan (e+f x)} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x]),x]","-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)}+\frac{(c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{(c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}+\frac{2 d^2 \sqrt{c+d \tan (e+f x)}}{b f}","-\frac{2 (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)}+\frac{(c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)}-\frac{(c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)}+\frac{2 d^2 \sqrt{c+d \tan (e+f x)}}{b f}",1,"((c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)*f) - ((c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)*f) - (2*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2)*f) + (2*d^2*Sqrt[c + d*Tan[e + f*x]])/(b*f)","A",12,7,27,0.2593,1,"{3566, 3653, 3539, 3537, 63, 208, 3634}"
1245,1,243,0,1.0781054,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^2} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^2,x]","-\frac{(b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{(b c-a d)^{3/2} \left(a^2 d+4 a b c+5 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)^2}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}","-\frac{(b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) (a+b \tan (e+f x))}-\frac{(b c-a d)^{3/2} \left(a^2 d+4 a b c+5 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{b^{3/2} f \left(a^2+b^2\right)^2}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2}",1,"((-I)*(c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*f) + (I*(c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*f) - ((b*c - a*d)^(3/2)*(4*a*b*c + a^2*d + 5*b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(b^(3/2)*(a^2 + b^2)^2*f) - ((b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/(b*(a^2 + b^2)*f*(a + b*Tan[e + f*x]))","A",12,7,27,0.2593,1,"{3565, 3653, 3539, 3537, 63, 208, 3634}"
1246,1,355,0,1.8577541,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^3} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^3,x]","\frac{\sqrt{b c-a d} \left(-6 a^2 b^2 \left(4 c^2-3 d^2\right)+8 a^3 b c d+a^4 d^2-56 a b^3 c d+b^4 \left(8 c^2-15 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} f \left(a^2+b^2\right)^3}-\frac{(b c-a d) \left(a^2 d+8 a b c+9 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 b f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}","\frac{\sqrt{b c-a d} \left(-6 a^2 b^2 \left(4 c^2-3 d^2\right)+8 a^3 b c d+a^4 d^2-56 a b^3 c d+b^4 \left(8 c^2-15 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} f \left(a^2+b^2\right)^3}-\frac{(b c-a d) \left(a^2 d+8 a b c+9 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{4 b f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))}-\frac{(b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{2 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^2}-\frac{(c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a)^3}+\frac{(c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a)^3}",1,"-(((c - I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((I*a + b)^3*f)) + ((c + I*d)^(5/2)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((I*a - b)^3*f) + (Sqrt[b*c - a*d]*(8*a^3*b*c*d - 56*a*b^3*c*d + a^4*d^2 + b^4*(8*c^2 - 15*d^2) - 6*a^2*b^2*(4*c^2 - 3*d^2))*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/(4*b^(3/2)*(a^2 + b^2)^3*f) - ((b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/(2*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^2) - ((b*c - a*d)*(8*a*b*c + a^2*d + 9*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(4*b*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x]))","A",13,8,27,0.2963,1,"{3565, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1247,1,248,0,0.7344484,"\int \frac{(a+b \tan (e+f x))^4}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^4/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{2 b^2 \left(-87 a^2 d^2+40 a b c d+b^2 \left(-\left(8 c^2-15 d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{15 d^3 f}-\frac{4 b^3 (2 b c-7 a d) \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{15 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d f}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}","-\frac{2 b^2 \left(-87 a^2 d^2+40 a b c d+b^2 \left(-\left(8 c^2-15 d^2\right)\right)\right) \sqrt{c+d \tan (e+f x)}}{15 d^3 f}-\frac{4 b^3 (2 b c-7 a d) \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{15 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}}{5 d f}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}",1,"((-I)*(a - I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) + (I*(a + I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) - (2*b^2*(40*a*b*c*d - 87*a^2*d^2 - b^2*(8*c^2 - 15*d^2))*Sqrt[c + d*Tan[e + f*x]])/(15*d^3*f) - (4*b^3*(2*b*c - 7*a*d)*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(15*d^2*f) + (2*b^2*(a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]])/(5*d*f)","A",10,7,27,0.2593,1,"{3566, 3637, 3630, 3539, 3537, 63, 208}"
1248,1,178,0,0.4302243,"\int \frac{(a+b \tan (e+f x))^3}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^3/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{4 b^2 (b c-4 a d) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}{3 d f}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}","-\frac{4 b^2 (b c-4 a d) \sqrt{c+d \tan (e+f x)}}{3 d^2 f}+\frac{2 b^2 (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}{3 d f}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}",1,"((I*a + b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) - ((I*a - b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) - (4*b^2*(b*c - 4*a*d)*Sqrt[c + d*Tan[e + f*x]])/(3*d^2*f) + (2*b^2*(a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])/(3*d*f)","A",9,6,27,0.2222,1,"{3566, 3630, 3539, 3537, 63, 208}"
1249,1,134,0,0.2467146,"\int \frac{(a+b \tan (e+f x))^2}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^2/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{d f}","-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}+\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{d f}",1,"((-I)*(a - I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f) + (I*(a + I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f) + (2*b^2*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",8,5,27,0.1852,1,"{3543, 3539, 3537, 63, 208}"
1250,1,102,0,0.1524541,"\int \frac{a+b \tan (e+f x)}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])/Sqrt[c + d*Tan[e + f*x]],x]","\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}","\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f \sqrt{c+i d}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f \sqrt{c-i d}}",1,"-(((I*a + b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/(Sqrt[c - I*d]*f)) + ((I*a - b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/(Sqrt[c + I*d]*f)","A",7,4,25,0.1600,1,"{3539, 3537, 63, 208}"
1251,1,170,0,0.4217908,"\int \frac{1}{(a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) \sqrt{b c-a d}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) \sqrt{c-i d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) \sqrt{c+i d}}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) \sqrt{b c-a d}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) \sqrt{c-i d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) \sqrt{c+i d}}",1,"ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]]/((I*a + b)*Sqrt[c - I*d]*f) - ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]]/((I*a - b)*Sqrt[c + I*d]*f) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*Sqrt[b*c - a*d]*f)","A",11,6,27,0.2222,1,"{3574, 3539, 3537, 63, 208, 3634}"
1252,1,244,0,0.8548002,"\int \frac{1}{(a+b \tan (e+f x))^2 \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + b*Tan[e + f*x])^2*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{b^2 \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}-\frac{b^{3/2} \left(-5 a^2 d+4 a b c-b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 \sqrt{c+i d}}","-\frac{b^2 \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))}-\frac{b^{3/2} \left(-5 a^2 d+4 a b c-b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 \sqrt{c+i d}}",1,"((-I)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*Sqrt[c - I*d]*f) + (I*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*Sqrt[c + I*d]*f) - (b^(3/2)*(4*a*b*c - 5*a^2*d - b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*(b*c - a*d)^(3/2)*f) - (b^2*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x]))","A",12,7,27,0.2593,1,"{3569, 3653, 3539, 3537, 63, 208, 3634}"
1253,1,317,0,0.9108646,"\int \frac{(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 b \left(15 a^2 b c d^2-6 a^3 d^3-12 a b^2 d \left(2 c^2+d^2\right)+b^3 \left(8 c^3+5 c d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}-\frac{2 b^2 \left(3 a d (2 b c-a d)-b^2 \left(4 c^2+d^2\right)\right) \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{3 d^2 f \left(c^2+d^2\right)}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}","-\frac{2 b \left(15 a^2 b c d^2-6 a^3 d^3-12 a b^2 d \left(2 c^2+d^2\right)+b^3 \left(8 c^3+5 c d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}-\frac{2 b^2 \left(3 a d (2 b c-a d)-b^2 \left(4 c^2+d^2\right)\right) \tan (e+f x) \sqrt{c+d \tan (e+f x)}}{3 d^2 f \left(c^2+d^2\right)}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*(a - I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) + (I*(a + I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^2)/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - (2*b*(15*a^2*b*c*d^2 - 6*a^3*d^3 - 12*a*b^2*d*(2*c^2 + d^2) + b^3*(8*c^3 + 5*c*d^2))*Sqrt[c + d*Tan[e + f*x]])/(3*d^3*(c^2 + d^2)*f) - (2*b^2*(3*a*d*(2*b*c - a*d) - b^2*(4*c^2 + d^2))*Tan[e + f*x]*Sqrt[c + d*Tan[e + f*x]])/(3*d^2*(c^2 + d^2)*f)","A",10,7,27,0.2593,1,"{3565, 3637, 3630, 3539, 3537, 63, 208}"
1254,1,216,0,0.5032538,"\int \frac{(a+b \tan (e+f x))^3}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 b \left(a d (2 b c-a d)-b^2 \left(2 c^2+d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}","-\frac{2 b \left(a d (2 b c-a d)-b^2 \left(2 c^2+d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}",1,"((I*a + b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) - ((I*a - b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x]))/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - (2*b*(a*d*(2*b*c - a*d) - b^2*(2*c^2 + d^2))*Sqrt[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)*f)","A",9,6,27,0.2222,1,"{3565, 3630, 3539, 3537, 63, 208}"
