1,1,175,0,0.663667," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{i a \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{6 A a - 8 i B a + \left(18 A a e^{2 i c} - 18 i B a e^{2 i c}\right) e^{2 i d x} + \left(12 A a e^{4 i c} - 18 i B a e^{4 i c}\right) e^{4 i d x}}{- 3 i d e^{6 i c} e^{6 i d x} - 9 i d e^{4 i c} e^{4 i d x} - 9 i d e^{2 i c} e^{2 i d x} - 3 i d}"," ",0,"I*a*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (6*A*a - 8*I*B*a + (18*A*a*exp(2*I*c) - 18*I*B*a*exp(2*I*c))*exp(2*I*d*x) + (12*A*a*exp(4*I*c) - 18*I*B*a*exp(4*I*c))*exp(4*I*d*x))/(-3*I*d*exp(6*I*c)*exp(6*I*d*x) - 9*I*d*exp(4*I*c)*exp(4*I*d*x) - 9*I*d*exp(2*I*c)*exp(2*I*d*x) - 3*I*d)","B",0
2,1,116,0,0.544433," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","- \frac{a \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 2 i A a - 2 B a + \left(- 2 i A a e^{2 i c} - 4 B a e^{2 i c}\right) e^{2 i d x}}{i d e^{4 i c} e^{4 i d x} + 2 i d e^{2 i c} e^{2 i d x} + i d}"," ",0,"-a*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-2*I*A*a - 2*B*a + (-2*I*A*a*exp(2*I*c) - 4*B*a*exp(2*I*c))*exp(2*I*d*x))/(I*d*exp(4*I*c)*exp(4*I*d*x) + 2*I*d*exp(2*I*c)*exp(2*I*d*x) + I*d)","B",0
3,1,53,0,0.421361," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 B a}{- d e^{2 i c} e^{2 i d x} - d} - \frac{i a \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d}"," ",0,"2*B*a/(-d*exp(2*I*c)*exp(2*I*d*x) - d) - I*a*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d","A",0
4,1,97,0,1.942115," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{A a \log{\left(\frac{A a + i B a}{- A a e^{2 i c} - i B a e^{2 i c}} + e^{2 i d x} \right)}}{d} - \frac{i B a \log{\left(\frac{- A a - i B a}{- A a e^{2 i c} - i B a e^{2 i c}} + e^{2 i d x} \right)}}{d}"," ",0,"A*a*log((A*a + I*B*a)/(-A*a*exp(2*I*c) - I*B*a*exp(2*I*c)) + exp(2*I*d*x))/d - I*B*a*log((-A*a - I*B*a)/(-A*a*exp(2*I*c) - I*B*a*exp(2*I*c)) + exp(2*I*d*x))/d","B",0
5,1,53,0,0.460349," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{2 i A a}{- d e^{2 i c} e^{2 i d x} + d} + \frac{i a \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d}"," ",0,"2*I*A*a/(-d*exp(2*I*c)*exp(2*I*d*x) + d) + I*a*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d","A",0
6,1,114,0,0.799050," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","- \frac{a \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 2 i A a - 2 B a + \left(4 i A a e^{2 i c} + 2 B a e^{2 i c}\right) e^{2 i d x}}{i d e^{4 i c} e^{4 i d x} - 2 i d e^{2 i c} e^{2 i d x} + i d}"," ",0,"-a*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-2*I*A*a - 2*B*a + (4*I*A*a*exp(2*I*c) + 2*B*a*exp(2*I*c))*exp(2*I*d*x))/(I*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*d*exp(2*I*c)*exp(2*I*d*x) + I*d)","B",0
7,1,168,0,0.778542," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","- \frac{i a \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 8 i A a - 6 B a + \left(18 i A a e^{2 i c} + 18 B a e^{2 i c}\right) e^{2 i d x} + \left(- 18 i A a e^{4 i c} - 12 B a e^{4 i c}\right) e^{4 i d x}}{- 3 d e^{6 i c} e^{6 i d x} + 9 d e^{4 i c} e^{4 i d x} - 9 d e^{2 i c} e^{2 i d x} + 3 d}"," ",0,"-I*a*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-8*I*A*a - 6*B*a + (18*I*A*a*exp(2*I*c) + 18*B*a*exp(2*I*c))*exp(2*I*d*x) + (-18*I*A*a*exp(4*I*c) - 12*B*a*exp(4*I*c))*exp(4*I*d*x))/(-3*d*exp(6*I*c)*exp(6*I*d*x) + 9*d*exp(4*I*c)*exp(4*I*d*x) - 9*d*exp(2*I*c)*exp(2*I*d*x) + 3*d)","B",0
8,1,218,0,3.769422," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\frac{a \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 8 A a + 8 i B a + \left(32 A a e^{2 i c} - 26 i B a e^{2 i c}\right) e^{2 i d x} + \left(- 36 A a e^{4 i c} + 36 i B a e^{4 i c}\right) e^{4 i d x} + \left(24 A a e^{6 i c} - 18 i B a e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} + 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} + 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"a*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-8*A*a + 8*I*B*a + (32*A*a*exp(2*I*c) - 26*I*B*a*exp(2*I*c))*exp(2*I*d*x) + (-36*A*a*exp(4*I*c) + 36*I*B*a*exp(4*I*c))*exp(4*I*d*x) + (24*A*a*exp(6*I*c) - 18*I*B*a*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) + 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) + 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","B",0
9,1,243,0,1.261732," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\frac{2 i a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 14 i A a^{2} - 16 B a^{2} + \left(- 50 i A a^{2} e^{2 i c} - 58 B a^{2} e^{2 i c}\right) e^{2 i d x} + \left(- 66 i A a^{2} e^{4 i c} - 72 B a^{2} e^{4 i c}\right) e^{4 i d x} + \left(- 30 i A a^{2} e^{6 i c} - 42 B a^{2} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} - 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} - 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"2*I*a**2*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-14*I*A*a**2 - 16*B*a**2 + (-50*I*A*a**2*exp(2*I*c) - 58*B*a**2*exp(2*I*c))*exp(2*I*d*x) + (-66*I*A*a**2*exp(4*I*c) - 72*B*a**2*exp(4*I*c))*exp(4*I*d*x) + (-30*I*A*a**2*exp(6*I*c) - 42*B*a**2*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) - 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) - 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","A",0
10,1,178,0,0.698407," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- \frac{2 a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 12 A a^{2} + 14 i B a^{2} + \left(- 30 A a^{2} e^{2 i c} + 36 i B a^{2} e^{2 i c}\right) e^{2 i d x} + \left(- 18 A a^{2} e^{4 i c} + 30 i B a^{2} e^{4 i c}\right) e^{4 i d x}}{3 d e^{6 i c} e^{6 i d x} + 9 d e^{4 i c} e^{4 i d x} + 9 d e^{2 i c} e^{2 i d x} + 3 d}"," ",0,"-2*a**2*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-12*A*a**2 + 14*I*B*a**2 + (-30*A*a**2*exp(2*I*c) + 36*I*B*a**2*exp(2*I*c))*exp(2*I*d*x) + (-18*A*a**2*exp(4*I*c) + 30*I*B*a**2*exp(4*I*c))*exp(4*I*d*x))/(3*d*exp(6*I*c)*exp(6*I*d*x) + 9*d*exp(4*I*c)*exp(4*I*d*x) + 9*d*exp(2*I*c)*exp(2*I*d*x) + 3*d)","B",0
11,1,128,0,0.612434," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- \frac{2 i a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 2 A a^{2} + 4 i B a^{2} + \left(- 2 A a^{2} e^{2 i c} + 6 i B a^{2} e^{2 i c}\right) e^{2 i d x}}{- i d e^{4 i c} e^{4 i d x} - 2 i d e^{2 i c} e^{2 i d x} - i d}"," ",0,"-2*I*a**2*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-2*A*a**2 + 4*I*B*a**2 + (-2*A*a**2*exp(2*I*c) + 6*I*B*a**2*exp(2*I*c))*exp(2*I*d*x))/(-I*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*d*exp(2*I*c)*exp(2*I*d*x) - I*d)","A",0
12,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
13,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
14,1,124,0,0.716628," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- \frac{2 a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 4 i A a^{2} - 2 B a^{2} + \left(6 i A a^{2} e^{2 i c} + 2 B a^{2} e^{2 i c}\right) e^{2 i d x}}{i d e^{4 i c} e^{4 i d x} - 2 i d e^{2 i c} e^{2 i d x} + i d}"," ",0,"-2*a**2*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-4*I*A*a**2 - 2*B*a**2 + (6*I*A*a**2*exp(2*I*c) + 2*B*a**2*exp(2*I*c))*exp(2*I*d*x))/(I*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*d*exp(2*I*c)*exp(2*I*d*x) + I*d)","A",0
15,1,182,0,2.356987," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- \frac{2 i a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 14 i A a^{2} - 12 B a^{2} + \left(36 i A a^{2} e^{2 i c} + 30 B a^{2} e^{2 i c}\right) e^{2 i d x} + \left(- 30 i A a^{2} e^{4 i c} - 18 B a^{2} e^{4 i c}\right) e^{4 i d x}}{- 3 d e^{6 i c} e^{6 i d x} + 9 d e^{4 i c} e^{4 i d x} - 9 d e^{2 i c} e^{2 i d x} + 3 d}"," ",0,"-2*I*a**2*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-14*I*A*a**2 - 12*B*a**2 + (36*I*A*a**2*exp(2*I*c) + 30*B*a**2*exp(2*I*c))*exp(2*I*d*x) + (-30*I*A*a**2*exp(4*I*c) - 18*B*a**2*exp(4*I*c))*exp(4*I*d*x))/(-3*d*exp(6*I*c)*exp(6*I*d*x) + 9*d*exp(4*I*c)*exp(4*I*d*x) - 9*d*exp(2*I*c)*exp(2*I*d*x) + 3*d)","A",0
16,1,235,0,1.388589," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\frac{2 a^{2} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 16 A a^{2} + 14 i B a^{2} + \left(58 A a^{2} e^{2 i c} - 50 i B a^{2} e^{2 i c}\right) e^{2 i d x} + \left(- 72 A a^{2} e^{4 i c} + 66 i B a^{2} e^{4 i c}\right) e^{4 i d x} + \left(42 A a^{2} e^{6 i c} - 30 i B a^{2} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} + 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} + 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"2*a**2*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-16*A*a**2 + 14*I*B*a**2 + (58*A*a**2*exp(2*I*c) - 50*I*B*a**2*exp(2*I*c))*exp(2*I*d*x) + (-72*A*a**2*exp(4*I*c) + 66*I*B*a**2*exp(4*I*c))*exp(4*I*d*x) + (42*A*a**2*exp(6*I*c) - 30*I*B*a**2*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) + 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) + 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","A",0
17,1,303,0,1.162905," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{4 i a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 150 A a^{3} + 166 i B a^{3} + \left(- 690 A a^{3} e^{2 i c} + 770 i B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(- 1230 A a^{3} e^{4 i c} + 1390 i B a^{3} e^{4 i c}\right) e^{4 i d x} + \left(- 1050 A a^{3} e^{6 i c} + 1170 i B a^{3} e^{6 i c}\right) e^{6 i d x} + \left(- 360 A a^{3} e^{8 i c} + 480 i B a^{3} e^{8 i c}\right) e^{8 i d x}}{15 i d e^{10 i c} e^{10 i d x} + 75 i d e^{8 i c} e^{8 i d x} + 150 i d e^{6 i c} e^{6 i d x} + 150 i d e^{4 i c} e^{4 i d x} + 75 i d e^{2 i c} e^{2 i d x} + 15 i d}"," ",0,"4*I*a**3*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-150*A*a**3 + 166*I*B*a**3 + (-690*A*a**3*exp(2*I*c) + 770*I*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (-1230*A*a**3*exp(4*I*c) + 1390*I*B*a**3*exp(4*I*c))*exp(4*I*d*x) + (-1050*A*a**3*exp(6*I*c) + 1170*I*B*a**3*exp(6*I*c))*exp(6*I*d*x) + (-360*A*a**3*exp(8*I*c) + 480*I*B*a**3*exp(8*I*c))*exp(8*I*d*x))/(15*I*d*exp(10*I*c)*exp(10*I*d*x) + 75*I*d*exp(8*I*c)*exp(8*I*d*x) + 150*I*d*exp(6*I*c)*exp(6*I*d*x) + 150*I*d*exp(4*I*c)*exp(4*I*d*x) + 75*I*d*exp(2*I*c)*exp(2*I*d*x) + 15*I*d)","A",0
18,1,236,0,1.109043," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- \frac{4 a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{26 A a^{3} - 30 i B a^{3} + \left(92 A a^{3} e^{2 i c} - 108 i B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(114 A a^{3} e^{4 i c} - 138 i B a^{3} e^{4 i c}\right) e^{4 i d x} + \left(48 A a^{3} e^{6 i c} - 72 i B a^{3} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} - 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} - 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"-4*a**3*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (26*A*a**3 - 30*I*B*a**3 + (92*A*a**3*exp(2*I*c) - 108*I*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (114*A*a**3*exp(4*I*c) - 138*I*B*a**3*exp(4*I*c))*exp(4*I*d*x) + (48*A*a**3*exp(6*I*c) - 72*I*B*a**3*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) - 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) - 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","B",0
19,1,187,0,0.771931," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- \frac{4 i a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{18 A a^{3} - 26 i B a^{3} + \left(42 A a^{3} e^{2 i c} - 66 i B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(24 A a^{3} e^{4 i c} - 48 i B a^{3} e^{4 i c}\right) e^{4 i d x}}{3 i d e^{6 i c} e^{6 i d x} + 9 i d e^{4 i c} e^{4 i d x} + 9 i d e^{2 i c} e^{2 i d x} + 3 i d}"," ",0,"-4*I*a**3*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (18*A*a**3 - 26*I*B*a**3 + (42*A*a**3*exp(2*I*c) - 66*I*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (24*A*a**3*exp(4*I*c) - 48*I*B*a**3*exp(4*I*c))*exp(4*I*d*x))/(3*I*d*exp(6*I*c)*exp(6*I*d*x) + 9*I*d*exp(4*I*c)*exp(4*I*d*x) + 9*I*d*exp(2*I*c)*exp(2*I*d*x) + 3*I*d)","B",0
20,1,233,0,3.188221," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{A a^{3} \log{\left(\frac{- A a^{3} + 2 i B a^{3}}{A a^{3} e^{2 i c} - 2 i B a^{3} e^{2 i c}} + e^{2 i d x} \right)}}{d} + \frac{a^{3} \left(3 A - 4 i B\right) \log{\left(e^{2 i d x} + \frac{- 2 A a^{3} + 2 i B a^{3} + a^{3} \left(3 A - 4 i B\right)}{A a^{3} e^{2 i c} - 2 i B a^{3} e^{2 i c}} \right)}}{d} + \frac{- 2 i A a^{3} - 6 B a^{3} + \left(- 2 i A a^{3} e^{2 i c} - 8 B a^{3} e^{2 i c}\right) e^{2 i d x}}{- i d e^{4 i c} e^{4 i d x} - 2 i d e^{2 i c} e^{2 i d x} - i d}"," ",0,"A*a**3*log((-A*a**3 + 2*I*B*a**3)/(A*a**3*exp(2*I*c) - 2*I*B*a**3*exp(2*I*c)) + exp(2*I*d*x))/d + a**3*(3*A - 4*I*B)*log(exp(2*I*d*x) + (-2*A*a**3 + 2*I*B*a**3 + a**3*(3*A - 4*I*B))/(A*a**3*exp(2*I*c) - 2*I*B*a**3*exp(2*I*c)))/d + (-2*I*A*a**3 - 6*B*a**3 + (-2*I*A*a**3*exp(2*I*c) - 8*B*a**3*exp(2*I*c))*exp(2*I*d*x))/(-I*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*d*exp(2*I*c)*exp(2*I*d*x) - I*d)","B",0
21,1,223,0,2.000005," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{i a^{3} \left(A - 3 i B\right) \log{\left(e^{2 i d x} + \frac{- 2 i A a^{3} - 2 B a^{3} + i a^{3} \left(A - 3 i B\right)}{- i A a^{3} e^{2 i c} + B a^{3} e^{2 i c}} \right)}}{d} + \frac{i a^{3} \left(3 A - i B\right) \log{\left(e^{2 i d x} + \frac{- 2 i A a^{3} - 2 B a^{3} + i a^{3} \left(3 A - i B\right)}{- i A a^{3} e^{2 i c} + B a^{3} e^{2 i c}} \right)}}{d} + \frac{2 i A a^{3} + 2 B a^{3} + \left(2 i A a^{3} e^{2 i c} - 2 B a^{3} e^{2 i c}\right) e^{2 i d x}}{- d e^{4 i c} e^{4 i d x} + d}"," ",0,"I*a**3*(A - 3*I*B)*log(exp(2*I*d*x) + (-2*I*A*a**3 - 2*B*a**3 + I*a**3*(A - 3*I*B))/(-I*A*a**3*exp(2*I*c) + B*a**3*exp(2*I*c)))/d + I*a**3*(3*A - I*B)*log(exp(2*I*d*x) + (-2*I*A*a**3 - 2*B*a**3 + I*a**3*(3*A - I*B))/(-I*A*a**3*exp(2*I*c) + B*a**3*exp(2*I*c)))/d + (2*I*A*a**3 + 2*B*a**3 + (2*I*A*a**3*exp(2*I*c) - 2*B*a**3*exp(2*I*c))*exp(2*I*d*x))/(-d*exp(4*I*c)*exp(4*I*d*x) + d)","B",0
22,1,233,0,2.547437," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{i B a^{3} \log{\left(\frac{2 A a^{3} - i B a^{3}}{2 A a^{3} e^{2 i c} - i B a^{3} e^{2 i c}} + e^{2 i d x} \right)}}{d} - \frac{a^{3} \left(4 A - 3 i B\right) \log{\left(e^{2 i d x} + \frac{2 A a^{3} - 2 i B a^{3} - a^{3} \left(4 A - 3 i B\right)}{2 A a^{3} e^{2 i c} - i B a^{3} e^{2 i c}} \right)}}{d} + \frac{6 i A a^{3} + 2 B a^{3} + \left(- 8 i A a^{3} e^{2 i c} - 2 B a^{3} e^{2 i c}\right) e^{2 i d x}}{- i d e^{4 i c} e^{4 i d x} + 2 i d e^{2 i c} e^{2 i d x} - i d}"," ",0,"I*B*a**3*log((2*A*a**3 - I*B*a**3)/(2*A*a**3*exp(2*I*c) - I*B*a**3*exp(2*I*c)) + exp(2*I*d*x))/d - a**3*(4*A - 3*I*B)*log(exp(2*I*d*x) + (2*A*a**3 - 2*I*B*a**3 - a**3*(4*A - 3*I*B))/(2*A*a**3*exp(2*I*c) - I*B*a**3*exp(2*I*c)))/d + (6*I*A*a**3 + 2*B*a**3 + (-8*I*A*a**3*exp(2*I*c) - 2*B*a**3*exp(2*I*c))*exp(2*I*d*x))/(-I*d*exp(4*I*c)*exp(4*I*d*x) + 2*I*d*exp(2*I*c)*exp(2*I*d*x) - I*d)","B",0
23,1,182,0,1.144424," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- \frac{4 i a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 26 i A a^{3} - 18 B a^{3} + \left(66 i A a^{3} e^{2 i c} + 42 B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(- 48 i A a^{3} e^{4 i c} - 24 B a^{3} e^{4 i c}\right) e^{4 i d x}}{- 3 d e^{6 i c} e^{6 i d x} + 9 d e^{4 i c} e^{4 i d x} - 9 d e^{2 i c} e^{2 i d x} + 3 d}"," ",0,"-4*I*a**3*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-26*I*A*a**3 - 18*B*a**3 + (66*I*A*a**3*exp(2*I*c) + 42*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (-48*I*A*a**3*exp(4*I*c) - 24*B*a**3*exp(4*I*c))*exp(4*I*d*x))/(-3*d*exp(6*I*c)*exp(6*I*d*x) + 9*d*exp(4*I*c)*exp(4*I*d*x) - 9*d*exp(2*I*c)*exp(2*I*d*x) + 3*d)","A",0
24,1,235,0,6.490187," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{4 a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 30 A a^{3} + 26 i B a^{3} + \left(108 A a^{3} e^{2 i c} - 92 i B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(- 138 A a^{3} e^{4 i c} + 114 i B a^{3} e^{4 i c}\right) e^{4 i d x} + \left(72 A a^{3} e^{6 i c} - 48 i B a^{3} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} + 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} + 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"4*a**3*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-30*A*a**3 + 26*I*B*a**3 + (108*A*a**3*exp(2*I*c) - 92*I*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (-138*A*a**3*exp(4*I*c) + 114*I*B*a**3*exp(4*I*c))*exp(4*I*d*x) + (72*A*a**3*exp(6*I*c) - 48*I*B*a**3*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) + 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) + 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","A",0
25,1,296,0,2.589846," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\frac{4 i a^{3} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 166 i A a^{3} - 150 B a^{3} + \left(770 i A a^{3} e^{2 i c} + 690 B a^{3} e^{2 i c}\right) e^{2 i d x} + \left(- 1390 i A a^{3} e^{4 i c} - 1230 B a^{3} e^{4 i c}\right) e^{4 i d x} + \left(1170 i A a^{3} e^{6 i c} + 1050 B a^{3} e^{6 i c}\right) e^{6 i d x} + \left(- 480 i A a^{3} e^{8 i c} - 360 B a^{3} e^{8 i c}\right) e^{8 i d x}}{15 d e^{10 i c} e^{10 i d x} - 75 d e^{8 i c} e^{8 i d x} + 150 d e^{6 i c} e^{6 i d x} - 150 d e^{4 i c} e^{4 i d x} + 75 d e^{2 i c} e^{2 i d x} - 15 d}"," ",0,"4*I*a**3*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-166*I*A*a**3 - 150*B*a**3 + (770*I*A*a**3*exp(2*I*c) + 690*B*a**3*exp(2*I*c))*exp(2*I*d*x) + (-1390*I*A*a**3*exp(4*I*c) - 1230*B*a**3*exp(4*I*c))*exp(4*I*d*x) + (1170*I*A*a**3*exp(6*I*c) + 1050*B*a**3*exp(6*I*c))*exp(6*I*d*x) + (-480*I*A*a**3*exp(8*I*c) - 360*B*a**3*exp(8*I*c))*exp(8*I*d*x))/(15*d*exp(10*I*c)*exp(10*I*d*x) - 75*d*exp(8*I*c)*exp(8*I*d*x) + 150*d*exp(6*I*c)*exp(6*I*d*x) - 150*d*exp(4*I*c)*exp(4*I*d*x) + 75*d*exp(2*I*c)*exp(2*I*d*x) - 15*d)","A",0
26,1,359,0,3.199288," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\frac{8 i a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 316 i A a^{4} - 344 B a^{4} + \left(- 1776 i A a^{4} e^{2 i c} - 1944 B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(- 4080 i A a^{4} e^{4 i c} - 4500 B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(- 4840 i A a^{4} e^{6 i c} - 5400 B a^{4} e^{6 i c}\right) e^{6 i d x} + \left(- 3060 i A a^{4} e^{8 i c} - 3420 B a^{4} e^{8 i c}\right) e^{8 i d x} + \left(- 840 i A a^{4} e^{10 i c} - 1080 B a^{4} e^{10 i c}\right) e^{10 i d x}}{- 15 d e^{12 i c} e^{12 i d x} - 90 d e^{10 i c} e^{10 i d x} - 225 d e^{8 i c} e^{8 i d x} - 300 d e^{6 i c} e^{6 i d x} - 225 d e^{4 i c} e^{4 i d x} - 90 d e^{2 i c} e^{2 i d x} - 15 d}"," ",0,"8*I*a**4*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-316*I*A*a**4 - 344*B*a**4 + (-1776*I*A*a**4*exp(2*I*c) - 1944*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (-4080*I*A*a**4*exp(4*I*c) - 4500*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (-4840*I*A*a**4*exp(6*I*c) - 5400*B*a**4*exp(6*I*c))*exp(6*I*d*x) + (-3060*I*A*a**4*exp(8*I*c) - 3420*B*a**4*exp(8*I*c))*exp(8*I*d*x) + (-840*I*A*a**4*exp(10*I*c) - 1080*B*a**4*exp(10*I*c))*exp(10*I*d*x))/(-15*d*exp(12*I*c)*exp(12*I*d*x) - 90*d*exp(10*I*c)*exp(10*I*d*x) - 225*d*exp(8*I*c)*exp(8*I*d*x) - 300*d*exp(6*I*c)*exp(6*I*d*x) - 225*d*exp(4*I*c)*exp(4*I*d*x) - 90*d*exp(2*I*c)*exp(2*I*d*x) - 15*d)","A",0
27,1,291,0,1.099017," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","- \frac{8 a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 280 A a^{4} + 316 i B a^{4} + \left(- 1280 A a^{4} e^{2 i c} + 1460 i B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(- 2260 A a^{4} e^{4 i c} + 2620 i B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(- 1860 A a^{4} e^{6 i c} + 2220 i B a^{4} e^{6 i c}\right) e^{6 i d x} + \left(- 600 A a^{4} e^{8 i c} + 840 i B a^{4} e^{8 i c}\right) e^{8 i d x}}{15 d e^{10 i c} e^{10 i d x} + 75 d e^{8 i c} e^{8 i d x} + 150 d e^{6 i c} e^{6 i d x} + 150 d e^{4 i c} e^{4 i d x} + 75 d e^{2 i c} e^{2 i d x} + 15 d}"," ",0,"-8*a**4*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-280*A*a**4 + 316*I*B*a**4 + (-1280*A*a**4*exp(2*I*c) + 1460*I*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (-2260*A*a**4*exp(4*I*c) + 2620*I*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (-1860*A*a**4*exp(6*I*c) + 2220*I*B*a**4*exp(6*I*c))*exp(6*I*d*x) + (-600*A*a**4*exp(8*I*c) + 840*I*B*a**4*exp(8*I*c))*exp(8*I*d*x))/(15*d*exp(10*I*c)*exp(10*I*d*x) + 75*d*exp(8*I*c)*exp(8*I*d*x) + 150*d*exp(6*I*c)*exp(6*I*d*x) + 150*d*exp(4*I*c)*exp(4*I*d*x) + 75*d*exp(2*I*c)*exp(2*I*d*x) + 15*d)","B",0
28,1,238,0,0.976928," ","integrate((a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","- \frac{8 i a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{44 i A a^{4} + 56 B a^{4} + \left(152 i A a^{4} e^{2 i c} + 200 B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(180 i A a^{4} e^{4 i c} + 252 B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(72 i A a^{4} e^{6 i c} + 120 B a^{4} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} - 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} - 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"-8*I*a**4*(A - I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/d + (44*I*A*a**4 + 56*B*a**4 + (152*I*A*a**4*exp(2*I*c) + 200*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (180*I*A*a**4*exp(4*I*c) + 252*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (72*I*A*a**4*exp(6*I*c) + 120*B*a**4*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) - 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) - 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","B",0
29,1,289,0,3.760945," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\frac{A a^{4} \log{\left(\frac{- 3 A a^{4} + 4 i B a^{4}}{3 A a^{4} e^{2 i c} - 4 i B a^{4} e^{2 i c}} + e^{2 i d x} \right)}}{d} + \frac{a^{4} \left(7 A - 8 i B\right) \log{\left(e^{2 i d x} + \frac{- 4 A a^{4} + 4 i B a^{4} + a^{4} \left(7 A - 8 i B\right)}{3 A a^{4} e^{2 i c} - 4 i B a^{4} e^{2 i c}} \right)}}{d} + \frac{24 A a^{4} - 44 i B a^{4} + \left(54 A a^{4} e^{2 i c} - 108 i B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(30 A a^{4} e^{4 i c} - 72 i B a^{4} e^{4 i c}\right) e^{4 i d x}}{3 d e^{6 i c} e^{6 i d x} + 9 d e^{4 i c} e^{4 i d x} + 9 d e^{2 i c} e^{2 i d x} + 3 d}"," ",0,"A*a**4*log((-3*A*a**4 + 4*I*B*a**4)/(3*A*a**4*exp(2*I*c) - 4*I*B*a**4*exp(2*I*c)) + exp(2*I*d*x))/d + a**4*(7*A - 8*I*B)*log(exp(2*I*d*x) + (-4*A*a**4 + 4*I*B*a**4 + a**4*(7*A - 8*I*B))/(3*A*a**4*exp(2*I*c) - 4*I*B*a**4*exp(2*I*c)))/d + (24*A*a**4 - 44*I*B*a**4 + (54*A*a**4*exp(2*I*c) - 108*I*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (30*A*a**4*exp(4*I*c) - 72*I*B*a**4*exp(4*I*c))*exp(4*I*d*x))/(3*d*exp(6*I*c)*exp(6*I*d*x) + 9*d*exp(4*I*c)*exp(4*I*d*x) + 9*d*exp(2*I*c)*exp(2*I*d*x) + 3*d)","B",0
30,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
31,-2,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
32,1,294,0,8.300851," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","- \frac{B a^{4} \log{\left(\frac{4 i A a^{4} + 3 B a^{4}}{4 i A a^{4} e^{2 i c} + 3 B a^{4} e^{2 i c}} + e^{2 i d x} \right)}}{d} - \frac{i a^{4} \left(8 A - 7 i B\right) \log{\left(e^{2 i d x} + \frac{4 i A a^{4} + 4 B a^{4} - i a^{4} \left(8 A - 7 i B\right)}{4 i A a^{4} e^{2 i c} + 3 B a^{4} e^{2 i c}} \right)}}{d} + \frac{44 i A a^{4} + 24 B a^{4} + \left(- 108 i A a^{4} e^{2 i c} - 54 B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(72 i A a^{4} e^{4 i c} + 30 B a^{4} e^{4 i c}\right) e^{4 i d x}}{3 d e^{6 i c} e^{6 i d x} - 9 d e^{4 i c} e^{4 i d x} + 9 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"-B*a**4*log((4*I*A*a**4 + 3*B*a**4)/(4*I*A*a**4*exp(2*I*c) + 3*B*a**4*exp(2*I*c)) + exp(2*I*d*x))/d - I*a**4*(8*A - 7*I*B)*log(exp(2*I*d*x) + (4*I*A*a**4 + 4*B*a**4 - I*a**4*(8*A - 7*I*B))/(4*I*A*a**4*exp(2*I*c) + 3*B*a**4*exp(2*I*c)))/d + (44*I*A*a**4 + 24*B*a**4 + (-108*I*A*a**4*exp(2*I*c) - 54*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (72*I*A*a**4*exp(4*I*c) + 30*B*a**4*exp(4*I*c))*exp(4*I*d*x))/(3*d*exp(6*I*c)*exp(6*I*d*x) - 9*d*exp(4*I*c)*exp(4*I*d*x) + 9*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","B",0
33,1,235,0,1.963665," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\frac{8 a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 56 A a^{4} + 44 i B a^{4} + \left(200 A a^{4} e^{2 i c} - 152 i B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(- 252 A a^{4} e^{4 i c} + 180 i B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(120 A a^{4} e^{6 i c} - 72 i B a^{4} e^{6 i c}\right) e^{6 i d x}}{- 3 d e^{8 i c} e^{8 i d x} + 12 d e^{6 i c} e^{6 i d x} - 18 d e^{4 i c} e^{4 i d x} + 12 d e^{2 i c} e^{2 i d x} - 3 d}"," ",0,"8*a**4*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-56*A*a**4 + 44*I*B*a**4 + (200*A*a**4*exp(2*I*c) - 152*I*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (-252*A*a**4*exp(4*I*c) + 180*I*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (120*A*a**4*exp(6*I*c) - 72*I*B*a**4*exp(6*I*c))*exp(6*I*d*x))/(-3*d*exp(8*I*c)*exp(8*I*d*x) + 12*d*exp(6*I*c)*exp(6*I*d*x) - 18*d*exp(4*I*c)*exp(4*I*d*x) + 12*d*exp(2*I*c)*exp(2*I*d*x) - 3*d)","A",0
34,1,296,0,17.310233," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\frac{8 i a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 316 i A a^{4} - 280 B a^{4} + \left(1460 i A a^{4} e^{2 i c} + 1280 B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(- 2620 i A a^{4} e^{4 i c} - 2260 B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(2220 i A a^{4} e^{6 i c} + 1860 B a^{4} e^{6 i c}\right) e^{6 i d x} + \left(- 840 i A a^{4} e^{8 i c} - 600 B a^{4} e^{8 i c}\right) e^{8 i d x}}{15 d e^{10 i c} e^{10 i d x} - 75 d e^{8 i c} e^{8 i d x} + 150 d e^{6 i c} e^{6 i d x} - 150 d e^{4 i c} e^{4 i d x} + 75 d e^{2 i c} e^{2 i d x} - 15 d}"," ",0,"8*I*a**4*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-316*I*A*a**4 - 280*B*a**4 + (1460*I*A*a**4*exp(2*I*c) + 1280*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (-2620*I*A*a**4*exp(4*I*c) - 2260*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (2220*I*A*a**4*exp(6*I*c) + 1860*B*a**4*exp(6*I*c))*exp(6*I*d*x) + (-840*I*A*a**4*exp(8*I*c) - 600*B*a**4*exp(8*I*c))*exp(8*I*d*x))/(15*d*exp(10*I*c)*exp(10*I*d*x) - 75*d*exp(8*I*c)*exp(8*I*d*x) + 150*d*exp(6*I*c)*exp(6*I*d*x) - 150*d*exp(4*I*c)*exp(4*I*d*x) + 75*d*exp(2*I*c)*exp(2*I*d*x) - 15*d)","A",0
35,1,347,0,4.930820," ","integrate(cot(d*x+c)**7*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","- \frac{8 a^{4} \left(A - i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{344 A a^{4} - 316 i B a^{4} + \left(- 1944 A a^{4} e^{2 i c} + 1776 i B a^{4} e^{2 i c}\right) e^{2 i d x} + \left(4500 A a^{4} e^{4 i c} - 4080 i B a^{4} e^{4 i c}\right) e^{4 i d x} + \left(- 5400 A a^{4} e^{6 i c} + 4840 i B a^{4} e^{6 i c}\right) e^{6 i d x} + \left(3420 A a^{4} e^{8 i c} - 3060 i B a^{4} e^{8 i c}\right) e^{8 i d x} + \left(- 1080 A a^{4} e^{10 i c} + 840 i B a^{4} e^{10 i c}\right) e^{10 i d x}}{- 15 d e^{12 i c} e^{12 i d x} + 90 d e^{10 i c} e^{10 i d x} - 225 d e^{8 i c} e^{8 i d x} + 300 d e^{6 i c} e^{6 i d x} - 225 d e^{4 i c} e^{4 i d x} + 90 d e^{2 i c} e^{2 i d x} - 15 d}"," ",0,"-8*a**4*(A - I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/d + (344*A*a**4 - 316*I*B*a**4 + (-1944*A*a**4*exp(2*I*c) + 1776*I*B*a**4*exp(2*I*c))*exp(2*I*d*x) + (4500*A*a**4*exp(4*I*c) - 4080*I*B*a**4*exp(4*I*c))*exp(4*I*d*x) + (-5400*A*a**4*exp(6*I*c) + 4840*I*B*a**4*exp(6*I*c))*exp(6*I*d*x) + (3420*A*a**4*exp(8*I*c) - 3060*I*B*a**4*exp(8*I*c))*exp(8*I*d*x) + (-1080*A*a**4*exp(10*I*c) + 840*I*B*a**4*exp(10*I*c))*exp(10*I*d*x))/(-15*d*exp(12*I*c)*exp(12*I*d*x) + 90*d*exp(10*I*c)*exp(10*I*d*x) - 225*d*exp(8*I*c)*exp(8*I*d*x) + 300*d*exp(6*I*c)*exp(6*I*d*x) - 225*d*exp(4*I*c)*exp(4*I*d*x) + 90*d*exp(2*I*c)*exp(2*I*d*x) - 15*d)","A",0
36,1,206,0,1.278940," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{- 2 A e^{2 i c} e^{2 i d x} - 2 A - 2 i B}{- a d e^{4 i c} e^{4 i d x} - 2 a d e^{2 i c} e^{2 i d x} - a d} + \begin{cases} - \frac{\left(- A - i B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{5 i A - 7 B}{2 a} - \frac{\left(- 5 i A e^{2 i c} + i A + 7 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 5 i A + 7 B\right)}{2 a} - \frac{\left(A + 2 i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"(-2*A*exp(2*I*c)*exp(2*I*d*x) - 2*A - 2*I*B)/(-a*d*exp(4*I*c)*exp(4*I*d*x) - 2*a*d*exp(2*I*c)*exp(2*I*d*x) - a*d) + Piecewise((-(-A - I*B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(5*I*A - 7*B)/(2*a) - (-5*I*A*exp(2*I*c) + I*A + 7*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(-5*I*A + 7*B)/(2*a) - (A + 2*I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
37,1,160,0,0.644670," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{2 B}{- a d e^{2 i c} e^{2 i d x} - a d} + \begin{cases} - \frac{\left(i A - B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{3 A + 5 i B}{2 a} + \frac{i \left(- 3 i A e^{2 i c} + i A + 5 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 3 A - 5 i B\right)}{2 a} + \frac{i \left(A + i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"-2*B/(-a*d*exp(2*I*c)*exp(2*I*d*x) - a*d) + Piecewise((-(I*A - B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(3*A + 5*I*B)/(2*a) + I*(-3*I*A*exp(2*I*c) + I*A + 5*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(-3*A - 5*I*B)/(2*a) + I*(A + I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
38,1,121,0,0.436694," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{i B \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d} + \begin{cases} - \frac{\left(A + i B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{- i A + 3 B}{2 a} + \frac{\left(- i A e^{2 i c} + i A + 3 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(i A - 3 B\right)}{2 a}"," ",0,"I*B*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d) + Piecewise((-(A + I*B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(-I*A + 3*B)/(2*a) + (-I*A*exp(2*I*c) + I*A + 3*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(I*A - 3*B)/(2*a)","A",0
39,1,90,0,0.256872," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\begin{cases} - \frac{\left(- i A + B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{A - i B}{2 a} + \frac{\left(A e^{2 i c} + A - i B e^{2 i c} + i B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{2 a}"," ",0,"Piecewise((-(-I*A + B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(A - I*B)/(2*a) + (A*exp(2*I*c) + A - I*B*exp(2*I*c) + I*B)*exp(-2*I*c)/(2*a)), True)) - x*(-A + I*B)/(2*a)","A",0
40,1,122,0,0.418339," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{A \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d} + \begin{cases} - \frac{\left(- A - i B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{- 3 i A + B}{2 a} - \frac{\left(3 i A e^{2 i c} + i A - B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(3 i A - B\right)}{2 a}"," ",0,"A*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d) + Piecewise((-(-A - I*B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(-3*I*A + B)/(2*a) - (3*I*A*exp(2*I*c) + I*A - B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(3*I*A - B)/(2*a)","A",0
41,1,160,0,0.651462," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{2 i A}{- a d e^{2 i c} e^{2 i d x} + a d} + \begin{cases} - \frac{\left(i A - B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{- 5 A - 3 i B}{2 a} + \frac{i \left(5 i A e^{2 i c} + i A - 3 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(5 A + 3 i B\right)}{2 a} - \frac{i \left(A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"2*I*A/(-a*d*exp(2*I*c)*exp(2*I*d*x) + a*d) + Piecewise((-(I*A - B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(-5*A - 3*I*B)/(2*a) + I*(5*I*A*exp(2*I*c) + I*A - 3*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(5*A + 3*I*B)/(2*a) - I*(A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
42,1,201,0,1.331754," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{2 A - 2 i B e^{2 i c} e^{2 i d x} + 2 i B}{a d e^{4 i c} e^{4 i d x} - 2 a d e^{2 i c} e^{2 i d x} + a d} + \begin{cases} - \frac{\left(A + i B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{7 i A - 5 B}{2 a} + \frac{\left(7 i A e^{2 i c} + i A - 5 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 7 i A + 5 B\right)}{2 a} - \frac{\left(2 A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"(2*A - 2*I*B*exp(2*I*c)*exp(2*I*d*x) + 2*I*B)/(a*d*exp(4*I*c)*exp(4*I*d*x) - 2*a*d*exp(2*I*c)*exp(2*I*d*x) + a*d) + Piecewise((-(A + I*B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(7*I*A - 5*B)/(2*a) + (7*I*A*exp(2*I*c) + I*A - 5*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(-7*I*A + 5*B)/(2*a) - (2*A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
43,1,262,0,1.023048," ","integrate(cot(d*x+c)**4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\frac{- 12 i A e^{4 i c} e^{4 i d x} - 14 i A + 6 B + \left(18 i A e^{2 i c} - 6 B e^{2 i c}\right) e^{2 i d x}}{- 3 a d e^{6 i c} e^{6 i d x} + 9 a d e^{4 i c} e^{4 i d x} - 9 a d e^{2 i c} e^{2 i d x} + 3 a d} + \begin{cases} - \frac{\left(- i A + B\right) e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(- \frac{9 A + 7 i B}{2 a} - \frac{i \left(9 i A e^{2 i c} + i A - 7 B e^{2 i c} - B\right) e^{- 2 i c}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 9 A - 7 i B\right)}{2 a} + \frac{2 i \left(A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"(-12*I*A*exp(4*I*c)*exp(4*I*d*x) - 14*I*A + 6*B + (18*I*A*exp(2*I*c) - 6*B*exp(2*I*c))*exp(2*I*d*x))/(-3*a*d*exp(6*I*c)*exp(6*I*d*x) + 9*a*d*exp(4*I*c)*exp(4*I*d*x) - 9*a*d*exp(2*I*c)*exp(2*I*d*x) + 3*a*d) + Piecewise((-(-I*A + B)*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-(9*A + 7*I*B)/(2*a) - I*(9*I*A*exp(2*I*c) + I*A - 7*B*exp(2*I*c) - B)*exp(-2*I*c)/(2*a)), True)) - x*(-9*A - 7*I*B)/(2*a) + 2*I*(A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
44,1,267,0,0.975518," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\frac{2 i B}{- a^{2} d e^{2 i c} e^{2 i d x} - a^{2} d} + \begin{cases} \frac{\left(\left(4 A a^{2} d e^{2 i c} + 4 i B a^{2} d e^{2 i c}\right) e^{- 4 i d x} + \left(- 32 A a^{2} d e^{4 i c} - 48 i B a^{2} d e^{4 i c}\right) e^{- 2 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{- 7 i A + 17 B}{4 a^{2}} - \frac{\left(7 i A e^{4 i c} - 4 i A e^{2 i c} + i A - 17 B e^{4 i c} + 6 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(7 i A - 17 B\right)}{4 a^{2}} + \frac{\left(A + 2 i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"2*I*B/(-a**2*d*exp(2*I*c)*exp(2*I*d*x) - a**2*d) + Piecewise((((4*A*a**2*d*exp(2*I*c) + 4*I*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x) + (-32*A*a**2*d*exp(4*I*c) - 48*I*B*a**2*d*exp(4*I*c))*exp(-2*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(-7*I*A + 17*B)/(4*a**2) - (7*I*A*exp(4*I*c) - 4*I*A*exp(2*I*c) + I*A - 17*B*exp(4*I*c) + 6*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(7*I*A - 17*B)/(4*a**2) + (A + 2*I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d)","A",0
45,1,224,0,0.855808," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\frac{B \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d} + \begin{cases} \frac{\left(\left(- 4 i A a^{2} d e^{2 i c} + 4 B a^{2} d e^{2 i c}\right) e^{- 4 i d x} + \left(16 i A a^{2} d e^{4 i c} - 32 B a^{2} d e^{4 i c}\right) e^{- 2 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{- A - 7 i B}{4 a^{2}} + \frac{i \left(i A e^{4 i c} - 2 i A e^{2 i c} + i A - 7 B e^{4 i c} + 4 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(A + 7 i B\right)}{4 a^{2}}"," ",0,"B*log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d) + Piecewise((((-4*I*A*a**2*d*exp(2*I*c) + 4*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x) + (16*I*A*a**2*d*exp(4*I*c) - 32*B*a**2*d*exp(4*I*c))*exp(-2*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(-A - 7*I*B)/(4*a**2) + I*(I*A*exp(4*I*c) - 2*I*A*exp(2*I*c) + I*A - 7*B*exp(4*I*c) + 4*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(A + 7*I*B)/(4*a**2)","A",0
46,1,167,0,0.368953," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(16 i B a^{2} d e^{4 i c} e^{- 2 i d x} + \left(- 4 A a^{2} d e^{2 i c} - 4 i B a^{2} d e^{2 i c}\right) e^{- 4 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{- i A - B}{4 a^{2}} + \frac{\left(- i A e^{4 i c} + i A - B e^{4 i c} + 2 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(i A + B\right)}{4 a^{2}}"," ",0,"Piecewise(((16*I*B*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + (-4*A*a**2*d*exp(2*I*c) - 4*I*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(-I*A - B)/(4*a**2) + (-I*A*exp(4*I*c) + I*A - B*exp(4*I*c) + 2*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(I*A + B)/(4*a**2)","A",0
47,1,163,0,0.367777," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(16 i A a^{2} d e^{4 i c} e^{- 2 i d x} + \left(4 i A a^{2} d e^{2 i c} - 4 B a^{2} d e^{2 i c}\right) e^{- 4 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{A - i B}{4 a^{2}} + \frac{\left(A e^{4 i c} + 2 A e^{2 i c} + A - i B e^{4 i c} + i B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{4 a^{2}}"," ",0,"Piecewise(((16*I*A*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + (4*I*A*a**2*d*exp(2*I*c) - 4*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(A - I*B)/(4*a**2) + (A*exp(4*I*c) + 2*A*exp(2*I*c) + A - I*B*exp(4*I*c) + I*B)*exp(-4*I*c)/(4*a**2)), True)) - x*(-A + I*B)/(4*a**2)","A",0
48,1,223,0,0.580608," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\frac{A \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d} + \begin{cases} \frac{\left(\left(4 A a^{2} d e^{2 i c} + 4 i B a^{2} d e^{2 i c}\right) e^{- 4 i d x} + \left(32 A a^{2} d e^{4 i c} + 16 i B a^{2} d e^{4 i c}\right) e^{- 2 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{- 7 i A + B}{4 a^{2}} - \frac{\left(7 i A e^{4 i c} + 4 i A e^{2 i c} + i A - B e^{4 i c} - 2 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(7 i A - B\right)}{4 a^{2}}"," ",0,"A*log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d) + Piecewise((((4*A*a**2*d*exp(2*I*c) + 4*I*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x) + (32*A*a**2*d*exp(4*I*c) + 16*I*B*a**2*d*exp(4*I*c))*exp(-2*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(-7*I*A + B)/(4*a**2) - (7*I*A*exp(4*I*c) + 4*I*A*exp(2*I*c) + I*A - B*exp(4*I*c) - 2*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(7*I*A - B)/(4*a**2)","A",0
49,1,267,0,1.345347," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\frac{2 i A}{- a^{2} d e^{2 i c} e^{2 i d x} + a^{2} d} + \begin{cases} \frac{\left(\left(- 4 i A a^{2} d e^{2 i c} + 4 B a^{2} d e^{2 i c}\right) e^{- 4 i d x} + \left(- 48 i A a^{2} d e^{4 i c} + 32 B a^{2} d e^{4 i c}\right) e^{- 2 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{- 17 A - 7 i B}{4 a^{2}} + \frac{i \left(17 i A e^{4 i c} + 6 i A e^{2 i c} + i A - 7 B e^{4 i c} - 4 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(17 A + 7 i B\right)}{4 a^{2}} - \frac{i \left(2 A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"2*I*A/(-a**2*d*exp(2*I*c)*exp(2*I*d*x) + a**2*d) + Piecewise((((-4*I*A*a**2*d*exp(2*I*c) + 4*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x) + (-48*I*A*a**2*d*exp(4*I*c) + 32*B*a**2*d*exp(4*I*c))*exp(-2*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(-17*A - 7*I*B)/(4*a**2) + I*(17*I*A*exp(4*I*c) + 6*I*A*exp(2*I*c) + I*A - 7*B*exp(4*I*c) - 4*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(17*A + 7*I*B)/(4*a**2) - I*(2*A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d)","A",0
50,1,323,0,1.106544," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","\frac{- 4 A - 2 i B + \left(2 A e^{2 i c} + 2 i B e^{2 i c}\right) e^{2 i d x}}{- a^{2} d e^{4 i c} e^{4 i d x} + 2 a^{2} d e^{2 i c} e^{2 i d x} - a^{2} d} + \begin{cases} \frac{\left(\left(- 4 A a^{2} d e^{2 i c} - 4 i B a^{2} d e^{2 i c}\right) e^{- 4 i d x} + \left(- 64 A a^{2} d e^{4 i c} - 48 i B a^{2} d e^{4 i c}\right) e^{- 2 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{31 i A - 17 B}{4 a^{2}} + \frac{\left(31 i A e^{4 i c} + 8 i A e^{2 i c} + i A - 17 B e^{4 i c} - 6 B e^{2 i c} - B\right) e^{- 4 i c}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 31 i A + 17 B\right)}{4 a^{2}} - \frac{2 \left(2 A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"(-4*A - 2*I*B + (2*A*exp(2*I*c) + 2*I*B*exp(2*I*c))*exp(2*I*d*x))/(-a**2*d*exp(4*I*c)*exp(4*I*d*x) + 2*a**2*d*exp(2*I*c)*exp(2*I*d*x) - a**2*d) + Piecewise((((-4*A*a**2*d*exp(2*I*c) - 4*I*B*a**2*d*exp(2*I*c))*exp(-4*I*d*x) + (-64*A*a**2*d*exp(4*I*c) - 48*I*B*a**2*d*exp(4*I*c))*exp(-2*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*(-(31*I*A - 17*B)/(4*a**2) + (31*I*A*exp(4*I*c) + 8*I*A*exp(2*I*c) + I*A - 17*B*exp(4*I*c) - 6*B*exp(2*I*c) - B)*exp(-4*I*c)/(4*a**2)), True)) - x*(-31*I*A + 17*B)/(4*a**2) - 2*(2*A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d)","A",0
51,1,342,0,1.565402," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","- \frac{2 B}{a^{3} d e^{2 i c} e^{2 i d x} + a^{3} d} + \begin{cases} - \frac{\left(\left(- 512 i A a^{6} d^{2} e^{6 i c} + 512 B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(3840 i A a^{6} d^{2} e^{8 i c} - 5376 B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 16896 i A a^{6} d^{2} e^{10 i c} + 35328 B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{- 15 A - 49 i B}{8 a^{3}} - \frac{i \left(- 15 i A e^{6 i c} + 11 i A e^{4 i c} - 5 i A e^{2 i c} + i A + 49 B e^{6 i c} - 23 B e^{4 i c} + 7 B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(15 A + 49 i B\right)}{8 a^{3}} - \frac{i \left(A + 3 i B\right) \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"-2*B/(a**3*d*exp(2*I*c)*exp(2*I*d*x) + a**3*d) + Piecewise((-((-512*I*A*a**6*d**2*exp(6*I*c) + 512*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (3840*I*A*a**6*d**2*exp(8*I*c) - 5376*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-16896*I*A*a**6*d**2*exp(10*I*c) + 35328*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(-15*A - 49*I*B)/(8*a**3) - I*(-15*I*A*exp(6*I*c) + 11*I*A*exp(4*I*c) - 5*I*A*exp(2*I*c) + I*A + 49*B*exp(6*I*c) - 23*B*exp(4*I*c) + 7*B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(15*A + 49*I*B)/(8*a**3) - I*(A + 3*I*B)*log(exp(2*I*d*x) + exp(-2*I*c))/(a**3*d)","A",0
52,1,303,0,2.424263," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","- \frac{i B \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{3} d} + \begin{cases} - \frac{\left(\left(- 512 A a^{6} d^{2} e^{6 i c} - 512 i B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(2304 A a^{6} d^{2} e^{8 i c} + 3840 i B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 4608 A a^{6} d^{2} e^{10 i c} - 16896 i B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{i A - 15 B}{8 a^{3}} - \frac{\left(- i A e^{6 i c} + 3 i A e^{4 i c} - 3 i A e^{2 i c} + i A + 15 B e^{6 i c} - 11 B e^{4 i c} + 5 B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- i A + 15 B\right)}{8 a^{3}}"," ",0,"-I*B*log(exp(2*I*d*x) + exp(-2*I*c))/(a**3*d) + Piecewise((-((-512*A*a**6*d**2*exp(6*I*c) - 512*I*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (2304*A*a**6*d**2*exp(8*I*c) + 3840*I*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-4608*A*a**6*d**2*exp(10*I*c) - 16896*I*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(I*A - 15*B)/(8*a**3) - (-I*A*exp(6*I*c) + 3*I*A*exp(4*I*c) - 3*I*A*exp(2*I*c) + I*A + 15*B*exp(6*I*c) - 11*B*exp(4*I*c) + 5*B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(-I*A + 15*B)/(8*a**3)","A",0
53,1,264,0,0.640136," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(\left(512 i A a^{6} d^{2} e^{6 i c} - 512 B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(- 768 i A a^{6} d^{2} e^{8 i c} + 2304 B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 1536 i A a^{6} d^{2} e^{10 i c} - 4608 B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{- A + i B}{8 a^{3}} + \frac{\left(- A e^{6 i c} + A e^{4 i c} + A e^{2 i c} - A + i B e^{6 i c} - 3 i B e^{4 i c} + 3 i B e^{2 i c} - i B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(A - i B\right)}{8 a^{3}}"," ",0,"Piecewise((-((512*I*A*a**6*d**2*exp(6*I*c) - 512*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (-768*I*A*a**6*d**2*exp(8*I*c) + 2304*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-1536*I*A*a**6*d**2*exp(10*I*c) - 4608*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(-A + I*B)/(8*a**3) + (-A*exp(6*I*c) + A*exp(4*I*c) + A*exp(2*I*c) - A + I*B*exp(6*I*c) - 3*I*B*exp(4*I*c) + 3*I*B*exp(2*I*c) - I*B)*exp(-6*I*c)/(8*a**3)), True)) - x*(A - I*B)/(8*a**3)","A",0
54,1,262,0,0.676646," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(\left(512 A a^{6} d^{2} e^{6 i c} + 512 i B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(768 A a^{6} d^{2} e^{8 i c} - 768 i B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 1536 A a^{6} d^{2} e^{10 i c} - 1536 i B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{- i A - B}{8 a^{3}} + \frac{\left(- i A e^{6 i c} - i A e^{4 i c} + i A e^{2 i c} + i A - B e^{6 i c} + B e^{4 i c} + B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(i A + B\right)}{8 a^{3}}"," ",0,"Piecewise((-((512*A*a**6*d**2*exp(6*I*c) + 512*I*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (768*A*a**6*d**2*exp(8*I*c) - 768*I*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-1536*A*a**6*d**2*exp(10*I*c) - 1536*I*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(-I*A - B)/(8*a**3) + (-I*A*exp(6*I*c) - I*A*exp(4*I*c) + I*A*exp(2*I*c) + I*A - B*exp(6*I*c) + B*exp(4*I*c) + B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(I*A + B)/(8*a**3)","A",0