1255,1,150,0,0.3284405,"\int \frac{(a+b \tan (e+f x))^2}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 (b c-a d)^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}","-\frac{2 (b c-a d)^2}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*(a - I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f) + (I*(a + I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) - (2*(b*c - a*d)^2)/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,27,0.1852,1,"{3542, 3539, 3537, 63, 208}"
1256,1,138,0,0.241404,"\int \frac{a+b \tan (e+f x)}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 (b c-a d)}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}","\frac{2 (b c-a d)}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{3/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{3/2}}",1,"-(((I*a + b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(3/2)*f)) + ((I*a - b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(3/2)*f) + (2*(b*c - a*d))/((c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,25,0.2000,1,"{3529, 3539, 3537, 63, 208}"
1257,1,211,0,0.937069,"\int \frac{1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{3/2}}+\frac{2 d^2}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) (c+i d)^{3/2}}","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{3/2}}+\frac{2 d^2}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) (c+i d)^{3/2}}",1,"ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]]/((I*a + b)*(c - I*d)^(3/2)*f) - ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]]/((I*a - b)*(c + I*d)^(3/2)*f) - (2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*(b*c - a*d)^(3/2)*f) + (2*d^2)/((b*c - a*d)*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",12,7,27,0.2593,1,"{3569, 3653, 3539, 3537, 63, 208, 3634}"
1258,1,314,0,1.4713581,"\int \frac{1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{d \left(2 a^2 d^2+b^2 \left(c^2+3 d^2\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{b^{5/2} \left(-7 a^2 d+4 a b c-3 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{3/2}}","-\frac{d \left(2 a^2 d^2+b^2 \left(c^2+3 d^2\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) \sqrt{c+d \tan (e+f x)}}-\frac{b^{5/2} \left(-7 a^2 d+4 a b c-3 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{5/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{3/2}}",1,"((-I)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*(c - I*d)^(3/2)*f) + (I*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*(c + I*d)^(3/2)*f) - (b^(5/2)*(4*a*b*c - 7*a^2*d - 3*b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*(b*c - a*d)^(5/2)*f) - (d*(2*a^2*d^2 + b^2*(c^2 + 3*d^2)))/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - b^2/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*Sqrt[c + d*Tan[e + f*x]])","A",13,8,27,0.2963,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1259,1,290,0,1.0093324,"\int \frac{(a+b \tan (e+f x))^4}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^4/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{2 b^2 \left(a d (2 b c-a d)-b^2 \left(4 c^2+3 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}+\frac{4 (b c-a d)^3 \left(3 a c d+2 b c^2+5 b d^2\right)}{3 d^3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}","-\frac{2 b^2 \left(a d (2 b c-a d)-b^2 \left(4 c^2+3 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{3 d^3 f \left(c^2+d^2\right)}+\frac{4 (b c-a d)^3 \left(3 a c d+2 b c^2+5 b d^2\right)}{3 d^3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^4 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^4*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^2)/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (4*(b*c - a*d)^3*(2*b*c^2 + 3*a*c*d + 5*b*d^2))/(3*d^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]]) - (2*b^2*(a*d*(2*b*c - a*d) - b^2*(4*c^2 + 3*d^2))*Sqrt[c + d*Tan[e + f*x]])/(3*d^3*(c^2 + d^2)*f)","A",10,7,27,0.2593,1,"{3565, 3635, 3630, 3539, 3537, 63, 208}"
1260,1,219,0,0.6499137,"\int \frac{(a+b \tan (e+f x))^3}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^3/(c + d*Tan[e + f*x])^(5/2),x]","-\frac{4 (b c-a d)^2 \left(3 a c d+b \left(c^2+4 d^2\right)\right)}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}","-\frac{4 (b c-a d)^2 \left(3 a c d+b \left(c^2+4 d^2\right)\right)}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{(-b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}+\frac{(b+i a)^3 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}",1,"((I*a + b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) - ((I*a - b)^3*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x]))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (4*(b*c - a*d)^2*(3*a*c*d + b*(c^2 + 4*d^2)))/(3*d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,27,0.2222,1,"{3565, 3628, 3539, 3537, 63, 208}"
1261,1,195,0,0.4983696,"\int \frac{(a+b \tan (e+f x))^2}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^2/(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 (b c-a d) (a c+b d)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}","\frac{4 (b c-a d) (a c+b d)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^2 \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^2*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) - (2*(b*c - a*d)^2)/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (4*(b*c - a*d)*(a*c + b*d))/((c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,27,0.2222,1,"{3542, 3529, 3539, 3537, 63, 208}"
1262,1,186,0,0.3841123,"\int \frac{a+b \tan (e+f x)}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 (b c-a d)}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(2 a c d-b \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}","\frac{2 (b c-a d)}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{2 \left(2 a c d-b \left(c^2-d^2\right)\right)}{f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{(b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (c-i d)^{5/2}}+\frac{(-b+i a) \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (c+i d)^{5/2}}",1,"-(((I*a + b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((c - I*d)^(5/2)*f)) + ((I*a - b)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((c + I*d)^(5/2)*f) + (2*(b*c - a*d))/(3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(2*a*c*d - b*(c^2 - d^2)))/((c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,5,25,0.2000,1,"{3529, 3539, 3537, 63, 208}"
1263,1,272,0,1.4232902,"\int \frac{1}{(a+b \tan (e+f x)) (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{2 b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{5/2}}-\frac{2 d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 d^2}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) (c+i d)^{5/2}}","-\frac{2 b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right) (b c-a d)^{5/2}}-\frac{2 d^2 \left(2 a c d-b \left(3 c^2+d^2\right)\right)}{f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 d^2}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (b+i a) (c-i d)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (-b+i a) (c+i d)^{5/2}}",1,"ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]]/((I*a + b)*(c - I*d)^(5/2)*f) - ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]]/((I*a - b)*(c + I*d)^(5/2)*f) - (2*b^(7/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)*(b*c - a*d)^(5/2)*f) + (2*d^2)/(3*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*d^2*(2*a*c*d - b*(3*c^2 + d^2)))/((b*c - a*d)^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",13,8,27,0.2963,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1264,1,425,0,2.5085194,"\int \frac{1}{(a+b \tan (e+f x))^2 (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^2*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{d \left(-4 a^2 b d^2 \left(2 c^2+d^2\right)+4 a^3 c d^3+4 a b^2 c d^3+b^3 \left(-\left(10 c^2 d^2+c^4+5 d^4\right)\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{d \left(2 a^2 d^2+b^2 \left(3 c^2+5 d^2\right)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{b^{7/2} \left(-9 a^2 d+4 a b c-5 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{7/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{5/2}}","\frac{d \left(-4 a^2 b d^2 \left(2 c^2+d^2\right)+4 a^3 c d^3+4 a b^2 c d^3+b^3 \left(-\left(10 c^2 d^2+c^4+5 d^4\right)\right)\right)}{f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{d \left(2 a^2 d^2+b^2 \left(3 c^2+5 d^2\right)\right)}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{b^2}{f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x)) (c+d \tan (e+f x))^{3/2}}-\frac{b^{7/2} \left(-9 a^2 d+4 a b c-5 b^2 d\right) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d \tan (e+f x)}}{\sqrt{b c-a d}}\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^{7/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c-i d}}\right)}{f (a-i b)^2 (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{c+i d}}\right)}{f (a+i b)^2 (c+i d)^{5/2}}",1,"((-I)*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c - I*d]])/((a - I*b)^2*(c - I*d)^(5/2)*f) + (I*ArcTanh[Sqrt[c + d*Tan[e + f*x]]/Sqrt[c + I*d]])/((a + I*b)^2*(c + I*d)^(5/2)*f) - (b^(7/2)*(4*a*b*c - 9*a^2*d - 5*b^2*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])/Sqrt[b*c - a*d]])/((a^2 + b^2)^2*(b*c - a*d)^(7/2)*f) - (d*(2*a^2*d^2 + b^2*(3*c^2 + 5*d^2)))/(3*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - b^2/((a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])*(c + d*Tan[e + f*x])^(3/2)) + (d*(4*a^3*c*d^3 + 4*a*b^2*c*d^3 - 4*a^2*b*d^2*(2*c^2 + d^2) - b^3*(c^4 + 10*c^2*d^2 + 5*d^4)))/((a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",14,8,27,0.2963,1,"{3569, 3649, 3653, 3539, 3537, 63, 208, 3634}"