55,1,264,0,0.528811," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(\left(- 512 i A a^{6} d^{2} e^{6 i c} + 512 B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(- 2304 i A a^{6} d^{2} e^{8 i c} + 768 B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 4608 i A a^{6} d^{2} e^{10 i c} - 1536 B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{A - i B}{8 a^{3}} + \frac{\left(A e^{6 i c} + 3 A e^{4 i c} + 3 A e^{2 i c} + A - i B e^{6 i c} - i B e^{4 i c} + i B e^{2 i c} + i B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{8 a^{3}}"," ",0,"Piecewise((-((-512*I*A*a**6*d**2*exp(6*I*c) + 512*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (-2304*I*A*a**6*d**2*exp(8*I*c) + 768*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-4608*I*A*a**6*d**2*exp(10*I*c) - 1536*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(A - I*B)/(8*a**3) + (A*exp(6*I*c) + 3*A*exp(4*I*c) + 3*A*exp(2*I*c) + A - I*B*exp(6*I*c) - I*B*exp(4*I*c) + I*B*exp(2*I*c) + I*B)*exp(-6*I*c)/(8*a**3)), True)) - x*(-A + I*B)/(8*a**3)","A",0
56,1,303,0,1.139161," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{A \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{3} d} + \begin{cases} - \frac{\left(\left(- 512 A a^{6} d^{2} e^{6 i c} - 512 i B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(- 3840 A a^{6} d^{2} e^{8 i c} - 2304 i B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(- 16896 A a^{6} d^{2} e^{10 i c} - 4608 i B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{- 15 i A + B}{8 a^{3}} - \frac{\left(15 i A e^{6 i c} + 11 i A e^{4 i c} + 5 i A e^{2 i c} + i A - B e^{6 i c} - 3 B e^{4 i c} - 3 B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(15 i A - B\right)}{8 a^{3}}"," ",0,"A*log(exp(2*I*d*x) - exp(-2*I*c))/(a**3*d) + Piecewise((-((-512*A*a**6*d**2*exp(6*I*c) - 512*I*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (-3840*A*a**6*d**2*exp(8*I*c) - 2304*I*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (-16896*A*a**6*d**2*exp(10*I*c) - 4608*I*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(-15*I*A + B)/(8*a**3) - (15*I*A*exp(6*I*c) + 11*I*A*exp(4*I*c) + 5*I*A*exp(2*I*c) + I*A - B*exp(6*I*c) - 3*B*exp(4*I*c) - 3*B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(15*I*A - B)/(8*a**3)","A",0
57,1,342,0,1.215440," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","- \frac{2 i A}{a^{3} d e^{2 i c} e^{2 i d x} - a^{3} d} + \begin{cases} - \frac{\left(\left(512 i A a^{6} d^{2} e^{6 i c} - 512 B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(5376 i A a^{6} d^{2} e^{8 i c} - 3840 B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(35328 i A a^{6} d^{2} e^{10 i c} - 16896 B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{- 49 A - 15 i B}{8 a^{3}} + \frac{i \left(49 i A e^{6 i c} + 23 i A e^{4 i c} + 7 i A e^{2 i c} + i A - 15 B e^{6 i c} - 11 B e^{4 i c} - 5 B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(49 A + 15 i B\right)}{8 a^{3}} - \frac{i \left(3 A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"-2*I*A/(a**3*d*exp(2*I*c)*exp(2*I*d*x) - a**3*d) + Piecewise((-((512*I*A*a**6*d**2*exp(6*I*c) - 512*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (5376*I*A*a**6*d**2*exp(8*I*c) - 3840*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (35328*I*A*a**6*d**2*exp(10*I*c) - 16896*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(-49*A - 15*I*B)/(8*a**3) + I*(49*I*A*exp(6*I*c) + 23*I*A*exp(4*I*c) + 7*I*A*exp(2*I*c) + I*A - 15*B*exp(6*I*c) - 11*B*exp(4*I*c) - 5*B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(49*A + 15*I*B)/(8*a**3) - I*(3*A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**3*d)","A",0
58,1,394,0,4.356707," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{- 6 A - 2 i B + \left(4 A e^{2 i c} + 2 i B e^{2 i c}\right) e^{2 i d x}}{- a^{3} d e^{4 i c} e^{4 i d x} + 2 a^{3} d e^{2 i c} e^{2 i d x} - a^{3} d} + \begin{cases} - \frac{\left(\left(512 A a^{6} d^{2} e^{6 i c} + 512 i B a^{6} d^{2} e^{6 i c}\right) e^{- 6 i d x} + \left(6912 A a^{6} d^{2} e^{8 i c} + 5376 i B a^{6} d^{2} e^{8 i c}\right) e^{- 4 i d x} + \left(59904 A a^{6} d^{2} e^{10 i c} + 35328 i B a^{6} d^{2} e^{10 i c}\right) e^{- 2 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(- \frac{111 i A - 49 B}{8 a^{3}} + \frac{\left(111 i A e^{6 i c} + 39 i A e^{4 i c} + 9 i A e^{2 i c} + i A - 49 B e^{6 i c} - 23 B e^{4 i c} - 7 B e^{2 i c} - B\right) e^{- 6 i c}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 111 i A + 49 B\right)}{8 a^{3}} - \frac{\left(7 A + 3 i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"(-6*A - 2*I*B + (4*A*exp(2*I*c) + 2*I*B*exp(2*I*c))*exp(2*I*d*x))/(-a**3*d*exp(4*I*c)*exp(4*I*d*x) + 2*a**3*d*exp(2*I*c)*exp(2*I*d*x) - a**3*d) + Piecewise((-((512*A*a**6*d**2*exp(6*I*c) + 512*I*B*a**6*d**2*exp(6*I*c))*exp(-6*I*d*x) + (6912*A*a**6*d**2*exp(8*I*c) + 5376*I*B*a**6*d**2*exp(8*I*c))*exp(-4*I*d*x) + (59904*A*a**6*d**2*exp(10*I*c) + 35328*I*B*a**6*d**2*exp(10*I*c))*exp(-2*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*(-(111*I*A - 49*B)/(8*a**3) + (111*I*A*exp(6*I*c) + 39*I*A*exp(4*I*c) + 9*I*A*exp(2*I*c) + I*A - 49*B*exp(6*I*c) - 23*B*exp(4*I*c) - 7*B*exp(2*I*c) - B)*exp(-6*I*c)/(8*a**3)), True)) - x*(-111*I*A + 49*B)/(8*a**3) - (7*A + 3*I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**3*d)","A",0
59,1,366,0,7.063994," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","- \frac{B \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{4} d} + \begin{cases} \frac{\left(\left(24576 i A a^{12} d^{3} e^{12 i c} - 24576 B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(- 131072 i A a^{12} d^{3} e^{14 i c} + 196608 B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(294912 i A a^{12} d^{3} e^{16 i c} - 786432 B a^{12} d^{3} e^{16 i c}\right) e^{- 4 i d x} + \left(- 393216 i A a^{12} d^{3} e^{18 i c} + 2555904 B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{A + 31 i B}{16 a^{4}} - \frac{i \left(i A e^{8 i c} - 4 i A e^{6 i c} + 6 i A e^{4 i c} - 4 i A e^{2 i c} + i A - 31 B e^{8 i c} + 26 B e^{6 i c} - 16 B e^{4 i c} + 6 B e^{2 i c} - B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A - 31 i B\right)}{16 a^{4}}"," ",0,"-B*log(exp(2*I*d*x) + exp(-2*I*c))/(a**4*d) + Piecewise((((24576*I*A*a**12*d**3*exp(12*I*c) - 24576*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (-131072*I*A*a**12*d**3*exp(14*I*c) + 196608*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (294912*I*A*a**12*d**3*exp(16*I*c) - 786432*B*a**12*d**3*exp(16*I*c))*exp(-4*I*d*x) + (-393216*I*A*a**12*d**3*exp(18*I*c) + 2555904*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(A + 31*I*B)/(16*a**4) - I*(I*A*exp(8*I*c) - 4*I*A*exp(6*I*c) + 6*I*A*exp(4*I*c) - 4*I*A*exp(2*I*c) + I*A - 31*B*exp(8*I*c) + 26*B*exp(6*I*c) - 16*B*exp(4*I*c) + 6*B*exp(2*I*c) - B)*exp(-8*I*c)/(16*a**4)), True)) - x*(-A - 31*I*B)/(16*a**4)","A",0
60,1,304,0,0.996995," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(294912 i B a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + \left(24576 A a^{12} d^{3} e^{12 i c} + 24576 i B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(- 65536 A a^{12} d^{3} e^{14 i c} - 131072 i B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(196608 A a^{12} d^{3} e^{18 i c} - 393216 i B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{i A + B}{16 a^{4}} + \frac{\left(i A e^{8 i c} - 2 i A e^{6 i c} + 2 i A e^{2 i c} - i A + B e^{8 i c} - 4 B e^{6 i c} + 6 B e^{4 i c} - 4 B e^{2 i c} + B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- i A - B\right)}{16 a^{4}}"," ",0,"Piecewise(((294912*I*B*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + (24576*A*a**12*d**3*exp(12*I*c) + 24576*I*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (-65536*A*a**12*d**3*exp(14*I*c) - 131072*I*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (196608*A*a**12*d**3*exp(18*I*c) - 393216*I*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(I*A + B)/(16*a**4) + (I*A*exp(8*I*c) - 2*I*A*exp(6*I*c) + 2*I*A*exp(2*I*c) - I*A + B*exp(8*I*c) - 4*B*exp(6*I*c) + 6*B*exp(4*I*c) - 4*B*exp(2*I*c) + B)*exp(-8*I*c)/(16*a**4)), True)) - x*(-I*A - B)/(16*a**4)","A",0
61,1,243,0,2.064606," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(98304 i A a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + 196608 B a^{12} d^{3} e^{18 i c} e^{- 2 i d x} - 65536 B a^{12} d^{3} e^{14 i c} e^{- 6 i d x} + \left(- 24576 i A a^{12} d^{3} e^{12 i c} + 24576 B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{- A + i B}{16 a^{4}} + \frac{\left(- A e^{8 i c} + 2 A e^{4 i c} - A + i B e^{8 i c} - 2 i B e^{6 i c} + 2 i B e^{2 i c} - i B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(A - i B\right)}{16 a^{4}}"," ",0,"Piecewise(((98304*I*A*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + 196608*B*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) - 65536*B*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) + (-24576*I*A*a**12*d**3*exp(12*I*c) + 24576*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(-A + I*B)/(16*a**4) + (-A*exp(8*I*c) + 2*A*exp(4*I*c) - A + I*B*exp(8*I*c) - 2*I*B*exp(6*I*c) + 2*I*B*exp(2*I*c) - I*B)*exp(-8*I*c)/(16*a**4)), True)) - x*(A - I*B)/(16*a**4)","A",0
62,1,246,0,0.678333," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(196608 A a^{12} d^{3} e^{18 i c} e^{- 2 i d x} - 65536 A a^{12} d^{3} e^{14 i c} e^{- 6 i d x} + 98304 i B a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + \left(- 24576 A a^{12} d^{3} e^{12 i c} - 24576 i B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{- i A - B}{16 a^{4}} + \frac{\left(- i A e^{8 i c} - 2 i A e^{6 i c} + 2 i A e^{2 i c} + i A - B e^{8 i c} + 2 B e^{4 i c} - B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(i A + B\right)}{16 a^{4}}"," ",0,"Piecewise(((196608*A*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) - 65536*A*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) + 98304*I*B*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + (-24576*A*a**12*d**3*exp(12*I*c) - 24576*I*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(-I*A - B)/(16*a**4) + (-I*A*exp(8*I*c) - 2*I*A*exp(6*I*c) + 2*I*A*exp(2*I*c) + I*A - B*exp(8*I*c) + 2*B*exp(4*I*c) - B)*exp(-8*I*c)/(16*a**4)), True)) - x*(I*A + B)/(16*a**4)","A",0
63,1,301,0,0.900051," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(294912 i A a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + \left(24576 i A a^{12} d^{3} e^{12 i c} - 24576 B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(131072 i A a^{12} d^{3} e^{14 i c} - 65536 B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(393216 i A a^{12} d^{3} e^{18 i c} + 196608 B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{A - i B}{16 a^{4}} + \frac{\left(A e^{8 i c} + 4 A e^{6 i c} + 6 A e^{4 i c} + 4 A e^{2 i c} + A - i B e^{8 i c} - 2 i B e^{6 i c} + 2 i B e^{2 i c} + i B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{16 a^{4}}"," ",0,"Piecewise(((294912*I*A*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + (24576*I*A*a**12*d**3*exp(12*I*c) - 24576*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (131072*I*A*a**12*d**3*exp(14*I*c) - 65536*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (393216*I*A*a**12*d**3*exp(18*I*c) + 196608*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(A - I*B)/(16*a**4) + (A*exp(8*I*c) + 4*A*exp(6*I*c) + 6*A*exp(4*I*c) + 4*A*exp(2*I*c) + A - I*B*exp(8*I*c) - 2*I*B*exp(6*I*c) + 2*I*B*exp(2*I*c) + I*B)*exp(-8*I*c)/(16*a**4)), True)) - x*(-A + I*B)/(16*a**4)","A",0
64,1,362,0,1.034751," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\frac{A \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{4} d} + \begin{cases} \frac{\left(\left(24576 A a^{12} d^{3} e^{12 i c} + 24576 i B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(196608 A a^{12} d^{3} e^{14 i c} + 131072 i B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(786432 A a^{12} d^{3} e^{16 i c} + 294912 i B a^{12} d^{3} e^{16 i c}\right) e^{- 4 i d x} + \left(2555904 A a^{12} d^{3} e^{18 i c} + 393216 i B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{- 31 i A + B}{16 a^{4}} - \frac{\left(31 i A e^{8 i c} + 26 i A e^{6 i c} + 16 i A e^{4 i c} + 6 i A e^{2 i c} + i A - B e^{8 i c} - 4 B e^{6 i c} - 6 B e^{4 i c} - 4 B e^{2 i c} - B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(31 i A - B\right)}{16 a^{4}}"," ",0,"A*log(exp(2*I*d*x) - exp(-2*I*c))/(a**4*d) + Piecewise((((24576*A*a**12*d**3*exp(12*I*c) + 24576*I*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (196608*A*a**12*d**3*exp(14*I*c) + 131072*I*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (786432*A*a**12*d**3*exp(16*I*c) + 294912*I*B*a**12*d**3*exp(16*I*c))*exp(-4*I*d*x) + (2555904*A*a**12*d**3*exp(18*I*c) + 393216*I*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(-31*I*A + B)/(16*a**4) - (31*I*A*exp(8*I*c) + 26*I*A*exp(6*I*c) + 16*I*A*exp(4*I*c) + 6*I*A*exp(2*I*c) + I*A - B*exp(8*I*c) - 4*B*exp(6*I*c) - 6*B*exp(4*I*c) - 4*B*exp(2*I*c) - B)*exp(-8*I*c)/(16*a**4)), True)) - x*(31*I*A - B)/(16*a**4)","A",0
65,1,406,0,4.099761," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\frac{2 i A}{- a^{4} d e^{2 i c} e^{2 i d x} + a^{4} d} + \begin{cases} \frac{\left(\left(- 24576 i A a^{12} d^{3} e^{12 i c} + 24576 B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(- 262144 i A a^{12} d^{3} e^{14 i c} + 196608 B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(- 1474560 i A a^{12} d^{3} e^{16 i c} + 786432 B a^{12} d^{3} e^{16 i c}\right) e^{- 4 i d x} + \left(- 7077888 i A a^{12} d^{3} e^{18 i c} + 2555904 B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{- 129 A - 31 i B}{16 a^{4}} + \frac{i \left(129 i A e^{8 i c} + 72 i A e^{6 i c} + 30 i A e^{4 i c} + 8 i A e^{2 i c} + i A - 31 B e^{8 i c} - 26 B e^{6 i c} - 16 B e^{4 i c} - 6 B e^{2 i c} - B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(129 A + 31 i B\right)}{16 a^{4}} - \frac{i \left(4 A + i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"2*I*A/(-a**4*d*exp(2*I*c)*exp(2*I*d*x) + a**4*d) + Piecewise((((-24576*I*A*a**12*d**3*exp(12*I*c) + 24576*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (-262144*I*A*a**12*d**3*exp(14*I*c) + 196608*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (-1474560*I*A*a**12*d**3*exp(16*I*c) + 786432*B*a**12*d**3*exp(16*I*c))*exp(-4*I*d*x) + (-7077888*I*A*a**12*d**3*exp(18*I*c) + 2555904*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(-129*A - 31*I*B)/(16*a**4) + I*(129*I*A*exp(8*I*c) + 72*I*A*exp(6*I*c) + 30*I*A*exp(4*I*c) + 8*I*A*exp(2*I*c) + I*A - 31*B*exp(8*I*c) - 26*B*exp(6*I*c) - 16*B*exp(4*I*c) - 6*B*exp(2*I*c) - B)*exp(-8*I*c)/(16*a**4)), True)) - x*(129*A + 31*I*B)/(16*a**4) - I*(4*A + I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**4*d)","A",0
66,1,471,0,2.116088," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\frac{8 i A - 2 B + \left(- 6 i A e^{2 i c} + 2 B e^{2 i c}\right) e^{2 i d x}}{i a^{4} d e^{4 i c} e^{4 i d x} - 2 i a^{4} d e^{2 i c} e^{2 i d x} + i a^{4} d} + \begin{cases} \frac{\left(\left(- 24576 A a^{12} d^{3} e^{12 i c} - 24576 i B a^{12} d^{3} e^{12 i c}\right) e^{- 8 i d x} + \left(- 327680 A a^{12} d^{3} e^{14 i c} - 262144 i B a^{12} d^{3} e^{14 i c}\right) e^{- 6 i d x} + \left(- 2359296 A a^{12} d^{3} e^{16 i c} - 1474560 i B a^{12} d^{3} e^{16 i c}\right) e^{- 4 i d x} + \left(- 14745600 A a^{12} d^{3} e^{18 i c} - 7077888 i B a^{12} d^{3} e^{18 i c}\right) e^{- 2 i d x}\right) e^{- 20 i c}}{3145728 a^{16} d^{4}} & \text{for}\: 3145728 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{351 i A - 129 B}{16 a^{4}} + \frac{\left(351 i A e^{8 i c} + 150 i A e^{6 i c} + 48 i A e^{4 i c} + 10 i A e^{2 i c} + i A - 129 B e^{8 i c} - 72 B e^{6 i c} - 30 B e^{4 i c} - 8 B e^{2 i c} - B\right) e^{- 8 i c}}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 351 i A + 129 B\right)}{16 a^{4}} - \frac{\left(11 A + 4 i B\right) \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"(8*I*A - 2*B + (-6*I*A*exp(2*I*c) + 2*B*exp(2*I*c))*exp(2*I*d*x))/(I*a**4*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*a**4*d*exp(2*I*c)*exp(2*I*d*x) + I*a**4*d) + Piecewise((((-24576*A*a**12*d**3*exp(12*I*c) - 24576*I*B*a**12*d**3*exp(12*I*c))*exp(-8*I*d*x) + (-327680*A*a**12*d**3*exp(14*I*c) - 262144*I*B*a**12*d**3*exp(14*I*c))*exp(-6*I*d*x) + (-2359296*A*a**12*d**3*exp(16*I*c) - 1474560*I*B*a**12*d**3*exp(16*I*c))*exp(-4*I*d*x) + (-14745600*A*a**12*d**3*exp(18*I*c) - 7077888*I*B*a**12*d**3*exp(18*I*c))*exp(-2*I*d*x))*exp(-20*I*c)/(3145728*a**16*d**4), Ne(3145728*a**16*d**4*exp(20*I*c), 0)), (x*(-(351*I*A - 129*B)/(16*a**4) + (351*I*A*exp(8*I*c) + 150*I*A*exp(6*I*c) + 48*I*A*exp(4*I*c) + 10*I*A*exp(2*I*c) + I*A - 129*B*exp(8*I*c) - 72*B*exp(6*I*c) - 30*B*exp(4*I*c) - 8*B*exp(2*I*c) - B)*exp(-8*I*c)/(16*a**4)), True)) - x*(-351*I*A + 129*B)/(16*a**4) - (11*A + 4*I*B)*log(exp(2*I*d*x) - exp(-2*I*c))/(a**4*d)","A",0
67,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**3*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*tan(c + d*x)**3, x)","F",0
68,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**2*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
69,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*tan(c + d*x), x)","F",0
70,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x)), x)","F",0
71,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*cot(c + d*x), x)","F",0
72,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
73,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*cot(c + d*x)**3, x)","F",0
74,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*cot(c + d*x)**4, x)","F",0
75,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
76,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*tan(c + d*x), x)","F",0
77,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x)), x)","F",0
78,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*cot(c + d*x), x)","F",0
79,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
80,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*(A + B*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
83,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*(A + B*tan(c + d*x))*tan(c + d*x), x)","F",0
84,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*(A + B*tan(c + d*x)), x)","F",0
85,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
91,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
92,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
93,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
94,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
95,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
96,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
97,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
101,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
102,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
104,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{4}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**4/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
106,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
108,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
109,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
110,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
111,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
112,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int A \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int B \tan^{\frac{9}{2}}{\left(c + d x \right)}\, dx + \int \left(- i A \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- i B \tan^{\frac{7}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(A*tan(c + d*x)**(7/2), x) + Integral(B*tan(c + d*x)**(9/2), x) + Integral(-I*A*tan(c + d*x)**(5/2), x) + Integral(-I*B*tan(c + d*x)**(7/2), x))","F",0
113,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int A \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int B \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int \left(- i A \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- i B \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(A*tan(c + d*x)**(5/2), x) + Integral(B*tan(c + d*x)**(7/2), x) + Integral(-I*A*tan(c + d*x)**(3/2), x) + Integral(-I*B*tan(c + d*x)**(5/2), x))","F",0
114,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int A \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int B \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int \left(- i A \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int \left(- i B \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(A*tan(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**(5/2), x) + Integral(-I*A*sqrt(tan(c + d*x)), x) + Integral(-I*B*tan(c + d*x)**(3/2), x))","F",0
115,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","i a \left(\int A \sqrt{\tan{\left(c + d x \right)}}\, dx + \int B \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- \frac{i A}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int \left(- i B \sqrt{\tan{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"I*a*(Integral(A*sqrt(tan(c + d*x)), x) + Integral(B*tan(c + d*x)**(3/2), x) + Integral(-I*A/sqrt(tan(c + d*x)), x) + Integral(-I*B*sqrt(tan(c + d*x)), x))","F",0
116,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","i a \left(\int \frac{A}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int B \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- \frac{i A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{i B}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"I*a*(Integral(A/sqrt(tan(c + d*x)), x) + Integral(B*sqrt(tan(c + d*x)), x) + Integral(-I*A/tan(c + d*x)**(3/2), x) + Integral(-I*B/sqrt(tan(c + d*x)), x))","F",0
117,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","i a \left(\int \frac{A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- \frac{i A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{i B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"I*a*(Integral(A/tan(c + d*x)**(3/2), x) + Integral(B/sqrt(tan(c + d*x)), x) + Integral(-I*A/tan(c + d*x)**(5/2), x) + Integral(-I*B/tan(c + d*x)**(3/2), x))","F",0
118,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","i a \left(\int \frac{A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{i A}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{i B}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"I*a*(Integral(A/tan(c + d*x)**(5/2), x) + Integral(B/tan(c + d*x)**(3/2), x) + Integral(-I*A/tan(c + d*x)**(7/2), x) + Integral(-I*B/tan(c + d*x)**(5/2), x))","F",0
119,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- a^{2} \left(\int \left(- A \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int A \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int \left(- B \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx + \int B \tan^{\frac{9}{2}}{\left(c + d x \right)}\, dx + \int \left(- 2 i A \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- 2 i B \tan^{\frac{7}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*tan(c + d*x)**(3/2), x) + Integral(A*tan(c + d*x)**(7/2), x) + Integral(-B*tan(c + d*x)**(5/2), x) + Integral(B*tan(c + d*x)**(9/2), x) + Integral(-2*I*A*tan(c + d*x)**(5/2), x) + Integral(-2*I*B*tan(c + d*x)**(7/2), x))","F",0
121,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- a^{2} \left(\int \left(- A \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int A \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int \left(- B \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int B \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int \left(- 2 i A \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- 2 i B \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*sqrt(tan(c + d*x)), x) + Integral(A*tan(c + d*x)**(5/2), x) + Integral(-B*tan(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**(7/2), x) + Integral(-2*I*A*tan(c + d*x)**(3/2), x) + Integral(-2*I*B*tan(c + d*x)**(5/2), x))","F",0
122,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","- a^{2} \left(\int \left(- \frac{A}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int A \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- B \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int B \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int \left(- 2 i A \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int \left(- 2 i B \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/sqrt(tan(c + d*x)), x) + Integral(A*tan(c + d*x)**(3/2), x) + Integral(-B*sqrt(tan(c + d*x)), x) + Integral(B*tan(c + d*x)**(5/2), x) + Integral(-2*I*A*sqrt(tan(c + d*x)), x) + Integral(-2*I*B*tan(c + d*x)**(3/2), x))","F",0
123,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","- a^{2} \left(\int \left(- \frac{A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int A \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- \frac{B}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int B \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- \frac{2 i A}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int \left(- 2 i B \sqrt{\tan{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/tan(c + d*x)**(3/2), x) + Integral(A*sqrt(tan(c + d*x)), x) + Integral(-B/sqrt(tan(c + d*x)), x) + Integral(B*tan(c + d*x)**(3/2), x) + Integral(-2*I*A/sqrt(tan(c + d*x)), x) + Integral(-2*I*B*sqrt(tan(c + d*x)), x))","F",0
124,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","- a^{2} \left(\int \left(- \frac{A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- \frac{B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int B \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- \frac{2 i A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{2 i B}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/tan(c + d*x)**(5/2), x) + Integral(A/sqrt(tan(c + d*x)), x) + Integral(-B/tan(c + d*x)**(3/2), x) + Integral(B*sqrt(tan(c + d*x)), x) + Integral(-2*I*A/tan(c + d*x)**(3/2), x) + Integral(-2*I*B/sqrt(tan(c + d*x)), x))","F",0
125,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","- a^{2} \left(\int \left(- \frac{A}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{B}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{B}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- \frac{2 i A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{2 i B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/tan(c + d*x)**(7/2), x) + Integral(A/tan(c + d*x)**(3/2), x) + Integral(-B/tan(c + d*x)**(5/2), x) + Integral(B/sqrt(tan(c + d*x)), x) + Integral(-2*I*A/tan(c + d*x)**(5/2), x) + Integral(-2*I*B/tan(c + d*x)**(3/2), x))","F",0
126,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","- a^{2} \left(\int \left(- \frac{A}{\tan^{\frac{9}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{B}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{2 i A}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{2 i B}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/tan(c + d*x)**(9/2), x) + Integral(A/tan(c + d*x)**(5/2), x) + Integral(-B/tan(c + d*x)**(7/2), x) + Integral(B/tan(c + d*x)**(3/2), x) + Integral(-2*I*A/tan(c + d*x)**(7/2), x) + Integral(-2*I*B/tan(c + d*x)**(5/2), x))","F",0
127,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- i a^{3} \left(\int \left(- 3 A \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int A \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 B \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx + \int B \tan^{\frac{9}{2}}{\left(c + d x \right)}\, dx + \int i A \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- 3 i A \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx + \int i B \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 i B \tan^{\frac{7}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A*tan(c + d*x)**(3/2), x) + Integral(A*tan(c + d*x)**(7/2), x) + Integral(-3*B*tan(c + d*x)**(5/2), x) + Integral(B*tan(c + d*x)**(9/2), x) + Integral(I*A*sqrt(tan(c + d*x)), x) + Integral(-3*I*A*tan(c + d*x)**(5/2), x) + Integral(I*B*tan(c + d*x)**(3/2), x) + Integral(-3*I*B*tan(c + d*x)**(7/2), x))","F",0
129,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","- i a^{3} \left(\int \left(- 3 A \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int A \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 B \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int B \tan^{\frac{7}{2}}{\left(c + d x \right)}\, dx + \int \frac{i A}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- 3 i A \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int i B \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- 3 i B \tan^{\frac{5}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A*sqrt(tan(c + d*x)), x) + Integral(A*tan(c + d*x)**(5/2), x) + Integral(-3*B*tan(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**(7/2), x) + Integral(I*A/sqrt(tan(c + d*x)), x) + Integral(-3*I*A*tan(c + d*x)**(3/2), x) + Integral(I*B*sqrt(tan(c + d*x)), x) + Integral(-3*I*B*tan(c + d*x)**(5/2), x))","F",0
130,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","- i a^{3} \left(\int \left(- \frac{3 A}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int A \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 B \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int B \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx + \int \frac{i A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- 3 i A \sqrt{\tan{\left(c + d x \right)}}\right)\, dx + \int \frac{i B}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- 3 i B \tan^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A/sqrt(tan(c + d*x)), x) + Integral(A*tan(c + d*x)**(3/2), x) + Integral(-3*B*sqrt(tan(c + d*x)), x) + Integral(B*tan(c + d*x)**(5/2), x) + Integral(I*A/tan(c + d*x)**(3/2), x) + Integral(-3*I*A*sqrt(tan(c + d*x)), x) + Integral(I*B/sqrt(tan(c + d*x)), x) + Integral(-3*I*B*tan(c + d*x)**(3/2), x))","F",0
131,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","- i a^{3} \left(\int \left(- \frac{3 A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int A \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 B}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int B \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \frac{i A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 i A}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx + \int \frac{i B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- 3 i B \sqrt{\tan{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A/tan(c + d*x)**(3/2), x) + Integral(A*sqrt(tan(c + d*x)), x) + Integral(-3*B/sqrt(tan(c + d*x)), x) + Integral(B*tan(c + d*x)**(3/2), x) + Integral(I*A/tan(c + d*x)**(5/2), x) + Integral(-3*I*A/sqrt(tan(c + d*x)), x) + Integral(I*B/tan(c + d*x)**(3/2), x) + Integral(-3*I*B*sqrt(tan(c + d*x)), x))","F",0
132,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","- i a^{3} \left(\int \left(- \frac{3 A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int B \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \frac{i A}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 i A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{i B}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 i B}{\sqrt{\tan{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A/tan(c + d*x)**(5/2), x) + Integral(A/sqrt(tan(c + d*x)), x) + Integral(-3*B/tan(c + d*x)**(3/2), x) + Integral(B*sqrt(tan(c + d*x)), x) + Integral(I*A/tan(c + d*x)**(7/2), x) + Integral(-3*I*A/tan(c + d*x)**(3/2), x) + Integral(I*B/tan(c + d*x)**(5/2), x) + Integral(-3*I*B/sqrt(tan(c + d*x)), x))","F",0
133,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","- i a^{3} \left(\int \left(- \frac{3 A}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 B}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{B}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \frac{i A}{\tan^{\frac{9}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 i A}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{i B}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{3 i B}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(-3*A/tan(c + d*x)**(7/2), x) + Integral(A/tan(c + d*x)**(3/2), x) + Integral(-3*B/tan(c + d*x)**(5/2), x) + Integral(B/sqrt(tan(c + d*x)), x) + Integral(I*A/tan(c + d*x)**(9/2), x) + Integral(-3*I*A/tan(c + d*x)**(5/2), x) + Integral(I*B/tan(c + d*x)**(7/2), x) + Integral(-3*I*B/tan(c + d*x)**(3/2), x))","F",0
134,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan^{\frac{7}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*tan(c + d*x)**(5/2)/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)**(7/2)/(tan(c + d*x) - I), x))/a","F",0
135,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*tan(c + d*x)**(3/2)/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)**(5/2)/(tan(c + d*x) - I), x))/a","F",0
136,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \sqrt{\tan{\left(c + d x \right)}}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*sqrt(tan(c + d*x))/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)**(3/2)/(tan(c + d*x) - I), x))/a","F",0
137,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
138,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c)),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
139,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan^{\frac{7}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*tan(c + d*x)**(5/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)**(7/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
141,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*tan(c + d*x)**(3/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)**(5/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
142,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \sqrt{\tan{\left(c + d x \right)}}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*sqrt(tan(c + d*x))/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)**(3/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
143,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
144,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
145,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{i \left(\int \frac{A \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx + \int \frac{B \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*tan(c + d*x)**(3/2)/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x) + Integral(B*tan(c + d*x)**(5/2)/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x))/a**3","F",0
150,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{i \left(\int \frac{A \sqrt{\tan{\left(c + d x \right)}}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx + \int \frac{B \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*sqrt(tan(c + d*x))/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x) + Integral(B*tan(c + d*x)**(3/2)/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x))/a**3","F",0
151,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
152,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
153,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**(3/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*tan(c + d*x)**(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
156,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
157,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
158,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
159,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
163,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
164,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
165,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
166,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*(A + B*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
173,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
180,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
181,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(I*a*(tan(c + d*x) - I))*sqrt(tan(c + d*x))), x)","F",0
182,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(3/2)), x)","F",0
183,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(5/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(5/2)), x)","F",0
184,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
186,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
187,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(tan(c + d*x))), x)","F",0
188,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
193,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/3)*(A+B*tan(d*x+c)),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*(A + B*tan(c + d*x)), x)","F",0
197,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(2/3)*(A + B*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
198,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}} \left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(2/3)*(A + B*tan(c + d*x))*tan(c + d*x), x)","F",0
199,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(2/3)*(A + B*tan(c + d*x)), x)","F",0
200,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}} \left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(2/3)*(A + B*tan(c + d*x))*cot(c + d*x), x)","F",0
201,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(2/3)*(A + B*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
202,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
203,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(2/3),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(2/3), x)","F",0
204,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","a^{4} \left(\int A \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 6 A \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int A \tan^{4}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 6 B \tan^{3}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int B \tan^{5}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int 4 i A \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 4 i A \tan^{3}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int 4 i B \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 4 i B \tan^{4}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"a**4*(Integral(A*tan(c + d*x)**m, x) + Integral(-6*A*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(A*tan(c + d*x)**4*tan(c + d*x)**m, x) + Integral(B*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(-6*B*tan(c + d*x)**3*tan(c + d*x)**m, x) + Integral(B*tan(c + d*x)**5*tan(c + d*x)**m, x) + Integral(4*I*A*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(-4*I*A*tan(c + d*x)**3*tan(c + d*x)**m, x) + Integral(4*I*B*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(-4*I*B*tan(c + d*x)**4*tan(c + d*x)**m, x))","F",0
205,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- i a^{3} \left(\int i A \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 3 A \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int A \tan^{3}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 3 B \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int B \tan^{4}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 3 i A \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int i B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 3 i B \tan^{3}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*tan(c + d*x)**m, x) + Integral(-3*A*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(A*tan(c + d*x)**3*tan(c + d*x)**m, x) + Integral(-3*B*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(B*tan(c + d*x)**4*tan(c + d*x)**m, x) + Integral(-3*I*A*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(I*B*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(-3*I*B*tan(c + d*x)**3*tan(c + d*x)**m, x))","F",0
206,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- a^{2} \left(\int \left(- A \tan^{m}{\left(c + d x \right)}\right)\, dx + \int A \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int B \tan^{3}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- 2 i A \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx + \int \left(- 2 i B \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*tan(c + d*x)**m, x) + Integral(A*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(-B*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(B*tan(c + d*x)**3*tan(c + d*x)**m, x) + Integral(-2*I*A*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(-2*I*B*tan(c + d*x)**2*tan(c + d*x)**m, x))","F",0
207,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int \left(- i A \tan^{m}{\left(c + d x \right)}\right)\, dx + \int A \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int B \tan^{2}{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\, dx + \int \left(- i B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*tan(c + d*x)**m, x) + Integral(A*tan(c + d*x)*tan(c + d*x)**m, x) + Integral(B*tan(c + d*x)**2*tan(c + d*x)**m, x) + Integral(-I*B*tan(c + d*x)*tan(c + d*x)**m, x))","F",0
208,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \tan^{m}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*tan(c + d*x)**m/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)*tan(c + d*x)**m/(tan(c + d*x) - I), x))/a","F",0
209,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \tan^{m}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*tan(c + d*x)**m/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)*tan(c + d*x)**m/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
210,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{i \left(\int \frac{A \tan^{m}{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx + \int \frac{B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*tan(c + d*x)**m/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x) + Integral(B*tan(c + d*x)*tan(c + d*x)**m/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x))/a**3","F",0
211,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**4,x)","\frac{\int \frac{A \tan^{m}{\left(c + d x \right)}}{\tan^{4}{\left(c + d x \right)} - 4 i \tan^{3}{\left(c + d x \right)} - 6 \tan^{2}{\left(c + d x \right)} + 4 i \tan{\left(c + d x \right)} + 1}\, dx + \int \frac{B \tan{\left(c + d x \right)} \tan^{m}{\left(c + d x \right)}}{\tan^{4}{\left(c + d x \right)} - 4 i \tan^{3}{\left(c + d x \right)} - 6 \tan^{2}{\left(c + d x \right)} + 4 i \tan{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"(Integral(A*tan(c + d*x)**m/(tan(c + d*x)**4 - 4*I*tan(c + d*x)**3 - 6*tan(c + d*x)**2 + 4*I*tan(c + d*x) + 1), x) + Integral(B*tan(c + d*x)*tan(c + d*x)**m/(tan(c + d*x)**4 - 4*I*tan(c + d*x)**3 - 6*tan(c + d*x)**2 + 4*I*tan(c + d*x) + 1), x))/a**4","F",0
212,-1,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
214,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
215,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
216,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
217,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
218,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
219,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*tan(c + d*x)**3, x)","F",0
220,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
221,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*tan(c + d*x), x)","F",0
222,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x)), x)","F",0
223,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*cot(c + d*x), x)","F",0
224,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
225,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*cot(c + d*x)**3, x)","F",0
226,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
229,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
230,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
231,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
232,1,136,0,0.381367," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} - A a x + \frac{A a \tan{\left(c + d x \right)}}{d} - \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b \tan^{2}{\left(c + d x \right)}}{2 d} - \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a \tan^{2}{\left(c + d x \right)}}{2 d} + B b x + \frac{B b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*x + A*a*tan(c + d*x)/d - A*b*log(tan(c + d*x)**2 + 1)/(2*d) + A*b*tan(c + d*x)**2/(2*d) - B*a*log(tan(c + d*x)**2 + 1)/(2*d) + B*a*tan(c + d*x)**2/(2*d) + B*b*x + B*b*tan(c + d*x)**3/(3*d) - B*b*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))*tan(c)**2, True))","A",0
233,1,104,0,0.236664," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} \frac{A a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - A b x + \frac{A b \tan{\left(c + d x \right)}}{d} - B a x + \frac{B a \tan{\left(c + d x \right)}}{d} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*log(tan(c + d*x)**2 + 1)/(2*d) - A*b*x + A*b*tan(c + d*x)/d - B*a*x + B*a*tan(c + d*x)/d - B*b*log(tan(c + d*x)**2 + 1)/(2*d) + B*b*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))*tan(c), True))","A",0
234,1,73,0,0.180152," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} A a x + \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B b x + \frac{B b \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x + A*b*log(tan(c + d*x)**2 + 1)/(2*d) + B*a*log(tan(c + d*x)**2 + 1)/(2*d) - B*b*x + B*b*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c)), True))","A",0
235,1,78,0,0.411276," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} - \frac{A a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + A b x + B a x + \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a*log(tan(c + d*x)**2 + 1)/(2*d) + A*a*log(tan(c + d*x))/d + A*b*x + B*a*x + B*b*log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))*cot(c), True))","A",0
236,1,121,0,0.849165," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a x & \text{for}\: c = 0 \wedge d = 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} A a x & \text{for}\: c = - d x \\- A a x - \frac{A a}{d \tan{\left(c + d x \right)}} - \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a*x, Eq(c, 0) & Eq(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))*cot(c)**2, Eq(d, 0)), (zoo*A*a*x, Eq(c, -d*x)), (-A*a*x - A*a/(d*tan(c + d*x)) - A*b*log(tan(c + d*x)**2 + 1)/(2*d) + A*b*log(tan(c + d*x))/d - B*a*log(tan(c + d*x)**2 + 1)/(2*d) + B*a*log(tan(c + d*x))/d + B*b*x, True))","A",0