1265,1,337,0,3.9485303,"\int (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]],x]","\frac{\sqrt{b} \left(15 a^2 d^2+10 a b c d+b^2 \left(-\left(c^2+8 d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{3/2} f}+\frac{b^2 \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}-\frac{b (b c-9 a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d f}-\frac{i (a-i b)^{5/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{5/2} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}","\frac{\sqrt{b} \left(15 a^2 d^2+10 a b c d+b^2 \left(-\left(c^2+8 d^2\right)\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 d^{3/2} f}+\frac{b^2 \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 d f}-\frac{b (b c-9 a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 d f}-\frac{i (a-i b)^{5/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{5/2} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"((-I)*(a - I*b)^(5/2)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*(a + I*b)^(5/2)*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (Sqrt[b]*(10*a*b*c*d + 15*a^2*d^2 - b^2*(c^2 + 8*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*d^(3/2)*f) - (b*(b*c - 9*a*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*d*f) + (b^2*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*d*f)","A",14,9,29,0.3103,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1266,1,258,0,2.2552416,"\int (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]],x]","\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^{3/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{b} (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}","\frac{b \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i (a-i b)^{3/2} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{b} (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}",1,"((-I)*(a - I*b)^(3/2)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*(a + I*b)^(3/2)*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (Sqrt[b]*(b*c + 3*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[d]*f) + (b*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/f","A",13,8,29,0.2759,1,"{3570, 3655, 6725, 63, 217, 206, 93, 208}"
1267,1,218,0,0.948188,"\int \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]],x]","-\frac{i \sqrt{a-i b} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{2 \sqrt{b} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{f}","-\frac{i \sqrt{a-i b} \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{2 \sqrt{b} \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"((-I)*Sqrt[a - I*b]*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*Sqrt[a + I*b]*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (2*Sqrt[b]*Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/f","A",11,8,29,0.2759,1,"{3575, 906, 63, 217, 206, 6725, 93, 208}"
1268,1,163,0,0.2257195,"\int \frac{\sqrt{c+d \tan (e+f x)}}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/Sqrt[a + b*Tan[e + f*x]],x]","\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}","\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}",1,"((-I)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f) + (I*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f)","A",7,4,29,0.1379,1,"{3575, 910, 93, 208}"
1269,1,206,0,0.7560964,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + b*Tan[e + f*x])^(3/2),x]","-\frac{2 b \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}","-\frac{2 b \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}",1,"((-I)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f) + (I*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) - (2*b*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3568, 3616, 3615, 93, 208}"
1270,1,280,0,1.2236555,"\int \frac{\sqrt{c+d \tan (e+f x)}}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[c + d*Tan[e + f*x]]/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{2 b \left(-5 a^2 d+6 a b c+b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{2 b \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}","-\frac{2 b \left(-5 a^2 d+6 a b c+b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{2 b \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i \sqrt{c-i d} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i \sqrt{c+i d} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}",1,"((-I)*Sqrt[c - I*d]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f) + (I*Sqrt[c + I*d]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) - (2*b*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2)) - (2*b*(6*a*b*c - 5*a^2*d + b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3568, 3649, 3616, 3615, 93, 208}"
1271,1,330,0,4.1505026,"\int (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2),x]","\frac{\left(3 a^2 d^2+18 a b c d+b^2 \left(3 c^2-8 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{b} \sqrt{d} f}+\frac{b \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 f}+\frac{(5 a d+3 b c) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}-\frac{i (a-i b)^{3/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}","\frac{\left(3 a^2 d^2+18 a b c d+b^2 \left(3 c^2-8 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 \sqrt{b} \sqrt{d} f}+\frac{b \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}{2 f}+\frac{(5 a d+3 b c) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 f}-\frac{i (a-i b)^{3/2} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"((-I)*(a - I*b)^(3/2)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*(a + I*b)^(3/2)*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + ((18*a*b*c*d + 3*a^2*d^2 + b^2*(3*c^2 - 8*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*Sqrt[b]*Sqrt[d]*f) + ((3*b*c + 5*a*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*f) + (b*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2))/(2*f)","A",14,9,29,0.3103,1,"{3570, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1272,1,258,0,2.1949987,"\int \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2),x]","\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i \sqrt{a-i b} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{d} (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} f}","\frac{d \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{f}-\frac{i \sqrt{a-i b} (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{\sqrt{d} (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} f}",1,"((-I)*Sqrt[a - I*b]*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*Sqrt[a + I*b]*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (Sqrt[d]*(3*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[b]*f) + (d*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/f","A",13,8,29,0.2759,1,"{3570, 3655, 6725, 63, 217, 206, 93, 208}"
1273,1,218,0,1.0788493,"\int \frac{(c+d \tan (e+f x))^{3/2}}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/Sqrt[a + b*Tan[e + f*x]],x]","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} f}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}","\frac{2 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{b} f}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}",1,"((-I)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f) + (I*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f) + (2*d^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[b]*f)","A",12,8,29,0.2759,1,"{3575, 910, 63, 217, 206, 6725, 93, 208}"
1274,1,213,0,0.8432016,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^(3/2),x]","-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}","-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}",1,"((-I)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f) + (I*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) - (2*(b*c - a*d)*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3567, 3616, 3615, 93, 208}"
1275,1,277,0,1.3358751,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{4 \left(a^2 (-d)+3 a b c+2 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}","-\frac{4 \left(a^2 (-d)+3 a b c+2 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}",1,"((-I)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f) + (I*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) - (2*(b*c - a*d)*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2)) - (4*(3*a*b*c - a^2*d + 2*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)^2*f*Sqrt[a + b*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3567, 3649, 3616, 3615, 93, 208}"
1276,1,391,0,2.0979375,"\int \frac{(c+d \tan (e+f x))^{3/2}}{(a+b \tan (e+f x))^{7/2}} \, dx","Int[(c + d*Tan[e + f*x])^(3/2)/(a + b*Tan[e + f*x])^(7/2),x]","\frac{2 \left(-a^2 b^2 \left(45 c^2-49 d^2\right)+50 a^3 b c d-8 a^4 d^2-70 a b^3 c d+3 b^4 \left(5 c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{15 f \left(a^2+b^2\right)^3 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{4 \left(-2 a^2 d+5 a b c+3 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{15 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{5 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}","\frac{2 \left(-a^2 b^2 \left(45 c^2-49 d^2\right)+50 a^3 b c d-8 a^4 d^2-70 a b^3 c d+3 b^4 \left(5 c^2-d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{15 f \left(a^2+b^2\right)^3 (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{4 \left(-2 a^2 d+5 a b c+3 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{15 f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{2 (b c-a d) \sqrt{c+d \tan (e+f x)}}{5 f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{i (c-i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}+\frac{i (c+i d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}",1,"((-I)*(c - I*d)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(7/2)*f) + (I*(c + I*d)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(7/2)*f) - (2*(b*c - a*d)*Sqrt[c + d*Tan[e + f*x]])/(5*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(5/2)) - (4*(5*a*b*c - 2*a^2*d + 3*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(15*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])^(3/2)) + (2*(50*a^3*b*c*d - 70*a*b^3*c*d - 8*a^4*d^2 - a^2*b^2*(45*c^2 - 49*d^2) + 3*b^4*(5*c^2 - d^2))*Sqrt[c + d*Tan[e + f*x]])/(15*(a^2 + b^2)^3*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]])","A",10,6,29,0.2069,1,"{3567, 3649, 3616, 3615, 93, 208}"
1277,1,429,0,5.4673061,"\int (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2),x]","\frac{\left(-a^2 d^2+14 a b c d+b^2 \left(11 c^2-8 d^2\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 b f}+\frac{\left(15 a^2 b c d^2-a^3 d^3+3 a b^2 d \left(15 c^2-8 d^2\right)+5 b^3 \left(c^3-8 c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{3/2} \sqrt{d} f}+\frac{d^2 (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}{3 b f}+\frac{d (13 b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{12 b f}-\frac{i (a-i b)^{3/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}","\frac{\left(-a^2 d^2+14 a b c d+b^2 \left(11 c^2-8 d^2\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{8 b f}+\frac{\left(15 a^2 b c d^2-a^3 d^3+3 a b^2 d \left(15 c^2-8 d^2\right)+5 b^3 \left(c^3-8 c d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{8 b^{3/2} \sqrt{d} f}+\frac{d^2 (a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}}{3 b f}+\frac{d (13 b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{12 b f}-\frac{i (a-i b)^{3/2} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i (a+i b)^{3/2} (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"((-I)*(a - I*b)^(3/2)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*(a + I*b)^(3/2)*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + ((15*a^2*b*c*d^2 - a^3*d^3 + 3*a*b^2*d*(15*c^2 - 8*d^2) + 5*b^3*(c^3 - 8*c*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(8*b^(3/2)*Sqrt[d]*f) + ((14*a*b*c*d - a^2*d^2 + b^2*(11*c^2 - 8*d^2))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(8*b*f) + (d*(13*b*c - a*d)*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]])/(12*b*f) + (d^2*(a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]])/(3*b*f)","A",15,9,29,0.3103,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1278,1,339,0,3.7812789,"\int \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2),x]","\frac{\sqrt{d} \left(-a^2 d^2+10 a b c d+b^2 \left(15 c^2-8 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{3/2} f}+\frac{d^2 (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 b f}+\frac{d (9 b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b f}-\frac{i \sqrt{a-i b} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}","\frac{\sqrt{d} \left(-a^2 d^2+10 a b c d+b^2 \left(15 c^2-8 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{4 b^{3/2} f}+\frac{d^2 (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}{2 b f}+\frac{d (9 b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{4 b f}-\frac{i \sqrt{a-i b} (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}+\frac{i \sqrt{a+i b} (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f}",1,"((-I)*Sqrt[a - I*b]*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (I*Sqrt[a + I*b]*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/f + (Sqrt[d]*(10*a*b*c*d - a^2*d^2 + b^2*(15*c^2 - 8*d^2))*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(4*b^(3/2)*f) + (d*(9*b*c - a*d)*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(4*b*f) + (d^2*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]])/(2*b*f)","A",14,9,29,0.3103,1,"{3566, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1279,1,264,0,2.5000436,"\int \frac{(c+d \tan (e+f x))^{5/2}}{\sqrt{a+b \tan (e+f x)}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/Sqrt[a + b*Tan[e + f*x]],x]","\frac{d^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}+\frac{d^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}","\frac{d^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}+\frac{d^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{b f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b}}",1,"((-I)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*f) + (I*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*f) + (d^(3/2)*(5*b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(3/2)*f) + (d^2*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(b*f)","A",13,8,29,0.2759,1,"{3566, 3655, 6725, 63, 217, 206, 93, 208}"
1280,1,273,0,3.0724452,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^{3/2}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^(3/2),x]","-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}","-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{b f \left(a^2+b^2\right) \sqrt{a+b \tan (e+f x)}}+\frac{2 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{b^{3/2} f}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2}}",1,"((-I)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*f) + (I*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*f) + (2*d^(5/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(b^(3/2)*f) - (2*(b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/(b*(a^2 + b^2)*f*Sqrt[a + b*Tan[e + f*x]])","A",13,8,29,0.2759,1,"{3565, 3655, 6725, 63, 217, 206, 93, 208}"
1281,1,292,0,1.5811323,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^{5/2}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^(5/2),x]","-\frac{2 (b c-a d) \left(a^2 d+6 a b c+7 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}","-\frac{2 (b c-a d) \left(a^2 d+6 a b c+7 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{3 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{3/2}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2}}",1,"((-I)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*f) + (I*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*f) - (2*(b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/(3*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(3/2)) - (2*(b*c - a*d)*(6*a*b*c + a^2*d + 7*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(3*b*(a^2 + b^2)^2*f*Sqrt[a + b*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3565, 3649, 3616, 3615, 93, 208}"
1282,1,398,0,2.3633226,"\int \frac{(c+d \tan (e+f x))^{5/2}}{(a+b \tan (e+f x))^{7/2}} \, dx","Int[(c + d*Tan[e + f*x])^(5/2)/(a + b*Tan[e + f*x])^(7/2),x]","\frac{2 \left(-3 a^2 b^2 \left(15 c^2-13 d^2\right)+20 a^3 b c d+2 a^4 d^2-100 a b^3 c d+b^4 \left(15 c^2-23 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{15 b f \left(a^2+b^2\right)^3 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d) \left(a^2 d+10 a b c+11 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{15 b f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}","\frac{2 \left(-3 a^2 b^2 \left(15 c^2-13 d^2\right)+20 a^3 b c d+2 a^4 d^2-100 a b^3 c d+b^4 \left(15 c^2-23 d^2\right)\right) \sqrt{c+d \tan (e+f x)}}{15 b f \left(a^2+b^2\right)^3 \sqrt{a+b \tan (e+f x)}}-\frac{2 (b c-a d) \left(a^2 d+10 a b c+11 b^2 d\right) \sqrt{c+d \tan (e+f x)}}{15 b f \left(a^2+b^2\right)^2 (a+b \tan (e+f x))^{3/2}}-\frac{2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}{5 b f \left(a^2+b^2\right) (a+b \tan (e+f x))^{5/2}}-\frac{i (c-i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{7/2}}+\frac{i (c+i d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{7/2}}",1,"((-I)*(c - I*d)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(7/2)*f) + (I*(c + I*d)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(7/2)*f) - (2*(b*c - a*d)^2*Sqrt[c + d*Tan[e + f*x]])/(5*b*(a^2 + b^2)*f*(a + b*Tan[e + f*x])^(5/2)) - (2*(b*c - a*d)*(10*a*b*c + a^2*d + 11*b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(15*b*(a^2 + b^2)^2*f*(a + b*Tan[e + f*x])^(3/2)) + (2*(20*a^3*b*c*d - 100*a*b^3*c*d + 2*a^4*d^2 + b^4*(15*c^2 - 23*d^2) - 3*a^2*b^2*(15*c^2 - 13*d^2))*Sqrt[c + d*Tan[e + f*x]])/(15*b*(a^2 + b^2)^3*f*Sqrt[a + b*Tan[e + f*x]])","A",10,6,29,0.2069,1,"{3565, 3649, 3616, 3615, 93, 208}"
1283,1,264,0,2.454081,"\int \frac{(a+b \tan (e+f x))^{5/2}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^(5/2)/Sqrt[c + d*Tan[e + f*x]],x]","-\frac{b^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{b^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}","-\frac{b^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}+\frac{b^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d f}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}",1,"((-I)*(a - I*b)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f) + (I*(a + I*b)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f) - (b^(3/2)*(b*c - 5*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(3/2)*f) + (b^2*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d*f)","A",13,8,29,0.2759,1,"{3566, 3655, 6725, 63, 217, 206, 93, 208}"
1284,1,218,0,1.0958346,"\int \frac{(a+b \tan (e+f x))^{3/2}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)/Sqrt[c + d*Tan[e + f*x]],x]","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{\sqrt{d} f}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}",1,"((-I)*(a - I*b)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f) + (I*(a + I*b)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f) + (2*b^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[d]*f)","A",12,8,29,0.2759,1,"{3575, 910, 63, 217, 206, 6725, 93, 208}"
1285,1,163,0,0.2173417,"\int \frac{\sqrt{a+b \tan (e+f x)}}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]/Sqrt[c + d*Tan[e + f*x]],x]","\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}","\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c+i d}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{c-i d}}",1,"((-I)*Sqrt[a - I*b]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c - I*d]*f) + (I*Sqrt[a + I*b]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[c + I*d]*f)","A",7,4,29,0.1379,1,"{3575, 910, 93, 208}"
1286,1,163,0,0.2084718,"\int \frac{1}{\sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/(Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]),x]","\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} \sqrt{c+i d}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} \sqrt{c-i d}}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} \sqrt{c+i d}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} \sqrt{c-i d}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*Sqrt[c - I*d]*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*Sqrt[c + I*d]*f)","A",7,4,29,0.1379,1,"{3575, 912, 93, 208}"
1287,1,218,0,0.7392842,"\int \frac{1}{(a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} \sqrt{c+i d}}","-\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} \sqrt{c+i d}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*Sqrt[c - I*d]*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*Sqrt[c + I*d]*f) - (2*b^2*Sqrt[c + d*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3569, 3616, 3615, 93, 208}"