237,1,150,0,1.276101," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{A a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a}{2 d \tan^{2}{\left(c + d x \right)}} - A b x - \frac{A b}{d \tan{\left(c + d x \right)}} - B a x - \frac{B a}{d \tan{\left(c + d x \right)}} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))*cot(c)**3, Eq(d, 0)), (A*a*log(tan(c + d*x)**2 + 1)/(2*d) - A*a*log(tan(c + d*x))/d - A*a/(2*d*tan(c + d*x)**2) - A*b*x - A*b/(d*tan(c + d*x)) - B*a*x - B*a/(d*tan(c + d*x)) - B*b*log(tan(c + d*x)**2 + 1)/(2*d) + B*b*log(tan(c + d*x))/d, True))","A",0
238,1,180,0,1.916838," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\A a x + \frac{A a}{d \tan{\left(c + d x \right)}} - \frac{A a}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A b}{2 d \tan^{2}{\left(c + d x \right)}} + \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a}{2 d \tan^{2}{\left(c + d x \right)}} - B b x - \frac{B b}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))*cot(c)**4, Eq(d, 0)), (A*a*x + A*a/(d*tan(c + d*x)) - A*a/(3*d*tan(c + d*x)**3) + A*b*log(tan(c + d*x)**2 + 1)/(2*d) - A*b*log(tan(c + d*x))/d - A*b/(2*d*tan(c + d*x)**2) + B*a*log(tan(c + d*x)**2 + 1)/(2*d) - B*a*log(tan(c + d*x))/d - B*a/(2*d*tan(c + d*x)**2) - B*b*x - B*b/(d*tan(c + d*x)), True))","A",0
239,1,211,0,2.614495," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right) \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{A a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A a}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A a}{4 d \tan^{4}{\left(c + d x \right)}} + A b x + \frac{A b}{d \tan{\left(c + d x \right)}} - \frac{A b}{3 d \tan^{3}{\left(c + d x \right)}} + B a x + \frac{B a}{d \tan{\left(c + d x \right)}} - \frac{B a}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B b}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))*cot(c)**5, Eq(d, 0)), (-A*a*log(tan(c + d*x)**2 + 1)/(2*d) + A*a*log(tan(c + d*x))/d + A*a/(2*d*tan(c + d*x)**2) - A*a/(4*d*tan(c + d*x)**4) + A*b*x + A*b/(d*tan(c + d*x)) - A*b/(3*d*tan(c + d*x)**3) + B*a*x + B*a/(d*tan(c + d*x)) - B*a/(3*d*tan(c + d*x)**3) + B*b*log(tan(c + d*x)**2 + 1)/(2*d) - B*b*log(tan(c + d*x))/d - B*b/(2*d*tan(c + d*x)**2), True))","A",0
240,1,246,0,0.604123," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} - A a^{2} x + \frac{A a^{2} \tan{\left(c + d x \right)}}{d} - \frac{A a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{A a b \tan^{2}{\left(c + d x \right)}}{d} + A b^{2} x + \frac{A b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{A b^{2} \tan{\left(c + d x \right)}}{d} - \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + 2 B a b x + \frac{2 B a b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{2 B a b \tan{\left(c + d x \right)}}{d} + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{2} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{B b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**2*x + A*a**2*tan(c + d*x)/d - A*a*b*log(tan(c + d*x)**2 + 1)/d + A*a*b*tan(c + d*x)**2/d + A*b**2*x + A*b**2*tan(c + d*x)**3/(3*d) - A*b**2*tan(c + d*x)/d - B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**2*tan(c + d*x)**2/(2*d) + 2*B*a*b*x + 2*B*a*b*tan(c + d*x)**3/(3*d) - 2*B*a*b*tan(c + d*x)/d + B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**2*tan(c + d*x)**4/(4*d) - B*b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**2*tan(c)**2, True))","A",0
241,1,192,0,0.424276," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} \frac{A a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 2 A a b x + \frac{2 A a b \tan{\left(c + d x \right)}}{d} - \frac{A b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} - B a^{2} x + \frac{B a^{2} \tan{\left(c + d x \right)}}{d} - \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{B a b \tan^{2}{\left(c + d x \right)}}{d} + B b^{2} x + \frac{B b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - 2*A*a*b*x + 2*A*a*b*tan(c + d*x)/d - A*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**2*tan(c + d*x)**2/(2*d) - B*a**2*x + B*a**2*tan(c + d*x)/d - B*a*b*log(tan(c + d*x)**2 + 1)/d + B*a*b*tan(c + d*x)**2/d + B*b**2*x + B*b**2*tan(c + d*x)**3/(3*d) - B*b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**2*tan(c), True))","A",0
242,1,143,0,0.296745," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} A a^{2} x + \frac{A a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - A b^{2} x + \frac{A b^{2} \tan{\left(c + d x \right)}}{d} + \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 2 B a b x + \frac{2 B a b \tan{\left(c + d x \right)}}{d} - \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x + A*a*b*log(tan(c + d*x)**2 + 1)/d - A*b**2*x + A*b**2*tan(c + d*x)/d + B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - 2*B*a*b*x + 2*B*a*b*tan(c + d*x)/d - B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**2, True))","A",0
243,1,129,0,0.688921," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} - \frac{A a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 2 A a b x + \frac{A b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + B a^{2} x + \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - B b^{2} x + \frac{B b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**2*log(tan(c + d*x))/d + 2*A*a*b*x + A*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**2*x + B*a*b*log(tan(c + d*x)**2 + 1)/d - B*b**2*x + B*b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**2*cot(c), True))","A",0
244,1,167,0,1.251448," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{2} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} A a^{2} x & \text{for}\: c = - d x \\- A a^{2} x - \frac{A a^{2}}{d \tan{\left(c + d x \right)}} - \frac{A a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 A a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + A b^{2} x - \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 2 B a b x + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**2*x, Eq(c, 0) & Eq(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**2*cot(c)**2, Eq(d, 0)), (zoo*A*a**2*x, Eq(c, -d*x)), (-A*a**2*x - A*a**2/(d*tan(c + d*x)) - A*a*b*log(tan(c + d*x)**2 + 1)/d + 2*A*a*b*log(tan(c + d*x))/d + A*b**2*x - B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**2*log(tan(c + d*x))/d + 2*B*a*b*x + B*b**2*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
245,1,214,0,1.805376," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{2} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{A a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - 2 A a b x - \frac{2 A a b}{d \tan{\left(c + d x \right)}} - \frac{A b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - B a^{2} x - \frac{B a^{2}}{d \tan{\left(c + d x \right)}} - \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 B a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**2*cot(c)**3, Eq(d, 0)), (A*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - A*a**2*log(tan(c + d*x))/d - A*a**2/(2*d*tan(c + d*x)**2) - 2*A*a*b*x - 2*A*a*b/(d*tan(c + d*x)) - A*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**2*log(tan(c + d*x))/d - B*a**2*x - B*a**2/(d*tan(c + d*x)) - B*a*b*log(tan(c + d*x)**2 + 1)/d + 2*B*a*b*log(tan(c + d*x))/d + B*b**2*x, True))","A",0
246,1,260,0,2.496149," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{2} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\A a^{2} x + \frac{A a^{2}}{d \tan{\left(c + d x \right)}} - \frac{A a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{A a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{2 A a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a b}{d \tan^{2}{\left(c + d x \right)}} - A b^{2} x - \frac{A b^{2}}{d \tan{\left(c + d x \right)}} + \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - 2 B a b x - \frac{2 B a b}{d \tan{\left(c + d x \right)}} - \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**2*cot(c)**4, Eq(d, 0)), (A*a**2*x + A*a**2/(d*tan(c + d*x)) - A*a**2/(3*d*tan(c + d*x)**3) + A*a*b*log(tan(c + d*x)**2 + 1)/d - 2*A*a*b*log(tan(c + d*x))/d - A*a*b/(d*tan(c + d*x)**2) - A*b**2*x - A*b**2/(d*tan(c + d*x)) + B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**2*log(tan(c + d*x))/d - B*a**2/(2*d*tan(c + d*x)**2) - 2*B*a*b*x - 2*B*a*b/(d*tan(c + d*x)) - B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**2*log(tan(c + d*x))/d, True))","A",0
247,1,313,0,4.664427," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{2} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{2} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{A a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{2}}{4 d \tan^{4}{\left(c + d x \right)}} + 2 A a b x + \frac{2 A a b}{d \tan{\left(c + d x \right)}} - \frac{2 A a b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{A b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} + B a^{2} x + \frac{B a^{2}}{d \tan{\left(c + d x \right)}} - \frac{B a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{2 B a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a b}{d \tan^{2}{\left(c + d x \right)}} - B b^{2} x - \frac{B b^{2}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**2*cot(c)**5, Eq(d, 0)), (-A*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**2*log(tan(c + d*x))/d + A*a**2/(2*d*tan(c + d*x)**2) - A*a**2/(4*d*tan(c + d*x)**4) + 2*A*a*b*x + 2*A*a*b/(d*tan(c + d*x)) - 2*A*a*b/(3*d*tan(c + d*x)**3) + A*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - A*b**2*log(tan(c + d*x))/d - A*b**2/(2*d*tan(c + d*x)**2) + B*a**2*x + B*a**2/(d*tan(c + d*x)) - B*a**2/(3*d*tan(c + d*x)**3) + B*a*b*log(tan(c + d*x)**2 + 1)/d - 2*B*a*b*log(tan(c + d*x))/d - B*a*b/(d*tan(c + d*x)**2) - B*b**2*x - B*b**2/(d*tan(c + d*x)), True))","A",0
248,1,384,0,0.961332," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} - A a^{3} x + \frac{A a^{3} \tan{\left(c + d x \right)}}{d} - \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 A a^{2} b \tan^{2}{\left(c + d x \right)}}{2 d} + 3 A a b^{2} x + \frac{A a b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 A a b^{2} \tan{\left(c + d x \right)}}{d} + \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{3} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{A b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} - \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{3} \tan^{2}{\left(c + d x \right)}}{2 d} + 3 B a^{2} b x + \frac{B a^{2} b \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 B a^{2} b \tan{\left(c + d x \right)}}{d} + \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a b^{2} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{3 B a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} - B b^{3} x + \frac{B b^{3} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{B b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**3*x + A*a**3*tan(c + d*x)/d - 3*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*A*a**2*b*tan(c + d*x)**2/(2*d) + 3*A*a*b**2*x + A*a*b**2*tan(c + d*x)**3/d - 3*A*a*b**2*tan(c + d*x)/d + A*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**3*tan(c + d*x)**4/(4*d) - A*b**3*tan(c + d*x)**2/(2*d) - B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**3*tan(c + d*x)**2/(2*d) + 3*B*a**2*b*x + B*a**2*b*tan(c + d*x)**3/d - 3*B*a**2*b*tan(c + d*x)/d + 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a*b**2*tan(c + d*x)**4/(4*d) - 3*B*a*b**2*tan(c + d*x)**2/(2*d) - B*b**3*x + B*b**3*tan(c + d*x)**5/(5*d) - B*b**3*tan(c + d*x)**3/(3*d) + B*b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**3*tan(c)**2, True))","A",0
249,1,311,0,0.659696," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \frac{A a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 A a^{2} b x + \frac{3 A a^{2} b \tan{\left(c + d x \right)}}{d} - \frac{3 A a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 A a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + A b^{3} x + \frac{A b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{A b^{3} \tan{\left(c + d x \right)}}{d} - B a^{3} x + \frac{B a^{3} \tan{\left(c + d x \right)}}{d} - \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a^{2} b \tan^{2}{\left(c + d x \right)}}{2 d} + 3 B a b^{2} x + \frac{B a b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 B a b^{2} \tan{\left(c + d x \right)}}{d} + \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{3} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{B b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - 3*A*a**2*b*x + 3*A*a**2*b*tan(c + d*x)/d - 3*A*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*A*a*b**2*tan(c + d*x)**2/(2*d) + A*b**3*x + A*b**3*tan(c + d*x)**3/(3*d) - A*b**3*tan(c + d*x)/d - B*a**3*x + B*a**3*tan(c + d*x)/d - 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a**2*b*tan(c + d*x)**2/(2*d) + 3*B*a*b**2*x + B*a*b**2*tan(c + d*x)**3/d - 3*B*a*b**2*tan(c + d*x)/d + B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**3*tan(c + d*x)**4/(4*d) - B*b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**3*tan(c), True))","A",0
250,1,240,0,0.460667," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} A a^{3} x + \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 A a b^{2} x + \frac{3 A a b^{2} \tan{\left(c + d x \right)}}{d} - \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} + \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 B a^{2} b x + \frac{3 B a^{2} b \tan{\left(c + d x \right)}}{d} - \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + B b^{3} x + \frac{B b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*x + 3*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*A*a*b**2*x + 3*A*a*b**2*tan(c + d*x)/d - A*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**3*tan(c + d*x)**2/(2*d) + B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a**2*b*x + 3*B*a**2*b*tan(c + d*x)/d - 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a*b**2*tan(c + d*x)**2/(2*d) + B*b**3*x + B*b**3*tan(c + d*x)**3/(3*d) - B*b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**3, True))","A",0
251,1,204,0,1.173782," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} - \frac{A a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 A a^{2} b x + \frac{3 A a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - A b^{3} x + \frac{A b^{3} \tan{\left(c + d x \right)}}{d} + B a^{3} x + \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 B a b^{2} x + \frac{3 B a b^{2} \tan{\left(c + d x \right)}}{d} - \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**3*log(tan(c + d*x))/d + 3*A*a**2*b*x + 3*A*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - A*b**3*x + A*b**3*tan(c + d*x)/d + B*a**3*x + 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a*b**2*x + 3*B*a*b**2*tan(c + d*x)/d - B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c), True))","A",0
252,1,223,0,1.943233," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{3} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} A a^{3} x & \text{for}\: c = - d x \\- A a^{3} x - \frac{A a^{3}}{d \tan{\left(c + d x \right)}} - \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 A a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 A a b^{2} x + \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 B a^{2} b x + \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B b^{3} x + \frac{B b^{3} \tan{\left(c + d x \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**3*x, Eq(c, 0) & Eq(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c)**2, Eq(d, 0)), (zoo*A*a**3*x, Eq(c, -d*x)), (-A*a**3*x - A*a**3/(d*tan(c + d*x)) - 3*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*A*a**2*b*log(tan(c + d*x))/d + 3*A*a*b**2*x + A*b**3*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**3*log(tan(c + d*x))/d + 3*B*a**2*b*x + 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - B*b**3*x + B*b**3*tan(c + d*x)/d, True))","A",0
253,1,262,0,2.468321," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{3} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{A a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - 3 A a^{2} b x - \frac{3 A a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{3 A a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 A a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + A b^{3} x - B a^{3} x - \frac{B a^{3}}{d \tan{\left(c + d x \right)}} - \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 B a b^{2} x + \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c)**3, Eq(d, 0)), (A*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - A*a**3*log(tan(c + d*x))/d - A*a**3/(2*d*tan(c + d*x)**2) - 3*A*a**2*b*x - 3*A*a**2*b/(d*tan(c + d*x)) - 3*A*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*A*a*b**2*log(tan(c + d*x))/d + A*b**3*x - B*a**3*x - B*a**3/(d*tan(c + d*x)) - 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a**2*b*log(tan(c + d*x))/d + 3*B*a*b**2*x + B*b**3*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
254,1,332,0,4.476868," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{3} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\A a^{3} x + \frac{A a^{3}}{d \tan{\left(c + d x \right)}} - \frac{A a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 A a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 A a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - 3 A a b^{2} x - \frac{3 A a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - 3 B a^{2} b x - \frac{3 B a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c)**4, Eq(d, 0)), (A*a**3*x + A*a**3/(d*tan(c + d*x)) - A*a**3/(3*d*tan(c + d*x)**3) + 3*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*A*a**2*b*log(tan(c + d*x))/d - 3*A*a**2*b/(2*d*tan(c + d*x)**2) - 3*A*a*b**2*x - 3*A*a*b**2/(d*tan(c + d*x)) - A*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**3*log(tan(c + d*x))/d + B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**3*log(tan(c + d*x))/d - B*a**3/(2*d*tan(c + d*x)**2) - 3*B*a**2*b*x - 3*B*a**2*b/(d*tan(c + d*x)) - 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a*b**2*log(tan(c + d*x))/d + B*b**3*x, True))","A",0
255,1,400,0,5.915842," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{3} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{A a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{3}}{4 d \tan^{4}{\left(c + d x \right)}} + 3 A a^{2} b x + \frac{3 A a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{A a^{2} b}{d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 A a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 A a b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - A b^{3} x - \frac{A b^{3}}{d \tan{\left(c + d x \right)}} + B a^{3} x + \frac{B a^{3}}{d \tan{\left(c + d x \right)}} - \frac{B a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 B a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - 3 B a b^{2} x - \frac{3 B a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c)**5, Eq(d, 0)), (-A*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**3*log(tan(c + d*x))/d + A*a**3/(2*d*tan(c + d*x)**2) - A*a**3/(4*d*tan(c + d*x)**4) + 3*A*a**2*b*x + 3*A*a**2*b/(d*tan(c + d*x)) - A*a**2*b/(d*tan(c + d*x)**3) + 3*A*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - 3*A*a*b**2*log(tan(c + d*x))/d - 3*A*a*b**2/(2*d*tan(c + d*x)**2) - A*b**3*x - A*b**3/(d*tan(c + d*x)) + B*a**3*x + B*a**3/(d*tan(c + d*x)) - B*a**3/(3*d*tan(c + d*x)**3) + 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a**2*b*log(tan(c + d*x))/d - 3*B*a**2*b/(2*d*tan(c + d*x)**2) - 3*B*a*b**2*x - 3*B*a*b**2/(d*tan(c + d*x)) - B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**3*log(tan(c + d*x))/d, True))","A",0
256,1,471,0,9.149468," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{3} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- A a^{3} x - \frac{A a^{3}}{d \tan{\left(c + d x \right)}} + \frac{A a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{3}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 A a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{3 A a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{3 A a^{2} b}{4 d \tan^{4}{\left(c + d x \right)}} + 3 A a b^{2} x + \frac{3 A a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{A a b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A b^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{3}}{4 d \tan^{4}{\left(c + d x \right)}} + 3 B a^{2} b x + \frac{3 B a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{B a^{2} b}{d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 B a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 B a b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - B b^{3} x - \frac{B b^{3}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**3*cot(c)**6, Eq(d, 0)), (-A*a**3*x - A*a**3/(d*tan(c + d*x)) + A*a**3/(3*d*tan(c + d*x)**3) - A*a**3/(5*d*tan(c + d*x)**5) - 3*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*A*a**2*b*log(tan(c + d*x))/d + 3*A*a**2*b/(2*d*tan(c + d*x)**2) - 3*A*a**2*b/(4*d*tan(c + d*x)**4) + 3*A*a*b**2*x + 3*A*a*b**2/(d*tan(c + d*x)) - A*a*b**2/(d*tan(c + d*x)**3) + A*b**3*log(tan(c + d*x)**2 + 1)/(2*d) - A*b**3*log(tan(c + d*x))/d - A*b**3/(2*d*tan(c + d*x)**2) - B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**3*log(tan(c + d*x))/d + B*a**3/(2*d*tan(c + d*x)**2) - B*a**3/(4*d*tan(c + d*x)**4) + 3*B*a**2*b*x + 3*B*a**2*b/(d*tan(c + d*x)) - B*a**2*b/(d*tan(c + d*x)**3) + 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a*b**2*log(tan(c + d*x))/d - 3*B*a*b**2/(2*d*tan(c + d*x)**2) - B*b**3*x - B*b**3/(d*tan(c + d*x)), True))","A",0
257,1,536,0,1.537341," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} - A a^{4} x + \frac{A a^{4} \tan{\left(c + d x \right)}}{d} - \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 A a^{3} b \tan^{2}{\left(c + d x \right)}}{d} + 6 A a^{2} b^{2} x + \frac{2 A a^{2} b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{6 A a^{2} b^{2} \tan{\left(c + d x \right)}}{d} + \frac{2 A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{A a b^{3} \tan^{4}{\left(c + d x \right)}}{d} - \frac{2 A a b^{3} \tan^{2}{\left(c + d x \right)}}{d} - A b^{4} x + \frac{A b^{4} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{A b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{A b^{4} \tan{\left(c + d x \right)}}{d} - \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{4} \tan^{2}{\left(c + d x \right)}}{2 d} + 4 B a^{3} b x + \frac{4 B a^{3} b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{4 B a^{3} b \tan{\left(c + d x \right)}}{d} + \frac{3 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 B a^{2} b^{2} \tan^{4}{\left(c + d x \right)}}{2 d} - \frac{3 B a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{d} - 4 B a b^{3} x + \frac{4 B a b^{3} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{4 B a b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{4 B a b^{3} \tan{\left(c + d x \right)}}{d} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{4} \tan^{6}{\left(c + d x \right)}}{6 d} - \frac{B b^{4} \tan^{4}{\left(c + d x \right)}}{4 d} + \frac{B b^{4} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**4*x + A*a**4*tan(c + d*x)/d - 2*A*a**3*b*log(tan(c + d*x)**2 + 1)/d + 2*A*a**3*b*tan(c + d*x)**2/d + 6*A*a**2*b**2*x + 2*A*a**2*b**2*tan(c + d*x)**3/d - 6*A*a**2*b**2*tan(c + d*x)/d + 2*A*a*b**3*log(tan(c + d*x)**2 + 1)/d + A*a*b**3*tan(c + d*x)**4/d - 2*A*a*b**3*tan(c + d*x)**2/d - A*b**4*x + A*b**4*tan(c + d*x)**5/(5*d) - A*b**4*tan(c + d*x)**3/(3*d) + A*b**4*tan(c + d*x)/d - B*a**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**4*tan(c + d*x)**2/(2*d) + 4*B*a**3*b*x + 4*B*a**3*b*tan(c + d*x)**3/(3*d) - 4*B*a**3*b*tan(c + d*x)/d + 3*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 3*B*a**2*b**2*tan(c + d*x)**4/(2*d) - 3*B*a**2*b**2*tan(c + d*x)**2/d - 4*B*a*b**3*x + 4*B*a*b**3*tan(c + d*x)**5/(5*d) - 4*B*a*b**3*tan(c + d*x)**3/(3*d) + 4*B*a*b**3*tan(c + d*x)/d - B*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**4*tan(c + d*x)**6/(6*d) - B*b**4*tan(c + d*x)**4/(4*d) + B*b**4*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**4*tan(c)**2, True))","A",0
258,1,437,0,1.075510," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 4 A a^{3} b x + \frac{4 A a^{3} b \tan{\left(c + d x \right)}}{d} - \frac{3 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 A a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{d} + 4 A a b^{3} x + \frac{4 A a b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{4 A a b^{3} \tan{\left(c + d x \right)}}{d} + \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{4} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{A b^{4} \tan^{2}{\left(c + d x \right)}}{2 d} - B a^{4} x + \frac{B a^{4} \tan{\left(c + d x \right)}}{d} - \frac{2 B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 B a^{3} b \tan^{2}{\left(c + d x \right)}}{d} + 6 B a^{2} b^{2} x + \frac{2 B a^{2} b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{6 B a^{2} b^{2} \tan{\left(c + d x \right)}}{d} + \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{B a b^{3} \tan^{4}{\left(c + d x \right)}}{d} - \frac{2 B a b^{3} \tan^{2}{\left(c + d x \right)}}{d} - B b^{4} x + \frac{B b^{4} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{B b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{4} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*log(tan(c + d*x)**2 + 1)/(2*d) - 4*A*a**3*b*x + 4*A*a**3*b*tan(c + d*x)/d - 3*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 3*A*a**2*b**2*tan(c + d*x)**2/d + 4*A*a*b**3*x + 4*A*a*b**3*tan(c + d*x)**3/(3*d) - 4*A*a*b**3*tan(c + d*x)/d + A*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**4*tan(c + d*x)**4/(4*d) - A*b**4*tan(c + d*x)**2/(2*d) - B*a**4*x + B*a**4*tan(c + d*x)/d - 2*B*a**3*b*log(tan(c + d*x)**2 + 1)/d + 2*B*a**3*b*tan(c + d*x)**2/d + 6*B*a**2*b**2*x + 2*B*a**2*b**2*tan(c + d*x)**3/d - 6*B*a**2*b**2*tan(c + d*x)/d + 2*B*a*b**3*log(tan(c + d*x)**2 + 1)/d + B*a*b**3*tan(c + d*x)**4/d - 2*B*a*b**3*tan(c + d*x)**2/d - B*b**4*x + B*b**4*tan(c + d*x)**5/(5*d) - B*b**4*tan(c + d*x)**3/(3*d) + B*b**4*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**4*tan(c), True))","A",0
259,1,347,0,0.717866," ","integrate((a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} A a^{4} x + \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 6 A a^{2} b^{2} x + \frac{6 A a^{2} b^{2} \tan{\left(c + d x \right)}}{d} - \frac{2 A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 A a b^{3} \tan^{2}{\left(c + d x \right)}}{d} + A b^{4} x + \frac{A b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{A b^{4} \tan{\left(c + d x \right)}}{d} + \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 4 B a^{3} b x + \frac{4 B a^{3} b \tan{\left(c + d x \right)}}{d} - \frac{3 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 B a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{d} + 4 B a b^{3} x + \frac{4 B a b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{4 B a b^{3} \tan{\left(c + d x \right)}}{d} + \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{4} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{B b^{4} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**4*x + 2*A*a**3*b*log(tan(c + d*x)**2 + 1)/d - 6*A*a**2*b**2*x + 6*A*a**2*b**2*tan(c + d*x)/d - 2*A*a*b**3*log(tan(c + d*x)**2 + 1)/d + 2*A*a*b**3*tan(c + d*x)**2/d + A*b**4*x + A*b**4*tan(c + d*x)**3/(3*d) - A*b**4*tan(c + d*x)/d + B*a**4*log(tan(c + d*x)**2 + 1)/(2*d) - 4*B*a**3*b*x + 4*B*a**3*b*tan(c + d*x)/d - 3*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 3*B*a**2*b**2*tan(c + d*x)**2/d + 4*B*a*b**3*x + 4*B*a*b**3*tan(c + d*x)**3/(3*d) - 4*B*a*b**3*tan(c + d*x)/d + B*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**4*tan(c + d*x)**4/(4*d) - B*b**4*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**4, True))","A",0
260,1,291,0,1.889236," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} - \frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 A a^{3} b x + \frac{3 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 4 A a b^{3} x + \frac{4 A a b^{3} \tan{\left(c + d x \right)}}{d} - \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{4} \tan^{2}{\left(c + d x \right)}}{2 d} + B a^{4} x + \frac{2 B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 6 B a^{2} b^{2} x + \frac{6 B a^{2} b^{2} \tan{\left(c + d x \right)}}{d} - \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 B a b^{3} \tan^{2}{\left(c + d x \right)}}{d} + B b^{4} x + \frac{B b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b^{4} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A*a**4*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**4*log(tan(c + d*x))/d + 4*A*a**3*b*x + 3*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 4*A*a*b**3*x + 4*A*a*b**3*tan(c + d*x)/d - A*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**4*tan(c + d*x)**2/(2*d) + B*a**4*x + 2*B*a**3*b*log(tan(c + d*x)**2 + 1)/d - 6*B*a**2*b**2*x + 6*B*a**2*b**2*tan(c + d*x)/d - 2*B*a*b**3*log(tan(c + d*x)**2 + 1)/d + 2*B*a*b**3*tan(c + d*x)**2/d + B*b**4*x + B*b**4*tan(c + d*x)**3/(3*d) - B*b**4*tan(c + d*x)/d, Ne(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c), True))","A",0
261,1,289,0,2.609640," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} A a^{4} x & \text{for}\: c = - d x \\- A a^{4} x - \frac{A a^{4}}{d \tan{\left(c + d x \right)}} - \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 A a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 6 A a^{2} b^{2} x + \frac{2 A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - A b^{4} x + \frac{A b^{4} \tan{\left(c + d x \right)}}{d} - \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 B a^{3} b x + \frac{3 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 4 B a b^{3} x + \frac{4 B a b^{3} \tan{\left(c + d x \right)}}{d} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{4} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, Eq(c, 0) & Eq(d, 0)), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**2, Eq(d, 0)), (zoo*A*a**4*x, Eq(c, -d*x)), (-A*a**4*x - A*a**4/(d*tan(c + d*x)) - 2*A*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*A*a**3*b*log(tan(c + d*x))/d + 6*A*a**2*b**2*x + 2*A*a*b**3*log(tan(c + d*x)**2 + 1)/d - A*b**4*x + A*b**4*tan(c + d*x)/d - B*a**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**4*log(tan(c + d*x))/d + 4*B*a**3*b*x + 3*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 4*B*a*b**3*x + 4*B*a*b**3*tan(c + d*x)/d - B*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**4*tan(c + d*x)**2/(2*d), True))","A",0
262,1,309,0,4.606835," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - 4 A a^{3} b x - \frac{4 A a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{3 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{6 A a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 A a b^{3} x + \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B a^{4} x - \frac{B a^{4}}{d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 B a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 6 B a^{2} b^{2} x + \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - B b^{4} x + \frac{B b^{4} \tan{\left(c + d x \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**3, Eq(d, 0)), (A*a**4*log(tan(c + d*x)**2 + 1)/(2*d) - A*a**4*log(tan(c + d*x))/d - A*a**4/(2*d*tan(c + d*x)**2) - 4*A*a**3*b*x - 4*A*a**3*b/(d*tan(c + d*x)) - 3*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 6*A*a**2*b**2*log(tan(c + d*x))/d + 4*A*a*b**3*x + A*b**4*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**4*x - B*a**4/(d*tan(c + d*x)) - 2*B*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*B*a**3*b*log(tan(c + d*x))/d + 6*B*a**2*b**2*x + 2*B*a*b**3*log(tan(c + d*x)**2 + 1)/d - B*b**4*x + B*b**4*tan(c + d*x)/d, True))","A",0
263,1,369,0,5.906840," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\A a^{4} x + \frac{A a^{4}}{d \tan{\left(c + d x \right)}} - \frac{A a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 A a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 A a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - 6 A a^{2} b^{2} x - \frac{6 A a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 A a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + A b^{4} x + \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - 4 B a^{3} b x - \frac{4 B a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{3 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{6 B a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 B a b^{3} x + \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**4, Eq(d, 0)), (A*a**4*x + A*a**4/(d*tan(c + d*x)) - A*a**4/(3*d*tan(c + d*x)**3) + 2*A*a**3*b*log(tan(c + d*x)**2 + 1)/d - 4*A*a**3*b*log(tan(c + d*x))/d - 2*A*a**3*b/(d*tan(c + d*x)**2) - 6*A*a**2*b**2*x - 6*A*a**2*b**2/(d*tan(c + d*x)) - 2*A*a*b**3*log(tan(c + d*x)**2 + 1)/d + 4*A*a*b**3*log(tan(c + d*x))/d + A*b**4*x + B*a**4*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**4*log(tan(c + d*x))/d - B*a**4/(2*d*tan(c + d*x)**2) - 4*B*a**3*b*x - 4*B*a**3*b/(d*tan(c + d*x)) - 3*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 6*B*a**2*b**2*log(tan(c + d*x))/d + 4*B*a*b**3*x + B*b**4*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
264,1,459,0,8.871057," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{4}}{4 d \tan^{4}{\left(c + d x \right)}} + 4 A a^{3} b x + \frac{4 A a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{4 A a^{3} b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{6 A a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 A a^{2} b^{2}}{d \tan^{2}{\left(c + d x \right)}} - 4 A a b^{3} x - \frac{4 A a b^{3}}{d \tan{\left(c + d x \right)}} - \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B a^{4} x + \frac{B a^{4}}{d \tan{\left(c + d x \right)}} - \frac{B a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 B a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 B a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - 6 B a^{2} b^{2} x - \frac{6 B a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 B a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b^{4} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**5, Eq(d, 0)), (-A*a**4*log(tan(c + d*x)**2 + 1)/(2*d) + A*a**4*log(tan(c + d*x))/d + A*a**4/(2*d*tan(c + d*x)**2) - A*a**4/(4*d*tan(c + d*x)**4) + 4*A*a**3*b*x + 4*A*a**3*b/(d*tan(c + d*x)) - 4*A*a**3*b/(3*d*tan(c + d*x)**3) + 3*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 6*A*a**2*b**2*log(tan(c + d*x))/d - 3*A*a**2*b**2/(d*tan(c + d*x)**2) - 4*A*a*b**3*x - 4*A*a*b**3/(d*tan(c + d*x)) - A*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + A*b**4*log(tan(c + d*x))/d + B*a**4*x + B*a**4/(d*tan(c + d*x)) - B*a**4/(3*d*tan(c + d*x)**3) + 2*B*a**3*b*log(tan(c + d*x)**2 + 1)/d - 4*B*a**3*b*log(tan(c + d*x))/d - 2*B*a**3*b/(d*tan(c + d*x)**2) - 6*B*a**2*b**2*x - 6*B*a**2*b**2/(d*tan(c + d*x)) - 2*B*a*b**3*log(tan(c + d*x)**2 + 1)/d + 4*B*a*b**3*log(tan(c + d*x))/d + B*b**4*x, True))","A",0
265,1,546,0,11.392485," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- A a^{4} x - \frac{A a^{4}}{d \tan{\left(c + d x \right)}} + \frac{A a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{4}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 A a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{2 A a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{3} b}{d \tan^{4}{\left(c + d x \right)}} + 6 A a^{2} b^{2} x + \frac{6 A a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{2 A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 A a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 A a b^{3}}{d \tan^{2}{\left(c + d x \right)}} - A b^{4} x - \frac{A b^{4}}{d \tan{\left(c + d x \right)}} - \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{4}}{4 d \tan^{4}{\left(c + d x \right)}} + 4 B a^{3} b x + \frac{4 B a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{4 B a^{3} b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{6 B a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 B a^{2} b^{2}}{d \tan^{2}{\left(c + d x \right)}} - 4 B a b^{3} x - \frac{4 B a b^{3}}{d \tan{\left(c + d x \right)}} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**6, Eq(d, 0)), (-A*a**4*x - A*a**4/(d*tan(c + d*x)) + A*a**4/(3*d*tan(c + d*x)**3) - A*a**4/(5*d*tan(c + d*x)**5) - 2*A*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*A*a**3*b*log(tan(c + d*x))/d + 2*A*a**3*b/(d*tan(c + d*x)**2) - A*a**3*b/(d*tan(c + d*x)**4) + 6*A*a**2*b**2*x + 6*A*a**2*b**2/(d*tan(c + d*x)) - 2*A*a**2*b**2/(d*tan(c + d*x)**3) + 2*A*a*b**3*log(tan(c + d*x)**2 + 1)/d - 4*A*a*b**3*log(tan(c + d*x))/d - 2*A*a*b**3/(d*tan(c + d*x)**2) - A*b**4*x - A*b**4/(d*tan(c + d*x)) - B*a**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**4*log(tan(c + d*x))/d + B*a**4/(2*d*tan(c + d*x)**2) - B*a**4/(4*d*tan(c + d*x)**4) + 4*B*a**3*b*x + 4*B*a**3*b/(d*tan(c + d*x)) - 4*B*a**3*b/(3*d*tan(c + d*x)**3) + 3*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 6*B*a**2*b**2*log(tan(c + d*x))/d - 3*B*a**2*b**2/(d*tan(c + d*x)**2) - 4*B*a*b**3*x - 4*B*a*b**3/(d*tan(c + d*x)) - B*b**4*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**4*log(tan(c + d*x))/d, True))","A",0
266,1,643,0,29.107550," ","integrate(cot(d*x+c)**7*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A a^{4} x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(A + B \tan{\left(c \right)}\right) \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{7}{\left(c \right)} & \text{for}\: d = 0 \\\frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} + \frac{A a^{4}}{4 d \tan^{4}{\left(c + d x \right)}} - \frac{A a^{4}}{6 d \tan^{6}{\left(c + d x \right)}} - 4 A a^{3} b x - \frac{4 A a^{3} b}{d \tan{\left(c + d x \right)}} + \frac{4 A a^{3} b}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{4 A a^{3} b}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{3 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{6 A a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{3 A a^{2} b^{2}}{d \tan^{2}{\left(c + d x \right)}} - \frac{3 A a^{2} b^{2}}{2 d \tan^{4}{\left(c + d x \right)}} + 4 A a b^{3} x + \frac{4 A a b^{3}}{d \tan{\left(c + d x \right)}} - \frac{4 A a b^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A b^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - B a^{4} x - \frac{B a^{4}}{d \tan{\left(c + d x \right)}} + \frac{B a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{B a^{4}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{2 B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 B a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{2 B a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{3} b}{d \tan^{4}{\left(c + d x \right)}} + 6 B a^{2} b^{2} x + \frac{6 B a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 B a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 B a b^{3}}{d \tan^{2}{\left(c + d x \right)}} - B b^{4} x - \frac{B b^{4}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(A + B*tan(c))*(a + b*tan(c))**4*cot(c)**7, Eq(d, 0)), (A*a**4*log(tan(c + d*x)**2 + 1)/(2*d) - A*a**4*log(tan(c + d*x))/d - A*a**4/(2*d*tan(c + d*x)**2) + A*a**4/(4*d*tan(c + d*x)**4) - A*a**4/(6*d*tan(c + d*x)**6) - 4*A*a**3*b*x - 4*A*a**3*b/(d*tan(c + d*x)) + 4*A*a**3*b/(3*d*tan(c + d*x)**3) - 4*A*a**3*b/(5*d*tan(c + d*x)**5) - 3*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 6*A*a**2*b**2*log(tan(c + d*x))/d + 3*A*a**2*b**2/(d*tan(c + d*x)**2) - 3*A*a**2*b**2/(2*d*tan(c + d*x)**4) + 4*A*a*b**3*x + 4*A*a*b**3/(d*tan(c + d*x)) - 4*A*a*b**3/(3*d*tan(c + d*x)**3) + A*b**4*log(tan(c + d*x)**2 + 1)/(2*d) - A*b**4*log(tan(c + d*x))/d - A*b**4/(2*d*tan(c + d*x)**2) - B*a**4*x - B*a**4/(d*tan(c + d*x)) + B*a**4/(3*d*tan(c + d*x)**3) - B*a**4/(5*d*tan(c + d*x)**5) - 2*B*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*B*a**3*b*log(tan(c + d*x))/d + 2*B*a**3*b/(d*tan(c + d*x)**2) - B*a**3*b/(d*tan(c + d*x)**4) + 6*B*a**2*b**2*x + 6*B*a**2*b**2/(d*tan(c + d*x)) - 2*B*a**2*b**2/(d*tan(c + d*x)**3) + 2*B*a*b**3*log(tan(c + d*x)**2 + 1)/d - 4*B*a*b**3*log(tan(c + d*x))/d - 2*B*a*b**3/(d*tan(c + d*x)**2) - B*b**4*x - B*b**4/(d*tan(c + d*x)), True))","A",0
267,1,1300,0,2.131157," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{3 i A d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 A d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i A \tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i A}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B \tan^{3}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\\frac{3 i A d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 A d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i A \tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i A}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B \tan^{3}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \tan^{2}{\left(c + d x \right)}}{2 d} + B x + \frac{B \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B \tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 A a^{3} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 A a^{2} b^{2} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 A b^{4} d x}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 A b^{4} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 B a^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 B a^{3} b \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{B a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 B a b^{3} d x}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 B a b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{B b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))*tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-3*I*A*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*A*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*A*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*A*tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*A/(2*I*b*d*tan(c + d*x) + 2*b*d) + 3*B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*tan(c + d*x)**3/(2*I*b*d*tan(c + d*x) + 2*b*d) - B*tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*B/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (3*I*A*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*A*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*A*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*A*tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*A/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*tan(c + d*x)**3/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B*tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*B/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*tan(c + d*x)**2/(2*d) + B*x + B*tan(c + d*x)**3/(3*d) - B*tan(c + d*x)/d)/a, Eq(b, 0)), (x*(A + B*tan(c))*tan(c)**3/(a + b*tan(c)), Eq(d, 0)), (-2*A*a**3*b*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) + 2*A*a**2*b**2*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - A*a*b**3*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) - 2*A*b**4*d*x/(2*a**2*b**3*d + 2*b**5*d) + 2*A*b**4*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + 2*B*a**4*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) - 2*B*a**3*b*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + B*a**2*b**2*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d) + 2*B*a*b**3*d*x/(2*a**2*b**3*d + 2*b**5*d) - 2*B*a*b**3*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - B*b**4*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) + B*b**4*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d), True))","A",0
268,1,1015,0,1.529318," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{i A d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{A d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i A}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 i B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{2 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\- \frac{i A d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{A d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i A}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 i B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{2 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{3 B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{- A x + \frac{A \tan{\left(c + d x \right)}}{d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \tan^{2}{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 A a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 A a b^{2} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{A b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 B a^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 B a^{2} b \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 B b^{3} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 B b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (I*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + A*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*A*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*A/(2*b*d*tan(c + d*x) - 2*I*b*d) - 3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 3*I*B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x) - 2*I*b*d) + 3*B/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (-I*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + A*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) + A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*A*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*A/(2*b*d*tan(c + d*x) + 2*I*b*d) - 3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) - 3*I*B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) + 2*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x) + 2*I*b*d) + 3*B/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), ((-A*x + A*tan(c + d*x)/d - B*log(tan(c + d*x)**2 + 1)/(2*d) + B*tan(c + d*x)**2/(2*d))/a, Eq(b, 0)), (x*(A + B*tan(c))*tan(c)**2/(a + b*tan(c)), Eq(d, 0)), (2*A*a**2*b*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) - 2*A*a*b**2*d*x/(2*a**2*b**2*d + 2*b**4*d) + A*b**3*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*B*a**3*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) + 2*B*a**2*b*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d) - B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*B*b**3*d*x/(2*a**2*b**2*d + 2*b**4*d) + 2*B*b**3*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d), True))","A",0