1288,1,295,0,1.2688817,"\int \frac{1}{(a+b \tan (e+f x))^{5/2} \sqrt{c+d \tan (e+f x)}} \, dx","Int[1/((a + b*Tan[e + f*x])^(5/2)*Sqrt[c + d*Tan[e + f*x]]),x]","-\frac{4 b^2 \left(-4 a^2 d+3 a b c-b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} \sqrt{c+i d}}","-\frac{4 b^2 \left(-4 a^2 d+3 a b c-b^2 d\right) \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}-\frac{2 b^2 \sqrt{c+d \tan (e+f x)}}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} \sqrt{c-i d}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} \sqrt{c+i d}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*Sqrt[c - I*d]*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*Sqrt[c + I*d]*f) - (2*b^2*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)) - (4*b^2*(3*a*b*c - 4*a^2*d - b^2*d)*Sqrt[c + d*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1289,1,356,0,4.0256102,"\int \frac{(a+b \tan (e+f x))^{7/2}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^(7/2)/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{b \left(2 a d (2 b c-a d)-b^2 \left(3 c^2+d^2\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{b^{5/2} (3 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{3/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}","-\frac{b \left(2 a d (2 b c-a d)-b^2 \left(3 c^2+d^2\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)}-\frac{b^{5/2} (3 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{3/2}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*(a - I*b)^(7/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) + (I*(a + I*b)^(7/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) - (b^(5/2)*(3*b*c - 7*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(5/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^(3/2))/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]]) - (b*(2*a*d*(2*b*c - a*d) - b^2*(3*c^2 + d^2))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d^2*(c^2 + d^2)*f)","A",14,9,29,0.3103,1,"{3565, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1290,1,273,0,2.8361952,"\int \frac{(a+b \tan (e+f x))^{5/2}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^(5/2)/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}","\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{3/2} f}-\frac{2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}{d f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*(a - I*b)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) + (I*(a + I*b)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) + (2*b^(5/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(3/2)*f) - (2*(b*c - a*d)^2*Sqrt[a + b*Tan[e + f*x]])/(d*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",13,8,29,0.2759,1,"{3565, 3655, 6725, 63, 217, 206, 93, 208}"
1291,1,213,0,0.8186104,"\int \frac{(a+b \tan (e+f x))^{3/2}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)/(c + d*Tan[e + f*x])^(3/2),x]","\frac{2 (b c-a d) \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}","\frac{2 (b c-a d) \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*(a - I*b)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) + (I*(a + I*b)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) + (2*(b*c - a*d)*Sqrt[a + b*Tan[e + f*x]])/((c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3567, 3616, 3615, 93, 208}"
1292,1,206,0,0.723656,"\int \frac{\sqrt{a+b \tan (e+f x)}}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]/(c + d*Tan[e + f*x])^(3/2),x]","-\frac{2 d \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}","-\frac{2 d \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) \sqrt{c+d \tan (e+f x)}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{3/2}}+\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{3/2}}",1,"((-I)*Sqrt[a - I*b]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(3/2)*f) + (I*Sqrt[a + I*b]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(3/2)*f) - (2*d*Sqrt[a + b*Tan[e + f*x]])/((c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3568, 3616, 3615, 93, 208}"
1293,1,218,0,0.7568964,"\int \frac{1}{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/(Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{2 d^2 \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{3/2}}","\frac{2 d^2 \sqrt{a+b \tan (e+f x)}}{f \left(c^2+d^2\right) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{3/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*(c - I*d)^(3/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*(c + I*d)^(3/2)*f) + (2*d^2*Sqrt[a + b*Tan[e + f*x]])/((b*c - a*d)*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",8,5,29,0.1724,1,"{3569, 3616, 3615, 93, 208}"
1294,1,301,0,1.2691826,"\int \frac{1}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)),x]","-\frac{2 d \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 b^2}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{3/2}}","-\frac{2 d \left(a^2 d^2+b^2 \left(c^2+2 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 b^2}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{3/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*(c - I*d)^(3/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*(c + I*d)^(3/2)*f) - (2*b^2)/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) - (2*d*(a^2*d^2 + b^2*(c^2 + 2*d^2))*Sqrt[a + b*Tan[e + f*x]])/((a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1295,1,417,0,1.9762904,"\int \frac{1}{(a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{3/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(3/2)),x]","\frac{2 d \left(a^2 b^2 d \left(11 c^2+17 d^2\right)+3 a^4 d^3-6 a b^3 c \left(c^2+d^2\right)+b^4 d \left(5 c^2+8 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{4 b^2 \left(-5 a^2 d+3 a b c-2 b^2 d\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{2 b^2}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{3/2}}","\frac{2 d \left(a^2 b^2 d \left(11 c^2+17 d^2\right)+3 a^4 d^3-6 a b^3 c \left(c^2+d^2\right)+b^4 d \left(5 c^2+8 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{4 b^2 \left(-5 a^2 d+3 a b c-2 b^2 d\right)}{3 f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}-\frac{2 b^2}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} \sqrt{c+d \tan (e+f x)}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{3/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{3/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*(c - I*d)^(3/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*(c + I*d)^(3/2)*f) - (2*b^2)/(3*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)*Sqrt[c + d*Tan[e + f*x]]) - (4*b^2*(3*a*b*c - 5*a^2*d - 2*b^2*d))/(3*(a^2 + b^2)^2*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]]) + (2*d*(3*a^4*d^3 - 6*a*b^3*c*(c^2 + d^2) + b^4*d*(5*c^2 + 8*d^2) + a^2*b^2*d*(11*c^2 + 17*d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^3*(c^2 + d^2)*f*Sqrt[c + d*Tan[e + f*x]])","A",10,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1296,1,470,0,6.2977665,"\int \frac{(a+b \tan (e+f x))^{9/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^(9/2)/(c + d*Tan[e + f*x])^(5/2),x]","\frac{b \left(-4 a^2 b d^2 \left(c^2-2 d^2\right)+4 a^3 c d^3-4 a b^2 c d \left(c^2+4 d^2\right)+b^3 \left(10 c^2 d^2+5 c^4+d^4\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^3 f \left(c^2+d^2\right)^2}-\frac{b^{7/2} (5 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{2 (b c-a d)^2 \left(6 a c d+5 b c^2+11 b d^2\right) (a+b \tan (e+f x))^{3/2}}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{5/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","\frac{b \left(-4 a^2 b d^2 \left(c^2-2 d^2\right)+4 a^3 c d^3-4 a b^2 c d \left(c^2+4 d^2\right)+b^3 \left(10 c^2 d^2+5 c^4+d^4\right)\right) \sqrt{a+b \tan (e+f x)} \sqrt{c+d \tan (e+f x)}}{d^3 f \left(c^2+d^2\right)^2}-\frac{b^{7/2} (5 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{7/2} f}-\frac{2 (b c-a d)^2 \left(6 a c d+5 b c^2+11 b d^2\right) (a+b \tan (e+f x))^{3/2}}{3 d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{5/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^(9/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^(9/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) - (b^(7/2)*(5*b*c - 9*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(7/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^(5/2))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*c - a*d)^2*(5*b*c^2 + 6*a*c*d + 11*b*d^2)*(a + b*Tan[e + f*x])^(3/2))/(3*d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]]) + (b*(4*a^3*c*d^3 - 4*a^2*b*d^2*(c^2 - 2*d^2) - 4*a*b^2*c*d*(c^2 + 4*d^2) + b^3*(5*c^4 + 10*c^2*d^2 + d^4))*Sqrt[a + b*Tan[e + f*x]]*Sqrt[c + d*Tan[e + f*x]])/(d^3*(c^2 + d^2)^2*f)","A",15,10,29,0.3448,1,"{3565, 3645, 3647, 3655, 6725, 63, 217, 206, 93, 208}"
1297,1,347,0,5.5605645,"\int \frac{(a+b \tan (e+f x))^{7/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^(7/2)/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 (b c-a d)^2 \left(2 a c d+b \left(c^2+3 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{3/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","\frac{2 b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b \tan (e+f x)}}{\sqrt{b} \sqrt{c+d \tan (e+f x)}}\right)}{d^{5/2} f}-\frac{2 (b c-a d)^2 \left(2 a c d+b \left(c^2+3 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{d^2 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 (a+b \tan (e+f x))^{3/2}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^(7/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^(7/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) + (2*b^(7/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[b]*Sqrt[c + d*Tan[e + f*x]])])/(d^(5/2)*f) - (2*(b*c - a*d)^2*(a + b*Tan[e + f*x])^(3/2))/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (2*(b*c - a*d)^2*(2*a*c*d + b*(c^2 + 3*d^2))*Sqrt[a + b*Tan[e + f*x]])/(d^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",14,9,29,0.3103,1,"{3565, 3645, 3655, 6725, 63, 217, 206, 93, 208}"
1298,1,292,0,1.5676237,"\int \frac{(a+b \tan (e+f x))^{5/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^(5/2)/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 (b c-a d) \left(6 a c d+b \left(c^2+7 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","\frac{2 (b c-a d) \left(6 a c d+b \left(c^2+7 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}-\frac{2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)}}{3 d f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^(5/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^(5/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) - (2*(b*c - a*d)^2*Sqrt[a + b*Tan[e + f*x]])/(3*d*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(b*c - a*d)*(6*a*c*d + b*(c^2 + 7*d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*d*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3565, 3649, 3616, 3615, 93, 208}"
1299,1,276,0,1.3521106,"\int \frac{(a+b \tan (e+f x))^{3/2}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^(3/2)/(c + d*Tan[e + f*x])^(5/2),x]","\frac{4 \left(-3 a c d+b c^2-2 b d^2\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 (b c-a d) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","\frac{4 \left(-3 a c d+b c^2-2 b d^2\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 (b c-a d) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i (a-i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*(a - I*b)^(3/2)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) + (I*(a + I*b)^(3/2)*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) + (2*(b*c - a*d)*Sqrt[a + b*Tan[e + f*x]])/(3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (4*(b*c^2 - 3*a*c*d - 2*b*d^2)*Sqrt[a + b*Tan[e + f*x]])/(3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3567, 3649, 3616, 3615, 93, 208}"
1300,1,283,0,1.2196383,"\int \frac{\sqrt{a+b \tan (e+f x)}}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[Sqrt[a + b*Tan[e + f*x]]/(c + d*Tan[e + f*x])^(5/2),x]","\frac{2 d \left(6 a c d-b \left(5 c^2-d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}","\frac{2 d \left(6 a c d-b \left(5 c^2-d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{2 d \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (c+d \tan (e+f x))^{3/2}}-\frac{i \sqrt{a-i b} \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c-i d)^{5/2}}+\frac{i \sqrt{a+i b} \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (c+i d)^{5/2}}",1,"((-I)*Sqrt[a - I*b]*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c - I*d)^(5/2)*f) + (I*Sqrt[a + I*b]*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((c + I*d)^(5/2)*f) - (2*d*Sqrt[a + b*Tan[e + f*x]])/(3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*d*(6*a*c*d - b*(5*c^2 - d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(b*c - a*d)*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3568, 3649, 3616, 3615, 93, 208}"
1301,1,295,0,1.2677406,"\int \frac{1}{\sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/(Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{4 d^2 \left(3 a c d-b \left(4 c^2+d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 d^2 \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{5/2}}","-\frac{4 d^2 \left(3 a c d-b \left(4 c^2+d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right)^2 (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}+\frac{2 d^2 \sqrt{a+b \tan (e+f x)}}{3 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a-i b} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f \sqrt{a+i b} (c+i d)^{5/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a - I*b]*(c - I*d)^(5/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/(Sqrt[a + I*b]*(c + I*d)^(5/2)*f) + (2*d^2*Sqrt[a + b*Tan[e + f*x]])/(3*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (4*d^2*(3*a*c*d - b*(4*c^2 + d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(b*c - a*d)^2*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",9,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1302,1,433,0,1.9575888,"\int \frac{1}{(a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(5/2)),x]","\frac{2 \left(-a^2 b d^3 \left(11 c^2+5 d^2\right)+6 a^3 c d^4+6 a b^2 c d^4-b^3 \left(17 c^2 d^3+3 c^4 d+8 d^5\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \left(a^2 d^2+b^2 \left(3 c^2+4 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{2 b^2}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{5/2}}","\frac{2 \left(-a^2 b d^3 \left(11 c^2+5 d^2\right)+6 a^3 c d^4+6 a b^2 c d^4-b^3 \left(17 c^2 d^3+3 c^4 d+8 d^5\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right)^2 (b c-a d)^3 \sqrt{c+d \tan (e+f x)}}-\frac{2 d \left(a^2 d^2+b^2 \left(3 c^2+4 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right) \left(c^2+d^2\right) (b c-a d)^2 (c+d \tan (e+f x))^{3/2}}-\frac{2 b^2}{f \left(a^2+b^2\right) (b c-a d) \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{3/2} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{3/2} (c+i d)^{5/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(3/2)*(c - I*d)^(5/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(3/2)*(c + I*d)^(5/2)*f) - (2*b^2)/((a^2 + b^2)*(b*c - a*d)*f*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) - (2*d*(a^2*d^2 + b^2*(3*c^2 + 4*d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)^2*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) + (2*(6*a^3*c*d^4 + 6*a*b^2*c*d^4 - a^2*b*d^3*(11*c^2 + 5*d^2) - b^3*(3*c^4*d + 17*c^2*d^3 + 8*d^5))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)*(b*c - a*d)^3*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",10,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1303,1,596,0,2.9969366,"\int \frac{1}{(a+b \tan (e+f x))^{5/2} (c+d \tan (e+f x))^{5/2}} \, dx","Int[1/((a + b*Tan[e + f*x])^(5/2)*(c + d*Tan[e + f*x])^(5/2)),x]","-\frac{4 d \left(-a^2 b^3 d \left(28 c^2 d^2+7 c^4+15 d^4\right)+6 a^3 b^2 c d^4-a^4 b d^3 \left(7 c^2+4 d^2\right)+3 a^5 c d^4+3 a b^4 c \left(2 c^2 d^2+c^4+2 d^4\right)-b^5 d \left(15 c^2 d^2+4 c^4+8 d^4\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2 (b c-a d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{2 d \left(a^2 b^2 d \left(13 c^2+15 d^2\right)+a^4 d^3-6 a b^3 c \left(c^2+d^2\right)+b^4 d \left(7 c^2+8 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 (c+d \tan (e+f x))^{3/2}}-\frac{4 b^2 \left(-2 a^2 d+a b c-b^2 d\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{2 b^2}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{5/2}}","-\frac{4 d \left(-a^2 b^3 d \left(28 c^2 d^2+7 c^4+15 d^4\right)+6 a^3 b^2 c d^4-a^4 b d^3 \left(7 c^2+4 d^2\right)+3 a^5 c d^4+3 a b^4 c \left(2 c^2 d^2+c^4+2 d^4\right)-b^5 d \left(15 c^2 d^2+4 c^4+8 d^4\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right)^2 (b c-a d)^4 \sqrt{c+d \tan (e+f x)}}+\frac{2 d \left(a^2 b^2 d \left(13 c^2+15 d^2\right)+a^4 d^3-6 a b^3 c \left(c^2+d^2\right)+b^4 d \left(7 c^2+8 d^2\right)\right) \sqrt{a+b \tan (e+f x)}}{3 f \left(a^2+b^2\right)^2 \left(c^2+d^2\right) (b c-a d)^3 (c+d \tan (e+f x))^{3/2}}-\frac{4 b^2 \left(-2 a^2 d+a b c-b^2 d\right)}{f \left(a^2+b^2\right)^2 (b c-a d)^2 \sqrt{a+b \tan (e+f x)} (c+d \tan (e+f x))^{3/2}}-\frac{2 b^2}{3 f \left(a^2+b^2\right) (b c-a d) (a+b \tan (e+f x))^{3/2} (c+d \tan (e+f x))^{3/2}}-\frac{i \tanh ^{-1}\left(\frac{\sqrt{c-i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a-i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a-i b)^{5/2} (c-i d)^{5/2}}+\frac{i \tanh ^{-1}\left(\frac{\sqrt{c+i d} \sqrt{a+b \tan (e+f x)}}{\sqrt{a+i b} \sqrt{c+d \tan (e+f x)}}\right)}{f (a+i b)^{5/2} (c+i d)^{5/2}}",1,"((-I)*ArcTanh[(Sqrt[c - I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a - I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a - I*b)^(5/2)*(c - I*d)^(5/2)*f) + (I*ArcTanh[(Sqrt[c + I*d]*Sqrt[a + b*Tan[e + f*x]])/(Sqrt[a + I*b]*Sqrt[c + d*Tan[e + f*x]])])/((a + I*b)^(5/2)*(c + I*d)^(5/2)*f) - (2*b^2)/(3*(a^2 + b^2)*(b*c - a*d)*f*(a + b*Tan[e + f*x])^(3/2)*(c + d*Tan[e + f*x])^(3/2)) - (4*b^2*(a*b*c - 2*a^2*d - b^2*d))/((a^2 + b^2)^2*(b*c - a*d)^2*f*Sqrt[a + b*Tan[e + f*x]]*(c + d*Tan[e + f*x])^(3/2)) + (2*d*(a^4*d^3 - 6*a*b^3*c*(c^2 + d^2) + b^4*d*(7*c^2 + 8*d^2) + a^2*b^2*d*(13*c^2 + 15*d^2))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^3*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^(3/2)) - (4*d*(3*a^5*c*d^4 + 6*a^3*b^2*c*d^4 - a^4*b*d^3*(7*c^2 + 4*d^2) + 3*a*b^4*c*(c^4 + 2*c^2*d^2 + 2*d^4) - b^5*d*(4*c^4 + 15*c^2*d^2 + 8*d^4) - a^2*b^3*d*(7*c^4 + 28*c^2*d^2 + 15*d^4))*Sqrt[a + b*Tan[e + f*x]])/(3*(a^2 + b^2)^2*(b*c - a*d)^4*(c^2 + d^2)^2*f*Sqrt[c + d*Tan[e + f*x]])","A",11,6,29,0.2069,1,"{3569, 3649, 3616, 3615, 93, 208}"
1304,1,257,0,0.304083,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^n \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^n,x]","\frac{(a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}","\frac{(a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(a+b \tan (e+f x))^{m+1} (c+d \tan (e+f x))^n \left(\frac{b (c+d \tan (e+f x))}{b c-a d}\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}",1,"(AppellF1[1 + m, -n, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^n)/(2*(I*a + b)*f*(1 + m)*((b*(c + d*Tan[e + f*x]))/(b*c - a*d))^n) - (AppellF1[1 + m, -n, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x])^n)/(2*(I*a - b)*f*(1 + m)*((b*(c + d*Tan[e + f*x]))/(b*c - a*d))^n)","A",7,4,25,0.1600,1,"{3575, 912, 137, 136}"
1305,1,234,0,0.4748963,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^3 \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^3,x]","-\frac{d^2 (a d-b c (2 m+5)) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+1) (m+2)}+\frac{d^2 (c+d \tan (e+f x)) (a+b \tan (e+f x))^{m+1}}{b f (m+2)}+\frac{(c-i d)^3 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(-d+i c)^3 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}","\frac{d^2 (3 b c-a d) (a+b \tan (e+f x))^{m+1}}{b^2 f (m+1)}+\frac{d^3 (a+b \tan (e+f x))^{m+2}}{b^2 f (m+2)}+\frac{(d+i c)^3 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (a-i b)}-\frac{(-d+i c)^3 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}",1,"-((d^2*(a*d - b*c*(5 + 2*m))*(a + b*Tan[e + f*x])^(1 + m))/(b^2*f*(1 + m)*(2 + m))) + ((c - I*d)^3*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) - ((I*c - d)^3*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*f*(1 + m)) + (d^2*(a + b*Tan[e + f*x])^(1 + m)*(c + d*Tan[e + f*x]))/(b*f*(2 + m))","A",7,5,25,0.2000,1,"{3566, 3630, 3539, 3537, 68}"
1306,1,176,0,0.2132984,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^2 \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^2,x]","\frac{(c-i d)^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d)^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{b f (m+1)}","\frac{(c-i d)^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}-\frac{(c+i d)^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a)}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{b f (m+1)}",1,"(d^2*(a + b*Tan[e + f*x])^(1 + m))/(b*f*(1 + m)) + ((c - I*d)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) - ((c + I*d)^2*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a - b)*f*(1 + m))","A",6,4,25,0.1600,1,"{3543, 3539, 3537, 68}"
1307,1,143,0,0.1342087,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x)) \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x]),x]","\frac{(c-i d) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(-d+i c) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}","\frac{(c-i d) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a)}+\frac{(-d+i c) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b)}",1,"((c - I*d)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*f*(1 + m)) + ((I*c - d)*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*f*(1 + m))","A",5,3,23,0.1304,1,"{3539, 3537, 68}"
1308,1,167,0,0.2511536,"\int (a+b \tan (e+f x))^m \, dx","Int[(a + b*Tan[e + f*x])^m,x]","\frac{b (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} f (m+1) \left(a-\sqrt{-b^2}\right)}-\frac{b (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} f (m+1) \left(a+\sqrt{-b^2}\right)}","\frac{b (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} f (m+1) \left(a-\sqrt{-b^2}\right)}-\frac{b (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+\sqrt{-b^2}}\right)}{2 \sqrt{-b^2} f (m+1) \left(a+\sqrt{-b^2}\right)}",1,"(b*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - Sqrt[-b^2])]*(a + b*Tan[e + f*x])^(1 + m))/(2*Sqrt[-b^2]*(a - Sqrt[-b^2])*f*(1 + m)) - (b*Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + Sqrt[-b^2])]*(a + b*Tan[e + f*x])^(1 + m))/(2*Sqrt[-b^2]*(a + Sqrt[-b^2])*f*(1 + m))","A",5,3,12,0.2500,1,"{3485, 712, 68}"