269,1,714,0,1.170402," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{A d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i A d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{A}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{B d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\- \frac{A d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i A d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{A}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{B d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B x + \frac{B \tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 A a b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b d + 2 b^{3} d} + \frac{A a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b d + 2 b^{3} d} + \frac{2 A b^{2} d x}{2 a^{2} b d + 2 b^{3} d} + \frac{2 B a^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b d + 2 b^{3} d} - \frac{2 B a b d x}{2 a^{2} b d + 2 b^{3} d} + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b d + 2 b^{3} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c)), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-A*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*A*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) + A/(-2*b*d*tan(c + d*x) + 2*I*b*d) - I*B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - B*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*B/(-2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (-A*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*A*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) + A/(-2*b*d*tan(c + d*x) - 2*I*b*d) + I*B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - B*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*B/(-2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, I*b)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - B*x + B*tan(c + d*x)/d)/a, Eq(b, 0)), (x*(A + B*tan(c))*tan(c)/(a + b*tan(c)), Eq(d, 0)), (-2*A*a*b*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) + A*a*b*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d) + 2*A*b**2*d*x/(2*a**2*b*d + 2*b**3*d) + 2*B*a**2*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) - 2*B*a*b*d*x/(2*a**2*b*d + 2*b**3*d) + B*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d), True))","A",0
270,1,524,0,0.950010," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(c \right)}\right)}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{i A d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{A d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i A}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\- \frac{i A d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{A d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i A}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right)}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{A x + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{2 A a d x}{2 a^{2} d + 2 b^{2} d} + \frac{2 A b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{2 B a \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 B b d x}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (I*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + A*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + I*A/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) - B/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (-I*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + A*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - I*A/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - B/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), (x*(A + B*tan(c))/(a + b*tan(c)), Eq(d, 0)), ((A*x + B*log(tan(c + d*x)**2 + 1)/(2*d))/a, Eq(b, 0)), (2*A*a*d*x/(2*a**2*d + 2*b**2*d) + 2*A*b*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) - A*b*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) - 2*B*a*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) + B*a*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*B*b*d*x/(2*a**2*d + 2*b**2*d), True))","A",0
271,1,952,0,2.362860," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) \cot{\left(c \right)}}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- A x - \frac{A}{d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{b} & \text{for}\: a = 0 \\\frac{i A d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{A d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i A \log{\left(\tan{\left(c + d x \right)} \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i A}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\- \frac{i A d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{A d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i A \log{\left(\tan{\left(c + d x \right)} \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i A}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B x}{a} & \text{for}\: b = 0 \\- \frac{A a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 A a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{2 A a b d x}{2 a^{3} d + 2 a b^{2} d} - \frac{2 A b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 A b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B a^{2} d x}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B a b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))*cot(c)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-A*x - A/(d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d)/b, Eq(a, 0)), (I*A*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + A*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) + A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - I*A*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*A*log(tan(c + d*x))*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*A*log(tan(c + d*x))/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*A/(2*I*b*d*tan(c + d*x) + 2*b*d) - B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - B/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (-I*A*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + A*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + I*A*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*A*log(tan(c + d*x))*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*A*log(tan(c + d*x))/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*A/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), (x*(A + B*tan(c))*cot(c)/(a + b*tan(c)), Eq(d, 0)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*log(tan(c + d*x))/d + B*x)/a, Eq(b, 0)), (-A*a**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d) + 2*A*a**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - 2*A*a*b*d*x/(2*a**3*d + 2*a*b**2*d) - 2*A*b**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*A*b**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*B*a**2*d*x/(2*a**3*d + 2*a*b**2*d) + 2*B*a*b*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - B*a*b*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d), True))","A",0
272,1,2067,0,4.497147," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{- A x - \frac{A}{d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - B x - \frac{B}{d \tan{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{3 A d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{3 i A \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 A}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{B \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{3 A d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{3 i A \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{2 A}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{B \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} A x}{a} & \text{for}\: c = - d x \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 A a^{3} d x \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 A a^{3}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 A a b^{2}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 A b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 A b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b d x \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((-A*x - A/(d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d)/a, Eq(b, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - A*log(tan(c + d*x))/d - A/(2*d*tan(c + d*x)**2) - B*x - B/(d*tan(c + d*x)))/b, Eq(a, 0)), (-3*I*A*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*A*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*I*A*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*I*A*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*A/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*B*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + B*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)), Eq(a, -I*b)), (3*I*A*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 3*A*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*A*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*I*A*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 3*I*A*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2*A/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*B*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + B*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)), Eq(a, I*b)), (zoo*A*x/a, Eq(c, -d*x)), (x*(A + B*tan(c))*cot(c)**2/(a + b*tan(c)), Eq(d, 0)), (-2*A*a**3*d*x*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*A*a**3/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + A*a**2*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*A*a**2*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*A*a*b**2/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*A*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*A*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - B*a**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*B*a**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a**2*b*d*x*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*B*a*b**2*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)), True))","A",0
273,1,2625,0,7.565619," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{A x + \frac{A}{d \tan{\left(c + d x \right)}} - \frac{A}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{3 A d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 A \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{i A \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{A}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i B d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i B \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 B \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{3 A d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{4 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 A \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{i A \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{A}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i B d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i B \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 B \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} A x}{a} & \text{for}\: c = - d x \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - B x - \frac{B}{d \tan{\left(c + d x \right)}}}{a} & \text{for}\: b = 0 \\\frac{A a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A a^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{4}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{3} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{3} b \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{A a^{2} b^{2}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a b^{3} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{4} d x \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{4} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{2} b^{2} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((A*x + A/(d*tan(c + d*x)) - A/(3*d*tan(c + d*x)**3) + B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2))/b, Eq(a, 0)), (3*A*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 3*I*A*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 4*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 4*A*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*A*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*A*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + A/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*I*B*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*B*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 2*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*I*B*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 2*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2), Eq(a, -I*b)), (3*A*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*I*A*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 4*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 4*A*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*A*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*A*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + A/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 3*I*B*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*B*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 3*I*B*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2), Eq(a, I*b)), (zoo*A*x/a, Eq(c, -d*x)), (x*(A + B*tan(c))*cot(c)**3/(a + b*tan(c)), Eq(d, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - A*log(tan(c + d*x))/d - A/(2*d*tan(c + d*x)**2) - B*x - B/(d*tan(c + d*x)))/a, Eq(b, 0)), (A*a**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*A*a**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - A*a**4/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*A*a**3*b*d*x*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*A*a**3*b*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - A*a**2*b**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*A*a*b**3*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*A*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*A*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**4*d*x*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**4*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + B*a**3*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**3*b*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**2*b**2*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a*b**3*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2), True))","A",0
274,1,3045,0,13.627356," ","integrate(cot(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} A x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{A x + \frac{A}{d \tan{\left(c + d x \right)}} - \frac{A}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}}}{a} & \text{for}\: b = 0 \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A}{4 d \tan^{4}{\left(c + d x \right)}} + B x + \frac{B}{d \tan{\left(c + d x \right)}} - \frac{B}{3 d \tan^{3}{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{15 i A d x \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{15 A d x \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{6 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{12 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{15 i A \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{9 A \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{i A \tan{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{2 A}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{9 B d x \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{9 i B d x \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{9 B \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{3 i B \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{3 B \tan{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} + 6 i b d \tan^{3}{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{15 i A d x \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{15 A d x \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{15 i A \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{9 A \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{i A \tan{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{2 A}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{9 B d x \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{9 i B d x \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{6 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{6 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} - \frac{12 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{12 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{9 B \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{3 i B \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} + \frac{3 B \tan{\left(c + d x \right)}}{- 6 b d \tan^{4}{\left(c + d x \right)} - 6 i b d \tan^{3}{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} A x}{a} & \text{for}\: c = - d x \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot^{4}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{6 A a^{5} d x \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A a^{5} \tan^{2}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{2 A a^{5}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{3 A a^{4} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A a^{4} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{4} b \tan{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{2 A a^{3} b^{2}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{2} b^{3} \tan{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{6 A a b^{4} \tan^{2}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{6 A b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{6 B a^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{3 B a^{5} \tan{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 B a^{4} b d x \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 B a^{4} b \tan^{2}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{3 B a^{3} b^{2} \tan{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 B a^{2} b^{3} \tan^{2}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} - \frac{6 B a b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} + \frac{6 B a b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{6 a^{6} d \tan^{3}{\left(c + d x \right)} + 6 a^{4} b^{2} d \tan^{3}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((A*x + A/(d*tan(c + d*x)) - A/(3*d*tan(c + d*x)**3) + B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2))/a, Eq(b, 0)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*log(tan(c + d*x))/d + A/(2*d*tan(c + d*x)**2) - A/(4*d*tan(c + d*x)**4) + B*x + B/(d*tan(c + d*x)) - B/(3*d*tan(c + d*x)**3))/b, Eq(a, 0)), (-15*I*A*d*x*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 15*A*d*x*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 6*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 6*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 12*A*log(tan(c + d*x))*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 12*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 15*I*A*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 9*A*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - I*A*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 2*A/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 9*B*d*x*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 9*I*B*d*x*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 6*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 6*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 12*I*B*log(tan(c + d*x))*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 12*B*log(tan(c + d*x))*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 9*B*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 3*I*B*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 3*B*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3), Eq(a, -I*b)), (15*I*A*d*x*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 15*A*d*x*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 6*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 6*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 12*A*log(tan(c + d*x))*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 12*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 15*I*A*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 9*A*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + I*A*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 2*A/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 9*B*d*x*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 9*I*B*d*x*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 6*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 6*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 12*I*B*log(tan(c + d*x))*tan(c + d*x)**4/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 12*B*log(tan(c + d*x))*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 9*B*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 3*I*B*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 3*B*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3), Eq(a, I*b)), (zoo*A*x/a, Eq(c, -d*x)), (x*(A + B*tan(c))*cot(c)**4/(a + b*tan(c)), Eq(d, 0)), (6*A*a**5*d*x*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*A*a**5*tan(c + d*x)**2/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 2*A*a**5/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 3*A*a**4*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*A*a**4*b*log(tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 3*A*a**4*b*tan(c + d*x)/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 2*A*a**3*b**2/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 3*A*a**2*b**3*tan(c + d*x)/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 6*A*a*b**4*tan(c + d*x)**2/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*A*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 6*A*b**5*log(tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 3*B*a**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 6*B*a**5*log(tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 3*B*a**5*tan(c + d*x)/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*B*a**4*b*d*x*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*B*a**4*b*tan(c + d*x)**2/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 3*B*a**3*b**2*tan(c + d*x)/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*B*a**2*b**3*tan(c + d*x)**2/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 6*B*a*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) + 6*B*a*b**4*log(tan(c + d*x))*tan(c + d*x)**3/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3), True))","A",0
275,1,4595,0,3.007685," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \tan^{2}{\left(c + d x \right)}}{2 d} + B x + \frac{B \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B \tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{3 A d x \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{6 i A d x \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{3 A d x}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{5 A \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{4 i A}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{9 i B d x \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{18 B d x \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{9 i B d x}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{8 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 i B \tan^{3}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{19 i B \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{14 B}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} & \text{for}\: a = - i b \\- \frac{3 A d x \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{6 i A d x \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{3 A d x}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{2 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{5 A \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 i A}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{9 i B d x \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{18 B d x \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{9 i B d x}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{8 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{4 i B \tan^{3}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{19 i B \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{14 B}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 A a^{5} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 A a^{5} b}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 A a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{6 A a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{A a^{3} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 A a^{3} b^{3}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 A a^{2} b^{4} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{6 A a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{A a^{2} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 A a b^{5} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{A a b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{A b^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 B a^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 B a^{6}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 B a^{5} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{8 B a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{4} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{6 B a^{4} b^{2}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} b^{3} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{8 B a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{2} b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{4 B a^{2} b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{4}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{5} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 B b^{6} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B b^{6} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*tan(c + d*x)**2/(2*d) + B*x + B*tan(c + d*x)**3/(3*d) - B*tan(c + d*x)/d)/a**2, Eq(b, 0)), (-3*A*d*x*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 6*I*A*d*x*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 3*A*d*x/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 2*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 2*I*A*log(tan(c + d*x)**2 + 1)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 5*A*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 4*I*A/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 9*I*B*d*x*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 18*B*d*x*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 9*I*B*d*x/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 4*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 8*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*B*log(tan(c + d*x)**2 + 1)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*I*B*tan(c + d*x)**3/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 19*I*B*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 14*B/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d), Eq(a, -I*b)), (-3*A*d*x*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 6*I*A*d*x*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 3*A*d*x/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 2*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 2*I*A*log(tan(c + d*x)**2 + 1)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 5*A*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*I*A/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 9*I*B*d*x*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 18*B*d*x*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 9*I*B*d*x/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 4*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 8*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*B*log(tan(c + d*x)**2 + 1)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 4*I*B*tan(c + d*x)**3/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 19*I*B*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 14*B/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d), Eq(a, I*b)), (x*(A + B*tan(c))*tan(c)**3/(a + b*tan(c))**2, Eq(d, 0)), (2*A*a**5*b*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*A*a**5*b/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*A*a**4*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 6*A*a**3*b**3*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - A*a**3*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*A*a**3*b**3/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*A*a**2*b**4*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 6*A*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - A*a**2*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*A*a*b**5*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + A*a*b**5*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + A*b**6*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*B*a**6*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*B*a**6/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*B*a**5*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 8*B*a**4*b**2*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**4*b**2*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 6*B*a**4*b**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**3*b**3*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 8*B*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**2*b**4*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*B*a**2*b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 4*B*a**2*b**4*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*B*a**2*b**4/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*B*a*b**5*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*B*a*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*B*b**6*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*b**6*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)), True))","A",0
276,1,3485,0,2.298705," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- A x + \frac{A \tan{\left(c + d x \right)}}{d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \tan^{2}{\left(c + d x \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{A d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{6 B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 i B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{5 i B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{A d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{6 B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{3 i B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{5 i B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 A a^{4} b}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 A a^{3} b^{2} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 A a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 A a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b^{3}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{4} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 A a b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 A b^{5} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a^{5}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a^{4} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{6 B a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{B a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} b^{2}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 B a^{2} b^{3} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{6 B a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{B a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 B a b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{B a b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{B b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c)), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-A*x + A*tan(c + d*x)/d - B*log(tan(c + d*x)**2 + 1)/(2*d) + B*tan(c + d*x)**2/(2*d))/a**2, Eq(b, 0)), (-A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*A*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + A*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*A/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 3*I*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 6*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*I*B*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*B*log(tan(c + d*x)**2 + 1)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 5*I*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*B/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, -I*b)), (-A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*A*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + A*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*A/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*I*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 6*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 3*I*B*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*B*log(tan(c + d*x)**2 + 1)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 5*I*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*B/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, I*b)), (x*(A + B*tan(c))*tan(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (-2*A*a**4*b/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*A*a**3*b**2*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*A*a**2*b**3*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*A*a**2*b**3*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*A*a**2*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*A*a**2*b**3/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*A*a*b**4*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*A*a*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*A*a*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*A*b**5*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a**5*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a**5/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a**4*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 6*B*a**3*b**2*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - B*a**3*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a**3*b**2/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*B*a**2*b**3*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 6*B*a**2*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - B*a**2*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*B*a*b**4*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + B*a*b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + B*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)), True))","A",0
277,1,2987,0,1.843320," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(c \right)}\right)}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B x + \frac{B \tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\\frac{i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{i A d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{i A d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right) \tan{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 A a^{3} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 A a^{3} b}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{4 A a^{2} b^{2} d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{4 A a b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{A a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{3}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 A b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{A b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 B a^{4}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} b d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{4 B a^{2} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{2}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{3} d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{4 B a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - B*x + B*tan(c + d*x)/d)/a**2, Eq(b, 0)), (I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - I*A*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*B/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, -I*b)), (-I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + I*A*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*B/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, I*b)), (x*(A + B*tan(c))*tan(c)/(a + b*tan(c))**2, Eq(d, 0)), (-2*A*a**3*b*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + A*a**3*b*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*A*a**3*b/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 4*A*a**2*b**2*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*A*a**2*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + A*a**2*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 4*A*a*b**3*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*A*a*b**3*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - A*a*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*A*a*b**3/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*A*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - A*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*B*a**4/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*B*a**3*b*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*B*a**2*b**2*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 4*B*a**2*b**2*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a**2*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*B*a**2*b**2/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a*b**3*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 4*B*a*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*b**4*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)), True))","A",0
278,1,2878,0,1.802981," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(c \right)}\right)}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{A d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - i b \\\frac{A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{A d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right)}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{A x + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 A a^{3} d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a^{2} b d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 A a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A a^{2} b}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A a b^{2} d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 A a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A b^{3}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{2} b d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a b^{2} d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{2}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*A*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - A*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*A/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*B*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, -I*b)), (A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*A*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - A*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*A/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*B*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, I*b)), (x*(A + B*tan(c))/(a + b*tan(c))**2, Eq(d, 0)), ((A*x + B*log(tan(c + d*x)**2 + 1)/(2*d))/a**2, Eq(b, 0)), (2*A*a**3*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*A*a**2*b*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*A*a**2*b*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*a**2*b*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*a**2*b/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*a*b**2*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*A*a*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*a*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*b**3*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*A*b**3/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a**3*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + B*a**3*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*B*a**3/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*B*a**2*b*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a**2*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + B*a**2*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*B*a*b**2*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*B*a*b**2*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*B*a*b**2/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*B*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - B*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)), True))","A",0
279,1,4447,0,4.154146," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(c \right)}\right) \cot{\left(c \right)}}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B x}{a^{2}} & \text{for}\: b = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - B x - \frac{B}{d \tan{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{6 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 i A d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{3 i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 A}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{3 i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{6 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{3 i A d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 A \log{\left(\tan{\left(c + d x \right)} \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 A}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{A a^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a^{5} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{4 A a^{4} b d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{A a^{4} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a^{4} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{4 A a^{3} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{6 A a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{A a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 A a^{3} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a^{3} b^{2}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{6 A a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{A a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 A a^{2} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A a b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A a b^{4}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 A b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 A b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{5} d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{4} b d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{4} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{4} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{4} b}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} b^{2} d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{3} d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{3}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(c))*cot(c)/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*log(tan(c + d*x))/d + B*x)/a**2, Eq(b, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - A*log(tan(c + d*x))/d - A/(2*d*tan(c + d*x)**2) - B*x - B/(d*tan(c + d*x)))/b**2, Eq(a, 0)), (3*I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 6*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*I*A*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*A*log(tan(c + d*x)**2 + 1)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*A*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 8*I*A*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*A*log(tan(c + d*x))/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 3*I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*A/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + B*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*B/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, -I*b)), (-3*I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 6*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 3*I*A*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*A*log(tan(c + d*x)**2 + 1)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*A*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 8*I*A*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*A*log(tan(c + d*x))/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*A/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + B*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*B/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, I*b)), (x*(A + B*tan(c))*cot(c)/(a + b*tan(c))**2, Eq(d, 0)), (-A*a**5*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*a**5*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 4*A*a**4*b*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - A*a**4*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*a**4*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 4*A*a**3*b**2*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 6*A*a**3*b**2*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + A*a**3*b**2*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*A*a**3*b**2*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*a**3*b**2/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 6*A*a**2*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + A*a**2*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*A*a**2*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*A*a*b**4*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*a*b**4*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*a*b**4/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*A*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*A*b**5*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a**5*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a**4*b*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*B*a**4*b*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**4*b*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**4*b/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**3*b**2*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*B*a**3*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**3*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**2*b**3*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a**2*b**3/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)), True))","A",0