1309,1,223,0,0.3741736,"\int \frac{(a+b \tan (e+f x))^m}{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^m/(c + d*Tan[e + f*x]),x]","\frac{d^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right) (b c-a d)}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)}-\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)}","\frac{d^2 (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right) (b c-a d)}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)}-\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)}",1,"(Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*(c - I*d)*f*(1 + m)) - (Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*(I*c - d)*f*(1 + m)) + (d^2*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)*(c^2 + d^2)*f*(1 + m))","A",8,5,25,0.2000,1,"{3574, 3539, 3537, 68, 3634}"
1310,1,299,0,0.8047987,"\int \frac{(a+b \tan (e+f x))^m}{(c+d \tan (e+f x))^2} \, dx","Int[(a + b*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^2,x]","-\frac{d^2 \left(2 a c d-b c^2 (2-m)+b d^2 m\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right)^2 (b c-a d)^2}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^2}-\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (c+i d)^2}","-\frac{d^2 \left(2 a c d-b \left(c^2 (2-m)-d^2 m\right)\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{f (m+1) \left(c^2+d^2\right)^2 (b c-a d)^2}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^2}-\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (c+i d)^2}",1,"(Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*(c - I*d)^2*f*(1 + m)) - (Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a - b)*(c + I*d)^2*f*(1 + m)) - (d^2*(2*a*c*d - b*c^2*(2 - m) + b*d^2*m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)^2*(c^2 + d^2)^2*f*(1 + m)) + (d^2*(a + b*Tan[e + f*x])^(1 + m))/((b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x]))","A",9,6,25,0.2400,1,"{3569, 3653, 3539, 3537, 68, 3634}"
1311,1,455,0,1.4905175,"\int \frac{(a+b \tan (e+f x))^m}{(c+d \tan (e+f x))^3} \, dx","Int[(a + b*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^3,x]","\frac{d^2 \left(2 a^2 d^2 \left(3 c^2-d^2\right)-4 a b c d \left(c^2 (3-m)-d^2 (m+1)\right)+b^2 \left(-\left(2 c^2 d^2 \left(-m^2+3 m+1\right)+c^4 \left(-\left(m^2-5 m+6\right)\right)+d^4 (1-m) m\right)\right)\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{2 f (m+1) \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{d^2 \left(4 a c d-b c^2 (5-m)-b d^2 (1-m)\right) (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^3}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)^3}","\frac{d^2 \left(2 a^2 d^2 \left(3 c^2-d^2\right)-4 a b c d \left(c^2 (3-m)-d^2 (m+1)\right)+b^2 \left(-\left(2 c^2 d^2 \left(-m^2+3 m+1\right)+c^4 \left(-\left(m^2-5 m+6\right)\right)+d^4 (1-m) m\right)\right)\right) (a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d}\right)}{2 f (m+1) \left(c^2+d^2\right)^3 (b c-a d)^3}-\frac{d^2 \left(4 a c d-b \left(c^2 (5-m)+d^2 (1-m)\right)\right) (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right)^2 (b c-a d)^2 (c+d \tan (e+f x))}+\frac{d^2 (a+b \tan (e+f x))^{m+1}}{2 f \left(c^2+d^2\right) (b c-a d) (c+d \tan (e+f x))^2}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (c-i d)^3}+\frac{(a+b \tan (e+f x))^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (a+i b) (-d+i c)^3}",1,"(Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(I*a + b)*(c - I*d)^3*f*(1 + m)) + (Hypergeometric2F1[1, 1 + m, 2 + m, (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m))/(2*(a + I*b)*(I*c - d)^3*f*(1 + m)) + (d^2*(2*a^2*d^2*(3*c^2 - d^2) - 4*a*b*c*d*(c^2*(3 - m) - d^2*(1 + m)) - b^2*(d^4*(1 - m)*m + 2*c^2*d^2*(1 + 3*m - m^2) - c^4*(6 - 5*m + m^2)))*Hypergeometric2F1[1, 1 + m, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d))]*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)^3*(c^2 + d^2)^3*f*(1 + m)) + (d^2*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)*(c^2 + d^2)*f*(c + d*Tan[e + f*x])^2) - (d^2*(4*a*c*d - b*d^2*(1 - m) - b*c^2*(5 - m))*(a + b*Tan[e + f*x])^(1 + m))/(2*(b*c - a*d)^2*(c^2 + d^2)^2*f*(c + d*Tan[e + f*x]))","A",10,7,25,0.2800,1,"{3569, 3649, 3653, 3539, 3537, 68, 3634}"
1312,1,283,0,0.357141,"\int (a+b \tan (e+f x))^m (c+d \tan (e+f x))^{3/2} \, dx","Int[(a + b*Tan[e + f*x])^m*(c + d*Tan[e + f*x])^(3/2),x]","\frac{(b c-a d) \sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 b f (m+1) (b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 b f (m+1) (-b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}","\frac{(b c-a d) \sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 b f (m+1) (b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}-\frac{(b c-a d) \sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 b f (m+1) (-b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}",1,"((b*c - a*d)*AppellF1[1 + m, -3/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[c + d*Tan[e + f*x]])/(2*b*(I*a + b)*f*(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)]) - ((b*c - a*d)*AppellF1[1 + m, -3/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[c + d*Tan[e + f*x]])/(2*(I*a - b)*b*f*(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])","A",7,4,27,0.1481,1,"{3575, 912, 137, 136}"
1313,1,261,0,0.2834939,"\int (a+b \tan (e+f x))^m \sqrt{c+d \tan (e+f x)} \, dx","Int[(a + b*Tan[e + f*x])^m*Sqrt[c + d*Tan[e + f*x]],x]","\frac{\sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}-\frac{\sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}","\frac{\sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}-\frac{\sqrt{c+d \tan (e+f x)} (a+b \tan (e+f x))^{m+1} F_1\left(m+1;-\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}}}",1,"(AppellF1[1 + m, -1/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[c + d*Tan[e + f*x]])/(2*(I*a + b)*f*(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)]) - (AppellF1[1 + m, -1/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[c + d*Tan[e + f*x]])/(2*(I*a - b)*f*(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])","A",7,4,27,0.1481,1,"{3575, 912, 137, 136}"
1314,1,261,0,0.2779978,"\int \frac{(a+b \tan (e+f x))^m}{\sqrt{c+d \tan (e+f x)}} \, dx","Int[(a + b*Tan[e + f*x])^m/Sqrt[c + d*Tan[e + f*x]],x]","\frac{(a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) \sqrt{c+d \tan (e+f x)}}-\frac{(a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) \sqrt{c+d \tan (e+f x)}}","\frac{(a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) \sqrt{c+d \tan (e+f x)}}-\frac{(a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{1}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) \sqrt{c+d \tan (e+f x)}}",1,"(AppellF1[1 + m, 1/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a + b)*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]]) - (AppellF1[1 + m, 1/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a - b)*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]])","A",7,4,27,0.1481,1,"{3575, 912, 137, 136}"
1315,1,283,0,0.3368094,"\int \frac{(a+b \tan (e+f x))^m}{(c+d \tan (e+f x))^{3/2}} \, dx","Int[(a + b*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^(3/2),x]","\frac{b (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{b (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (b c-a d) \sqrt{c+d \tan (e+f x)}}","\frac{b (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (b c-a d) \sqrt{c+d \tan (e+f x)}}-\frac{b (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{3}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (b c-a d) \sqrt{c+d \tan (e+f x)}}",1,"(b*AppellF1[1 + m, 3/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a + b)*(b*c - a*d)*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]]) - (b*AppellF1[1 + m, 3/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a - b)*(b*c - a*d)*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]])","A",7,4,27,0.1481,1,"{3575, 912, 137, 136}"
1316,1,287,0,0.3580106,"\int \frac{(a+b \tan (e+f x))^m}{(c+d \tan (e+f x))^{5/2}} \, dx","Int[(a + b*Tan[e + f*x])^m/(c + d*Tan[e + f*x])^(5/2),x]","\frac{b^2 (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{b^2 (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}","\frac{b^2 (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a-i b}\right)}{2 f (m+1) (b+i a) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}-\frac{b^2 (a+b \tan (e+f x))^{m+1} \sqrt{\frac{b (c+d \tan (e+f x))}{b c-a d}} F_1\left(m+1;\frac{5}{2},1;m+2;-\frac{d (a+b \tan (e+f x))}{b c-a d},\frac{a+b \tan (e+f x)}{a+i b}\right)}{2 f (m+1) (-b+i a) (b c-a d)^2 \sqrt{c+d \tan (e+f x)}}",1,"(b^2*AppellF1[1 + m, 5/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a - I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a + b)*(b*c - a*d)^2*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]]) - (b^2*AppellF1[1 + m, 5/2, 1, 2 + m, -((d*(a + b*Tan[e + f*x]))/(b*c - a*d)), (a + b*Tan[e + f*x])/(a + I*b)]*(a + b*Tan[e + f*x])^(1 + m)*Sqrt[(b*(c + d*Tan[e + f*x]))/(b*c - a*d)])/(2*(I*a - b)*(b*c - a*d)^2*f*(1 + m)*Sqrt[c + d*Tan[e + f*x]])","A",7,4,27,0.1481,1,"{3575, 912, 137, 136}"
1317,1,99,0,0.1872865,"\int \left(c (d \tan (e+f x))^p\right)^n (a+i a \tan (e+f x))^m \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + I*a*Tan[e + f*x])^m,x]","\frac{\tan (e+f x) (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m F_1(n p+1;1-m,1;n p+2;-i \tan (e+f x),i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}","\frac{\tan (e+f x) (1+i \tan (e+f x))^{-m} (a+i a \tan (e+f x))^m F_1(n p+1;1-m,1;n p+2;-i \tan (e+f x),i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}",1,"(AppellF1[1 + n*p, 1 - m, 1, 2 + n*p, (-I)*Tan[e + f*x], I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n*(a + I*a*Tan[e + f*x])^m)/(f*(1 + n*p)*(1 + I*Tan[e + f*x])^m)","A",4,4,30,0.1333,1,"{3578, 3564, 135, 133}"
1318,1,132,0,0.3106868,"\int \left(c (d \tan (e+f x))^p\right)^n (a+i a \tan (e+f x))^3 \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + I*a*Tan[e + f*x])^3,x]","\frac{4 a^3 \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}-\frac{i a^3 \tan ^2(e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}-\frac{3 a^3 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}","\frac{4 a^3 \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}-\frac{i a^3 \tan ^2(e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}-\frac{3 a^3 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}",1,"(-3*a^3*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + (4*a^3*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) - (I*a^3*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(f*(2 + n*p))","A",8,5,30,0.1667,1,"{1586, 6677, 88, 64, 43}"