280,1,8102,0,7.158746," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} A x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{A x + \frac{A}{d \tan{\left(c + d x \right)}} - \frac{A}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{9 A d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{18 i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{9 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{9 A \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{14 i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 A}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i B d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{6 B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i B \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{9 A d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{18 i A d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{9 A d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{9 A \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{14 i A \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 A}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i B d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{6 B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i B \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} A x}{a^{2}} & \text{for}\: c = - d x \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{- A x - \frac{A}{d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2 A a^{6} d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A a^{6}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A a^{5} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{5} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A a^{5} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A a^{5} b \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{4} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{4} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A a^{4} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A a^{4} b^{2}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A a^{3} b^{3} d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{8 A a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{8 A a^{3} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 A a^{3} b^{3} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{8 A a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{8 A a^{2} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 A a^{2} b^{4}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 A a b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A a b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A a b^{5} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 A b^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 A b^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a^{5} b d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{5} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{5} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a^{4} b^{2} d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 B a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{B a^{4} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B a^{4} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{4} b^{2} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 B a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{B a^{3} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B a^{3} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{2} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{2} b^{4} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((A*x + A/(d*tan(c + d*x)) - A/(3*d*tan(c + d*x)**3) + B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2))/b**2, Eq(a, 0)), (9*A*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 18*I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 9*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 16*A*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*A*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 9*A*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 14*I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*A/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*B*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 6*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*B*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*B*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)), Eq(a, -I*b)), (9*A*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 18*I*A*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 9*A*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 16*A*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*A*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 9*A*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 14*I*A*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*A/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*B*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 6*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*B*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*B*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)), Eq(a, I*b)), (zoo*A*x/a**2, Eq(c, -d*x)), (x*(A + B*tan(c))*cot(c)**2/(a + b*tan(c))**2, Eq(d, 0)), ((-A*x - A/(d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d)/a**2, Eq(b, 0)), (-2*A*a**6*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*A*a**6/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*A*a**5*b*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*A*a**5*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*a**5*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*A*a**5*b*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*A*a**4*b**2*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*A*a**4*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*a**4*b**2*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*a**4*b**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*A*a**3*b**3*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 8*A*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 8*A*a**3*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*A*a**3*b**3*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 8*A*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 8*A*a**2*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*A*a**2*b**4/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*A*a*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*a*b**5*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*a*b**5*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*A*b**6*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*A*b**6*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - B*a**6*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**6*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a**5*b*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - B*a**5*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**5*b*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a**4*b**2*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*B*a**4*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + B*a**4*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*B*a**4*b**2*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**4*b**2*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*B*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + B*a**3*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*B*a**3*b**3*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**2*b**4*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**2*b**4*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a*b**5*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2), True))","A",0
281,1,9840,0,10.763031," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} A x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{- \frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{A}{4 d \tan^{4}{\left(c + d x \right)}} + B x + \frac{B}{d \tan{\left(c + d x \right)}} - \frac{B}{3 d \tan^{3}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{15 i A d x \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{30 A d x \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{15 i A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{16 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{32 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{15 i A \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{22 A \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{4 i A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{9 B d x \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{18 i B d x \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{9 B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{16 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{9 B \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{14 i B \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} + 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = - i b \\- \frac{15 i A d x \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{30 A d x \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{15 i A d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{16 i A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{8 A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{32 i A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{16 A \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{15 i A \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{22 A \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{4 i A \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 A}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{9 B d x \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{18 i B d x \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{9 B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{16 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{9 B \tan^{3}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{14 i B \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{4}{\left(c + d x \right)} - 8 i b^{2} d \tan^{3}{\left(c + d x \right)} + 4 b^{2} d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} A x}{a^{2}} & \text{for}\: c = - d x \\\frac{x \left(A + B \tan{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{A \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{A}{2 d \tan^{2}{\left(c + d x \right)}} - B x - \frac{B}{d \tan{\left(c + d x \right)}}}{a^{2}} & \text{for}\: b = 0 \\\frac{A a^{7} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 A a^{7} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{7}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{4 A a^{6} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{A a^{6} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 A a^{6} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{6} b \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{4 A a^{5} b^{2} d x \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{5} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 A a^{5} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{4 A a^{5} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 A a^{5} b^{2}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{4} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 A a^{4} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A a^{4} b^{3} \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{10 A a^{3} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{10 A a^{3} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{10 A a^{3} b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{A a^{3} b^{4}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{10 A a^{2} b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{10 A a^{2} b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{3 A a^{2} b^{5} \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{6 A a b^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A a b^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A a b^{6} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{6 A b^{7} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{6 A b^{7} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 B a^{7} d x \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 B a^{7} \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 B a^{6} b d x \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a^{6} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a^{6} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 B a^{6} b \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a^{5} b^{2} d x \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a^{5} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a^{5} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a^{5} b^{2} \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{2 B a^{4} b^{3} d x \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{8 B a^{4} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{8 B a^{4} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{6 B a^{4} b^{3} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{8 B a^{3} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{8 B a^{3} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{2 B a^{3} b^{4} \tan{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{4 B a^{2} b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a^{2} b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a^{2} b^{5} \tan^{2}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} + \frac{4 B a b^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} - \frac{4 B a b^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 a^{9} d \tan^{2}{\left(c + d x \right)} + 2 a^{8} b d \tan^{3}{\left(c + d x \right)} + 4 a^{7} b^{2} d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{3} d \tan^{3}{\left(c + d x \right)} + 2 a^{5} b^{4} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{5} d \tan^{3}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*A*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((-A*log(tan(c + d*x)**2 + 1)/(2*d) + A*log(tan(c + d*x))/d + A/(2*d*tan(c + d*x)**2) - A/(4*d*tan(c + d*x)**4) + B*x + B/(d*tan(c + d*x)) - B/(3*d*tan(c + d*x)**3))/b**2, Eq(a, 0)), (15*I*A*d*x*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 30*A*d*x*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 15*I*A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 16*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 16*A*log(tan(c + d*x))*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 32*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 16*A*log(tan(c + d*x))*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 15*I*A*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 22*A*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 4*I*A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 2*A/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 9*B*d*x*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 18*I*B*d*x*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 9*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 16*B*log(tan(c + d*x))*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 9*B*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 14*I*B*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 4*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**4 + 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2), Eq(a, -I*b)), (-15*I*A*d*x*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 30*A*d*x*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 15*I*A*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 16*I*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 8*A*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 16*A*log(tan(c + d*x))*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 32*I*A*log(tan(c + d*x))*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 16*A*log(tan(c + d*x))*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 15*I*A*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 22*A*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 4*I*A*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 2*A/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 9*B*d*x*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 18*I*B*d*x*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 9*B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 16*B*log(tan(c + d*x))*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 9*B*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) - 14*I*B*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2) + 4*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**4 - 8*I*b**2*d*tan(c + d*x)**3 + 4*b**2*d*tan(c + d*x)**2), Eq(a, I*b)), (zoo*A*x/a**2, Eq(c, -d*x)), (x*(A + B*tan(c))*cot(c)**3/(a + b*tan(c))**2, Eq(d, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) - A*log(tan(c + d*x))/d - A/(2*d*tan(c + d*x)**2) - B*x - B/(d*tan(c + d*x)))/a**2, Eq(b, 0)), (A*a**7*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*A*a**7*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - A*a**7/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 4*A*a**6*b*d*x*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + A*a**6*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*A*a**6*b*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 3*A*a**6*b*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 4*A*a**5*b**2*d*x*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - A*a**5*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*A*a**5*b**2*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 4*A*a**5*b**2*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*A*a**5*b**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - A*a**4*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*A*a**4*b**3*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 6*A*a**4*b**3*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 10*A*a**3*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 10*A*a**3*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 10*A*a**3*b**4*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - A*a**3*b**4/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 10*A*a**2*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 10*A*a**2*b**5*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 3*A*a**2*b**5*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 6*A*a*b**6*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 6*A*a*b**6*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 6*A*a*b**6*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 6*A*b**7*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 6*A*b**7*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*B*a**7*d*x*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*B*a**7*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*B*a**6*b*d*x*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*B*a**6*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a**6*b*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*B*a**6*b*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*B*a**5*b**2*d*x*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*B*a**5*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a**5*b**2*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a**5*b**2*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 2*B*a**4*b**3*d*x*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 8*B*a**4*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 8*B*a**4*b**3*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 6*B*a**4*b**3*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 8*B*a**3*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 8*B*a**3*b**4*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 2*B*a**3*b**4*tan(c + d*x)/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 4*B*a**2*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a**2*b**5*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a**2*b**5*tan(c + d*x)**2/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) + 4*B*a*b**6*log(a/b + tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3) - 4*B*a*b**6*log(tan(c + d*x))*tan(c + d*x)**3/(2*a**9*d*tan(c + d*x)**2 + 2*a**8*b*d*tan(c + d*x)**3 + 4*a**7*b**2*d*tan(c + d*x)**2 + 4*a**6*b**3*d*tan(c + d*x)**3 + 2*a**5*b**4*d*tan(c + d*x)**2 + 2*a**4*b**5*d*tan(c + d*x)**3), True))","A",0
282,-2,0,0,0.000000," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
283,-2,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
284,-2,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
285,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
286,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
287,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
288,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
289,-2,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
290,-2,0,0,0.000000," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
291,-2,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
292,-2,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
293,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
294,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
295,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
296,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
297,-2,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
298,1,53,0,0.837327," ","integrate(tan(d*x+c)**3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(B*a + B*b*tan(c))*tan(c)**3/(a + b*tan(c)), True))","A",0
299,1,36,0,0.605768," ","integrate(tan(d*x+c)**2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} - B x + \frac{B \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*x + B*tan(c + d*x)/d, Ne(d, 0)), (x*(B*a + B*b*tan(c))*tan(c)**2/(a + b*tan(c)), True))","A",0
300,1,37,0,0.560216," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*(B*a + B*b*tan(c))*tan(c)/(a + b*tan(c)), True))","A",0
301,1,2,0,0.142318," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B x"," ",0,"B*x","A",0
302,1,49,0,0.800115," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d, Ne(d, 0)), (x*(B*a + B*b*tan(c))*cot(c)/(a + b*tan(c)), True))","A",0
303,1,37,0,0.993141," ","integrate(cot(d*x+c)**2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} - B x - \frac{B \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*x - B*cot(c + d*x)/d, Ne(d, 0)), (x*(B*a + B*b*tan(c))*cot(c)**2/(a + b*tan(c)), True))","A",0
304,1,80,0,1.986048," ","integrate(cot(d*x+c)**3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} B x & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(B*a + B*b*tan(c))*cot(c)**3/(a + b*tan(c)), Eq(d, 0)), (B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2), True))","A",0
305,1,49,0,3.416452," ","integrate(cot(d*x+c)**4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} B x - \frac{B \cot^{3}{\left(c + d x \right)}}{3 d} + \frac{B \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot^{4}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*x - B*cot(c + d*x)**3/(3*d) + B*cot(c + d*x)/d, Ne(d, 0)), (x*(B*a + B*b*tan(c))*cot(c)**4/(a + b*tan(c)), True))","A",0
306,1,782,0,2.796531," ","integrate(tan(d*x+c)**4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x \tan^{3}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{3 B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B \tan^{3}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{4 B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\\frac{3 B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B \tan^{3}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{4 B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{B \left(x + \frac{\tan^{3}{\left(c + d x \right)}}{3 d} - \frac{\tan{\left(c + d x \right)}}{d}\right)}{a} & \text{for}\: b = 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan^{4}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 B a^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 B a^{3} b \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{B a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 B a b^{3} d x}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 B a b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{B b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x*tan(c)**3, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (3*B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*tan(c + d*x)**3/(2*I*b*d*tan(c + d*x) + 2*b*d) - B*tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 4*B/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (3*B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*tan(c + d*x)**3/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B*tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 4*B/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), (B*(x + tan(c + d*x)**3/(3*d) - tan(c + d*x)/d)/a, Eq(b, 0)), (x*(B*a + B*b*tan(c))*tan(c)**4/(a + b*tan(c))**2, Eq(d, 0)), (2*B*a**4*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) - 2*B*a**3*b*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + B*a**2*b**2*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d) + 2*B*a*b**3*d*x/(2*a**2*b**3*d + 2*b**5*d) - 2*B*a*b**3*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - B*b**4*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) + B*b**4*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d), True))","A",0
307,1,660,0,2.142986," ","integrate(tan(d*x+c)**3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x \tan^{2}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 i B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{2 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{2 i B \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{5 B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\- \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 i B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{2 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{2 i B \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{5 B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{B \left(- \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{2}{\left(c + d x \right)}}{2 d}\right)}{a} & \text{for}\: b = 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 B a^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 B a^{2} b \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 B b^{3} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 B b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x*tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 3*I*B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*I*B*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 5*B/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (-3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) - 3*I*B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) + 2*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x) + 2*I*b*d) - 2*I*B*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + 5*B/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), (B*(-log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**2/(2*d))/a, Eq(b, 0)), (x*(B*a + B*b*tan(c))*tan(c)**3/(a + b*tan(c))**2, Eq(d, 0)), (-2*B*a**3*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) + 2*B*a**2*b*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d) - B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*B*b**3*d*x/(2*a**2*b**2*d + 2*b**4*d) + 2*B*b**3*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d), True))","A",0
308,1,447,0,1.600458," ","integrate(tan(d*x+c)**2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{i B d x}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{B}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = - i b \\\frac{B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} - 2 b d} + \frac{i B d x}{2 i b d \tan{\left(c + d x \right)} - 2 b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{B}{2 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = i b \\\frac{B \left(- x + \frac{\tan{\left(c + d x \right)}}{d}\right)}{a} & \text{for}\: b = 0 \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 B a^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b d + 2 b^{3} d} - \frac{2 B a b d x}{2 a^{2} b d + 2 b^{3} d} + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b d + 2 b^{3} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) - 2*b*d) - I*B*d*x/(-2*I*b*d*tan(c + d*x) - 2*b*d) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) - 2*b*d) - B*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) - 2*b*d) - B/(-2*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, -I*b)), (B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) - 2*b*d) + I*B*d*x/(2*I*b*d*tan(c + d*x) - 2*b*d) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) - 2*b*d) - B*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) - 2*b*d) - B/(2*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, I*b)), (B*(-x + tan(c + d*x)/d)/a, Eq(b, 0)), (x*(B*a + B*b*tan(c))*tan(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (2*B*a**2*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) - 2*B*a*b*d*x/(2*a**2*b*d + 2*b**3*d) + B*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d), True))","A",0
309,1,282,0,1.267219," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\\frac{B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \tan{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a d} & \text{for}\: b = 0 \\- \frac{2 B a \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 B b d x}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) - B/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - B/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), (x*(B*a + B*b*tan(c))*tan(c)/(a + b*tan(c))**2, Eq(d, 0)), (B*log(tan(c + d*x)**2 + 1)/(2*a*d), Eq(b, 0)), (-2*B*a*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) + B*a*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*B*b*d*x/(2*a**2*d + 2*b**2*d), True))","A",0
310,1,270,0,1.240317," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} B x}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\- \frac{B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{x \left(B a + B b \tan{\left(c \right)}\right)}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{B x}{a} & \text{for}\: b = 0 \\\frac{2 B a d x}{2 a^{2} d + 2 b^{2} d} + \frac{2 B b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - B/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (-B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), (x*(B*a + B*b*tan(c))/(a + b*tan(c))**2, Eq(d, 0)), (B*x/a, Eq(b, 0)), (2*B*a*d*x/(2*a**2*d + 2*b**2*d) + 2*B*b*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) - B*b*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d), True))","A",0
311,1,683,0,3.323299," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} B x \cot{\left(c \right)}}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{B \left(- x - \frac{1}{d \tan{\left(c + d x \right)}}\right)}{b} & \text{for}\: a = 0 \\- \frac{B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{B}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\- \frac{B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{B}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{B \left(- \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\log{\left(\tan{\left(c + d x \right)} \right)}}{d}\right)}{a} & \text{for}\: b = 0 \\- \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{2 B a b d x}{2 a^{3} d + 2 a b^{2} d} - \frac{2 B b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x*cot(c)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (B*(-x - 1/(d*tan(c + d*x)))/b, Eq(a, 0)), (-B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - 2*B*log(tan(c + d*x))/(-2*b*d*tan(c + d*x) + 2*I*b*d) - B/(-2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (-B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) - 2*I*b*d) + 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - 2*B*log(tan(c + d*x))/(-2*b*d*tan(c + d*x) - 2*I*b*d) - B/(-2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, I*b)), (x*(B*a + B*b*tan(c))*cot(c)/(a + b*tan(c))**2, Eq(d, 0)), (B*(-log(tan(c + d*x)**2 + 1)/(2*d) + log(tan(c + d*x))/d)/a, Eq(b, 0)), (-B*a**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d) + 2*B*a**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - 2*B*a*b*d*x/(2*a**3*d + 2*a*b**2*d) - 2*B*b**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*B*b**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d), True))","A",0
312,1,1151,0,6.477366," ","integrate(cot(d*x+c)**2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{B \left(- x - \frac{\cot{\left(c + d x \right)}}{d}\right)}{a} & \text{for}\: b = 0 \\\frac{B \left(\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{\log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{1}{2 d \tan^{2}{\left(c + d x \right)}}\right)}{b} & \text{for}\: a = 0 \\\frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{3 B d x \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{3 i B \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B}{- 2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = - i b \\- \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{3 B d x \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{3 i B \tan{\left(c + d x \right)}}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B}{- 2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} B x}{a} & \text{for}\: c = - d x \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 B a^{3} d x \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{2}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), (B*(-x - cot(c + d*x)/d)/a, Eq(b, 0)), (B*(log(tan(c + d*x)**2 + 1)/(2*d) - log(tan(c + d*x))/d - 1/(2*d*tan(c + d*x)**2))/b, Eq(a, 0)), (3*I*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 3*B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 3*I*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*B/(-2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)), Eq(a, -I*b)), (-3*I*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 3*B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*I*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*B/(-2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)), Eq(a, I*b)), (zoo*B*x/a, Eq(c, -d*x)), (x*(B*a + B*b*tan(c))*cot(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (-2*B*a**3*d*x*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a**3/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + B*a**2*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a**2*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a*b**2/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*B*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)), True))","A",0
313,1,1397,0,10.068126," ","integrate(cot(d*x+c)**3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} B x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{B \left(x + \frac{1}{d \tan{\left(c + d x \right)}} - \frac{1}{3 d \tan^{3}{\left(c + d x \right)}}\right)}{b} & \text{for}\: a = 0 \\- \frac{3 B d x \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{i B \tan{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{B}{2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = - i b \\- \frac{3 B d x \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 B \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{i B \tan{\left(c + d x \right)}}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{B}{2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{\tilde{\infty} B x}{a} & \text{for}\: c = - d x \\\frac{x \left(B a + B b \tan{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{B \left(\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{\log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{1}{2 d \tan^{2}{\left(c + d x \right)}}\right)}{a} & \text{for}\: b = 0 \\\frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{4}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{3} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{3} b \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{2} b^{2}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a b^{3} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*B*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), (B*(x + 1/(d*tan(c + d*x)) - 1/(3*d*tan(c + d*x)**3))/b, Eq(a, 0)), (-3*B*d*x*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*I*B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 4*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 3*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*B*tan(c + d*x)/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - B/(2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2), Eq(a, -I*b)), (-3*B*d*x*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 3*I*B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 4*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 3*B*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*B*tan(c + d*x)/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - B/(2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2), Eq(a, I*b)), (zoo*B*x/a, Eq(c, -d*x)), (x*(B*a + B*b*tan(c))*cot(c)**3/(a + b*tan(c))**2, Eq(d, 0)), (B*(log(tan(c + d*x)**2 + 1)/(2*d) - log(tan(c + d*x))/d - 1/(2*d*tan(c + d*x)**2))/a, Eq(b, 0)), (B*a**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - B*a**4/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a**3*b*d*x*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a**3*b*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - B*a**2*b**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a*b**3*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2), True))","A",0
314,1,39,0,0.329974," ","integrate((3+tan(d*x+c))/(2-tan(d*x+c)),x)","\begin{cases} x - \frac{\log{\left(\tan{\left(c + d x \right)} - 2 \right)}}{d} + \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\\frac{x \left(\tan{\left(c \right)} + 3\right)}{2 - \tan{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x - log(tan(c + d*x) - 2)/d + log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*(tan(c) + 3)/(2 - tan(c)), True))","A",0
315,1,235,0,0.873246," ","integrate((b*B/a+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\begin{cases} \text{NaN} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{B}{b d \tan{\left(c + d x \right)} - i b d} & \text{for}\: a = - i b \\- \frac{B}{b d \tan{\left(c + d x \right)} + i b d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + \frac{B b}{a}\right)}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a d} & \text{for}\: b = 0 \\- \frac{2 B a^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{4 B a b d x}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-B/(b*d*tan(c + d*x) - I*b*d), Eq(a, -I*b)), (-B/(b*d*tan(c + d*x) + I*b*d), Eq(a, I*b)), (x*(B*tan(c) + B*b/a)/(a + b*tan(c)), Eq(d, 0)), (B*log(tan(c + d*x)**2 + 1)/(2*a*d), Eq(b, 0)), (-2*B*a**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + B*a**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d) + 4*B*a*b*d*x/(2*a**3*d + 2*a*b**2*d) + 2*B*b**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - B*b**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d), True))","A",0
316,1,1346,0,1.568313," ","integrate((a+b*tan(d*x+c))/(b+a*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{1}{2 b d \tan^{2}{\left(c + d x \right)} + 4 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = - i b \\\frac{1}{2 b d \tan^{2}{\left(c + d x \right)} - 4 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = i b \\\frac{x \left(a + b \tan{\left(c \right)}\right)}{\left(a \tan{\left(c \right)} + b\right)^{2}} & \text{for}\: d = 0 \\\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d} & \text{for}\: a = 0 \\- \frac{2 a^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{2 a^{4}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{2 a^{3} b d x}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{6 a^{3} b \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{3 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{6 a^{2} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{6 a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{6 a b^{3} d x}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{2 a b^{3} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} - \frac{2 b^{4} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} + \frac{2 b^{4}}{2 a^{5} d \tan{\left(c + d x \right)} + 2 a^{4} b d + 4 a^{3} b^{2} d \tan{\left(c + d x \right)} + 4 a^{2} b^{3} d + 2 a b^{4} d \tan{\left(c + d x \right)} + 2 b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (1/(2*b*d*tan(c + d*x)**2 + 4*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, -I*b)), (1/(2*b*d*tan(c + d*x)**2 - 4*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, I*b)), (x*(a + b*tan(c))/(a*tan(c) + b)**2, Eq(d, 0)), (log(tan(c + d*x)**2 + 1)/(2*b*d), Eq(a, 0)), (-2*a**4*d*x*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 2*a**4/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 2*a**3*b*d*x/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + 6*a**3*b*log(tan(c + d*x) + b/a)*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 3*a**3*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + 6*a**2*b**2*d*x*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + 6*a**2*b**2*log(tan(c + d*x) + b/a)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + 6*a*b**3*d*x/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 2*a*b**3*log(tan(c + d*x) + b/a)*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + a*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) - 2*b**4*log(tan(c + d*x) + b/a)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d) + 2*b**4/(2*a**5*d*tan(c + d*x) + 2*a**4*b*d + 4*a**3*b**2*d*tan(c + d*x) + 4*a**2*b**3*d + 2*a*b**4*d*tan(c + d*x) + 2*b**5*d), True))","A",0
317,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**3*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**3, x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*tan(c + d*x), x)","F",0
320,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x)), x)","F",0
321,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*cot(c + d*x), x)","F",0
322,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
323,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*cot(c + d*x)**3, x)","F",0
324,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*cot(c + d*x)**4, x)","F",0
325,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**2, x)","F",0
326,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*tan(c + d*x), x)","F",0
327,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2), x)","F",0
328,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*cot(c + d*x), x)","F",0
329,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*cot(c + d*x)**2, x)","F",0
330,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*cot(c + d*x)**3, x)","F",0
331,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*cot(c + d*x)**4, x)","F",0
332,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(5/2)*tan(c + d*x)**2, x)","F",0
333,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(5/2)*tan(c + d*x), x)","F",0
334,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(5/2), x)","F",0
335,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))**(5/2),x)","- \int a^{3} \sqrt{a + b \tan{\left(c + d x \right)}}\, dx - \int \left(- b^{3} \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{3}{\left(c + d x \right)}\right)\, dx - \int \left(- a b^{2} \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}\right)\, dx - \int a^{2} b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}\, dx"," ",0,"-Integral(a**3*sqrt(a + b*tan(c + d*x)), x) - Integral(-b**3*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**3, x) - Integral(-a*b**2*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2, x) - Integral(a**2*b*sqrt(a + b*tan(c + d*x))*tan(c + d*x), x)","F",0
341,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))**(3/2),x)","- \int a^{2} \sqrt{a + b \tan{\left(c + d x \right)}}\, dx - \int \left(- b^{2} \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(a**2*sqrt(a + b*tan(c + d*x)), x) - Integral(-b**2*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
342,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))*(a+b*tan(d*x+c))**(1/2),x)","- \int a \sqrt{a + b \tan{\left(c + d x \right)}}\, dx - \int \left(- b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(a*sqrt(a + b*tan(c + d*x)), x) - Integral(-b*sqrt(a + b*tan(c + d*x))*tan(c + d*x), x)","F",0
343,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/sqrt(a + b*tan(c + d*x)), x)","F",0
344,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/sqrt(a + b*tan(c + d*x)), x)","F",0
345,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
346,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
347,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
348,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/sqrt(a + b*tan(c + d*x)), x)","F",0
349,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/sqrt(a + b*tan(c + d*x)), x)","F",0
350,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/(a + b*tan(c + d*x))**(3/2), x)","F",0
351,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/(a + b*tan(c + d*x))**(3/2), x)","F",0
352,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/(a + b*tan(c + d*x))**(3/2), x)","F",0
353,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(a + b*tan(c + d*x))**(3/2), x)","F",0
354,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/(a + b*tan(c + d*x))**(3/2), x)","F",0
355,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/(a + b*tan(c + d*x))**(3/2), x)","F",0
356,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/(a + b*tan(c + d*x))**(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{4}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**4/(a + b*tan(c + d*x))**(5/2), x)","F",0
358,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**3/(a + b*tan(c + d*x))**(5/2), x)","F",0
359,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**2/(a + b*tan(c + d*x))**(5/2), x)","F",0
360,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)/(a + b*tan(c + d*x))**(5/2), x)","F",0
361,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(a + b*tan(c + d*x))**(5/2), x)","F",0
362,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)/(a + b*tan(c + d*x))**(5/2), x)","F",0
363,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**2/(a + b*tan(c + d*x))**(5/2), x)","F",0
364,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**3/(a + b*tan(c + d*x))**(5/2), x)","F",0
365,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","B \int \sqrt{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(a + b*tan(c + d*x)), x)","F",0
366,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/sqrt(a + b*tan(c + d*x)), x)","F",0
367,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{\cot{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(cot(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
368,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","B \int \frac{1}{a \sqrt{a + b \tan{\left(c + d x \right)}} + b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(a*sqrt(a + b*tan(c + d*x)) + b*sqrt(a + b*tan(c + d*x))*tan(c + d*x)), x)","F",0
369,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","B \int \frac{\cot{\left(c + d x \right)}}{a \sqrt{a + b \tan{\left(c + d x \right)}} + b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(cot(c + d*x)/(a*sqrt(a + b*tan(c + d*x)) + b*sqrt(a + b*tan(c + d*x))*tan(c + d*x)), x)","F",0
370,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","- \int \frac{a}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx - \int \left(- \frac{b \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\right)\, dx"," ",0,"-Integral(a/sqrt(a + b*tan(c + d*x)), x) - Integral(-b*tan(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
371,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","- \int \frac{a}{a \sqrt{a + b \tan{\left(c + d x \right)}} + b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}}\, dx - \int \left(- \frac{b \tan{\left(c + d x \right)}}{a \sqrt{a + b \tan{\left(c + d x \right)}} + b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}}\right)\, dx"," ",0,"-Integral(a/(a*sqrt(a + b*tan(c + d*x)) + b*sqrt(a + b*tan(c + d*x))*tan(c + d*x)), x) - Integral(-b*tan(c + d*x)/(a*sqrt(a + b*tan(c + d*x)) + b*sqrt(a + b*tan(c + d*x))*tan(c + d*x)), x)","F",0
372,0,0,0,0.000000," ","integrate((-a+b*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","- \int \frac{a}{a^{2} \sqrt{a + b \tan{\left(c + d x \right)}} + 2 a b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)} + b^{2} \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}}\, dx - \int \left(- \frac{b \tan{\left(c + d x \right)}}{a^{2} \sqrt{a + b \tan{\left(c + d x \right)}} + 2 a b \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)} + b^{2} \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}}\right)\, dx"," ",0,"-Integral(a/(a**2*sqrt(a + b*tan(c + d*x)) + 2*a*b*sqrt(a + b*tan(c + d*x))*tan(c + d*x) + b**2*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2), x) - Integral(-b*tan(c + d*x)/(a**2*sqrt(a + b*tan(c + d*x)) + 2*a*b*sqrt(a + b*tan(c + d*x))*tan(c + d*x) + b**2*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2), x)","F",0
373,0,0,0,0.000000," ","integrate((1+I*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","i \left(\int \left(- \frac{i}{\sqrt{a + b \tan{\left(c + d x \right)}}}\right)\, dx + \int \frac{\tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx\right)"," ",0,"I*(Integral(-I/sqrt(a + b*tan(c + d*x)), x) + Integral(tan(c + d*x)/sqrt(a + b*tan(c + d*x)), x))","F",0
374,0,0,0,0.000000," ","integrate((1-I*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","- i \left(\int \frac{i}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx + \int \frac{\tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx\right)"," ",0,"-I*(Integral(I/sqrt(a + b*tan(c + d*x)), x) + Integral(tan(c + d*x)/sqrt(a + b*tan(c + d*x)), x))","F",0
375,0,0,0,0.000000," ","integrate((3+tan(x))/(4+3*tan(x))**(1/2),x)","\int \frac{\tan{\left(x \right)} + 3}{\sqrt{3 \tan{\left(x \right)} + 4}}\, dx"," ",0,"Integral((tan(x) + 3)/sqrt(3*tan(x) + 4), x)","F",0
376,0,0,0,0.000000," ","integrate((1-3*tan(x))/(4+3*tan(x))**(1/2),x)","- \int \frac{3 \tan{\left(x \right)}}{\sqrt{3 \tan{\left(x \right)} + 4}}\, dx - \int \left(- \frac{1}{\sqrt{3 \tan{\left(x \right)} + 4}}\right)\, dx"," ",0,"-Integral(3*tan(x)/sqrt(3*tan(x) + 4), x) - Integral(-1/sqrt(3*tan(x) + 4), x)","F",0
377,0,0,0,0.000000," ","integrate((4-3*tan(b*x+a))/(4+3*tan(b*x+a))**(1/2),x)","- \int \frac{3 \tan{\left(a + b x \right)}}{\sqrt{3 \tan{\left(a + b x \right)} + 4}}\, dx - \int \left(- \frac{4}{\sqrt{3 \tan{\left(a + b x \right)} + 4}}\right)\, dx"," ",0,"-Integral(3*tan(a + b*x)/sqrt(3*tan(a + b*x) + 4), x) - Integral(-4/sqrt(3*tan(a + b*x) + 4), x)","F",0
378,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*tan(c + d*x)**(5/2), x)","F",0
379,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*tan(c + d*x)**(3/2), x)","F",0
380,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
381,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
382,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
383,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
384,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))/tan(c + d*x)**(7/2), x)","F",0
385,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2*tan(c + d*x)**(3/2), x)","F",0
387,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2*sqrt(tan(c + d*x)), x)","F",0
388,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2/sqrt(tan(c + d*x)), x)","F",0
389,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2/tan(c + d*x)**(3/2), x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2/tan(c + d*x)**(5/2), x)","F",0
391,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2/tan(c + d*x)**(7/2), x)","F",0
392,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3*sqrt(tan(c + d*x)), x)","F",0
394,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3/sqrt(tan(c + d*x)), x)","F",0
395,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3/tan(c + d*x)**(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3/tan(c + d*x)**(5/2), x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3/tan(c + d*x)**(7/2), x)","F",0
398,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(5/2)/(a + b*tan(c + d*x)), x)","F",0
399,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/(a + b*tan(c + d*x)), x)","F",0
400,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(a + b*tan(c + d*x)), x)","F",0
401,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
402,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))*tan(c + d*x)**(3/2)), x)","F",0
403,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**2, x)","F",0
405,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**2, x)","F",0
406,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**2, x)","F",0
407,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B \int \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx"," ",0,"B*Integral(tan(c + d*x)**(5/2), x)","F",0
417,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B \int \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"B*Integral(tan(c + d*x)**(3/2), x)","F",0
418,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B \int \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(tan(c + d*x)), x)","F",0
419,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/sqrt(tan(c + d*x)), x)","F",0
420,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(tan(c + d*x)**(-3/2), x)","F",0
421,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(tan(c + d*x)**(-5/2), x)","F",0
422,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","B \int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x)), x)","F",0
423,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","B \int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x)), x)","F",0
424,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","B \int \frac{\sqrt{\tan{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x)), x)","F",0
425,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","B \int \frac{1}{a \sqrt{\tan{\left(c + d x \right)}} + b \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(a*sqrt(tan(c + d*x)) + b*tan(c + d*x)**(3/2)), x)","F",0
426,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","B \int \frac{1}{a \tan^{\frac{3}{2}}{\left(c + d x \right)} + b \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(a*tan(c + d*x)**(3/2) + b*tan(c + d*x)**(5/2)), x)","F",0
427,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(3/2), x)","F",0
428,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
429,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
430,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
431,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
432,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*sqrt(tan(c + d*x)), x)","F",0
436,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)/sqrt(tan(c + d*x)), x)","F",0
437,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)/tan(c + d*x)**(3/2), x)","F",0
438,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)/tan(c + d*x)**(5/2), x)","F",0
439,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(5/2)/tan(c + d*x)**(3/2), x)","F",0
446,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(5/2)/tan(c + d*x)**(5/2), x)","F",0
447,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\frac{B \left(\int \frac{2 a^{3} \sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{3 b^{3} \sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx + \int \frac{6 a b^{2} \sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int 2 a b^{2} \sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}\, dx + \int \frac{3 a^{2} b \sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx + \int \frac{4 a^{2} b \sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx\right)}{2 a}"," ",0,"B*(Integral(2*a**3*sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(3/2), x) + Integral(3*b**3*sqrt(a + b*tan(c + d*x))/sqrt(tan(c + d*x)), x) + Integral(6*a*b**2*sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(3/2), x) + Integral(2*a*b**2*sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x) + Integral(3*a**2*b*sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(5/2), x) + Integral(4*a**2*b*sqrt(a + b*tan(c + d*x))/sqrt(tan(c + d*x)), x))/(2*a)","F",0
452,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
453,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
454,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
455,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(3/2)), x)","F",0
456,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(5/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(5/2)), x)","F",0
457,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**(3/2), x)","F",0
459,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**(3/2), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**(3/2)*sqrt(tan(c + d*x))), x)","F",0
461,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**(3/2)), x)","F",0
462,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**(5/2), x)","F",0
464,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**(5/2), x)","F",0
465,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**(5/2), x)","F",0
466,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(tan(c + d*x)**(3/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
470,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(sqrt(tan(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
471,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
472,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(3/2)), x)","F",0
473,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(2/3)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(2/3), x)","F",0
474,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/3)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt[3]{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(1/3), x)","F",0
475,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/3),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt[3]{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(a + b*tan(c + d*x))**(1/3), x)","F",0
476,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(2/3),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(a + b*tan(c + d*x))**(2/3), x)","F",0
477,0,0,0,0.000000," ","integrate((I-tan(f*x+e))/(c+d*tan(f*x+e))**(1/3),x)","- \int \left(- \frac{i}{\sqrt[3]{c + d \tan{\left(e + f x \right)}}}\right)\, dx - \int \frac{\tan{\left(e + f x \right)}}{\sqrt[3]{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"-Integral(-I/(c + d*tan(e + f*x))**(1/3), x) - Integral(tan(e + f*x)/(c + d*tan(e + f*x))**(1/3), x)","F",0
478,0,0,0,0.000000," ","integrate((d-c*tan(f*x+e))/(c+d*tan(f*x+e))**(2/3),x)","- \int \left(- \frac{d}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{2}{3}}}\right)\, dx - \int \frac{c \tan{\left(e + f x \right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"-Integral(-d/(c + d*tan(e + f*x))**(2/3), x) - Integral(c*tan(e + f*x)/(c + d*tan(e + f*x))**(2/3), x)","F",0
479,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**4*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{4} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**4*tan(c + d*x)**m, x)","F",0
480,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3*tan(c + d*x)**m, x)","F",0
481,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2*tan(c + d*x)**m, x)","F",0
482,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
483,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x)), x)","F",0
484,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x))**2, x)","F",0
485,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x))**3, x)","F",0
486,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**4,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x))**4, x)","F",0
487,-1,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**m, x)","F",0
489,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
490,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/sqrt(a + b*tan(c + d*x)), x)","F",0
491,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x))**(3/2), x)","F",0
492,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*tan(c + d*x)**m/(a + b*tan(c + d*x))**(5/2), x)","F",0
493,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*tan(c + d*x)**m, x)","F",0
494,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \tan^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*tan(c + d*x)**4, x)","F",0
495,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*tan(c + d*x)**3, x)","F",0
496,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*tan(c + d*x)**2, x)","F",0
497,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*tan(c + d*x), x)","F",0
498,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n, x)","F",0
499,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*cot(c + d*x), x)","F",0
500,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*cot(c + d*x)**2, x)","F",0
501,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int \left(- i A \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int A \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int B \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- i B \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*cot(c + d*x)**(3/2), x) + Integral(A*tan(c + d*x)*cot(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**2*cot(c + d*x)**(3/2), x) + Integral(-I*B*tan(c + d*x)*cot(c + d*x)**(3/2), x))","F",0
505,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x)","i a \left(\int \left(- i A \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int A \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int B \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- i B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**2*sqrt(cot(c + d*x)), x) + Integral(-I*B*tan(c + d*x)*sqrt(cot(c + d*x)), x))","F",0
506,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","i a \left(\int \left(- \frac{i A}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{A \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \frac{B \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{i B \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**2/sqrt(cot(c + d*x)), x) + Integral(-I*B*tan(c + d*x)/sqrt(cot(c + d*x)), x))","F",0
507,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","i a \left(\int \left(- \frac{i A}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{A \tan{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \tan^{2}{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{i B \tan{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/cot(c + d*x)**(3/2), x) + Integral(A*tan(c + d*x)/cot(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**2/cot(c + d*x)**(3/2), x) + Integral(-I*B*tan(c + d*x)/cot(c + d*x)**(3/2), x))","F",0
508,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- a^{2} \left(\int \left(- A \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int A \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- B \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int B \tan^{3}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 2 i A \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- 2 i B \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*cot(c + d*x)**(3/2), x) + Integral(A*tan(c + d*x)**2*cot(c + d*x)**(3/2), x) + Integral(-B*tan(c + d*x)*cot(c + d*x)**(3/2), x) + Integral(B*tan(c + d*x)**3*cot(c + d*x)**(3/2), x) + Integral(-2*I*A*tan(c + d*x)*cot(c + d*x)**(3/2), x) + Integral(-2*I*B*tan(c + d*x)**2*cot(c + d*x)**(3/2), x))","F",0
511,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","- a^{2} \left(\int \left(- A \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int A \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int B \tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 2 i A \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int \left(- 2 i B \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)**2*sqrt(cot(c + d*x)), x) + Integral(-B*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**3*sqrt(cot(c + d*x)), x) + Integral(-2*I*A*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(-2*I*B*tan(c + d*x)**2*sqrt(cot(c + d*x)), x))","F",0
512,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","- a^{2} \left(\int \left(- \frac{A}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{A \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{B \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{B \tan^{3}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{2 i A \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \left(- \frac{2 i B \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)**2/sqrt(cot(c + d*x)), x) + Integral(-B*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**3/sqrt(cot(c + d*x)), x) + Integral(-2*I*A*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(-2*I*B*tan(c + d*x)**2/sqrt(cot(c + d*x)), x))","F",0
513,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","- i a^{3} \left(\int i A \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 A \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int A \tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 B \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int B \tan^{4}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 i A \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int i B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 i B \tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*sqrt(cot(c + d*x)), x) + Integral(-3*A*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)**3*sqrt(cot(c + d*x)), x) + Integral(-3*B*tan(c + d*x)**2*sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**4*sqrt(cot(c + d*x)), x) + Integral(-3*I*A*tan(c + d*x)**2*sqrt(cot(c + d*x)), x) + Integral(I*B*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(-3*I*B*tan(c + d*x)**3*sqrt(cot(c + d*x)), x))","F",0
518,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","- i a^{3} \left(\int \frac{i A}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 A \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{A \tan^{3}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 B \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{B \tan^{4}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 i A \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{i B \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 i B \tan^{3}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A/sqrt(cot(c + d*x)), x) + Integral(-3*A*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(A*tan(c + d*x)**3/sqrt(cot(c + d*x)), x) + Integral(-3*B*tan(c + d*x)**2/sqrt(cot(c + d*x)), x) + Integral(B*tan(c + d*x)**4/sqrt(cot(c + d*x)), x) + Integral(-3*I*A*tan(c + d*x)**2/sqrt(cot(c + d*x)), x) + Integral(I*B*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(-3*I*B*tan(c + d*x)**3/sqrt(cot(c + d*x)), x))","F",0
519,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*cot(c + d*x)**(3/2)/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)*cot(c + d*x)**(3/2)/(tan(c + d*x) - I), x))/a","F",0
521,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A \sqrt{\cot{\left(c + d x \right)}}}{\tan{\left(c + d x \right)} - i}\, dx + \int \frac{B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}}{\tan{\left(c + d x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*sqrt(cot(c + d*x))/(tan(c + d*x) - I), x) + Integral(B*tan(c + d*x)*sqrt(cot(c + d*x))/(tan(c + d*x) - I), x))/a","F",0
522,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A}{\tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - i \sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \frac{B \tan{\left(c + d x \right)}}{\tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - i \sqrt{\cot{\left(c + d x \right)}}}\, dx\right)}{a}"," ",0,"-I*(Integral(A/(tan(c + d*x)*sqrt(cot(c + d*x)) - I*sqrt(cot(c + d*x))), x) + Integral(B*tan(c + d*x)/(tan(c + d*x)*sqrt(cot(c + d*x)) - I*sqrt(cot(c + d*x))), x))/a","F",0
523,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \left(\int \frac{A}{\tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - i \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \frac{B \tan{\left(c + d x \right)}}{\tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - i \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)}{a}"," ",0,"-I*(Integral(A/(tan(c + d*x)*cot(c + d*x)**(3/2) - I*cot(c + d*x)**(3/2)), x) + Integral(B*tan(c + d*x)/(tan(c + d*x)*cot(c + d*x)**(3/2) - I*cot(c + d*x)**(3/2)), x))/a","F",0
524,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*cot(c + d*x)**(3/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)*cot(c + d*x)**(3/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
526,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A \sqrt{\cot{\left(c + d x \right)}}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx + \int \frac{B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}}{\tan^{2}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*sqrt(cot(c + d*x))/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x) + Integral(B*tan(c + d*x)*sqrt(cot(c + d*x))/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x))/a**2","F",0
527,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{A}{\tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 2 i \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - \sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \frac{B \tan{\left(c + d x \right)}}{\tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 2 i \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - \sqrt{\cot{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"-(Integral(A/(tan(c + d*x)**2*sqrt(cot(c + d*x)) - 2*I*tan(c + d*x)*sqrt(cot(c + d*x)) - sqrt(cot(c + d*x))), x) + Integral(B*tan(c + d*x)/(tan(c + d*x)**2*sqrt(cot(c + d*x)) - 2*I*tan(c + d*x)*sqrt(cot(c + d*x)) - sqrt(cot(c + d*x))), x))/a**2","F",0
528,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**3,x)","\frac{i \left(\int \frac{A \sqrt{\cot{\left(c + d x \right)}}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx + \int \frac{B \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}}{\tan^{3}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} - 3 \tan{\left(c + d x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*sqrt(cot(c + d*x))/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x) + Integral(B*tan(c + d*x)*sqrt(cot(c + d*x))/(tan(c + d*x)**3 - 3*I*tan(c + d*x)**2 - 3*tan(c + d*x) + I), x))/a**3","F",0
532,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**3,x)","\frac{i \left(\int \frac{A}{\tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 3 i \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 3 \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} + i \sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \frac{B \tan{\left(c + d x \right)}}{\tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 3 i \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - 3 \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} + i \sqrt{\cot{\left(c + d x \right)}}}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A/(tan(c + d*x)**3*sqrt(cot(c + d*x)) - 3*I*tan(c + d*x)**2*sqrt(cot(c + d*x)) - 3*tan(c + d*x)*sqrt(cot(c + d*x)) + I*sqrt(cot(c + d*x))), x) + Integral(B*tan(c + d*x)/(tan(c + d*x)**3*sqrt(cot(c + d*x)) - 3*I*tan(c + d*x)**2*sqrt(cot(c + d*x)) - 3*tan(c + d*x)*sqrt(cot(c + d*x)) + I*sqrt(cot(c + d*x))), x))/a**3","F",0
533,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))*sqrt(cot(c + d*x)), x)","F",0
540,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*(A + B*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
541,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*(A + B*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
547,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(11/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
557,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(I*a*(tan(c + d*x) - I))*sqrt(cot(c + d*x))), x)","F",0
558,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
560,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(cot(c + d*x))), x)","F",0
561,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,0,0,0,0.000000," ","integrate(cot(d*x+c)**m*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \cot^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*cot(c + d*x)**m, x)","F",0
568,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))*sqrt(cot(c + d*x)), x)","F",0
571,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \left(A + B \tan{\left(c + d x \right)}\right)}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*(A + B*tan(c + d*x))/cot(c + d*x)**(3/2), x)","F",0
573,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n*(A+B*tan(d*x+c))/cot(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*cot(c + d*x)**(3/2), x)","F",0
576,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))*sqrt(cot(c + d*x)), x)","F",0
577,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
578,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2*cot(c + d*x)**(3/2), x)","F",0
581,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**2*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2*sqrt(cot(c + d*x)), x)","F",0
582,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**2/sqrt(cot(c + d*x)), x)","F",0
583,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**3*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3*sqrt(cot(c + d*x)), x)","F",0
588,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**3/sqrt(cot(c + d*x)), x)","F",0
589,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**(3/2)/(a + b*tan(c + d*x)), x)","F",0
591,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(a + b*tan(c + d*x)), x)","F",0
592,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))*sqrt(cot(c + d*x))), x)","F",0
593,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))*cot(c + d*x)**(3/2)), x)","F",0
594,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right) \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))*cot(c + d*x)**(5/2)), x)","F",0
595,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**(3/2)/(a + b*tan(c + d*x))**2, x)","F",0
596,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**2,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**2, x)","F",0
597,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**2*sqrt(cot(c + d*x))), x)","F",0
598,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**2*cot(c + d*x)**(3/2)), x)","F",0
599,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**(3/2)/(a + b*tan(c + d*x))**3, x)","F",0
601,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**3,x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**3, x)","F",0
602,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**3*sqrt(cot(c + d*x))), x)","F",0
603,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(7/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B \int \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"B*Integral(cot(c + d*x)**(3/2), x)","F",0
608,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x)","B \int \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(sqrt(cot(c + d*x)), x)","F",0
609,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/sqrt(cot(c + d*x)), x)","F",0
610,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(cot(c + d*x)**(-3/2), x)","F",0
611,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","B \int \frac{1}{\cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(cot(c + d*x)**(-5/2), x)","F",0
612,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))*sqrt(cot(c + d*x)), x)","F",0
617,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
618,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{a + b \tan{\left(c + d x \right)}}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(a + b*tan(c + d*x))/cot(c + d*x)**(3/2), x)","F",0
619,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(11/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)*sqrt(cot(c + d*x)), x)","F",0
625,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)/sqrt(cot(c + d*x)), x)","F",0
626,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**(3/2)/cot(c + d*x)**(3/2), x)","F",0
627,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(13/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(11/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*cot(c + d*x)**(3/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
639,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
640,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(a + b*tan(c + d*x))*sqrt(cot(c + d*x))), x)","F",0
641,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**(3/2)), x)","F",0
642,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**(3/2), x)","F",0
645,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**(3/2)*sqrt(cot(c + d*x))), x)","F",0
646,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{A + B \tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))/((a + b*tan(c + d*x))**(3/2)*cot(c + d*x)**(3/2)), x)","F",0
647,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**(5/2), x)","F",0
650,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(sqrt(cot(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
654,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*tan(c + d*x))*sqrt(cot(c + d*x))), x)","F",0
655,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","B \int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"B*Integral(1/(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**(3/2)), x)","F",0
656,-1,0,0,0.000000," ","integrate(cot(d*x+c)**m*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
657,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
658,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*sqrt(cot(c + d*x)), x)","F",0
659,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n*(A+B*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n/sqrt(cot(c + d*x)), x)","F",0
660,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n*(A+B*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
661,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
662,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**n*(A+B*tan(d*x+c)),x)","\int \left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n*sqrt(tan(c + d*x)), x)","F",0
663,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n*(A+B*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n/sqrt(tan(c + d*x)), x)","F",0
664,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n*(A+B*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)}\right) \left(a + b \tan{\left(c + d x \right)}\right)^{n}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*tan(c + d*x))*(a + b*tan(c + d*x))**n/tan(c + d*x)**(3/2), x)","F",0
665,1,394,0,1.623609," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \left(A + B \tan{\left(e \right)}\right) \left(i a \tan{\left(e \right)} + a\right) \left(- i c \tan{\left(e \right)} + c\right)^{n} & \text{for}\: f = 0 \\\frac{2 i A a}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{2 B a f x \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{2 i B a f x}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{i B a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{B a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{2 B a}{2 i c f \tan{\left(e + f x \right)} - 2 c f} & \text{for}\: n = -1 \\A a x + \frac{i A a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - i B a x + \frac{B a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{i B a \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\\frac{i A a n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{2} + f n} + \frac{i A a \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{2} + f n} + \frac{i B a n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{2} + f n} + \frac{B a \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{2} + f n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*tan(e))*(I*a*tan(e) + a)*(-I*c*tan(e) + c)**n, Eq(f, 0)), (2*I*A*a/(2*I*c*f*tan(e + f*x) - 2*c*f) - 2*B*a*f*x*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) - 2*I*B*a*f*x/(2*I*c*f*tan(e + f*x) - 2*c*f) - I*B*a*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) + B*a*log(tan(e + f*x)**2 + 1)/(2*I*c*f*tan(e + f*x) - 2*c*f) + 2*B*a/(2*I*c*f*tan(e + f*x) - 2*c*f), Eq(n, -1)), (A*a*x + I*A*a*log(tan(e + f*x)**2 + 1)/(2*f) - I*B*a*x + B*a*log(tan(e + f*x)**2 + 1)/(2*f) + I*B*a*tan(e + f*x)/f, Eq(n, 0)), (I*A*a*n*(-I*c*tan(e + f*x) + c)**n/(f*n**2 + f*n) + I*A*a*(-I*c*tan(e + f*x) + c)**n/(f*n**2 + f*n) + I*B*a*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**2 + f*n) + B*a*(-I*c*tan(e + f*x) + c)**n/(f*n**2 + f*n), True))","A",0
666,1,158,0,0.681664," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4,x)","\frac{- 20 i A a c^{4} + 12 B a c^{4} + \left(- 20 i A a c^{4} e^{2 i e} - 20 B a c^{4} e^{2 i e}\right) e^{2 i f x}}{- 5 f e^{10 i e} e^{10 i f x} - 25 f e^{8 i e} e^{8 i f x} - 50 f e^{6 i e} e^{6 i f x} - 50 f e^{4 i e} e^{4 i f x} - 25 f e^{2 i e} e^{2 i f x} - 5 f}"," ",0,"(-20*I*A*a*c**4 + 12*B*a*c**4 + (-20*I*A*a*c**4*exp(2*I*e) - 20*B*a*c**4*exp(2*I*e))*exp(2*I*f*x))/(-5*f*exp(10*I*e)*exp(10*I*f*x) - 25*f*exp(8*I*e)*exp(8*I*f*x) - 50*f*exp(6*I*e)*exp(6*I*f*x) - 50*f*exp(4*I*e)*exp(4*I*f*x) - 25*f*exp(2*I*e)*exp(2*I*f*x) - 5*f)","B",0
667,1,144,0,0.571067," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3,x)","\frac{- 8 A a c^{3} - 4 i B a c^{3} + \left(- 8 A a c^{3} e^{2 i e} + 8 i B a c^{3} e^{2 i e}\right) e^{2 i f x}}{3 i f e^{8 i e} e^{8 i f x} + 12 i f e^{6 i e} e^{6 i f x} + 18 i f e^{4 i e} e^{4 i f x} + 12 i f e^{2 i e} e^{2 i f x} + 3 i f}"," ",0,"(-8*A*a*c**3 - 4*I*B*a*c**3 + (-8*A*a*c**3*exp(2*I*e) + 8*I*B*a*c**3*exp(2*I*e))*exp(2*I*f*x))/(3*I*f*exp(8*I*e)*exp(8*I*f*x) + 12*I*f*exp(6*I*e)*exp(6*I*f*x) + 18*I*f*exp(4*I*e)*exp(4*I*f*x) + 12*I*f*exp(2*I*e)*exp(2*I*f*x) + 3*I*f)","B",0
668,1,117,0,0.423183," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2,x)","\frac{6 i A a c^{2} - 2 B a c^{2} + \left(6 i A a c^{2} e^{2 i e} + 6 B a c^{2} e^{2 i e}\right) e^{2 i f x}}{3 f e^{6 i e} e^{6 i f x} + 9 f e^{4 i e} e^{4 i f x} + 9 f e^{2 i e} e^{2 i f x} + 3 f}"," ",0,"(6*I*A*a*c**2 - 2*B*a*c**2 + (6*I*A*a*c**2*exp(2*I*e) + 6*B*a*c**2*exp(2*I*e))*exp(2*I*f*x))/(3*f*exp(6*I*e)*exp(6*I*f*x) + 9*f*exp(4*I*e)*exp(4*I*f*x) + 9*f*exp(2*I*e)*exp(2*I*f*x) + 3*f)","B",0
669,1,82,0,0.308167," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{2 i A a c + \left(2 i A a c e^{2 i e} + 2 B a c e^{2 i e}\right) e^{2 i f x}}{f e^{4 i e} e^{4 i f x} + 2 f e^{2 i e} e^{2 i f x} + f}"," ",0,"(2*I*A*a*c + (2*I*A*a*c*exp(2*I*e) + 2*B*a*c*exp(2*I*e))*exp(2*I*f*x))/(f*exp(4*I*e)*exp(4*I*f*x) + 2*f*exp(2*I*e)*exp(2*I*f*x) + f)","C",0
670,1,53,0,0.417150," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x)","\frac{2 B a}{- f e^{2 i e} e^{2 i f x} - f} - \frac{i a \left(A - i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f}"," ",0,"2*B*a/(-f*exp(2*I*e)*exp(2*I*f*x) - f) - I*a*(A - I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/f","A",0
671,1,92,0,0.376065," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{B a \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \begin{cases} - \frac{\left(i A a e^{2 i e} + B a e^{2 i e}\right) e^{2 i f x}}{2 c f} & \text{for}\: 2 c f \neq 0 \\- \frac{x \left(- A a e^{2 i e} + i B a e^{2 i e}\right)}{c} & \text{otherwise} \end{cases}"," ",0,"B*a*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + Piecewise((-(I*A*a*exp(2*I*e) + B*a*exp(2*I*e))*exp(2*I*f*x)/(2*c*f), Ne(2*c*f, 0)), (-x*(-A*a*exp(2*I*e) + I*B*a*exp(2*I*e))/c, True))","A",0
672,1,155,0,0.382816," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(- 8 i A a c^{2} f e^{2 i e} + 8 B a c^{2} f e^{2 i e}\right) e^{2 i f x} + \left(- 4 i A a c^{2} f e^{4 i e} - 4 B a c^{2} f e^{4 i e}\right) e^{4 i f x}}{32 c^{4} f^{2}} & \text{for}\: 32 c^{4} f^{2} \neq 0 \\\frac{x \left(A a e^{4 i e} + A a e^{2 i e} - i B a e^{4 i e} + i B a e^{2 i e}\right)}{2 c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-8*I*A*a*c**2*f*exp(2*I*e) + 8*B*a*c**2*f*exp(2*I*e))*exp(2*I*f*x) + (-4*I*A*a*c**2*f*exp(4*I*e) - 4*B*a*c**2*f*exp(4*I*e))*exp(4*I*f*x))/(32*c**4*f**2), Ne(32*c**4*f**2, 0)), (x*(A*a*exp(4*I*e) + A*a*exp(2*I*e) - I*B*a*exp(4*I*e) + I*B*a*exp(2*I*e))/(2*c**2), True))","A",0
673,1,202,0,0.511886," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} - \frac{192 i A a c^{6} f^{2} e^{4 i e} e^{4 i f x} + \left(192 i A a c^{6} f^{2} e^{2 i e} - 192 B a c^{6} f^{2} e^{2 i e}\right) e^{2 i f x} + \left(64 i A a c^{6} f^{2} e^{6 i e} + 64 B a c^{6} f^{2} e^{6 i e}\right) e^{6 i f x}}{1536 c^{9} f^{3}} & \text{for}\: 1536 c^{9} f^{3} \neq 0 \\\frac{x \left(A a e^{6 i e} + 2 A a e^{4 i e} + A a e^{2 i e} - i B a e^{6 i e} + i B a e^{2 i e}\right)}{4 c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(192*I*A*a*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + (192*I*A*a*c**6*f**2*exp(2*I*e) - 192*B*a*c**6*f**2*exp(2*I*e))*exp(2*I*f*x) + (64*I*A*a*c**6*f**2*exp(6*I*e) + 64*B*a*c**6*f**2*exp(6*I*e))*exp(6*I*f*x))/(1536*c**9*f**3), Ne(1536*c**9*f**3, 0)), (x*(A*a*exp(6*I*e) + 2*A*a*exp(4*I*e) + A*a*exp(2*I*e) - I*B*a*exp(6*I*e) + I*B*a*exp(2*I*e))/(4*c**3), True))","A",0
674,1,306,0,0.638740," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{\left(- 98304 i A a c^{12} f^{3} e^{2 i e} + 98304 B a c^{12} f^{3} e^{2 i e}\right) e^{2 i f x} + \left(- 147456 i A a c^{12} f^{3} e^{4 i e} + 49152 B a c^{12} f^{3} e^{4 i e}\right) e^{4 i f x} + \left(- 98304 i A a c^{12} f^{3} e^{6 i e} - 32768 B a c^{12} f^{3} e^{6 i e}\right) e^{6 i f x} + \left(- 24576 i A a c^{12} f^{3} e^{8 i e} - 24576 B a c^{12} f^{3} e^{8 i e}\right) e^{8 i f x}}{1572864 c^{16} f^{4}} & \text{for}\: 1572864 c^{16} f^{4} \neq 0 \\\frac{x \left(A a e^{8 i e} + 3 A a e^{6 i e} + 3 A a e^{4 i e} + A a e^{2 i e} - i B a e^{8 i e} - i B a e^{6 i e} + i B a e^{4 i e} + i B a e^{2 i e}\right)}{8 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-98304*I*A*a*c**12*f**3*exp(2*I*e) + 98304*B*a*c**12*f**3*exp(2*I*e))*exp(2*I*f*x) + (-147456*I*A*a*c**12*f**3*exp(4*I*e) + 49152*B*a*c**12*f**3*exp(4*I*e))*exp(4*I*f*x) + (-98304*I*A*a*c**12*f**3*exp(6*I*e) - 32768*B*a*c**12*f**3*exp(6*I*e))*exp(6*I*f*x) + (-24576*I*A*a*c**12*f**3*exp(8*I*e) - 24576*B*a*c**12*f**3*exp(8*I*e))*exp(8*I*f*x))/(1572864*c**16*f**4), Ne(1572864*c**16*f**4, 0)), (x*(A*a*exp(8*I*e) + 3*A*a*exp(6*I*e) + 3*A*a*exp(4*I*e) + A*a*exp(2*I*e) - I*B*a*exp(8*I*e) - I*B*a*exp(6*I*e) + I*B*a*exp(4*I*e) + I*B*a*exp(2*I*e))/(8*c**4), True))","B",0
675,1,348,0,0.902074," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**5,x)","\begin{cases} - \frac{10485760 i A a c^{20} f^{4} e^{6 i e} e^{6 i f x} + \left(5242880 i A a c^{20} f^{4} e^{2 i e} - 5242880 B a c^{20} f^{4} e^{2 i e}\right) e^{2 i f x} + \left(10485760 i A a c^{20} f^{4} e^{4 i e} - 5242880 B a c^{20} f^{4} e^{4 i e}\right) e^{4 i f x} + \left(5242880 i A a c^{20} f^{4} e^{8 i e} + 2621440 B a c^{20} f^{4} e^{8 i e}\right) e^{8 i f x} + \left(1048576 i A a c^{20} f^{4} e^{10 i e} + 1048576 B a c^{20} f^{4} e^{10 i e}\right) e^{10 i f x}}{167772160 c^{25} f^{5}} & \text{for}\: 167772160 c^{25} f^{5} \neq 0 \\\frac{x \left(A a e^{10 i e} + 4 A a e^{8 i e} + 6 A a e^{6 i e} + 4 A a e^{4 i e} + A a e^{2 i e} - i B a e^{10 i e} - 2 i B a e^{8 i e} + 2 i B a e^{4 i e} + i B a e^{2 i e}\right)}{16 c^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(10485760*I*A*a*c**20*f**4*exp(6*I*e)*exp(6*I*f*x) + (5242880*I*A*a*c**20*f**4*exp(2*I*e) - 5242880*B*a*c**20*f**4*exp(2*I*e))*exp(2*I*f*x) + (10485760*I*A*a*c**20*f**4*exp(4*I*e) - 5242880*B*a*c**20*f**4*exp(4*I*e))*exp(4*I*f*x) + (5242880*I*A*a*c**20*f**4*exp(8*I*e) + 2621440*B*a*c**20*f**4*exp(8*I*e))*exp(8*I*f*x) + (1048576*I*A*a*c**20*f**4*exp(10*I*e) + 1048576*B*a*c**20*f**4*exp(10*I*e))*exp(10*I*f*x))/(167772160*c**25*f**5), Ne(167772160*c**25*f**5, 0)), (x*(A*a*exp(10*I*e) + 4*A*a*exp(8*I*e) + 6*A*a*exp(6*I*e) + 4*A*a*exp(4*I*e) + A*a*exp(2*I*e) - I*B*a*exp(10*I*e) - 2*I*B*a*exp(8*I*e) + 2*I*B*a*exp(4*I*e) + I*B*a*exp(2*I*e))/(16*c**5), True))","B",0