1319,1,93,0,0.2051801,"\int \left(c (d \tan (e+f x))^p\right)^n (a+i a \tan (e+f x))^2 \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + I*a*Tan[e + f*x])^2,x]","-\frac{a^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{2 a^2 \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}","-\frac{a^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{2 a^2 \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}",1,"-((a^2*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p))) + (2*a^2*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p))","A",5,4,30,0.1333,1,"{1586, 6677, 80, 64}"
1320,1,54,0,0.1045386,"\int \left(c (d \tan (e+f x))^p\right)^n (a+i a \tan (e+f x)) \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + I*a*Tan[e + f*x]),x]","\frac{a \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}","\frac{a \tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}",1,"(a*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p))","A",4,3,28,0.1071,1,"{12, 6677, 64}"
1321,1,134,0,0.2762767,"\int \frac{\left(c (d \tan (e+f x))^p\right)^n}{a+i a \tan (e+f x)} \, dx","Int[(c*(d*Tan[e + f*x])^p)^n/(a + I*a*Tan[e + f*x]),x]","\frac{\tan (e+f x) \, _2F_1\left(2,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{a f (n p+1)}-\frac{i \tan ^2(e+f x) \, _2F_1\left(2,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{a f (n p+2)}","\frac{\tan (e+f x) \, _2F_1\left(2,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{a f (n p+1)}-\frac{i \tan ^2(e+f x) \, _2F_1\left(2,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{a f (n p+2)}",1,"(Hypergeometric2F1[2, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(a*f*(1 + n*p)) - (I*Hypergeometric2F1[2, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(a*f*(2 + n*p))","A",8,5,30,0.1667,1,"{6677, 848, 82, 73, 364}"
1322,1,227,0,0.4142282,"\int \frac{\left(c (d \tan (e+f x))^p\right)^n}{(a+i a \tan (e+f x))^2} \, dx","Int[(c*(d*Tan[e + f*x])^p)^n/(a + I*a*Tan[e + f*x])^2,x]","\frac{\left(2 n^2 p^2-4 n p+1\right) \tan (e+f x) \, _2F_1(1,n p+1;n p+2;-i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{8 a^2 f (n p+1)}+\frac{\tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{8 a^2 f (n p+1)}+\frac{(2-n p) \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{4 a^2 f (1+i \tan (e+f x))}+\frac{\tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{4 a^2 f (1+i \tan (e+f x))^2}","\frac{\left(2 n^2 p^2-4 n p+1\right) \tan (e+f x) \, _2F_1(1,n p+1;n p+2;-i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{8 a^2 f (n p+1)}+\frac{\tan (e+f x) \, _2F_1(1,n p+1;n p+2;i \tan (e+f x)) \left(c (d \tan (e+f x))^p\right)^n}{8 a^2 f (n p+1)}+\frac{(2-n p) \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{4 a^2 f (1+i \tan (e+f x))}+\frac{\tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{4 a^2 f (1+i \tan (e+f x))^2}",1,"((1 - 4*n*p + 2*n^2*p^2)*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, (-I)*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(8*a^2*f*(1 + n*p)) + (Hypergeometric2F1[1, 1 + n*p, 2 + n*p, I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(8*a^2*f*(1 + n*p)) + (Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(4*a^2*f*(1 + I*Tan[e + f*x])^2) + ((2 - n*p)*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(4*a^2*f*(1 + I*Tan[e + f*x]))","A",8,6,30,0.2000,1,"{6677, 848, 103, 151, 156, 64}"
1323,1,201,0,0.2728856,"\int \left(c (d \tan (e+f x))^p\right)^n (a+b \tan (e+f x))^m \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x])^m,x]","\frac{\tan (e+f x) (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} \left(c (d \tan (e+f x))^p\right)^n F_1\left(n p+1;-m,1;n p+2;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 f (n p+1)}+\frac{\tan (e+f x) (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} \left(c (d \tan (e+f x))^p\right)^n F_1\left(n p+1;-m,1;n p+2;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 f (n p+1)}","\frac{\tan (e+f x) (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} \left(c (d \tan (e+f x))^p\right)^n F_1\left(n p+1;-m,1;n p+2;-\frac{b \tan (e+f x)}{a},-i \tan (e+f x)\right)}{2 f (n p+1)}+\frac{\tan (e+f x) (a+b \tan (e+f x))^m \left(\frac{b \tan (e+f x)}{a}+1\right)^{-m} \left(c (d \tan (e+f x))^p\right)^n F_1\left(n p+1;-m,1;n p+2;-\frac{b \tan (e+f x)}{a},i \tan (e+f x)\right)}{2 f (n p+1)}",1,"(AppellF1[1 + n*p, -m, 1, 2 + n*p, -((b*Tan[e + f*x])/a), (-I)*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x])^m)/(2*f*(1 + n*p)*(1 + (b*Tan[e + f*x])/a)^m) + (AppellF1[1 + n*p, -m, 1, 2 + n*p, -((b*Tan[e + f*x])/a), I*Tan[e + f*x]]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x])^m)/(2*f*(1 + n*p)*(1 + (b*Tan[e + f*x])/a)^m)","A",8,5,27,0.1852,1,"{3578, 3575, 912, 135, 133}"
1324,1,219,0,0.3671514,"\int \left(c (d \tan (e+f x))^p\right)^n (a+b \tan (e+f x))^3 \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x])^3,x]","\frac{b \left(3 a^2-b^2\right) \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}+\frac{a \left(a^2-3 b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{3 a b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{b^3 \tan ^2(e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}","\frac{b \left(3 a^2-b^2\right) \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}+\frac{a \left(a^2-3 b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{3 a b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{b^3 \tan ^2(e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}",1,"(3*a*b^2*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + (a*(a^2 - 3*b^2)*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + (b^3*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(f*(2 + n*p)) + (b*(3*a^2 - b^2)*Hypergeometric2F1[1, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(f*(2 + n*p))","A",7,4,27,0.1481,1,"{6677, 1802, 808, 364}"
1325,1,171,0,0.3200684,"\int \left(c (d \tan (e+f x))^p\right)^n (a+b \tan (e+f x))^2 \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x])^2,x]","\frac{\left(a^2-b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{2 a b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}","\frac{\left(a^2-b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{2 a b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}",1,"(b^2*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + ((a^2 - b^2)*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + (2*a*b*Hypergeometric2F1[1, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(f*(2 + n*p))","A",7,4,27,0.1481,1,"{6677, 1802, 808, 364}"
1326,1,127,0,0.1781317,"\int \left(c (d \tan (e+f x))^p\right)^n (a+b \tan (e+f x)) \, dx","Int[(c*(d*Tan[e + f*x])^p)^n*(a + b*Tan[e + f*x]),x]","\frac{a \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}","\frac{a \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+1)}+\frac{b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f (n p+2)}",1,"(a*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(f*(1 + n*p)) + (b*Hypergeometric2F1[1, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/(f*(2 + n*p))","A",5,3,25,0.1200,1,"{6677, 808, 364}"
1327,1,216,0,0.3909991,"\int \frac{\left(c (d \tan (e+f x))^p\right)^n}{a+b \tan (e+f x)} \, dx","Int[(c*(d*Tan[e + f*x])^p)^n/(a + b*Tan[e + f*x]),x]","-\frac{b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right) (n p+2)}+\frac{a \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right) (n p+1)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(1,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{a f \left(a^2+b^2\right) (n p+1)}","-\frac{b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right) (n p+2)}+\frac{a \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right) (n p+1)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(1,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{a f \left(a^2+b^2\right) (n p+1)}",1,"(a*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/((a^2 + b^2)*f*(1 + n*p)) + (b^2*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, -((b*Tan[e + f*x])/a)]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(a*(a^2 + b^2)*f*(1 + n*p)) - (b*Hypergeometric2F1[1, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/((a^2 + b^2)*f*(2 + n*p))","A",8,5,27,0.1852,1,"{6677, 961, 64, 808, 364}"
1328,1,293,0,0.4815207,"\int \frac{\left(c (d \tan (e+f x))^p\right)^n}{(a+b \tan (e+f x))^2} \, dx","Int[(c*(d*Tan[e + f*x])^p)^n/(a + b*Tan[e + f*x])^2,x]","-\frac{2 a b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right)^2 (n p+2)}+\frac{\left(a^2-b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right)^2 (n p+1)}+\frac{2 b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(1,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{f \left(a^2+b^2\right)^2 (n p+1)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(2,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{a^2 f \left(a^2+b^2\right) (n p+1)}","-\frac{2 a b \tan ^2(e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+2);\frac{1}{2} (n p+4);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right)^2 (n p+2)}+\frac{\left(a^2-b^2\right) \tan (e+f x) \, _2F_1\left(1,\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);-\tan ^2(e+f x)\right) \left(c (d \tan (e+f x))^p\right)^n}{f \left(a^2+b^2\right)^2 (n p+1)}+\frac{2 b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(1,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{f \left(a^2+b^2\right)^2 (n p+1)}+\frac{b^2 \tan (e+f x) \left(c (d \tan (e+f x))^p\right)^n \, _2F_1\left(2,n p+1;n p+2;-\frac{b \tan (e+f x)}{a}\right)}{a^2 f \left(a^2+b^2\right) (n p+1)}",1,"((a^2 - b^2)*Hypergeometric2F1[1, (1 + n*p)/2, (3 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/((a^2 + b^2)^2*f*(1 + n*p)) + (2*b^2*Hypergeometric2F1[1, 1 + n*p, 2 + n*p, -((b*Tan[e + f*x])/a)]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/((a^2 + b^2)^2*f*(1 + n*p)) + (b^2*Hypergeometric2F1[2, 1 + n*p, 2 + n*p, -((b*Tan[e + f*x])/a)]*Tan[e + f*x]*(c*(d*Tan[e + f*x])^p)^n)/(a^2*(a^2 + b^2)*f*(1 + n*p)) - (2*a*b*Hypergeometric2F1[1, (2 + n*p)/2, (4 + n*p)/2, -Tan[e + f*x]^2]*Tan[e + f*x]^2*(c*(d*Tan[e + f*x])^p)^n)/((a^2 + b^2)^2*f*(2 + n*p))","A",9,5,27,0.1852,1,"{6677, 961, 64, 808, 364}"