676,1,1499,0,4.399810," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \left(A + B \tan{\left(e \right)}\right) \left(i a \tan{\left(e \right)} + a\right)^{2} \left(- i c \tan{\left(e \right)} + c\right)^{n} & \text{for}\: f = 0 \\- \frac{2 A a^{2} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{2 i B a^{2} f x \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{4 B a^{2} f x \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{2 i B a^{2} f x}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{2 i B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{6 i B a^{2} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{4 B a^{2}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} & \text{for}\: n = -2 \\- \frac{2 i A a^{2} f x \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{2 A a^{2} f x}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{A a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{i A a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{4 i A a^{2}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{6 B a^{2} f x \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{6 i B a^{2} f x}{2 i c f \tan{\left(e + f x \right)} - 2 c f} - \frac{3 i B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{3 B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{2 B a^{2} \tan^{2}{\left(e + f x \right)}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} + \frac{6 B a^{2}}{2 i c f \tan{\left(e + f x \right)} - 2 c f} & \text{for}\: n = -1 \\2 A a^{2} x + \frac{i A a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{A a^{2} \tan{\left(e + f x \right)}}{f} - 2 i B a^{2} x + \frac{B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{B a^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{2 i B a^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\\frac{A a^{2} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{i A a^{2} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{- f n^{3} - 3 f n^{2} - 2 f n} + \frac{2 A a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{4 i A a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{4 i A a^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{- f n^{3} - 3 f n^{2} - 2 f n} + \frac{B a^{2} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{i B a^{2} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} + \frac{B a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{4 i B a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{B a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{- f n^{3} - 3 f n^{2} - 2 f n} - \frac{4 B a^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{- f n^{3} - 3 f n^{2} - 2 f n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*tan(e))*(I*a*tan(e) + a)**2*(-I*c*tan(e) + c)**n, Eq(f, 0)), (-2*A*a**2*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 2*I*B*a**2*f*x*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 4*B*a**2*f*x*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 2*I*B*a**2*f*x/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + B*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 2*I*B*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - B*a**2*log(tan(e + f*x)**2 + 1)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 6*I*B*a**2*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 4*B*a**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f), Eq(n, -2)), (-2*I*A*a**2*f*x*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) + 2*A*a**2*f*x/(2*I*c*f*tan(e + f*x) - 2*c*f) + A*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) + I*A*a**2*log(tan(e + f*x)**2 + 1)/(2*I*c*f*tan(e + f*x) - 2*c*f) + 4*I*A*a**2/(2*I*c*f*tan(e + f*x) - 2*c*f) - 6*B*a**2*f*x*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) - 6*I*B*a**2*f*x/(2*I*c*f*tan(e + f*x) - 2*c*f) - 3*I*B*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*c*f*tan(e + f*x) - 2*c*f) + 3*B*a**2*log(tan(e + f*x)**2 + 1)/(2*I*c*f*tan(e + f*x) - 2*c*f) + 2*B*a**2*tan(e + f*x)**2/(2*I*c*f*tan(e + f*x) - 2*c*f) + 6*B*a**2/(2*I*c*f*tan(e + f*x) - 2*c*f), Eq(n, -1)), (2*A*a**2*x + I*A*a**2*log(tan(e + f*x)**2 + 1)/f - A*a**2*tan(e + f*x)/f - 2*I*B*a**2*x + B*a**2*log(tan(e + f*x)**2 + 1)/f - B*a**2*tan(e + f*x)**2/(2*f) + 2*I*B*a**2*tan(e + f*x)/f, Eq(n, 0)), (A*a**2*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(-f*n**3 - 3*f*n**2 - 2*f*n) - I*A*a**2*n**2*(-I*c*tan(e + f*x) + c)**n/(-f*n**3 - 3*f*n**2 - 2*f*n) + 2*A*a**2*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(-f*n**3 - 3*f*n**2 - 2*f*n) - 4*I*A*a**2*n*(-I*c*tan(e + f*x) + c)**n/(-f*n**3 - 3*f*n**2 - 2*f*n) - 4*I*A*a**2*(-I*c*tan(e + f*x) + c)**n/(-f*n**3 - 3*f*n**2 - 2*f*n) + B*a**2*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(-f*n**3 - 3*f*n**2 - 2*f*n) - I*B*a**2*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(-f*n**3 - 3*f*n**2 - 2*f*n) + B*a**2*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(-f*n**3 - 3*f*n**2 - 2*f*n) - 4*I*B*a**2*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(-f*n**3 - 3*f*n**2 - 2*f*n) - B*a**2*n*(-I*c*tan(e + f*x) + c)**n/(-f*n**3 - 3*f*n**2 - 2*f*n) - 4*B*a**2*(-I*c*tan(e + f*x) + c)**n/(-f*n**3 - 3*f*n**2 - 2*f*n), True))","A",0
677,1,258,0,1.406769," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**5,x)","\frac{- 224 A a^{2} c^{5} - 96 i B a^{2} c^{5} + \left(- 1568 A a^{2} c^{5} e^{2 i e} - 672 i B a^{2} c^{5} e^{2 i e}\right) e^{2 i f x} + \left(- 1344 A a^{2} c^{5} e^{4 i e} + 1344 i B a^{2} c^{5} e^{4 i e}\right) e^{4 i f x}}{105 i f e^{14 i e} e^{14 i f x} + 735 i f e^{12 i e} e^{12 i f x} + 2205 i f e^{10 i e} e^{10 i f x} + 3675 i f e^{8 i e} e^{8 i f x} + 3675 i f e^{6 i e} e^{6 i f x} + 2205 i f e^{4 i e} e^{4 i f x} + 735 i f e^{2 i e} e^{2 i f x} + 105 i f}"," ",0,"(-224*A*a**2*c**5 - 96*I*B*a**2*c**5 + (-1568*A*a**2*c**5*exp(2*I*e) - 672*I*B*a**2*c**5*exp(2*I*e))*exp(2*I*f*x) + (-1344*A*a**2*c**5*exp(4*I*e) + 1344*I*B*a**2*c**5*exp(4*I*e))*exp(4*I*f*x))/(105*I*f*exp(14*I*e)*exp(14*I*f*x) + 735*I*f*exp(12*I*e)*exp(12*I*f*x) + 2205*I*f*exp(10*I*e)*exp(10*I*f*x) + 3675*I*f*exp(8*I*e)*exp(8*I*f*x) + 3675*I*f*exp(6*I*e)*exp(6*I*f*x) + 2205*I*f*exp(4*I*e)*exp(4*I*f*x) + 735*I*f*exp(2*I*e)*exp(2*I*f*x) + 105*I*f)","B",0
678,1,238,0,1.154835," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4,x)","\frac{- 24 A a^{2} c^{4} - 8 i B a^{2} c^{4} + \left(- 144 A a^{2} c^{4} e^{2 i e} - 48 i B a^{2} c^{4} e^{2 i e}\right) e^{2 i f x} + \left(- 120 A a^{2} c^{4} e^{4 i e} + 120 i B a^{2} c^{4} e^{4 i e}\right) e^{4 i f x}}{15 i f e^{12 i e} e^{12 i f x} + 90 i f e^{10 i e} e^{10 i f x} + 225 i f e^{8 i e} e^{8 i f x} + 300 i f e^{6 i e} e^{6 i f x} + 225 i f e^{4 i e} e^{4 i f x} + 90 i f e^{2 i e} e^{2 i f x} + 15 i f}"," ",0,"(-24*A*a**2*c**4 - 8*I*B*a**2*c**4 + (-144*A*a**2*c**4*exp(2*I*e) - 48*I*B*a**2*c**4*exp(2*I*e))*exp(2*I*f*x) + (-120*A*a**2*c**4*exp(4*I*e) + 120*I*B*a**2*c**4*exp(4*I*e))*exp(4*I*f*x))/(15*I*f*exp(12*I*e)*exp(12*I*f*x) + 90*I*f*exp(10*I*e)*exp(10*I*f*x) + 225*I*f*exp(8*I*e)*exp(8*I*f*x) + 300*I*f*exp(6*I*e)*exp(6*I*f*x) + 225*I*f*exp(4*I*e)*exp(4*I*f*x) + 90*I*f*exp(2*I*e)*exp(2*I*f*x) + 15*I*f)","B",0
679,1,218,0,0.866240," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3,x)","\frac{20 A a^{2} c^{3} + 4 i B a^{2} c^{3} + \left(100 A a^{2} c^{3} e^{2 i e} + 20 i B a^{2} c^{3} e^{2 i e}\right) e^{2 i f x} + \left(80 A a^{2} c^{3} e^{4 i e} - 80 i B a^{2} c^{3} e^{4 i e}\right) e^{4 i f x}}{- 15 i f e^{10 i e} e^{10 i f x} - 75 i f e^{8 i e} e^{8 i f x} - 150 i f e^{6 i e} e^{6 i f x} - 150 i f e^{4 i e} e^{4 i f x} - 75 i f e^{2 i e} e^{2 i f x} - 15 i f}"," ",0,"(20*A*a**2*c**3 + 4*I*B*a**2*c**3 + (100*A*a**2*c**3*exp(2*I*e) + 20*I*B*a**2*c**3*exp(2*I*e))*exp(2*I*f*x) + (80*A*a**2*c**3*exp(4*I*e) - 80*I*B*a**2*c**3*exp(4*I*e))*exp(4*I*f*x))/(-15*I*f*exp(10*I*e)*exp(10*I*f*x) - 75*I*f*exp(8*I*e)*exp(8*I*f*x) - 150*I*f*exp(6*I*e)*exp(6*I*f*x) - 150*I*f*exp(4*I*e)*exp(4*I*f*x) - 75*I*f*exp(2*I*e)*exp(2*I*f*x) - 15*I*f)","B",0
680,1,167,0,0.598578," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2,x)","\frac{16 A a^{2} c^{2} e^{2 i e} e^{2 i f x} + 4 A a^{2} c^{2} + \left(12 A a^{2} c^{2} e^{4 i e} - 12 i B a^{2} c^{2} e^{4 i e}\right) e^{4 i f x}}{- 3 i f e^{8 i e} e^{8 i f x} - 12 i f e^{6 i e} e^{6 i f x} - 18 i f e^{4 i e} e^{4 i f x} - 12 i f e^{2 i e} e^{2 i f x} - 3 i f}"," ",0,"(16*A*a**2*c**2*exp(2*I*e)*exp(2*I*f*x) + 4*A*a**2*c**2 + (12*A*a**2*c**2*exp(4*I*e) - 12*I*B*a**2*c**2*exp(4*I*e))*exp(4*I*f*x))/(-3*I*f*exp(8*I*e)*exp(8*I*f*x) - 12*I*f*exp(6*I*e)*exp(6*I*f*x) - 18*I*f*exp(4*I*e)*exp(4*I*f*x) - 12*I*f*exp(2*I*e)*exp(2*I*f*x) - 3*I*f)","C",0
681,1,167,0,0.446274," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{6 A a^{2} c - 2 i B a^{2} c + \left(18 A a^{2} c e^{2 i e} - 6 i B a^{2} c e^{2 i e}\right) e^{2 i f x} + \left(12 A a^{2} c e^{4 i e} - 12 i B a^{2} c e^{4 i e}\right) e^{4 i f x}}{- 3 i f e^{6 i e} e^{6 i f x} - 9 i f e^{4 i e} e^{4 i f x} - 9 i f e^{2 i e} e^{2 i f x} - 3 i f}"," ",0,"(6*A*a**2*c - 2*I*B*a**2*c + (18*A*a**2*c*exp(2*I*e) - 6*I*B*a**2*c*exp(2*I*e))*exp(2*I*f*x) + (12*A*a**2*c*exp(4*I*e) - 12*I*B*a**2*c*exp(4*I*e))*exp(4*I*f*x))/(-3*I*f*exp(6*I*e)*exp(6*I*f*x) - 9*I*f*exp(4*I*e)*exp(4*I*f*x) - 9*I*f*exp(2*I*e)*exp(2*I*f*x) - 3*I*f)","B",0
682,1,128,0,0.595065," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e)),x)","- \frac{2 i a^{2} \left(A - i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{- 2 A a^{2} + 4 i B a^{2} + \left(- 2 A a^{2} e^{2 i e} + 6 i B a^{2} e^{2 i e}\right) e^{2 i f x}}{- i f e^{4 i e} e^{4 i f x} - 2 i f e^{2 i e} e^{2 i f x} - i f}"," ",0,"-2*I*a**2*(A - I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/f + (-2*A*a**2 + 4*I*B*a**2 + (-2*A*a**2*exp(2*I*e) + 6*I*B*a**2*exp(2*I*e))*exp(2*I*f*x))/(-I*f*exp(4*I*e)*exp(4*I*f*x) - 2*I*f*exp(2*I*e)*exp(2*I*f*x) - I*f)","A",0
683,1,138,0,0.722995," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","- \frac{2 B a^{2}}{- c f e^{2 i e} e^{2 i f x} - c f} + \frac{i a^{2} \left(A - 3 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \begin{cases} - \frac{\left(i A a^{2} e^{2 i e} + B a^{2} e^{2 i e}\right) e^{2 i f x}}{c f} & \text{for}\: c f \neq 0 \\- \frac{x \left(- 2 A a^{2} e^{2 i e} + 2 i B a^{2} e^{2 i e}\right)}{c} & \text{otherwise} \end{cases}"," ",0,"-2*B*a**2/(-c*f*exp(2*I*e)*exp(2*I*f*x) - c*f) + I*a**2*(A - 3*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + Piecewise((-(I*A*a**2*exp(2*I*e) + B*a**2*exp(2*I*e))*exp(2*I*f*x)/(c*f), Ne(c*f, 0)), (-x*(-2*A*a**2*exp(2*I*e) + 2*I*B*a**2*exp(2*I*e))/c, True))","A",0
684,1,163,0,0.630535," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","- \frac{B a^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{2} f} + \begin{cases} - \frac{- 4 B a^{2} c^{2} f e^{2 i e} e^{2 i f x} + \left(i A a^{2} c^{2} f e^{4 i e} + B a^{2} c^{2} f e^{4 i e}\right) e^{4 i f x}}{4 c^{4} f^{2}} & \text{for}\: 4 c^{4} f^{2} \neq 0 \\- \frac{x \left(- A a^{2} e^{4 i e} + i B a^{2} e^{4 i e} - 2 i B a^{2} e^{2 i e}\right)}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"-B*a**2*log(exp(2*I*f*x) + exp(-2*I*e))/(c**2*f) + Piecewise((-(-4*B*a**2*c**2*f*exp(2*I*e)*exp(2*I*f*x) + (I*A*a**2*c**2*f*exp(4*I*e) + B*a**2*c**2*f*exp(4*I*e))*exp(4*I*f*x))/(4*c**4*f**2), Ne(4*c**4*f**2, 0)), (-x*(-A*a**2*exp(4*I*e) + I*B*a**2*exp(4*I*e) - 2*I*B*a**2*exp(2*I*e))/c**2, True))","A",0
685,1,168,0,0.563475," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(- 12 i A a^{2} c^{3} f e^{4 i e} + 12 B a^{2} c^{3} f e^{4 i e}\right) e^{4 i f x} + \left(- 8 i A a^{2} c^{3} f e^{6 i e} - 8 B a^{2} c^{3} f e^{6 i e}\right) e^{6 i f x}}{96 c^{6} f^{2}} & \text{for}\: 96 c^{6} f^{2} \neq 0 \\\frac{x \left(A a^{2} e^{6 i e} + A a^{2} e^{4 i e} - i B a^{2} e^{6 i e} + i B a^{2} e^{4 i e}\right)}{2 c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-12*I*A*a**2*c**3*f*exp(4*I*e) + 12*B*a**2*c**3*f*exp(4*I*e))*exp(4*I*f*x) + (-8*I*A*a**2*c**3*f*exp(6*I*e) - 8*B*a**2*c**3*f*exp(6*I*e))*exp(6*I*f*x))/(96*c**6*f**2), Ne(96*c**6*f**2, 0)), (x*(A*a**2*exp(6*I*e) + A*a**2*exp(4*I*e) - I*B*a**2*exp(6*I*e) + I*B*a**2*exp(4*I*e))/(2*c**3), True))","A",0
686,1,219,0,0.771407," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{512 i A a^{2} c^{8} f^{2} e^{6 i e} e^{6 i f x} + \left(384 i A a^{2} c^{8} f^{2} e^{4 i e} - 384 B a^{2} c^{8} f^{2} e^{4 i e}\right) e^{4 i f x} + \left(192 i A a^{2} c^{8} f^{2} e^{8 i e} + 192 B a^{2} c^{8} f^{2} e^{8 i e}\right) e^{8 i f x}}{6144 c^{12} f^{3}} & \text{for}\: 6144 c^{12} f^{3} \neq 0 \\\frac{x \left(A a^{2} e^{8 i e} + 2 A a^{2} e^{6 i e} + A a^{2} e^{4 i e} - i B a^{2} e^{8 i e} + i B a^{2} e^{4 i e}\right)}{4 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(512*I*A*a**2*c**8*f**2*exp(6*I*e)*exp(6*I*f*x) + (384*I*A*a**2*c**8*f**2*exp(4*I*e) - 384*B*a**2*c**8*f**2*exp(4*I*e))*exp(4*I*f*x) + (192*I*A*a**2*c**8*f**2*exp(8*I*e) + 192*B*a**2*c**8*f**2*exp(8*I*e))*exp(8*I*f*x))/(6144*c**12*f**3), Ne(6144*c**12*f**3, 0)), (x*(A*a**2*exp(8*I*e) + 2*A*a**2*exp(6*I*e) + A*a**2*exp(4*I*e) - I*B*a**2*exp(8*I*e) + I*B*a**2*exp(4*I*e))/(4*c**4), True))","A",0
687,1,333,0,0.899744," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**5,x)","\begin{cases} \frac{\left(- 245760 i A a^{2} c^{15} f^{3} e^{4 i e} + 245760 B a^{2} c^{15} f^{3} e^{4 i e}\right) e^{4 i f x} + \left(- 491520 i A a^{2} c^{15} f^{3} e^{6 i e} + 163840 B a^{2} c^{15} f^{3} e^{6 i e}\right) e^{6 i f x} + \left(- 368640 i A a^{2} c^{15} f^{3} e^{8 i e} - 122880 B a^{2} c^{15} f^{3} e^{8 i e}\right) e^{8 i f x} + \left(- 98304 i A a^{2} c^{15} f^{3} e^{10 i e} - 98304 B a^{2} c^{15} f^{3} e^{10 i e}\right) e^{10 i f x}}{7864320 c^{20} f^{4}} & \text{for}\: 7864320 c^{20} f^{4} \neq 0 \\\frac{x \left(A a^{2} e^{10 i e} + 3 A a^{2} e^{8 i e} + 3 A a^{2} e^{6 i e} + A a^{2} e^{4 i e} - i B a^{2} e^{10 i e} - i B a^{2} e^{8 i e} + i B a^{2} e^{6 i e} + i B a^{2} e^{4 i e}\right)}{8 c^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-245760*I*A*a**2*c**15*f**3*exp(4*I*e) + 245760*B*a**2*c**15*f**3*exp(4*I*e))*exp(4*I*f*x) + (-491520*I*A*a**2*c**15*f**3*exp(6*I*e) + 163840*B*a**2*c**15*f**3*exp(6*I*e))*exp(6*I*f*x) + (-368640*I*A*a**2*c**15*f**3*exp(8*I*e) - 122880*B*a**2*c**15*f**3*exp(8*I*e))*exp(8*I*f*x) + (-98304*I*A*a**2*c**15*f**3*exp(10*I*e) - 98304*B*a**2*c**15*f**3*exp(10*I*e))*exp(10*I*f*x))/(7864320*c**20*f**4), Ne(7864320*c**20*f**4, 0)), (x*(A*a**2*exp(10*I*e) + 3*A*a**2*exp(8*I*e) + 3*A*a**2*exp(6*I*e) + A*a**2*exp(4*I*e) - I*B*a**2*exp(10*I*e) - I*B*a**2*exp(8*I*e) + I*B*a**2*exp(6*I*e) + I*B*a**2*exp(4*I*e))/(8*c**5), True))","A",0
688,1,379,0,1.324769," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**6,x)","\begin{cases} - \frac{141557760 i A a^{2} c^{24} f^{4} e^{8 i e} e^{8 i f x} + \left(47185920 i A a^{2} c^{24} f^{4} e^{4 i e} - 47185920 B a^{2} c^{24} f^{4} e^{4 i e}\right) e^{4 i f x} + \left(125829120 i A a^{2} c^{24} f^{4} e^{6 i e} - 62914560 B a^{2} c^{24} f^{4} e^{6 i e}\right) e^{6 i f x} + \left(75497472 i A a^{2} c^{24} f^{4} e^{10 i e} + 37748736 B a^{2} c^{24} f^{4} e^{10 i e}\right) e^{10 i f x} + \left(15728640 i A a^{2} c^{24} f^{4} e^{12 i e} + 15728640 B a^{2} c^{24} f^{4} e^{12 i e}\right) e^{12 i f x}}{3019898880 c^{30} f^{5}} & \text{for}\: 3019898880 c^{30} f^{5} \neq 0 \\\frac{x \left(A a^{2} e^{12 i e} + 4 A a^{2} e^{10 i e} + 6 A a^{2} e^{8 i e} + 4 A a^{2} e^{6 i e} + A a^{2} e^{4 i e} - i B a^{2} e^{12 i e} - 2 i B a^{2} e^{10 i e} + 2 i B a^{2} e^{6 i e} + i B a^{2} e^{4 i e}\right)}{16 c^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(141557760*I*A*a**2*c**24*f**4*exp(8*I*e)*exp(8*I*f*x) + (47185920*I*A*a**2*c**24*f**4*exp(4*I*e) - 47185920*B*a**2*c**24*f**4*exp(4*I*e))*exp(4*I*f*x) + (125829120*I*A*a**2*c**24*f**4*exp(6*I*e) - 62914560*B*a**2*c**24*f**4*exp(6*I*e))*exp(6*I*f*x) + (75497472*I*A*a**2*c**24*f**4*exp(10*I*e) + 37748736*B*a**2*c**24*f**4*exp(10*I*e))*exp(10*I*f*x) + (15728640*I*A*a**2*c**24*f**4*exp(12*I*e) + 15728640*B*a**2*c**24*f**4*exp(12*I*e))*exp(12*I*f*x))/(3019898880*c**30*f**5), Ne(3019898880*c**30*f**5, 0)), (x*(A*a**2*exp(12*I*e) + 4*A*a**2*exp(10*I*e) + 6*A*a**2*exp(8*I*e) + 4*A*a**2*exp(6*I*e) + A*a**2*exp(4*I*e) - I*B*a**2*exp(12*I*e) - 2*I*B*a**2*exp(10*I*e) + 2*I*B*a**2*exp(6*I*e) + I*B*a**2*exp(4*I*e))/(16*c**6), True))","A",0
689,1,3669,0,13.118504," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \left(A + B \tan{\left(e \right)}\right) \left(i a \tan{\left(e \right)} + a\right)^{3} \left(- i c \tan{\left(e \right)} + c\right)^{n} & \text{for}\: f = 0 \\\frac{6 i A a^{3} \tan^{2}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{2 i A a^{3}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{6 B a^{3} f x \tan^{3}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{18 i B a^{3} f x \tan^{2}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{18 B a^{3} f x \tan{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{6 i B a^{3} f x}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{3 i B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{3}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{9 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{9 i B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{3 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{30 B a^{3} \tan^{2}{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} + \frac{36 i B a^{3} \tan{\left(e + f x \right)}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} - \frac{14 B a^{3}}{6 i c^{3} f \tan^{3}{\left(e + f x \right)} - 18 c^{3} f \tan^{2}{\left(e + f x \right)} - 18 i c^{3} f \tan{\left(e + f x \right)} + 6 c^{3} f} & \text{for}\: n = -3 \\\frac{2 A a^{3} f x \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{4 i A a^{3} f x \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{2 A a^{3} f x}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{i A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{2 A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{i A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{8 A a^{3} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{4 i A a^{3}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{10 i B a^{3} f x \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{20 B a^{3} f x \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{10 i B a^{3} f x}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{5 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{10 i B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{5 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{2 i B a^{3} \tan^{3}{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} + \frac{22 i B a^{3} \tan{\left(e + f x \right)}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} - \frac{16 B a^{3}}{2 c^{2} f \tan^{2}{\left(e + f x \right)} + 4 i c^{2} f \tan{\left(e + f x \right)} - 2 c^{2} f} & \text{for}\: n = -2 \\\frac{8 i A a^{3} f x \tan{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{8 A a^{3} f x}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{4 A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{4 i A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{2 i A a^{3} \tan^{2}{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{10 i A a^{3}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} + \frac{16 B a^{3} f x \tan{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} + \frac{16 i B a^{3} f x}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} + \frac{8 i B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{8 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{i B a^{3} \tan^{3}{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{7 B a^{3} \tan^{2}{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{16 B a^{3}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} & \text{for}\: n = -1 \\4 A a^{3} x + \frac{2 i A a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{i A a^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{3 A a^{3} \tan{\left(e + f x \right)}}{f} - 4 i B a^{3} x + \frac{2 B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{i B a^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{3 B a^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{4 i B a^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\- \frac{i A a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{2 A a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{i A a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{4 i A a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{12 A a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{8 i A a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{3 i A a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{18 A a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{23 i A a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{24 i A a^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{i B a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{3}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{2 B a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{i B a^{3} n^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{3 i B a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{3}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{11 B a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{9 i B a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{B a^{3} n^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{2 i B a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{3}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} - \frac{9 B a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan^{2}{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{24 i B a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{9 B a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} + \frac{24 B a^{3} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{4} + 6 f n^{3} + 11 f n^{2} + 6 f n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*tan(e))*(I*a*tan(e) + a)**3*(-I*c*tan(e) + c)**n, Eq(f, 0)), (6*I*A*a**3*tan(e + f*x)**2/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 2*I*A*a**3/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 6*B*a**3*f*x*tan(e + f*x)**3/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 18*I*B*a**3*f*x*tan(e + f*x)**2/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 18*B*a**3*f*x*tan(e + f*x)/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 6*I*B*a**3*f*x/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 3*I*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**3/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 9*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 9*I*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 3*B*a**3*log(tan(e + f*x)**2 + 1)/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 30*B*a**3*tan(e + f*x)**2/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) + 36*I*B*a**3*tan(e + f*x)/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f) - 14*B*a**3/(6*I*c**3*f*tan(e + f*x)**3 - 18*c**3*f*tan(e + f*x)**2 - 18*I*c**3*f*tan(e + f*x) + 6*c**3*f), Eq(n, -3)), (2*A*a**3*f*x*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 4*I*A*a**3*f*x*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 2*A*a**3*f*x/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + I*A*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 2*A*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - I*A*a**3*log(tan(e + f*x)**2 + 1)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 8*A*a**3*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 4*I*A*a**3/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 10*I*B*a**3*f*x*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 20*B*a**3*f*x*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 10*I*B*a**3*f*x/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 5*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 10*I*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 5*B*a**3*log(tan(e + f*x)**2 + 1)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 2*I*B*a**3*tan(e + f*x)**3/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) + 22*I*B*a**3*tan(e + f*x)/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f) - 16*B*a**3/(2*c**2*f*tan(e + f*x)**2 + 4*I*c**2*f*tan(e + f*x) - 2*c**2*f), Eq(n, -2)), (8*I*A*a**3*f*x*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 8*A*a**3*f*x/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 4*A*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 4*I*A*a**3*log(tan(e + f*x)**2 + 1)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 2*I*A*a**3*tan(e + f*x)**2/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 10*I*A*a**3/(-2*I*c*f*tan(e + f*x) + 2*c*f) + 16*B*a**3*f*x*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) + 16*I*B*a**3*f*x/(-2*I*c*f*tan(e + f*x) + 2*c*f) + 8*I*B*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 8*B*a**3*log(tan(e + f*x)**2 + 1)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - I*B*a**3*tan(e + f*x)**3/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 7*B*a**3*tan(e + f*x)**2/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 16*B*a**3/(-2*I*c*f*tan(e + f*x) + 2*c*f), Eq(n, -1)), (4*A*a**3*x + 2*I*A*a**3*log(tan(e + f*x)**2 + 1)/f - I*A*a**3*tan(e + f*x)**2/(2*f) - 3*A*a**3*tan(e + f*x)/f - 4*I*B*a**3*x + 2*B*a**3*log(tan(e + f*x)**2 + 1)/f - I*B*a**3*tan(e + f*x)**3/(3*f) - 3*B*a**3*tan(e + f*x)**2/(2*f) + 4*I*B*a**3*tan(e + f*x)/f, Eq(n, 0)), (-I*A*a**3*n**3*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 2*A*a**3*n**3*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + I*A*a**3*n**3*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 4*I*A*a**3*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 12*A*a**3*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 8*I*A*a**3*n**2*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 3*I*A*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 18*A*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 23*I*A*a**3*n*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 24*I*A*a**3*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - I*B*a**3*n**3*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**3/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 2*B*a**3*n**3*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + I*B*a**3*n**3*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 3*I*B*a**3*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**3/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 11*B*a**3*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 9*I*B*a**3*n**2*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + B*a**3*n**2*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 2*I*B*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**3/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) - 9*B*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 24*I*B*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 9*B*a**3*n*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 24*B*a**3*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n), True))","A",0
690,1,345,0,2.135633," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**6,x)","\frac{- 96 A a^{3} c^{6} - 32 i B a^{3} c^{6} + \left(- 864 A a^{3} c^{6} e^{2 i e} - 288 i B a^{3} c^{6} e^{2 i e}\right) e^{2 i f x} + \left(- 3456 A a^{3} c^{6} e^{4 i e} - 1152 i B a^{3} c^{6} e^{4 i e}\right) e^{4 i f x} + \left(- 2688 A a^{3} c^{6} e^{6 i e} + 2688 i B a^{3} c^{6} e^{6 i e}\right) e^{6 i f x}}{63 i f e^{18 i e} e^{18 i f x} + 567 i f e^{16 i e} e^{16 i f x} + 2268 i f e^{14 i e} e^{14 i f x} + 5292 i f e^{12 i e} e^{12 i f x} + 7938 i f e^{10 i e} e^{10 i f x} + 7938 i f e^{8 i e} e^{8 i f x} + 5292 i f e^{6 i e} e^{6 i f x} + 2268 i f e^{4 i e} e^{4 i f x} + 567 i f e^{2 i e} e^{2 i f x} + 63 i f}"," ",0,"(-96*A*a**3*c**6 - 32*I*B*a**3*c**6 + (-864*A*a**3*c**6*exp(2*I*e) - 288*I*B*a**3*c**6*exp(2*I*e))*exp(2*I*f*x) + (-3456*A*a**3*c**6*exp(4*I*e) - 1152*I*B*a**3*c**6*exp(4*I*e))*exp(4*I*f*x) + (-2688*A*a**3*c**6*exp(6*I*e) + 2688*I*B*a**3*c**6*exp(6*I*e))*exp(6*I*f*x))/(63*I*f*exp(18*I*e)*exp(18*I*f*x) + 567*I*f*exp(16*I*e)*exp(16*I*f*x) + 2268*I*f*exp(14*I*e)*exp(14*I*f*x) + 5292*I*f*exp(12*I*e)*exp(12*I*f*x) + 7938*I*f*exp(10*I*e)*exp(10*I*f*x) + 7938*I*f*exp(8*I*e)*exp(8*I*f*x) + 5292*I*f*exp(6*I*e)*exp(6*I*f*x) + 2268*I*f*exp(4*I*e)*exp(4*I*f*x) + 567*I*f*exp(2*I*e)*exp(2*I*f*x) + 63*I*f)","B",0
691,1,323,0,1.829361," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**5,x)","\frac{128 A a^{3} c^{5} + 32 i B a^{3} c^{5} + \left(1024 A a^{3} c^{5} e^{2 i e} + 256 i B a^{3} c^{5} e^{2 i e}\right) e^{2 i f x} + \left(3584 A a^{3} c^{5} e^{4 i e} + 896 i B a^{3} c^{5} e^{4 i e}\right) e^{4 i f x} + \left(2688 A a^{3} c^{5} e^{6 i e} - 2688 i B a^{3} c^{5} e^{6 i e}\right) e^{6 i f x}}{- 105 i f e^{16 i e} e^{16 i f x} - 840 i f e^{14 i e} e^{14 i f x} - 2940 i f e^{12 i e} e^{12 i f x} - 5880 i f e^{10 i e} e^{10 i f x} - 7350 i f e^{8 i e} e^{8 i f x} - 5880 i f e^{6 i e} e^{6 i f x} - 2940 i f e^{4 i e} e^{4 i f x} - 840 i f e^{2 i e} e^{2 i f x} - 105 i f}"," ",0,"(128*A*a**3*c**5 + 32*I*B*a**3*c**5 + (1024*A*a**3*c**5*exp(2*I*e) + 256*I*B*a**3*c**5*exp(2*I*e))*exp(2*I*f*x) + (3584*A*a**3*c**5*exp(4*I*e) + 896*I*B*a**3*c**5*exp(4*I*e))*exp(4*I*f*x) + (2688*A*a**3*c**5*exp(6*I*e) - 2688*I*B*a**3*c**5*exp(6*I*e))*exp(6*I*f*x))/(-105*I*f*exp(16*I*e)*exp(16*I*f*x) - 840*I*f*exp(14*I*e)*exp(14*I*f*x) - 2940*I*f*exp(12*I*e)*exp(12*I*f*x) - 5880*I*f*exp(10*I*e)*exp(10*I*f*x) - 7350*I*f*exp(8*I*e)*exp(8*I*f*x) - 5880*I*f*exp(6*I*e)*exp(6*I*f*x) - 2940*I*f*exp(4*I*e)*exp(4*I*f*x) - 840*I*f*exp(2*I*e)*exp(2*I*f*x) - 105*I*f)","B",0
692,1,303,0,1.435536," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4,x)","\frac{112 A a^{3} c^{4} + 16 i B a^{3} c^{4} + \left(784 A a^{3} c^{4} e^{2 i e} + 112 i B a^{3} c^{4} e^{2 i e}\right) e^{2 i f x} + \left(2352 A a^{3} c^{4} e^{4 i e} + 336 i B a^{3} c^{4} e^{4 i e}\right) e^{4 i f x} + \left(1680 A a^{3} c^{4} e^{6 i e} - 1680 i B a^{3} c^{4} e^{6 i e}\right) e^{6 i f x}}{- 105 i f e^{14 i e} e^{14 i f x} - 735 i f e^{12 i e} e^{12 i f x} - 2205 i f e^{10 i e} e^{10 i f x} - 3675 i f e^{8 i e} e^{8 i f x} - 3675 i f e^{6 i e} e^{6 i f x} - 2205 i f e^{4 i e} e^{4 i f x} - 735 i f e^{2 i e} e^{2 i f x} - 105 i f}"," ",0,"(112*A*a**3*c**4 + 16*I*B*a**3*c**4 + (784*A*a**3*c**4*exp(2*I*e) + 112*I*B*a**3*c**4*exp(2*I*e))*exp(2*I*f*x) + (2352*A*a**3*c**4*exp(4*I*e) + 336*I*B*a**3*c**4*exp(4*I*e))*exp(4*I*f*x) + (1680*A*a**3*c**4*exp(6*I*e) - 1680*I*B*a**3*c**4*exp(6*I*e))*exp(6*I*f*x))/(-105*I*f*exp(14*I*e)*exp(14*I*f*x) - 735*I*f*exp(12*I*e)*exp(12*I*f*x) - 2205*I*f*exp(10*I*e)*exp(10*I*f*x) - 3675*I*f*exp(8*I*e)*exp(8*I*f*x) - 3675*I*f*exp(6*I*e)*exp(6*I*f*x) - 2205*I*f*exp(4*I*e)*exp(4*I*f*x) - 735*I*f*exp(2*I*e)*exp(2*I*f*x) - 105*I*f)","B",0
693,1,231,0,1.013551," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3,x)","\frac{- 240 A a^{3} c^{3} e^{4 i e} e^{4 i f x} - 96 A a^{3} c^{3} e^{2 i e} e^{2 i f x} - 16 A a^{3} c^{3} + \left(- 160 A a^{3} c^{3} e^{6 i e} + 160 i B a^{3} c^{3} e^{6 i e}\right) e^{6 i f x}}{15 i f e^{12 i e} e^{12 i f x} + 90 i f e^{10 i e} e^{10 i f x} + 225 i f e^{8 i e} e^{8 i f x} + 300 i f e^{6 i e} e^{6 i f x} + 225 i f e^{4 i e} e^{4 i f x} + 90 i f e^{2 i e} e^{2 i f x} + 15 i f}"," ",0,"(-240*A*a**3*c**3*exp(4*I*e)*exp(4*I*f*x) - 96*A*a**3*c**3*exp(2*I*e)*exp(2*I*f*x) - 16*A*a**3*c**3 + (-160*A*a**3*c**3*exp(6*I*e) + 160*I*B*a**3*c**3*exp(6*I*e))*exp(6*I*f*x))/(15*I*f*exp(12*I*e)*exp(12*I*f*x) + 90*I*f*exp(10*I*e)*exp(10*I*f*x) + 225*I*f*exp(8*I*e)*exp(8*I*f*x) + 300*I*f*exp(6*I*e)*exp(6*I*f*x) + 225*I*f*exp(4*I*e)*exp(4*I*f*x) + 90*I*f*exp(2*I*e)*exp(2*I*f*x) + 15*I*f)","C",0
694,1,260,0,0.904972," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2,x)","\frac{- 20 A a^{3} c^{2} + 4 i B a^{3} c^{2} + \left(- 100 A a^{3} c^{2} e^{2 i e} + 20 i B a^{3} c^{2} e^{2 i e}\right) e^{2 i f x} + \left(- 200 A a^{3} c^{2} e^{4 i e} + 40 i B a^{3} c^{2} e^{4 i e}\right) e^{4 i f x} + \left(- 120 A a^{3} c^{2} e^{6 i e} + 120 i B a^{3} c^{2} e^{6 i e}\right) e^{6 i f x}}{15 i f e^{10 i e} e^{10 i f x} + 75 i f e^{8 i e} e^{8 i f x} + 150 i f e^{6 i e} e^{6 i f x} + 150 i f e^{4 i e} e^{4 i f x} + 75 i f e^{2 i e} e^{2 i f x} + 15 i f}"," ",0,"(-20*A*a**3*c**2 + 4*I*B*a**3*c**2 + (-100*A*a**3*c**2*exp(2*I*e) + 20*I*B*a**3*c**2*exp(2*I*e))*exp(2*I*f*x) + (-200*A*a**3*c**2*exp(4*I*e) + 40*I*B*a**3*c**2*exp(4*I*e))*exp(4*I*f*x) + (-120*A*a**3*c**2*exp(6*I*e) + 120*I*B*a**3*c**2*exp(6*I*e))*exp(6*I*f*x))/(15*I*f*exp(10*I*e)*exp(10*I*f*x) + 75*I*f*exp(8*I*e)*exp(8*I*f*x) + 150*I*f*exp(6*I*e)*exp(6*I*f*x) + 150*I*f*exp(4*I*e)*exp(4*I*f*x) + 75*I*f*exp(2*I*e)*exp(2*I*f*x) + 15*I*f)","B",0
695,1,224,0,0.635458," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","\frac{- 8 i A a^{3} c - 4 B a^{3} c + \left(- 32 i A a^{3} c e^{2 i e} - 16 B a^{3} c e^{2 i e}\right) e^{2 i f x} + \left(- 48 i A a^{3} c e^{4 i e} - 24 B a^{3} c e^{4 i e}\right) e^{4 i f x} + \left(- 24 i A a^{3} c e^{6 i e} - 24 B a^{3} c e^{6 i e}\right) e^{6 i f x}}{- 3 f e^{8 i e} e^{8 i f x} - 12 f e^{6 i e} e^{6 i f x} - 18 f e^{4 i e} e^{4 i f x} - 12 f e^{2 i e} e^{2 i f x} - 3 f}"," ",0,"(-8*I*A*a**3*c - 4*B*a**3*c + (-32*I*A*a**3*c*exp(2*I*e) - 16*B*a**3*c*exp(2*I*e))*exp(2*I*f*x) + (-48*I*A*a**3*c*exp(4*I*e) - 24*B*a**3*c*exp(4*I*e))*exp(4*I*f*x) + (-24*I*A*a**3*c*exp(6*I*e) - 24*B*a**3*c*exp(6*I*e))*exp(6*I*f*x))/(-3*f*exp(8*I*e)*exp(8*I*f*x) - 12*f*exp(6*I*e)*exp(6*I*f*x) - 18*f*exp(4*I*e)*exp(4*I*f*x) - 12*f*exp(2*I*e)*exp(2*I*f*x) - 3*f)","B",0
696,1,187,0,0.731049," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e)),x)","- \frac{4 i a^{3} \left(A - i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{18 A a^{3} - 26 i B a^{3} + \left(42 A a^{3} e^{2 i e} - 66 i B a^{3} e^{2 i e}\right) e^{2 i f x} + \left(24 A a^{3} e^{4 i e} - 48 i B a^{3} e^{4 i e}\right) e^{4 i f x}}{3 i f e^{6 i e} e^{6 i f x} + 9 i f e^{4 i e} e^{4 i f x} + 9 i f e^{2 i e} e^{2 i f x} + 3 i f}"," ",0,"-4*I*a**3*(A - I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/f + (18*A*a**3 - 26*I*B*a**3 + (42*A*a**3*exp(2*I*e) - 66*I*B*a**3*exp(2*I*e))*exp(2*I*f*x) + (24*A*a**3*exp(4*I*e) - 48*I*B*a**3*exp(4*I*e))*exp(4*I*f*x))/(3*I*f*exp(6*I*e)*exp(6*I*f*x) + 9*I*f*exp(4*I*e)*exp(4*I*f*x) + 9*I*f*exp(2*I*e)*exp(2*I*f*x) + 3*I*f)","B",0
697,1,214,0,1.006684," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{4 i a^{3} \left(A - 2 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \frac{2 A a^{3} - 8 i B a^{3} + \left(2 A a^{3} e^{2 i e} - 10 i B a^{3} e^{2 i e}\right) e^{2 i f x}}{- i c f e^{4 i e} e^{4 i f x} - 2 i c f e^{2 i e} e^{2 i f x} - i c f} + \begin{cases} - \frac{\left(2 i A a^{3} e^{2 i e} + 2 B a^{3} e^{2 i e}\right) e^{2 i f x}}{c f} & \text{for}\: c f \neq 0 \\- \frac{x \left(- 4 A a^{3} e^{2 i e} + 4 i B a^{3} e^{2 i e}\right)}{c} & \text{otherwise} \end{cases}"," ",0,"4*I*a**3*(A - 2*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + (2*A*a**3 - 8*I*B*a**3 + (2*A*a**3*exp(2*I*e) - 10*I*B*a**3*exp(2*I*e))*exp(2*I*f*x))/(-I*c*f*exp(4*I*e)*exp(4*I*f*x) - 2*I*c*f*exp(2*I*e)*exp(2*I*f*x) - I*c*f) + Piecewise((-(2*I*A*a**3*exp(2*I*e) + 2*B*a**3*exp(2*I*e))*exp(2*I*f*x)/(c*f), Ne(c*f, 0)), (-x*(-4*A*a**3*exp(2*I*e) + 4*I*B*a**3*exp(2*I*e))/c, True))","A",0
698,1,241,0,1.000704," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","\frac{2 B a^{3}}{- c^{2} f e^{2 i e} e^{2 i f x} - c^{2} f} - \frac{i a^{3} \left(A - 5 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{2} f} + \begin{cases} \frac{\left(2 i A a^{3} c^{2} f e^{2 i e} + 6 B a^{3} c^{2} f e^{2 i e}\right) e^{2 i f x} + \left(- i A a^{3} c^{2} f e^{4 i e} - B a^{3} c^{2} f e^{4 i e}\right) e^{4 i f x}}{2 c^{4} f^{2}} & \text{for}\: 2 c^{4} f^{2} \neq 0 \\- \frac{x \left(- 2 A a^{3} e^{4 i e} + 2 A a^{3} e^{2 i e} + 2 i B a^{3} e^{4 i e} - 6 i B a^{3} e^{2 i e}\right)}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"2*B*a**3/(-c**2*f*exp(2*I*e)*exp(2*I*f*x) - c**2*f) - I*a**3*(A - 5*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(c**2*f) + Piecewise((((2*I*A*a**3*c**2*f*exp(2*I*e) + 6*B*a**3*c**2*f*exp(2*I*e))*exp(2*I*f*x) + (-I*A*a**3*c**2*f*exp(4*I*e) - B*a**3*c**2*f*exp(4*I*e))*exp(4*I*f*x))/(2*c**4*f**2), Ne(2*c**4*f**2, 0)), (-x*(-2*A*a**3*exp(4*I*e) + 2*A*a**3*exp(2*I*e) + 2*I*B*a**3*exp(4*I*e) - 6*I*B*a**3*exp(2*I*e))/c**2, True))","A",0
699,1,216,0,0.982366," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\frac{B a^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{3} f} + \begin{cases} - \frac{- 6 B a^{3} c^{6} f^{2} e^{4 i e} e^{4 i f x} + 12 B a^{3} c^{6} f^{2} e^{2 i e} e^{2 i f x} + \left(2 i A a^{3} c^{6} f^{2} e^{6 i e} + 2 B a^{3} c^{6} f^{2} e^{6 i e}\right) e^{6 i f x}}{12 c^{9} f^{3}} & \text{for}\: 12 c^{9} f^{3} \neq 0 \\- \frac{x \left(- A a^{3} e^{6 i e} + i B a^{3} e^{6 i e} - 2 i B a^{3} e^{4 i e} + 2 i B a^{3} e^{2 i e}\right)}{c^{3}} & \text{otherwise} \end{cases}"," ",0,"B*a**3*log(exp(2*I*f*x) + exp(-2*I*e))/(c**3*f) + Piecewise((-(-6*B*a**3*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + 12*B*a**3*c**6*f**2*exp(2*I*e)*exp(2*I*f*x) + (2*I*A*a**3*c**6*f**2*exp(6*I*e) + 2*B*a**3*c**6*f**2*exp(6*I*e))*exp(6*I*f*x))/(12*c**9*f**3), Ne(12*c**9*f**3, 0)), (-x*(-A*a**3*exp(6*I*e) + I*B*a**3*exp(6*I*e) - 2*I*B*a**3*exp(4*I*e) + 2*I*B*a**3*exp(2*I*e))/c**3, True))","A",0
700,1,168,0,0.782495," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{\left(- 16 i A a^{3} c^{4} f e^{6 i e} + 16 B a^{3} c^{4} f e^{6 i e}\right) e^{6 i f x} + \left(- 12 i A a^{3} c^{4} f e^{8 i e} - 12 B a^{3} c^{4} f e^{8 i e}\right) e^{8 i f x}}{192 c^{8} f^{2}} & \text{for}\: 192 c^{8} f^{2} \neq 0 \\\frac{x \left(A a^{3} e^{8 i e} + A a^{3} e^{6 i e} - i B a^{3} e^{8 i e} + i B a^{3} e^{6 i e}\right)}{2 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-16*I*A*a**3*c**4*f*exp(6*I*e) + 16*B*a**3*c**4*f*exp(6*I*e))*exp(6*I*f*x) + (-12*I*A*a**3*c**4*f*exp(8*I*e) - 12*B*a**3*c**4*f*exp(8*I*e))*exp(8*I*f*x))/(192*c**8*f**2), Ne(192*c**8*f**2, 0)), (x*(A*a**3*exp(8*I*e) + A*a**3*exp(6*I*e) - I*B*a**3*exp(8*I*e) + I*B*a**3*exp(6*I*e))/(2*c**4), True))","A",0
701,1,219,0,1.117233," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**5,x)","\begin{cases} - \frac{960 i A a^{3} c^{10} f^{2} e^{8 i e} e^{8 i f x} + \left(640 i A a^{3} c^{10} f^{2} e^{6 i e} - 640 B a^{3} c^{10} f^{2} e^{6 i e}\right) e^{6 i f x} + \left(384 i A a^{3} c^{10} f^{2} e^{10 i e} + 384 B a^{3} c^{10} f^{2} e^{10 i e}\right) e^{10 i f x}}{15360 c^{15} f^{3}} & \text{for}\: 15360 c^{15} f^{3} \neq 0 \\\frac{x \left(A a^{3} e^{10 i e} + 2 A a^{3} e^{8 i e} + A a^{3} e^{6 i e} - i B a^{3} e^{10 i e} + i B a^{3} e^{6 i e}\right)}{4 c^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(960*I*A*a**3*c**10*f**2*exp(8*I*e)*exp(8*I*f*x) + (640*I*A*a**3*c**10*f**2*exp(6*I*e) - 640*B*a**3*c**10*f**2*exp(6*I*e))*exp(6*I*f*x) + (384*I*A*a**3*c**10*f**2*exp(10*I*e) + 384*B*a**3*c**10*f**2*exp(10*I*e))*exp(10*I*f*x))/(15360*c**15*f**3), Ne(15360*c**15*f**3, 0)), (x*(A*a**3*exp(10*I*e) + 2*A*a**3*exp(8*I*e) + A*a**3*exp(6*I*e) - I*B*a**3*exp(10*I*e) + I*B*a**3*exp(6*I*e))/(4*c**5), True))","A",0
702,1,333,0,1.203891," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**6,x)","\begin{cases} \frac{\left(- 491520 i A a^{3} c^{18} f^{3} e^{6 i e} + 491520 B a^{3} c^{18} f^{3} e^{6 i e}\right) e^{6 i f x} + \left(- 1105920 i A a^{3} c^{18} f^{3} e^{8 i e} + 368640 B a^{3} c^{18} f^{3} e^{8 i e}\right) e^{8 i f x} + \left(- 884736 i A a^{3} c^{18} f^{3} e^{10 i e} - 294912 B a^{3} c^{18} f^{3} e^{10 i e}\right) e^{10 i f x} + \left(- 245760 i A a^{3} c^{18} f^{3} e^{12 i e} - 245760 B a^{3} c^{18} f^{3} e^{12 i e}\right) e^{12 i f x}}{23592960 c^{24} f^{4}} & \text{for}\: 23592960 c^{24} f^{4} \neq 0 \\\frac{x \left(A a^{3} e^{12 i e} + 3 A a^{3} e^{10 i e} + 3 A a^{3} e^{8 i e} + A a^{3} e^{6 i e} - i B a^{3} e^{12 i e} - i B a^{3} e^{10 i e} + i B a^{3} e^{8 i e} + i B a^{3} e^{6 i e}\right)}{8 c^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-491520*I*A*a**3*c**18*f**3*exp(6*I*e) + 491520*B*a**3*c**18*f**3*exp(6*I*e))*exp(6*I*f*x) + (-1105920*I*A*a**3*c**18*f**3*exp(8*I*e) + 368640*B*a**3*c**18*f**3*exp(8*I*e))*exp(8*I*f*x) + (-884736*I*A*a**3*c**18*f**3*exp(10*I*e) - 294912*B*a**3*c**18*f**3*exp(10*I*e))*exp(10*I*f*x) + (-245760*I*A*a**3*c**18*f**3*exp(12*I*e) - 245760*B*a**3*c**18*f**3*exp(12*I*e))*exp(12*I*f*x))/(23592960*c**24*f**4), Ne(23592960*c**24*f**4, 0)), (x*(A*a**3*exp(12*I*e) + 3*A*a**3*exp(10*I*e) + 3*A*a**3*exp(8*I*e) + A*a**3*exp(6*I*e) - I*B*a**3*exp(12*I*e) - I*B*a**3*exp(10*I*e) + I*B*a**3*exp(8*I*e) + I*B*a**3*exp(6*I*e))/(8*c**6), True))","A",0
703,1,379,0,1.862089," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**7,x)","\begin{cases} - \frac{396361728 i A a^{3} c^{28} f^{4} e^{10 i e} e^{10 i f x} + \left(110100480 i A a^{3} c^{28} f^{4} e^{6 i e} - 110100480 B a^{3} c^{28} f^{4} e^{6 i e}\right) e^{6 i f x} + \left(330301440 i A a^{3} c^{28} f^{4} e^{8 i e} - 165150720 B a^{3} c^{28} f^{4} e^{8 i e}\right) e^{8 i f x} + \left(220200960 i A a^{3} c^{28} f^{4} e^{12 i e} + 110100480 B a^{3} c^{28} f^{4} e^{12 i e}\right) e^{12 i f x} + \left(47185920 i A a^{3} c^{28} f^{4} e^{14 i e} + 47185920 B a^{3} c^{28} f^{4} e^{14 i e}\right) e^{14 i f x}}{10569646080 c^{35} f^{5}} & \text{for}\: 10569646080 c^{35} f^{5} \neq 0 \\\frac{x \left(A a^{3} e^{14 i e} + 4 A a^{3} e^{12 i e} + 6 A a^{3} e^{10 i e} + 4 A a^{3} e^{8 i e} + A a^{3} e^{6 i e} - i B a^{3} e^{14 i e} - 2 i B a^{3} e^{12 i e} + 2 i B a^{3} e^{8 i e} + i B a^{3} e^{6 i e}\right)}{16 c^{7}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(396361728*I*A*a**3*c**28*f**4*exp(10*I*e)*exp(10*I*f*x) + (110100480*I*A*a**3*c**28*f**4*exp(6*I*e) - 110100480*B*a**3*c**28*f**4*exp(6*I*e))*exp(6*I*f*x) + (330301440*I*A*a**3*c**28*f**4*exp(8*I*e) - 165150720*B*a**3*c**28*f**4*exp(8*I*e))*exp(8*I*f*x) + (220200960*I*A*a**3*c**28*f**4*exp(12*I*e) + 110100480*B*a**3*c**28*f**4*exp(12*I*e))*exp(12*I*f*x) + (47185920*I*A*a**3*c**28*f**4*exp(14*I*e) + 47185920*B*a**3*c**28*f**4*exp(14*I*e))*exp(14*I*f*x))/(10569646080*c**35*f**5), Ne(10569646080*c**35*f**5, 0)), (x*(A*a**3*exp(14*I*e) + 4*A*a**3*exp(12*I*e) + 6*A*a**3*exp(10*I*e) + 4*A*a**3*exp(8*I*e) + A*a**3*exp(6*I*e) - I*B*a**3*exp(14*I*e) - 2*I*B*a**3*exp(12*I*e) + 2*I*B*a**3*exp(8*I*e) + I*B*a**3*exp(6*I*e))/(16*c**7), True))","A",0
704,1,498,0,1.718317," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**8,x)","\begin{cases} \frac{\left(- 1803886264320 i A a^{3} c^{40} f^{5} e^{6 i e} + 1803886264320 B a^{3} c^{40} f^{5} e^{6 i e}\right) e^{6 i f x} + \left(- 6764573491200 i A a^{3} c^{40} f^{5} e^{8 i e} + 4058744094720 B a^{3} c^{40} f^{5} e^{8 i e}\right) e^{8 i f x} + \left(- 10823317585920 i A a^{3} c^{40} f^{5} e^{10 i e} + 2164663517184 B a^{3} c^{40} f^{5} e^{10 i e}\right) e^{10 i f x} + \left(- 9019431321600 i A a^{3} c^{40} f^{5} e^{12 i e} - 1803886264320 B a^{3} c^{40} f^{5} e^{12 i e}\right) e^{12 i f x} + \left(- 3865470566400 i A a^{3} c^{40} f^{5} e^{14 i e} - 2319282339840 B a^{3} c^{40} f^{5} e^{14 i e}\right) e^{14 i f x} + \left(- 676457349120 i A a^{3} c^{40} f^{5} e^{16 i e} - 676457349120 B a^{3} c^{40} f^{5} e^{16 i e}\right) e^{16 i f x}}{346346162749440 c^{48} f^{6}} & \text{for}\: 346346162749440 c^{48} f^{6} \neq 0 \\\frac{x \left(A a^{3} e^{16 i e} + 5 A a^{3} e^{14 i e} + 10 A a^{3} e^{12 i e} + 10 A a^{3} e^{10 i e} + 5 A a^{3} e^{8 i e} + A a^{3} e^{6 i e} - i B a^{3} e^{16 i e} - 3 i B a^{3} e^{14 i e} - 2 i B a^{3} e^{12 i e} + 2 i B a^{3} e^{10 i e} + 3 i B a^{3} e^{8 i e} + i B a^{3} e^{6 i e}\right)}{32 c^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((-1803886264320*I*A*a**3*c**40*f**5*exp(6*I*e) + 1803886264320*B*a**3*c**40*f**5*exp(6*I*e))*exp(6*I*f*x) + (-6764573491200*I*A*a**3*c**40*f**5*exp(8*I*e) + 4058744094720*B*a**3*c**40*f**5*exp(8*I*e))*exp(8*I*f*x) + (-10823317585920*I*A*a**3*c**40*f**5*exp(10*I*e) + 2164663517184*B*a**3*c**40*f**5*exp(10*I*e))*exp(10*I*f*x) + (-9019431321600*I*A*a**3*c**40*f**5*exp(12*I*e) - 1803886264320*B*a**3*c**40*f**5*exp(12*I*e))*exp(12*I*f*x) + (-3865470566400*I*A*a**3*c**40*f**5*exp(14*I*e) - 2319282339840*B*a**3*c**40*f**5*exp(14*I*e))*exp(14*I*f*x) + (-676457349120*I*A*a**3*c**40*f**5*exp(16*I*e) - 676457349120*B*a**3*c**40*f**5*exp(16*I*e))*exp(16*I*f*x))/(346346162749440*c**48*f**6), Ne(346346162749440*c**48*f**6, 0)), (x*(A*a**3*exp(16*I*e) + 5*A*a**3*exp(14*I*e) + 10*A*a**3*exp(12*I*e) + 10*A*a**3*exp(10*I*e) + 5*A*a**3*exp(8*I*e) + A*a**3*exp(6*I*e) - I*B*a**3*exp(16*I*e) - 3*I*B*a**3*exp(14*I*e) - 2*I*B*a**3*exp(12*I*e) + 2*I*B*a**3*exp(10*I*e) + 3*I*B*a**3*exp(8*I*e) + I*B*a**3*exp(6*I*e))/(32*c**8), True))","A",0
705,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{A \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{B \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*(-I*c*tan(e + f*x) + c)**n/(tan(e + f*x) - I), x) + Integral(B*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
706,1,340,0,1.092061," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e)),x)","\frac{- 30 A c^{4} - 74 i B c^{4} + \left(- 54 A c^{4} e^{2 i e} - 114 i B c^{4} e^{2 i e}\right) e^{2 i f x} + \left(- 24 A c^{4} e^{4 i e} - 48 i B c^{4} e^{4 i e}\right) e^{4 i f x}}{3 i a f e^{6 i e} e^{6 i f x} + 9 i a f e^{4 i e} e^{4 i f x} + 9 i a f e^{2 i e} e^{2 i f x} + 3 i a f} + \begin{cases} - \frac{\left(- 4 i A c^{4} + 4 B c^{4}\right) e^{- 2 i e} e^{- 2 i f x}}{a f} & \text{for}\: a f e^{2 i e} \neq 0 \\x \left(- \frac{- 24 A c^{4} - 40 i B c^{4}}{a} + \frac{i \left(24 i A c^{4} e^{2 i e} - 8 i A c^{4} - 40 B c^{4} e^{2 i e} + 8 B c^{4}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{4 i c^{4} \left(3 A + 5 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} - \frac{x \left(24 A c^{4} + 40 i B c^{4}\right)}{a}"," ",0,"(-30*A*c**4 - 74*I*B*c**4 + (-54*A*c**4*exp(2*I*e) - 114*I*B*c**4*exp(2*I*e))*exp(2*I*f*x) + (-24*A*c**4*exp(4*I*e) - 48*I*B*c**4*exp(4*I*e))*exp(4*I*f*x))/(3*I*a*f*exp(6*I*e)*exp(6*I*f*x) + 9*I*a*f*exp(4*I*e)*exp(4*I*f*x) + 9*I*a*f*exp(2*I*e)*exp(2*I*f*x) + 3*I*a*f) + Piecewise((-(-4*I*A*c**4 + 4*B*c**4)*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(-(-24*A*c**4 - 40*I*B*c**4)/a + I*(24*I*A*c**4*exp(2*I*e) - 8*I*A*c**4 - 40*B*c**4*exp(2*I*e) + 8*B*c**4)*exp(-2*I*e)/a), True)) - 4*I*c**4*(3*A + 5*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) - x*(24*A*c**4 + 40*I*B*c**4)/a","A",0
707,1,269,0,0.952719," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e)),x)","\frac{- 2 i A c^{3} + 8 B c^{3} + \left(- 2 i A c^{3} e^{2 i e} + 6 B c^{3} e^{2 i e}\right) e^{2 i f x}}{- a f e^{4 i e} e^{4 i f x} - 2 a f e^{2 i e} e^{2 i f x} - a f} + \begin{cases} - \frac{\left(- 2 i A c^{3} + 2 B c^{3}\right) e^{- 2 i e} e^{- 2 i f x}}{a f} & \text{for}\: a f e^{2 i e} \neq 0 \\x \left(- \frac{- 8 A c^{3} - 16 i B c^{3}}{a} + \frac{i \left(8 i A c^{3} e^{2 i e} - 4 i A c^{3} - 16 B c^{3} e^{2 i e} + 4 B c^{3}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{4 i c^{3} \left(A + 2 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} - \frac{x \left(8 A c^{3} + 16 i B c^{3}\right)}{a}"," ",0,"(-2*I*A*c**3 + 8*B*c**3 + (-2*I*A*c**3*exp(2*I*e) + 6*B*c**3*exp(2*I*e))*exp(2*I*f*x))/(-a*f*exp(4*I*e)*exp(4*I*f*x) - 2*a*f*exp(2*I*e)*exp(2*I*f*x) - a*f) + Piecewise((-(-2*I*A*c**3 + 2*B*c**3)*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(-(-8*A*c**3 - 16*I*B*c**3)/a + I*(8*I*A*c**3*exp(2*I*e) - 4*I*A*c**3 - 16*B*c**3*exp(2*I*e) + 4*B*c**3)*exp(-2*I*e)/a), True)) - 4*I*c**3*(A + 2*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) - x*(8*A*c**3 + 16*I*B*c**3)/a","A",0
708,1,197,0,0.732468," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e)),x)","\frac{2 B c^{2}}{- a f e^{2 i e} e^{2 i f x} - a f} + \begin{cases} - \frac{\left(- i A c^{2} + B c^{2}\right) e^{- 2 i e} e^{- 2 i f x}}{a f} & \text{for}\: a f e^{2 i e} \neq 0 \\x \left(- \frac{- 2 A c^{2} - 6 i B c^{2}}{a} + \frac{i \left(2 i A c^{2} e^{2 i e} - 2 i A c^{2} - 6 B c^{2} e^{2 i e} + 2 B c^{2}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{i c^{2} \left(A + 3 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} - \frac{x \left(2 A c^{2} + 6 i B c^{2}\right)}{a}"," ",0,"2*B*c**2/(-a*f*exp(2*I*e)*exp(2*I*f*x) - a*f) + Piecewise((-(-I*A*c**2 + B*c**2)*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(-(-2*A*c**2 - 6*I*B*c**2)/a + I*(2*I*A*c**2*exp(2*I*e) - 2*I*A*c**2 - 6*B*c**2*exp(2*I*e) + 2*B*c**2)*exp(-2*I*e)/a), True)) - I*c**2*(A + 3*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) - x*(2*A*c**2 + 6*I*B*c**2)/a","A",0
709,1,116,0,0.385991," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","- \frac{2 i B c x}{a} + \frac{B c \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} + \begin{cases} - \frac{\left(- i A c + B c\right) e^{- 2 i e} e^{- 2 i f x}}{2 a f} & \text{for}\: 2 a f e^{2 i e} \neq 0 \\x \left(\frac{2 i B c}{a} + \frac{i \left(- i A c - 2 B c e^{2 i e} + B c\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases}"," ",0,"-2*I*B*c*x/a + B*c*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) + Piecewise((-(-I*A*c + B*c)*exp(-2*I*e)*exp(-2*I*f*x)/(2*a*f), Ne(2*a*f*exp(2*I*e), 0)), (x*(2*I*B*c/a + I*(-I*A*c - 2*B*c*exp(2*I*e) + B*c)*exp(-2*I*e)/a), True))","A",0
710,1,90,0,0.254379," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\begin{cases} - \frac{\left(- i A + B\right) e^{- 2 i e} e^{- 2 i f x}}{4 a f} & \text{for}\: 4 a f e^{2 i e} \neq 0 \\x \left(- \frac{A - i B}{2 a} + \frac{\left(A e^{2 i e} + A - i B e^{2 i e} + i B\right) e^{- 2 i e}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{2 a}"," ",0,"Piecewise((-(-I*A + B)*exp(-2*I*e)*exp(-2*I*f*x)/(4*a*f), Ne(4*a*f*exp(2*I*e), 0)), (x*(-(A - I*B)/(2*a) + (A*exp(2*I*e) + A - I*B*exp(2*I*e) + I*B)*exp(-2*I*e)/(2*a)), True)) - x*(-A + I*B)/(2*a)","A",0
711,1,167,0,0.367702," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\frac{A x}{2 a c} + \begin{cases} \frac{\left(\left(8 i A a c f - 8 B a c f\right) e^{- 2 i f x} + \left(- 8 i A a c f e^{4 i e} - 8 B a c f e^{4 i e}\right) e^{2 i f x}\right) e^{- 2 i e}}{64 a^{2} c^{2} f^{2}} & \text{for}\: 64 a^{2} c^{2} f^{2} e^{2 i e} \neq 0 \\x \left(- \frac{A}{2 a c} + \frac{\left(A e^{4 i e} + 2 A e^{2 i e} + A - i B e^{4 i e} + i B\right) e^{- 2 i e}}{4 a c}\right) & \text{otherwise} \end{cases}"," ",0,"A*x/(2*a*c) + Piecewise((((8*I*A*a*c*f - 8*B*a*c*f)*exp(-2*I*f*x) + (-8*I*A*a*c*f*exp(4*I*e) - 8*B*a*c*f*exp(4*I*e))*exp(2*I*f*x))*exp(-2*I*e)/(64*a**2*c**2*f**2), Ne(64*a**2*c**2*f**2*exp(2*I*e), 0)), (x*(-A/(2*a*c) + (A*exp(4*I*e) + 2*A*exp(2*I*e) + A - I*B*exp(4*I*e) + I*B)*exp(-2*I*e)/(4*a*c)), True))","A",0
712,1,286,0,0.522943," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} - \frac{\left(\left(- 512 i A a^{2} c^{4} f^{2} + 512 B a^{2} c^{4} f^{2}\right) e^{- 2 i f x} + \left(1536 i A a^{2} c^{4} f^{2} e^{4 i e} + 512 B a^{2} c^{4} f^{2} e^{4 i e}\right) e^{2 i f x} + \left(256 i A a^{2} c^{4} f^{2} e^{6 i e} + 256 B a^{2} c^{4} f^{2} e^{6 i e}\right) e^{4 i f x}\right) e^{- 2 i e}}{8192 a^{3} c^{6} f^{3}} & \text{for}\: 8192 a^{3} c^{6} f^{3} e^{2 i e} \neq 0 \\x \left(- \frac{3 A + i B}{8 a c^{2}} + \frac{\left(A e^{6 i e} + 3 A e^{4 i e} + 3 A e^{2 i e} + A - i B e^{6 i e} - i B e^{4 i e} + i B e^{2 i e} + i B\right) e^{- 2 i e}}{8 a c^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 3 A - i B\right)}{8 a c^{2}}"," ",0,"Piecewise((-((-512*I*A*a**2*c**4*f**2 + 512*B*a**2*c**4*f**2)*exp(-2*I*f*x) + (1536*I*A*a**2*c**4*f**2*exp(4*I*e) + 512*B*a**2*c**4*f**2*exp(4*I*e))*exp(2*I*f*x) + (256*I*A*a**2*c**4*f**2*exp(6*I*e) + 256*B*a**2*c**4*f**2*exp(6*I*e))*exp(4*I*f*x))*exp(-2*I*e)/(8192*a**3*c**6*f**3), Ne(8192*a**3*c**6*f**3*exp(2*I*e), 0)), (x*(-(3*A + I*B)/(8*a*c**2) + (A*exp(6*I*e) + 3*A*exp(4*I*e) + 3*A*exp(2*I*e) + A - I*B*exp(6*I*e) - I*B*exp(4*I*e) + I*B*exp(2*I*e) + I*B)*exp(-2*I*e)/(8*a*c**2)), True)) - x*(-3*A - I*B)/(8*a*c**2)","A",0
713,1,332,0,0.689855," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(- 294912 i A a^{3} c^{9} f^{3} e^{4 i e} e^{2 i f x} + \left(49152 i A a^{3} c^{9} f^{3} - 49152 B a^{3} c^{9} f^{3}\right) e^{- 2 i f x} + \left(- 98304 i A a^{3} c^{9} f^{3} e^{6 i e} - 49152 B a^{3} c^{9} f^{3} e^{6 i e}\right) e^{4 i f x} + \left(- 16384 i A a^{3} c^{9} f^{3} e^{8 i e} - 16384 B a^{3} c^{9} f^{3} e^{8 i e}\right) e^{6 i f x}\right) e^{- 2 i e}}{1572864 a^{4} c^{12} f^{4}} & \text{for}\: 1572864 a^{4} c^{12} f^{4} e^{2 i e} \neq 0 \\x \left(- \frac{2 A + i B}{8 a c^{3}} + \frac{\left(A e^{8 i e} + 4 A e^{6 i e} + 6 A e^{4 i e} + 4 A e^{2 i e} + A - i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{2 i e} + i B\right) e^{- 2 i e}}{16 a c^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 2 A - i B\right)}{8 a c^{3}}"," ",0,"Piecewise(((-294912*I*A*a**3*c**9*f**3*exp(4*I*e)*exp(2*I*f*x) + (49152*I*A*a**3*c**9*f**3 - 49152*B*a**3*c**9*f**3)*exp(-2*I*f*x) + (-98304*I*A*a**3*c**9*f**3*exp(6*I*e) - 49152*B*a**3*c**9*f**3*exp(6*I*e))*exp(4*I*f*x) + (-16384*I*A*a**3*c**9*f**3*exp(8*I*e) - 16384*B*a**3*c**9*f**3*exp(8*I*e))*exp(6*I*f*x))*exp(-2*I*e)/(1572864*a**4*c**12*f**4), Ne(1572864*a**4*c**12*f**4*exp(2*I*e), 0)), (x*(-(2*A + I*B)/(8*a*c**3) + (A*exp(8*I*e) + 4*A*exp(6*I*e) + 6*A*exp(4*I*e) + 4*A*exp(2*I*e) + A - I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(2*I*e) + I*B)*exp(-2*I*e)/(16*a*c**3)), True)) - x*(-2*A - I*B)/(8*a*c**3)","A",0
714,1,439,0,0.789765," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{\left(\left(- 100663296 i A a^{4} c^{16} f^{4} + 100663296 B a^{4} c^{16} f^{4}\right) e^{- 2 i f x} + \left(1006632960 i A a^{4} c^{16} f^{4} e^{4 i e} - 201326592 B a^{4} c^{16} f^{4} e^{4 i e}\right) e^{2 i f x} + \left(503316480 i A a^{4} c^{16} f^{4} e^{6 i e} + 100663296 B a^{4} c^{16} f^{4} e^{6 i e}\right) e^{4 i f x} + \left(167772160 i A a^{4} c^{16} f^{4} e^{8 i e} + 100663296 B a^{4} c^{16} f^{4} e^{8 i e}\right) e^{6 i f x} + \left(25165824 i A a^{4} c^{16} f^{4} e^{10 i e} + 25165824 B a^{4} c^{16} f^{4} e^{10 i e}\right) e^{8 i f x}\right) e^{- 2 i e}}{6442450944 a^{5} c^{20} f^{5}} & \text{for}\: 6442450944 a^{5} c^{20} f^{5} e^{2 i e} \neq 0 \\x \left(- \frac{5 A + 3 i B}{32 a c^{4}} + \frac{\left(A e^{10 i e} + 5 A e^{8 i e} + 10 A e^{6 i e} + 10 A e^{4 i e} + 5 A e^{2 i e} + A - i B e^{10 i e} - 3 i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{4 i e} + 3 i B e^{2 i e} + i B\right) e^{- 2 i e}}{32 a c^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 5 A - 3 i B\right)}{32 a c^{4}}"," ",0,"Piecewise((-((-100663296*I*A*a**4*c**16*f**4 + 100663296*B*a**4*c**16*f**4)*exp(-2*I*f*x) + (1006632960*I*A*a**4*c**16*f**4*exp(4*I*e) - 201326592*B*a**4*c**16*f**4*exp(4*I*e))*exp(2*I*f*x) + (503316480*I*A*a**4*c**16*f**4*exp(6*I*e) + 100663296*B*a**4*c**16*f**4*exp(6*I*e))*exp(4*I*f*x) + (167772160*I*A*a**4*c**16*f**4*exp(8*I*e) + 100663296*B*a**4*c**16*f**4*exp(8*I*e))*exp(6*I*f*x) + (25165824*I*A*a**4*c**16*f**4*exp(10*I*e) + 25165824*B*a**4*c**16*f**4*exp(10*I*e))*exp(8*I*f*x))*exp(-2*I*e)/(6442450944*a**5*c**20*f**5), Ne(6442450944*a**5*c**20*f**5*exp(2*I*e), 0)), (x*(-(5*A + 3*I*B)/(32*a*c**4) + (A*exp(10*I*e) + 5*A*exp(8*I*e) + 10*A*exp(6*I*e) + 10*A*exp(4*I*e) + 5*A*exp(2*I*e) + A - I*B*exp(10*I*e) - 3*I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(4*I*e) + 3*I*B*exp(2*I*e) + I*B)*exp(-2*I*e)/(32*a*c**4)), True)) - x*(-5*A - 3*I*B)/(32*a*c**4)","A",0
715,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{A \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{B \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*(-I*c*tan(e + f*x) + c)**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(B*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
716,1,461,0,1.486204," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**5/(a+I*a*tan(f*x+e))**2,x)","\frac{- 42 A c^{5} - 146 i B c^{5} + \left(- 78 A c^{5} e^{2 i e} - 246 i B c^{5} e^{2 i e}\right) e^{2 i f x} + \left(- 36 A c^{5} e^{4 i e} - 108 i B c^{5} e^{4 i e}\right) e^{4 i f x}}{- 3 i a^{2} f e^{6 i e} e^{6 i f x} - 9 i a^{2} f e^{4 i e} e^{4 i f x} - 9 i a^{2} f e^{2 i e} e^{2 i f x} - 3 i a^{2} f} + \begin{cases} \frac{\left(\left(2 i A a^{2} c^{5} f e^{2 i e} - 2 B a^{2} c^{5} f e^{2 i e}\right) e^{- 4 i f x} + \left(- 12 i A a^{2} c^{5} f e^{4 i e} + 20 B a^{2} c^{5} f e^{4 i e}\right) e^{- 2 i f x}\right) e^{- 6 i e}}{a^{4} f^{2}} & \text{for}\: a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{48 A c^{5} + 112 i B c^{5}}{a^{2}} + \frac{i \left(- 48 i A c^{5} e^{4 i e} + 24 i A c^{5} e^{2 i e} - 8 i A c^{5} + 112 B c^{5} e^{4 i e} - 40 B c^{5} e^{2 i e} + 8 B c^{5}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases} + \frac{8 i c^{5} \left(3 A + 7 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f} - \frac{x \left(- 48 A c^{5} - 112 i B c^{5}\right)}{a^{2}}"," ",0,"(-42*A*c**5 - 146*I*B*c**5 + (-78*A*c**5*exp(2*I*e) - 246*I*B*c**5*exp(2*I*e))*exp(2*I*f*x) + (-36*A*c**5*exp(4*I*e) - 108*I*B*c**5*exp(4*I*e))*exp(4*I*f*x))/(-3*I*a**2*f*exp(6*I*e)*exp(6*I*f*x) - 9*I*a**2*f*exp(4*I*e)*exp(4*I*f*x) - 9*I*a**2*f*exp(2*I*e)*exp(2*I*f*x) - 3*I*a**2*f) + Piecewise((((2*I*A*a**2*c**5*f*exp(2*I*e) - 2*B*a**2*c**5*f*exp(2*I*e))*exp(-4*I*f*x) + (-12*I*A*a**2*c**5*f*exp(4*I*e) + 20*B*a**2*c**5*f*exp(4*I*e))*exp(-2*I*f*x))*exp(-6*I*e)/(a**4*f**2), Ne(a**4*f**2*exp(6*I*e), 0)), (x*(-(48*A*c**5 + 112*I*B*c**5)/a**2 + I*(-48*I*A*c**5*exp(4*I*e) + 24*I*A*c**5*exp(2*I*e) - 8*I*A*c**5 + 112*B*c**5*exp(4*I*e) - 40*B*c**5*exp(2*I*e) + 8*B*c**5)*exp(-4*I*e)/a**2), True)) + 8*I*c**5*(3*A + 7*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f) - x*(-48*A*c**5 - 112*I*B*c**5)/a**2","A",0
717,1,382,0,1.311235," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**2,x)","\frac{2 i A c^{4} - 12 B c^{4} + \left(2 i A c^{4} e^{2 i e} - 10 B c^{4} e^{2 i e}\right) e^{2 i f x}}{- a^{2} f e^{4 i e} e^{4 i f x} - 2 a^{2} f e^{2 i e} e^{2 i f x} - a^{2} f} + \begin{cases} \frac{\left(\left(i A a^{2} c^{4} f e^{2 i e} - B a^{2} c^{4} f e^{2 i e}\right) e^{- 4 i f x} + \left(- 4 i A a^{2} c^{4} f e^{4 i e} + 8 B a^{2} c^{4} f e^{4 i e}\right) e^{- 2 i f x}\right) e^{- 6 i e}}{a^{4} f^{2}} & \text{for}\: a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{12 A c^{4} + 36 i B c^{4}}{a^{2}} + \frac{i \left(- 12 i A c^{4} e^{4 i e} + 8 i A c^{4} e^{2 i e} - 4 i A c^{4} + 36 B c^{4} e^{4 i e} - 16 B c^{4} e^{2 i e} + 4 B c^{4}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases} + \frac{6 i c^{4} \left(A + 3 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f} - \frac{x \left(- 12 A c^{4} - 36 i B c^{4}\right)}{a^{2}}"," ",0,"(2*I*A*c**4 - 12*B*c**4 + (2*I*A*c**4*exp(2*I*e) - 10*B*c**4*exp(2*I*e))*exp(2*I*f*x))/(-a**2*f*exp(4*I*e)*exp(4*I*f*x) - 2*a**2*f*exp(2*I*e)*exp(2*I*f*x) - a**2*f) + Piecewise((((I*A*a**2*c**4*f*exp(2*I*e) - B*a**2*c**4*f*exp(2*I*e))*exp(-4*I*f*x) + (-4*I*A*a**2*c**4*f*exp(4*I*e) + 8*B*a**2*c**4*f*exp(4*I*e))*exp(-2*I*f*x))*exp(-6*I*e)/(a**4*f**2), Ne(a**4*f**2*exp(6*I*e), 0)), (x*(-(12*A*c**4 + 36*I*B*c**4)/a**2 + I*(-12*I*A*c**4*exp(4*I*e) + 8*I*A*c**4*exp(2*I*e) - 4*I*A*c**4 + 36*B*c**4*exp(4*I*e) - 16*B*c**4*exp(2*I*e) + 4*B*c**4)*exp(-4*I*e)/a**2), True)) + 6*I*c**4*(A + 3*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f) - x*(-12*A*c**4 - 36*I*B*c**4)/a**2","A",0
718,1,316,0,1.043385," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**2,x)","- \frac{2 B c^{3}}{- a^{2} f e^{2 i e} e^{2 i f x} - a^{2} f} + \begin{cases} \frac{\left(\left(i A a^{2} c^{3} f e^{2 i e} - B a^{2} c^{3} f e^{2 i e}\right) e^{- 4 i f x} + \left(- 2 i A a^{2} c^{3} f e^{4 i e} + 6 B a^{2} c^{3} f e^{4 i e}\right) e^{- 2 i f x}\right) e^{- 6 i e}}{2 a^{4} f^{2}} & \text{for}\: 2 a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{2 A c^{3} + 10 i B c^{3}}{a^{2}} + \frac{i \left(- 2 i A c^{3} e^{4 i e} + 2 i A c^{3} e^{2 i e} - 2 i A c^{3} + 10 B c^{3} e^{4 i e} - 6 B c^{3} e^{2 i e} + 2 B c^{3}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases} + \frac{i c^{3} \left(A + 5 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f} - \frac{x \left(- 2 A c^{3} - 10 i B c^{3}\right)}{a^{2}}"," ",0,"-2*B*c**3/(-a**2*f*exp(2*I*e)*exp(2*I*f*x) - a**2*f) + Piecewise((((I*A*a**2*c**3*f*exp(2*I*e) - B*a**2*c**3*f*exp(2*I*e))*exp(-4*I*f*x) + (-2*I*A*a**2*c**3*f*exp(4*I*e) + 6*B*a**2*c**3*f*exp(4*I*e))*exp(-2*I*f*x))*exp(-6*I*e)/(2*a**4*f**2), Ne(2*a**4*f**2*exp(6*I*e), 0)), (x*(-(2*A*c**3 + 10*I*B*c**3)/a**2 + I*(-2*I*A*c**3*exp(4*I*e) + 2*I*A*c**3*exp(2*I*e) - 2*I*A*c**3 + 10*B*c**3*exp(4*I*e) - 6*B*c**3*exp(2*I*e) + 2*B*c**3)*exp(-4*I*e)/a**2), True)) + I*c**3*(A + 5*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f) - x*(-2*A*c**3 - 10*I*B*c**3)/a**2","A",0
719,1,207,0,0.623590," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**2,x)","\frac{2 i B c^{2} x}{a^{2}} - \frac{B c^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f} + \begin{cases} - \frac{\left(- 4 B a^{2} c^{2} f e^{4 i e} e^{- 2 i f x} + \left(- i A a^{2} c^{2} f e^{2 i e} + B a^{2} c^{2} f e^{2 i e}\right) e^{- 4 i f x}\right) e^{- 6 i e}}{4 a^{4} f^{2}} & \text{for}\: 4 a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{2 i B c^{2}}{a^{2}} + \frac{i \left(- i A c^{2} + 2 B c^{2} e^{4 i e} - 2 B c^{2} e^{2 i e} + B c^{2}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases}"," ",0,"2*I*B*c**2*x/a**2 - B*c**2*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f) + Piecewise((-(-4*B*a**2*c**2*f*exp(4*I*e)*exp(-2*I*f*x) + (-I*A*a**2*c**2*f*exp(2*I*e) + B*a**2*c**2*f*exp(2*I*e))*exp(-4*I*f*x))*exp(-6*I*e)/(4*a**4*f**2), Ne(4*a**4*f**2*exp(6*I*e), 0)), (x*(-2*I*B*c**2/a**2 + I*(-I*A*c**2 + 2*B*c**2*exp(4*I*e) - 2*B*c**2*exp(2*I*e) + B*c**2)*exp(-4*I*e)/a**2), True))","A",0
720,1,160,0,0.380911," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(\left(4 i A a^{2} c f e^{2 i e} - 4 B a^{2} c f e^{2 i e}\right) e^{- 4 i f x} + \left(8 i A a^{2} c f e^{4 i e} + 8 B a^{2} c f e^{4 i e}\right) e^{- 2 i f x}\right) e^{- 6 i e}}{32 a^{4} f^{2}} & \text{for}\: 32 a^{4} f^{2} e^{6 i e} \neq 0 \\\frac{x \left(A c e^{2 i e} + A c - i B c e^{2 i e} + i B c\right) e^{- 4 i e}}{2 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((4*I*A*a**2*c*f*exp(2*I*e) - 4*B*a**2*c*f*exp(2*I*e))*exp(-4*I*f*x) + (8*I*A*a**2*c*f*exp(4*I*e) + 8*B*a**2*c*f*exp(4*I*e))*exp(-2*I*f*x))*exp(-6*I*e)/(32*a**4*f**2), Ne(32*a**4*f**2*exp(6*I*e), 0)), (x*(A*c*exp(2*I*e) + A*c - I*B*c*exp(2*I*e) + I*B*c)*exp(-4*I*e)/(2*a**2), True))","A",0
721,1,163,0,0.363232," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(16 i A a^{2} f e^{4 i e} e^{- 2 i f x} + \left(4 i A a^{2} f e^{2 i e} - 4 B a^{2} f e^{2 i e}\right) e^{- 4 i f x}\right) e^{- 6 i e}}{64 a^{4} f^{2}} & \text{for}\: 64 a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{A - i B}{4 a^{2}} + \frac{\left(A e^{4 i e} + 2 A e^{2 i e} + A - i B e^{4 i e} + i B\right) e^{- 4 i e}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{4 a^{2}}"," ",0,"Piecewise(((16*I*A*a**2*f*exp(4*I*e)*exp(-2*I*f*x) + (4*I*A*a**2*f*exp(2*I*e) - 4*B*a**2*f*exp(2*I*e))*exp(-4*I*f*x))*exp(-6*I*e)/(64*a**4*f**2), Ne(64*a**4*f**2*exp(6*I*e), 0)), (x*(-(A - I*B)/(4*a**2) + (A*exp(4*I*e) + 2*A*exp(2*I*e) + A - I*B*exp(4*I*e) + I*B)*exp(-4*I*e)/(4*a**2)), True)) - x*(-A + I*B)/(4*a**2)","A",0
722,1,298,0,0.524608," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e)),x)","\begin{cases} - \frac{\left(\left(- 256 i A a^{4} c^{2} f^{2} e^{2 i e} + 256 B a^{4} c^{2} f^{2} e^{2 i e}\right) e^{- 4 i f x} + \left(- 1536 i A a^{4} c^{2} f^{2} e^{4 i e} + 512 B a^{4} c^{2} f^{2} e^{4 i e}\right) e^{- 2 i f x} + \left(512 i A a^{4} c^{2} f^{2} e^{8 i e} + 512 B a^{4} c^{2} f^{2} e^{8 i e}\right) e^{2 i f x}\right) e^{- 6 i e}}{8192 a^{6} c^{3} f^{3}} & \text{for}\: 8192 a^{6} c^{3} f^{3} e^{6 i e} \neq 0 \\x \left(- \frac{3 A - i B}{8 a^{2} c} + \frac{\left(A e^{6 i e} + 3 A e^{4 i e} + 3 A e^{2 i e} + A - i B e^{6 i e} - i B e^{4 i e} + i B e^{2 i e} + i B\right) e^{- 4 i e}}{8 a^{2} c}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 3 A + i B\right)}{8 a^{2} c}"," ",0,"Piecewise((-((-256*I*A*a**4*c**2*f**2*exp(2*I*e) + 256*B*a**4*c**2*f**2*exp(2*I*e))*exp(-4*I*f*x) + (-1536*I*A*a**4*c**2*f**2*exp(4*I*e) + 512*B*a**4*c**2*f**2*exp(4*I*e))*exp(-2*I*f*x) + (512*I*A*a**4*c**2*f**2*exp(8*I*e) + 512*B*a**4*c**2*f**2*exp(8*I*e))*exp(2*I*f*x))*exp(-6*I*e)/(8192*a**6*c**3*f**3), Ne(8192*a**6*c**3*f**3*exp(6*I*e), 0)), (x*(-(3*A - I*B)/(8*a**2*c) + (A*exp(6*I*e) + 3*A*exp(4*I*e) + 3*A*exp(2*I*e) + A - I*B*exp(6*I*e) - I*B*exp(4*I*e) + I*B*exp(2*I*e) + I*B)*exp(-4*I*e)/(8*a**2*c)), True)) - x*(-3*A + I*B)/(8*a**2*c)","A",0
723,1,362,0,0.733177," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**2,x)","\frac{3 A x}{8 a^{2} c^{2}} + \begin{cases} \frac{\left(\left(16384 i A a^{6} c^{6} f^{3} e^{2 i e} - 16384 B a^{6} c^{6} f^{3} e^{2 i e}\right) e^{- 4 i f x} + \left(131072 i A a^{6} c^{6} f^{3} e^{4 i e} - 65536 B a^{6} c^{6} f^{3} e^{4 i e}\right) e^{- 2 i f x} + \left(- 131072 i A a^{6} c^{6} f^{3} e^{8 i e} - 65536 B a^{6} c^{6} f^{3} e^{8 i e}\right) e^{2 i f x} + \left(- 16384 i A a^{6} c^{6} f^{3} e^{10 i e} - 16384 B a^{6} c^{6} f^{3} e^{10 i e}\right) e^{4 i f x}\right) e^{- 6 i e}}{1048576 a^{8} c^{8} f^{4}} & \text{for}\: 1048576 a^{8} c^{8} f^{4} e^{6 i e} \neq 0 \\x \left(- \frac{3 A}{8 a^{2} c^{2}} + \frac{\left(A e^{8 i e} + 4 A e^{6 i e} + 6 A e^{4 i e} + 4 A e^{2 i e} + A - i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{2 i e} + i B\right) e^{- 4 i e}}{16 a^{2} c^{2}}\right) & \text{otherwise} \end{cases}"," ",0,"3*A*x/(8*a**2*c**2) + Piecewise((((16384*I*A*a**6*c**6*f**3*exp(2*I*e) - 16384*B*a**6*c**6*f**3*exp(2*I*e))*exp(-4*I*f*x) + (131072*I*A*a**6*c**6*f**3*exp(4*I*e) - 65536*B*a**6*c**6*f**3*exp(4*I*e))*exp(-2*I*f*x) + (-131072*I*A*a**6*c**6*f**3*exp(8*I*e) - 65536*B*a**6*c**6*f**3*exp(8*I*e))*exp(2*I*f*x) + (-16384*I*A*a**6*c**6*f**3*exp(10*I*e) - 16384*B*a**6*c**6*f**3*exp(10*I*e))*exp(4*I*f*x))*exp(-6*I*e)/(1048576*a**8*c**8*f**4), Ne(1048576*a**8*c**8*f**4*exp(6*I*e), 0)), (x*(-3*A/(8*a**2*c**2) + (A*exp(8*I*e) + 4*A*exp(6*I*e) + 6*A*exp(4*I*e) + 4*A*exp(2*I*e) + A - I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(2*I*e) + I*B)*exp(-4*I*e)/(16*a**2*c**2)), True))","A",0
724,1,454,0,0.872319," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(\left(- 50331648 i A a^{8} c^{12} f^{4} e^{2 i e} + 50331648 B a^{8} c^{12} f^{4} e^{2 i e}\right) e^{- 4 i f x} + \left(- 503316480 i A a^{8} c^{12} f^{4} e^{4 i e} + 301989888 B a^{8} c^{12} f^{4} e^{4 i e}\right) e^{- 2 i f x} + \left(1006632960 i A a^{8} c^{12} f^{4} e^{8 i e} + 201326592 B a^{8} c^{12} f^{4} e^{8 i e}\right) e^{2 i f x} + \left(251658240 i A a^{8} c^{12} f^{4} e^{10 i e} + 150994944 B a^{8} c^{12} f^{4} e^{10 i e}\right) e^{4 i f x} + \left(33554432 i A a^{8} c^{12} f^{4} e^{12 i e} + 33554432 B a^{8} c^{12} f^{4} e^{12 i e}\right) e^{6 i f x}\right) e^{- 6 i e}}{6442450944 a^{10} c^{15} f^{5}} & \text{for}\: 6442450944 a^{10} c^{15} f^{5} e^{6 i e} \neq 0 \\x \left(- \frac{5 A + i B}{16 a^{2} c^{3}} + \frac{\left(A e^{10 i e} + 5 A e^{8 i e} + 10 A e^{6 i e} + 10 A e^{4 i e} + 5 A e^{2 i e} + A - i B e^{10 i e} - 3 i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{4 i e} + 3 i B e^{2 i e} + i B\right) e^{- 4 i e}}{32 a^{2} c^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 5 A - i B\right)}{16 a^{2} c^{3}}"," ",0,"Piecewise((-((-50331648*I*A*a**8*c**12*f**4*exp(2*I*e) + 50331648*B*a**8*c**12*f**4*exp(2*I*e))*exp(-4*I*f*x) + (-503316480*I*A*a**8*c**12*f**4*exp(4*I*e) + 301989888*B*a**8*c**12*f**4*exp(4*I*e))*exp(-2*I*f*x) + (1006632960*I*A*a**8*c**12*f**4*exp(8*I*e) + 201326592*B*a**8*c**12*f**4*exp(8*I*e))*exp(2*I*f*x) + (251658240*I*A*a**8*c**12*f**4*exp(10*I*e) + 150994944*B*a**8*c**12*f**4*exp(10*I*e))*exp(4*I*f*x) + (33554432*I*A*a**8*c**12*f**4*exp(12*I*e) + 33554432*B*a**8*c**12*f**4*exp(12*I*e))*exp(6*I*f*x))*exp(-6*I*e)/(6442450944*a**10*c**15*f**5), Ne(6442450944*a**10*c**15*f**5*exp(6*I*e), 0)), (x*(-(5*A + I*B)/(16*a**2*c**3) + (A*exp(10*I*e) + 5*A*exp(8*I*e) + 10*A*exp(6*I*e) + 10*A*exp(4*I*e) + 5*A*exp(2*I*e) + A - I*B*exp(10*I*e) - 3*I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(4*I*e) + 3*I*B*exp(2*I*e) + I*B)*exp(-4*I*e)/(32*a**2*c**3)), True)) - x*(-5*A - I*B)/(16*a**2*c**3)","A",0
725,1,502,0,1.224251," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{\left(- 2061584302080 i A a^{10} c^{20} f^{5} e^{8 i e} e^{2 i f x} + \left(51539607552 i A a^{10} c^{20} f^{5} e^{2 i e} - 51539607552 B a^{10} c^{20} f^{5} e^{2 i e}\right) e^{- 4 i f x} + \left(618475290624 i A a^{10} c^{20} f^{5} e^{4 i e} - 412316860416 B a^{10} c^{20} f^{5} e^{4 i e}\right) e^{- 2 i f x} + \left(- 773094113280 i A a^{10} c^{20} f^{5} e^{10 i e} - 257698037760 B a^{10} c^{20} f^{5} e^{10 i e}\right) e^{4 i f x} + \left(- 206158430208 i A a^{10} c^{20} f^{5} e^{12 i e} - 137438953472 B a^{10} c^{20} f^{5} e^{12 i e}\right) e^{6 i f x} + \left(- 25769803776 i A a^{10} c^{20} f^{5} e^{14 i e} - 25769803776 B a^{10} c^{20} f^{5} e^{14 i e}\right) e^{8 i f x}\right) e^{- 6 i e}}{13194139533312 a^{12} c^{24} f^{6}} & \text{for}\: 13194139533312 a^{12} c^{24} f^{6} e^{6 i e} \neq 0 \\x \left(- \frac{15 A + 5 i B}{64 a^{2} c^{4}} + \frac{\left(A e^{12 i e} + 6 A e^{10 i e} + 15 A e^{8 i e} + 20 A e^{6 i e} + 15 A e^{4 i e} + 6 A e^{2 i e} + A - i B e^{12 i e} - 4 i B e^{10 i e} - 5 i B e^{8 i e} + 5 i B e^{4 i e} + 4 i B e^{2 i e} + i B\right) e^{- 4 i e}}{64 a^{2} c^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 15 A - 5 i B\right)}{64 a^{2} c^{4}}"," ",0,"Piecewise(((-2061584302080*I*A*a**10*c**20*f**5*exp(8*I*e)*exp(2*I*f*x) + (51539607552*I*A*a**10*c**20*f**5*exp(2*I*e) - 51539607552*B*a**10*c**20*f**5*exp(2*I*e))*exp(-4*I*f*x) + (618475290624*I*A*a**10*c**20*f**5*exp(4*I*e) - 412316860416*B*a**10*c**20*f**5*exp(4*I*e))*exp(-2*I*f*x) + (-773094113280*I*A*a**10*c**20*f**5*exp(10*I*e) - 257698037760*B*a**10*c**20*f**5*exp(10*I*e))*exp(4*I*f*x) + (-206158430208*I*A*a**10*c**20*f**5*exp(12*I*e) - 137438953472*B*a**10*c**20*f**5*exp(12*I*e))*exp(6*I*f*x) + (-25769803776*I*A*a**10*c**20*f**5*exp(14*I*e) - 25769803776*B*a**10*c**20*f**5*exp(14*I*e))*exp(8*I*f*x))*exp(-6*I*e)/(13194139533312*a**12*c**24*f**6), Ne(13194139533312*a**12*c**24*f**6*exp(6*I*e), 0)), (x*(-(15*A + 5*I*B)/(64*a**2*c**4) + (A*exp(12*I*e) + 6*A*exp(10*I*e) + 15*A*exp(8*I*e) + 20*A*exp(6*I*e) + 15*A*exp(4*I*e) + 6*A*exp(2*I*e) + A - I*B*exp(12*I*e) - 4*I*B*exp(10*I*e) - 5*I*B*exp(8*I*e) + 5*I*B*exp(4*I*e) + 4*I*B*exp(2*I*e) + I*B)*exp(-4*I*e)/(64*a**2*c**4)), True)) - x*(-15*A - 5*I*B)/(64*a**2*c**4)","A",0
726,1,604,0,1.260517," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**5,x)","\begin{cases} - \frac{\left(\left(- 11258999068426240 i A a^{12} c^{30} f^{6} e^{2 i e} + 11258999068426240 B a^{12} c^{30} f^{6} e^{2 i e}\right) e^{- 4 i f x} + \left(- 157625986957967360 i A a^{12} c^{30} f^{6} e^{4 i e} + 112589990684262400 B a^{12} c^{30} f^{6} e^{4 i e}\right) e^{- 2 i f x} + \left(788129934789836800 i A a^{12} c^{30} f^{6} e^{8 i e} - 112589990684262400 B a^{12} c^{30} f^{6} e^{8 i e}\right) e^{2 i f x} + \left(394064967394918400 i A a^{12} c^{30} f^{6} e^{10 i e} + 56294995342131200 B a^{12} c^{30} f^{6} e^{10 i e}\right) e^{4 i f x} + \left(157625986957967360 i A a^{12} c^{30} f^{6} e^{12 i e} + 67553994410557440 B a^{12} c^{30} f^{6} e^{12 i e}\right) e^{6 i f x} + \left(39406496739491840 i A a^{12} c^{30} f^{6} e^{14 i e} + 28147497671065600 B a^{12} c^{30} f^{6} e^{14 i e}\right) e^{8 i f x} + \left(4503599627370496 i A a^{12} c^{30} f^{6} e^{16 i e} + 4503599627370496 B a^{12} c^{30} f^{6} e^{16 i e}\right) e^{10 i f x}\right) e^{- 6 i e}}{5764607523034234880 a^{14} c^{35} f^{7}} & \text{for}\: 5764607523034234880 a^{14} c^{35} f^{7} e^{6 i e} \neq 0 \\x \left(- \frac{21 A + 9 i B}{128 a^{2} c^{5}} + \frac{\left(A e^{14 i e} + 7 A e^{12 i e} + 21 A e^{10 i e} + 35 A e^{8 i e} + 35 A e^{6 i e} + 21 A e^{4 i e} + 7 A e^{2 i e} + A - i B e^{14 i e} - 5 i B e^{12 i e} - 9 i B e^{10 i e} - 5 i B e^{8 i e} + 5 i B e^{6 i e} + 9 i B e^{4 i e} + 5 i B e^{2 i e} + i B\right) e^{- 4 i e}}{128 a^{2} c^{5}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 21 A - 9 i B\right)}{128 a^{2} c^{5}}"," ",0,"Piecewise((-((-11258999068426240*I*A*a**12*c**30*f**6*exp(2*I*e) + 11258999068426240*B*a**12*c**30*f**6*exp(2*I*e))*exp(-4*I*f*x) + (-157625986957967360*I*A*a**12*c**30*f**6*exp(4*I*e) + 112589990684262400*B*a**12*c**30*f**6*exp(4*I*e))*exp(-2*I*f*x) + (788129934789836800*I*A*a**12*c**30*f**6*exp(8*I*e) - 112589990684262400*B*a**12*c**30*f**6*exp(8*I*e))*exp(2*I*f*x) + (394064967394918400*I*A*a**12*c**30*f**6*exp(10*I*e) + 56294995342131200*B*a**12*c**30*f**6*exp(10*I*e))*exp(4*I*f*x) + (157625986957967360*I*A*a**12*c**30*f**6*exp(12*I*e) + 67553994410557440*B*a**12*c**30*f**6*exp(12*I*e))*exp(6*I*f*x) + (39406496739491840*I*A*a**12*c**30*f**6*exp(14*I*e) + 28147497671065600*B*a**12*c**30*f**6*exp(14*I*e))*exp(8*I*f*x) + (4503599627370496*I*A*a**12*c**30*f**6*exp(16*I*e) + 4503599627370496*B*a**12*c**30*f**6*exp(16*I*e))*exp(10*I*f*x))*exp(-6*I*e)/(5764607523034234880*a**14*c**35*f**7), Ne(5764607523034234880*a**14*c**35*f**7*exp(6*I*e), 0)), (x*(-(21*A + 9*I*B)/(128*a**2*c**5) + (A*exp(14*I*e) + 7*A*exp(12*I*e) + 21*A*exp(10*I*e) + 35*A*exp(8*I*e) + 35*A*exp(6*I*e) + 21*A*exp(4*I*e) + 7*A*exp(2*I*e) + A - I*B*exp(14*I*e) - 5*I*B*exp(12*I*e) - 9*I*B*exp(10*I*e) - 5*I*B*exp(8*I*e) + 5*I*B*exp(6*I*e) + 9*I*B*exp(4*I*e) + 5*I*B*exp(2*I*e) + I*B)*exp(-4*I*e)/(128*a**2*c**5)), True)) - x*(-21*A - 9*I*B)/(128*a**2*c**5)","A",0
727,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{A \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \frac{B \left(- i c \tan{\left(e + f x \right)} + c\right)^{n} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*(-I*c*tan(e + f*x) + c)**n/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(B*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x))/a**3","F",0
728,1,476,0,1.817542," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**5/(a+I*a*tan(f*x+e))**3,x)","\frac{2 i A c^{5} - 16 B c^{5} + \left(2 i A c^{5} e^{2 i e} - 14 B c^{5} e^{2 i e}\right) e^{2 i f x}}{a^{3} f e^{4 i e} e^{4 i f x} + 2 a^{3} f e^{2 i e} e^{2 i f x} + a^{3} f} + \begin{cases} - \frac{\left(\left(- 2 i A a^{6} c^{5} f^{2} e^{6 i e} + 2 B a^{6} c^{5} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(6 i A a^{6} c^{5} f^{2} e^{8 i e} - 12 B a^{6} c^{5} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 18 i A a^{6} c^{5} f^{2} e^{10 i e} + 54 B a^{6} c^{5} f^{2} e^{10 i e}\right) e^{- 2 i f x}\right) e^{- 12 i e}}{3 a^{9} f^{3}} & \text{for}\: 3 a^{9} f^{3} e^{12 i e} \neq 0 \\x \left(- \frac{- 16 A c^{5} - 64 i B c^{5}}{a^{3}} + \frac{i \left(16 i A c^{5} e^{6 i e} - 12 i A c^{5} e^{4 i e} + 8 i A c^{5} e^{2 i e} - 4 i A c^{5} - 64 B c^{5} e^{6 i e} + 36 B c^{5} e^{4 i e} - 16 B c^{5} e^{2 i e} + 4 B c^{5}\right) e^{- 6 i e}}{a^{3}}\right) & \text{otherwise} \end{cases} - \frac{8 i c^{5} \left(A + 4 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{3} f} - \frac{x \left(16 A c^{5} + 64 i B c^{5}\right)}{a^{3}}"," ",0,"(2*I*A*c**5 - 16*B*c**5 + (2*I*A*c**5*exp(2*I*e) - 14*B*c**5*exp(2*I*e))*exp(2*I*f*x))/(a**3*f*exp(4*I*e)*exp(4*I*f*x) + 2*a**3*f*exp(2*I*e)*exp(2*I*f*x) + a**3*f) + Piecewise((-((-2*I*A*a**6*c**5*f**2*exp(6*I*e) + 2*B*a**6*c**5*f**2*exp(6*I*e))*exp(-6*I*f*x) + (6*I*A*a**6*c**5*f**2*exp(8*I*e) - 12*B*a**6*c**5*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-18*I*A*a**6*c**5*f**2*exp(10*I*e) + 54*B*a**6*c**5*f**2*exp(10*I*e))*exp(-2*I*f*x))*exp(-12*I*e)/(3*a**9*f**3), Ne(3*a**9*f**3*exp(12*I*e), 0)), (x*(-(-16*A*c**5 - 64*I*B*c**5)/a**3 + I*(16*I*A*c**5*exp(6*I*e) - 12*I*A*c**5*exp(4*I*e) + 8*I*A*c**5*exp(2*I*e) - 4*I*A*c**5 - 64*B*c**5*exp(6*I*e) + 36*B*c**5*exp(4*I*e) - 16*B*c**5*exp(2*I*e) + 4*B*c**5)*exp(-6*I*e)/a**3), True)) - 8*I*c**5*(A + 4*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a**3*f) - x*(16*A*c**5 + 64*I*B*c**5)/a**3","A",0
729,1,408,0,1.398220," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**3,x)","\frac{2 B c^{4}}{- a^{3} f e^{2 i e} e^{2 i f x} - a^{3} f} + \begin{cases} - \frac{\left(\left(- 2 i A a^{6} c^{4} f^{2} e^{6 i e} + 2 B a^{6} c^{4} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(3 i A a^{6} c^{4} f^{2} e^{8 i e} - 9 B a^{6} c^{4} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 6 i A a^{6} c^{4} f^{2} e^{10 i e} + 30 B a^{6} c^{4} f^{2} e^{10 i e}\right) e^{- 2 i f x}\right) e^{- 12 i e}}{6 a^{9} f^{3}} & \text{for}\: 6 a^{9} f^{3} e^{12 i e} \neq 0 \\x \left(- \frac{- 2 A c^{4} - 14 i B c^{4}}{a^{3}} + \frac{i \left(2 i A c^{4} e^{6 i e} - 2 i A c^{4} e^{4 i e} + 2 i A c^{4} e^{2 i e} - 2 i A c^{4} - 14 B c^{4} e^{6 i e} + 10 B c^{4} e^{4 i e} - 6 B c^{4} e^{2 i e} + 2 B c^{4}\right) e^{- 6 i e}}{a^{3}}\right) & \text{otherwise} \end{cases} - \frac{i c^{4} \left(A + 7 i B\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{3} f} - \frac{x \left(2 A c^{4} + 14 i B c^{4}\right)}{a^{3}}"," ",0,"2*B*c**4/(-a**3*f*exp(2*I*e)*exp(2*I*f*x) - a**3*f) + Piecewise((-((-2*I*A*a**6*c**4*f**2*exp(6*I*e) + 2*B*a**6*c**4*f**2*exp(6*I*e))*exp(-6*I*f*x) + (3*I*A*a**6*c**4*f**2*exp(8*I*e) - 9*B*a**6*c**4*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-6*I*A*a**6*c**4*f**2*exp(10*I*e) + 30*B*a**6*c**4*f**2*exp(10*I*e))*exp(-2*I*f*x))*exp(-12*I*e)/(6*a**9*f**3), Ne(6*a**9*f**3*exp(12*I*e), 0)), (x*(-(-2*A*c**4 - 14*I*B*c**4)/a**3 + I*(2*I*A*c**4*exp(6*I*e) - 2*I*A*c**4*exp(4*I*e) + 2*I*A*c**4*exp(2*I*e) - 2*I*A*c**4 - 14*B*c**4*exp(6*I*e) + 10*B*c**4*exp(4*I*e) - 6*B*c**4*exp(2*I*e) + 2*B*c**4)*exp(-6*I*e)/a**3), True)) - I*c**4*(A + 7*I*B)*log(exp(2*I*f*x) + exp(-2*I*e))/(a**3*f) - x*(2*A*c**4 + 14*I*B*c**4)/a**3","A",0
730,1,258,0,0.905941," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**3,x)","- \frac{2 i B c^{3} x}{a^{3}} + \frac{B c^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{3} f} + \begin{cases} - \frac{\left(12 B a^{6} c^{3} f^{2} e^{10 i e} e^{- 2 i f x} - 6 B a^{6} c^{3} f^{2} e^{8 i e} e^{- 4 i f x} + \left(- 2 i A a^{6} c^{3} f^{2} e^{6 i e} + 2 B a^{6} c^{3} f^{2} e^{6 i e}\right) e^{- 6 i f x}\right) e^{- 12 i e}}{12 a^{9} f^{3}} & \text{for}\: 12 a^{9} f^{3} e^{12 i e} \neq 0 \\x \left(\frac{2 i B c^{3}}{a^{3}} + \frac{i \left(- i A c^{3} - 2 B c^{3} e^{6 i e} + 2 B c^{3} e^{4 i e} - 2 B c^{3} e^{2 i e} + B c^{3}\right) e^{- 6 i e}}{a^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"-2*I*B*c**3*x/a**3 + B*c**3*log(exp(2*I*f*x) + exp(-2*I*e))/(a**3*f) + Piecewise((-(12*B*a**6*c**3*f**2*exp(10*I*e)*exp(-2*I*f*x) - 6*B*a**6*c**3*f**2*exp(8*I*e)*exp(-4*I*f*x) + (-2*I*A*a**6*c**3*f**2*exp(6*I*e) + 2*B*a**6*c**3*f**2*exp(6*I*e))*exp(-6*I*f*x))*exp(-12*I*e)/(12*a**9*f**3), Ne(12*a**9*f**3*exp(12*I*e), 0)), (x*(2*I*B*c**3/a**3 + I*(-I*A*c**3 - 2*B*c**3*exp(6*I*e) + 2*B*c**3*exp(4*I*e) - 2*B*c**3*exp(2*I*e) + B*c**3)*exp(-6*I*e)/a**3), True))","A",0
731,1,173,0,0.548686," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(\left(8 i A a^{3} c^{2} f e^{4 i e} - 8 B a^{3} c^{2} f e^{4 i e}\right) e^{- 6 i f x} + \left(12 i A a^{3} c^{2} f e^{6 i e} + 12 B a^{3} c^{2} f e^{6 i e}\right) e^{- 4 i f x}\right) e^{- 10 i e}}{96 a^{6} f^{2}} & \text{for}\: 96 a^{6} f^{2} e^{10 i e} \neq 0 \\\frac{x \left(A c^{2} e^{2 i e} + A c^{2} - i B c^{2} e^{2 i e} + i B c^{2}\right) e^{- 6 i e}}{2 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((((8*I*A*a**3*c**2*f*exp(4*I*e) - 8*B*a**3*c**2*f*exp(4*I*e))*exp(-6*I*f*x) + (12*I*A*a**3*c**2*f*exp(6*I*e) + 12*B*a**3*c**2*f*exp(6*I*e))*exp(-4*I*f*x))*exp(-10*I*e)/(96*a**6*f**2), Ne(96*a**6*f**2*exp(10*I*e), 0)), (x*(A*c**2*exp(2*I*e) + A*c**2 - I*B*c**2*exp(2*I*e) + I*B*c**2)*exp(-6*I*e)/(2*a**3), True))","A",0
732,1,211,0,0.567642," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(- 192 i A a^{6} c f^{2} e^{8 i e} e^{- 4 i f x} + \left(- 64 i A a^{6} c f^{2} e^{6 i e} + 64 B a^{6} c f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(- 192 i A a^{6} c f^{2} e^{10 i e} - 192 B a^{6} c f^{2} e^{10 i e}\right) e^{- 2 i f x}\right) e^{- 12 i e}}{1536 a^{9} f^{3}} & \text{for}\: 1536 a^{9} f^{3} e^{12 i e} \neq 0 \\\frac{x \left(A c e^{4 i e} + 2 A c e^{2 i e} + A c - i B c e^{4 i e} + i B c\right) e^{- 6 i e}}{4 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-192*I*A*a**6*c*f**2*exp(8*I*e)*exp(-4*I*f*x) + (-64*I*A*a**6*c*f**2*exp(6*I*e) + 64*B*a**6*c*f**2*exp(6*I*e))*exp(-6*I*f*x) + (-192*I*A*a**6*c*f**2*exp(10*I*e) - 192*B*a**6*c*f**2*exp(10*I*e))*exp(-2*I*f*x))*exp(-12*I*e)/(1536*a**9*f**3), Ne(1536*a**9*f**3*exp(12*I*e), 0)), (x*(A*c*exp(4*I*e) + 2*A*c*exp(2*I*e) + A*c - I*B*c*exp(4*I*e) + I*B*c)*exp(-6*I*e)/(4*a**3), True))","A",0
733,1,264,0,0.512912," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(\left(- 512 i A a^{6} f^{2} e^{6 i e} + 512 B a^{6} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(- 2304 i A a^{6} f^{2} e^{8 i e} + 768 B a^{6} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 4608 i A a^{6} f^{2} e^{10 i e} - 1536 B a^{6} f^{2} e^{10 i e}\right) e^{- 2 i f x}\right) e^{- 12 i e}}{24576 a^{9} f^{3}} & \text{for}\: 24576 a^{9} f^{3} e^{12 i e} \neq 0 \\x \left(- \frac{A - i B}{8 a^{3}} + \frac{\left(A e^{6 i e} + 3 A e^{4 i e} + 3 A e^{2 i e} + A - i B e^{6 i e} - i B e^{4 i e} + i B e^{2 i e} + i B\right) e^{- 6 i e}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A + i B\right)}{8 a^{3}}"," ",0,"Piecewise((-((-512*I*A*a**6*f**2*exp(6*I*e) + 512*B*a**6*f**2*exp(6*I*e))*exp(-6*I*f*x) + (-2304*I*A*a**6*f**2*exp(8*I*e) + 768*B*a**6*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-4608*I*A*a**6*f**2*exp(10*I*e) - 1536*B*a**6*f**2*exp(10*I*e))*exp(-2*I*f*x))*exp(-12*I*e)/(24576*a**9*f**3), Ne(24576*a**9*f**3*exp(12*I*e), 0)), (x*(-(A - I*B)/(8*a**3) + (A*exp(6*I*e) + 3*A*exp(4*I*e) + 3*A*exp(2*I*e) + A - I*B*exp(6*I*e) - I*B*exp(4*I*e) + I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(8*a**3)), True)) - x*(-A + I*B)/(8*a**3)","A",0
734,1,342,0,0.789592," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e)),x)","\begin{cases} \frac{\left(294912 i A a^{9} c^{3} f^{3} e^{10 i e} e^{- 2 i f x} + \left(16384 i A a^{9} c^{3} f^{3} e^{6 i e} - 16384 B a^{9} c^{3} f^{3} e^{6 i e}\right) e^{- 6 i f x} + \left(98304 i A a^{9} c^{3} f^{3} e^{8 i e} - 49152 B a^{9} c^{3} f^{3} e^{8 i e}\right) e^{- 4 i f x} + \left(- 49152 i A a^{9} c^{3} f^{3} e^{14 i e} - 49152 B a^{9} c^{3} f^{3} e^{14 i e}\right) e^{2 i f x}\right) e^{- 12 i e}}{1572864 a^{12} c^{4} f^{4}} & \text{for}\: 1572864 a^{12} c^{4} f^{4} e^{12 i e} \neq 0 \\x \left(- \frac{2 A - i B}{8 a^{3} c} + \frac{\left(A e^{8 i e} + 4 A e^{6 i e} + 6 A e^{4 i e} + 4 A e^{2 i e} + A - i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{2 i e} + i B\right) e^{- 6 i e}}{16 a^{3} c}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 2 A + i B\right)}{8 a^{3} c}"," ",0,"Piecewise(((294912*I*A*a**9*c**3*f**3*exp(10*I*e)*exp(-2*I*f*x) + (16384*I*A*a**9*c**3*f**3*exp(6*I*e) - 16384*B*a**9*c**3*f**3*exp(6*I*e))*exp(-6*I*f*x) + (98304*I*A*a**9*c**3*f**3*exp(8*I*e) - 49152*B*a**9*c**3*f**3*exp(8*I*e))*exp(-4*I*f*x) + (-49152*I*A*a**9*c**3*f**3*exp(14*I*e) - 49152*B*a**9*c**3*f**3*exp(14*I*e))*exp(2*I*f*x))*exp(-12*I*e)/(1572864*a**12*c**4*f**4), Ne(1572864*a**12*c**4*f**4*exp(12*I*e), 0)), (x*(-(2*A - I*B)/(8*a**3*c) + (A*exp(8*I*e) + 4*A*exp(6*I*e) + 6*A*exp(4*I*e) + 4*A*exp(2*I*e) + A - I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(16*a**3*c)), True)) - x*(-2*A + I*B)/(8*a**3*c)","A",0
735,1,452,0,0.892550," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} - \frac{\left(\left(- 33554432 i A a^{12} c^{8} f^{4} e^{6 i e} + 33554432 B a^{12} c^{8} f^{4} e^{6 i e}\right) e^{- 6 i f x} + \left(- 251658240 i A a^{12} c^{8} f^{4} e^{8 i e} + 150994944 B a^{12} c^{8} f^{4} e^{8 i e}\right) e^{- 4 i f x} + \left(- 1006632960 i A a^{12} c^{8} f^{4} e^{10 i e} + 201326592 B a^{12} c^{8} f^{4} e^{10 i e}\right) e^{- 2 i f x} + \left(503316480 i A a^{12} c^{8} f^{4} e^{14 i e} + 301989888 B a^{12} c^{8} f^{4} e^{14 i e}\right) e^{2 i f x} + \left(50331648 i A a^{12} c^{8} f^{4} e^{16 i e} + 50331648 B a^{12} c^{8} f^{4} e^{16 i e}\right) e^{4 i f x}\right) e^{- 12 i e}}{6442450944 a^{15} c^{10} f^{5}} & \text{for}\: 6442450944 a^{15} c^{10} f^{5} e^{12 i e} \neq 0 \\x \left(- \frac{5 A - i B}{16 a^{3} c^{2}} + \frac{\left(A e^{10 i e} + 5 A e^{8 i e} + 10 A e^{6 i e} + 10 A e^{4 i e} + 5 A e^{2 i e} + A - i B e^{10 i e} - 3 i B e^{8 i e} - 2 i B e^{6 i e} + 2 i B e^{4 i e} + 3 i B e^{2 i e} + i B\right) e^{- 6 i e}}{32 a^{3} c^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 5 A + i B\right)}{16 a^{3} c^{2}}"," ",0,"Piecewise((-((-33554432*I*A*a**12*c**8*f**4*exp(6*I*e) + 33554432*B*a**12*c**8*f**4*exp(6*I*e))*exp(-6*I*f*x) + (-251658240*I*A*a**12*c**8*f**4*exp(8*I*e) + 150994944*B*a**12*c**8*f**4*exp(8*I*e))*exp(-4*I*f*x) + (-1006632960*I*A*a**12*c**8*f**4*exp(10*I*e) + 201326592*B*a**12*c**8*f**4*exp(10*I*e))*exp(-2*I*f*x) + (503316480*I*A*a**12*c**8*f**4*exp(14*I*e) + 301989888*B*a**12*c**8*f**4*exp(14*I*e))*exp(2*I*f*x) + (50331648*I*A*a**12*c**8*f**4*exp(16*I*e) + 50331648*B*a**12*c**8*f**4*exp(16*I*e))*exp(4*I*f*x))*exp(-12*I*e)/(6442450944*a**15*c**10*f**5), Ne(6442450944*a**15*c**10*f**5*exp(12*I*e), 0)), (x*(-(5*A - I*B)/(16*a**3*c**2) + (A*exp(10*I*e) + 5*A*exp(8*I*e) + 10*A*exp(6*I*e) + 10*A*exp(4*I*e) + 5*A*exp(2*I*e) + A - I*B*exp(10*I*e) - 3*I*B*exp(8*I*e) - 2*I*B*exp(6*I*e) + 2*I*B*exp(4*I*e) + 3*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(32*a**3*c**2)), True)) - x*(-5*A + I*B)/(16*a**3*c**2)","A",0
736,1,510,0,1.255538," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**3,x)","\frac{5 A x}{16 a^{3} c^{3}} + \begin{cases} \frac{\left(\left(103079215104 i A a^{15} c^{15} f^{5} e^{6 i e} - 103079215104 B a^{15} c^{15} f^{5} e^{6 i e}\right) e^{- 6 i f x} + \left(927712935936 i A a^{15} c^{15} f^{5} e^{8 i e} - 618475290624 B a^{15} c^{15} f^{5} e^{8 i e}\right) e^{- 4 i f x} + \left(4638564679680 i A a^{15} c^{15} f^{5} e^{10 i e} - 1546188226560 B a^{15} c^{15} f^{5} e^{10 i e}\right) e^{- 2 i f x} + \left(- 4638564679680 i A a^{15} c^{15} f^{5} e^{14 i e} - 1546188226560 B a^{15} c^{15} f^{5} e^{14 i e}\right) e^{2 i f x} + \left(- 927712935936 i A a^{15} c^{15} f^{5} e^{16 i e} - 618475290624 B a^{15} c^{15} f^{5} e^{16 i e}\right) e^{4 i f x} + \left(- 103079215104 i A a^{15} c^{15} f^{5} e^{18 i e} - 103079215104 B a^{15} c^{15} f^{5} e^{18 i e}\right) e^{6 i f x}\right) e^{- 12 i e}}{39582418599936 a^{18} c^{18} f^{6}} & \text{for}\: 39582418599936 a^{18} c^{18} f^{6} e^{12 i e} \neq 0 \\x \left(- \frac{5 A}{16 a^{3} c^{3}} + \frac{\left(A e^{12 i e} + 6 A e^{10 i e} + 15 A e^{8 i e} + 20 A e^{6 i e} + 15 A e^{4 i e} + 6 A e^{2 i e} + A - i B e^{12 i e} - 4 i B e^{10 i e} - 5 i B e^{8 i e} + 5 i B e^{4 i e} + 4 i B e^{2 i e} + i B\right) e^{- 6 i e}}{64 a^{3} c^{3}}\right) & \text{otherwise} \end{cases}"," ",0,"5*A*x/(16*a**3*c**3) + Piecewise((((103079215104*I*A*a**15*c**15*f**5*exp(6*I*e) - 103079215104*B*a**15*c**15*f**5*exp(6*I*e))*exp(-6*I*f*x) + (927712935936*I*A*a**15*c**15*f**5*exp(8*I*e) - 618475290624*B*a**15*c**15*f**5*exp(8*I*e))*exp(-4*I*f*x) + (4638564679680*I*A*a**15*c**15*f**5*exp(10*I*e) - 1546188226560*B*a**15*c**15*f**5*exp(10*I*e))*exp(-2*I*f*x) + (-4638564679680*I*A*a**15*c**15*f**5*exp(14*I*e) - 1546188226560*B*a**15*c**15*f**5*exp(14*I*e))*exp(2*I*f*x) + (-927712935936*I*A*a**15*c**15*f**5*exp(16*I*e) - 618475290624*B*a**15*c**15*f**5*exp(16*I*e))*exp(4*I*f*x) + (-103079215104*I*A*a**15*c**15*f**5*exp(18*I*e) - 103079215104*B*a**15*c**15*f**5*exp(18*I*e))*exp(6*I*f*x))*exp(-12*I*e)/(39582418599936*a**18*c**18*f**6), Ne(39582418599936*a**18*c**18*f**6*exp(12*I*e), 0)), (x*(-5*A/(16*a**3*c**3) + (A*exp(12*I*e) + 6*A*exp(10*I*e) + 15*A*exp(8*I*e) + 20*A*exp(6*I*e) + 15*A*exp(4*I*e) + 6*A*exp(2*I*e) + A - I*B*exp(12*I*e) - 4*I*B*exp(10*I*e) - 5*I*B*exp(8*I*e) + 5*I*B*exp(4*I*e) + 4*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(64*a**3*c**3)), True))","A",0
737,1,604,0,1.263436," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{\left(\left(- 13510798882111488 i A a^{18} c^{24} f^{6} e^{6 i e} + 13510798882111488 B a^{18} c^{24} f^{6} e^{6 i e}\right) e^{- 6 i f x} + \left(- 141863388262170624 i A a^{18} c^{24} f^{6} e^{8 i e} + 101330991615836160 B a^{18} c^{24} f^{6} e^{8 i e}\right) e^{- 4 i f x} + \left(- 851180329573023744 i A a^{18} c^{24} f^{6} e^{10 i e} + 364791569817010176 B a^{18} c^{24} f^{6} e^{10 i e}\right) e^{- 2 i f x} + \left(1418633882621706240 i A a^{18} c^{24} f^{6} e^{14 i e} + 202661983231672320 B a^{18} c^{24} f^{6} e^{14 i e}\right) e^{2 i f x} + \left(425590164786511872 i A a^{18} c^{24} f^{6} e^{16 i e} + 182395784908505088 B a^{18} c^{24} f^{6} e^{16 i e}\right) e^{4 i f x} + \left(94575592174780416 i A a^{18} c^{24} f^{6} e^{18 i e} + 67553994410557440 B a^{18} c^{24} f^{6} e^{18 i e}\right) e^{6 i f x} + \left(10133099161583616 i A a^{18} c^{24} f^{6} e^{20 i e} + 10133099161583616 B a^{18} c^{24} f^{6} e^{20 i e}\right) e^{8 i f x}\right) e^{- 12 i e}}{10376293541461622784 a^{21} c^{28} f^{7}} & \text{for}\: 10376293541461622784 a^{21} c^{28} f^{7} e^{12 i e} \neq 0 \\x \left(- \frac{35 A + 5 i B}{128 a^{3} c^{4}} + \frac{\left(A e^{14 i e} + 7 A e^{12 i e} + 21 A e^{10 i e} + 35 A e^{8 i e} + 35 A e^{6 i e} + 21 A e^{4 i e} + 7 A e^{2 i e} + A - i B e^{14 i e} - 5 i B e^{12 i e} - 9 i B e^{10 i e} - 5 i B e^{8 i e} + 5 i B e^{6 i e} + 9 i B e^{4 i e} + 5 i B e^{2 i e} + i B\right) e^{- 6 i e}}{128 a^{3} c^{4}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 35 A - 5 i B\right)}{128 a^{3} c^{4}}"," ",0,"Piecewise((-((-13510798882111488*I*A*a**18*c**24*f**6*exp(6*I*e) + 13510798882111488*B*a**18*c**24*f**6*exp(6*I*e))*exp(-6*I*f*x) + (-141863388262170624*I*A*a**18*c**24*f**6*exp(8*I*e) + 101330991615836160*B*a**18*c**24*f**6*exp(8*I*e))*exp(-4*I*f*x) + (-851180329573023744*I*A*a**18*c**24*f**6*exp(10*I*e) + 364791569817010176*B*a**18*c**24*f**6*exp(10*I*e))*exp(-2*I*f*x) + (1418633882621706240*I*A*a**18*c**24*f**6*exp(14*I*e) + 202661983231672320*B*a**18*c**24*f**6*exp(14*I*e))*exp(2*I*f*x) + (425590164786511872*I*A*a**18*c**24*f**6*exp(16*I*e) + 182395784908505088*B*a**18*c**24*f**6*exp(16*I*e))*exp(4*I*f*x) + (94575592174780416*I*A*a**18*c**24*f**6*exp(18*I*e) + 67553994410557440*B*a**18*c**24*f**6*exp(18*I*e))*exp(6*I*f*x) + (10133099161583616*I*A*a**18*c**24*f**6*exp(20*I*e) + 10133099161583616*B*a**18*c**24*f**6*exp(20*I*e))*exp(8*I*f*x))*exp(-12*I*e)/(10376293541461622784*a**21*c**28*f**7), Ne(10376293541461622784*a**21*c**28*f**7*exp(12*I*e), 0)), (x*(-(35*A + 5*I*B)/(128*a**3*c**4) + (A*exp(14*I*e) + 7*A*exp(12*I*e) + 21*A*exp(10*I*e) + 35*A*exp(8*I*e) + 35*A*exp(6*I*e) + 21*A*exp(4*I*e) + 7*A*exp(2*I*e) + A - I*B*exp(14*I*e) - 5*I*B*exp(12*I*e) - 9*I*B*exp(10*I*e) - 5*I*B*exp(8*I*e) + 5*I*B*exp(6*I*e) + 9*I*B*exp(4*I*e) + 5*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(128*a**3*c**4)), True)) - x*(-35*A - 5*I*B)/(128*a**3*c**4)","A",0
738,1,649,0,1.969951," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**5,x)","\begin{cases} \frac{\left(- 7263405479023135948800 i A a^{21} c^{35} f^{7} e^{14 i e} e^{2 i f x} + \left(34587645138205409280 i A a^{21} c^{35} f^{7} e^{6 i e} - 34587645138205409280 B a^{21} c^{35} f^{7} e^{6 i e}\right) e^{- 6 i f x} + \left(415051741658464911360 i A a^{21} c^{35} f^{7} e^{8 i e} - 311288806243848683520 B a^{21} c^{35} f^{7} e^{8 i e}\right) e^{- 4 i f x} + \left(2905362191609254379520 i A a^{21} c^{35} f^{7} e^{10 i e} - 1452681095804627189760 B a^{21} c^{35} f^{7} e^{10 i e}\right) e^{- 2 i f x} + \left(- 2905362191609254379520 i A a^{21} c^{35} f^{7} e^{16 i e} - 726340547902313594880 B a^{21} c^{35} f^{7} e^{16 i e}\right) e^{4 i f x} + \left(- 968454063869751459840 i A a^{21} c^{35} f^{7} e^{18 i e} - 484227031934875729920 B a^{21} c^{35} f^{7} e^{18 i e}\right) e^{6 i f x} + \left(- 207525870829232455680 i A a^{21} c^{35} f^{7} e^{20 i e} - 155644403121924341760 B a^{21} c^{35} f^{7} e^{20 i e}\right) e^{8 i f x} + \left(- 20752587082923245568 i A a^{21} c^{35} f^{7} e^{22 i e} - 20752587082923245568 B a^{21} c^{35} f^{7} e^{22 i e}\right) e^{10 i f x}\right) e^{- 12 i e}}{53126622932283508654080 a^{24} c^{40} f^{8}} & \text{for}\: 53126622932283508654080 a^{24} c^{40} f^{8} e^{12 i e} \neq 0 \\x \left(- \frac{28 A + 7 i B}{128 a^{3} c^{5}} + \frac{\left(A e^{16 i e} + 8 A e^{14 i e} + 28 A e^{12 i e} + 56 A e^{10 i e} + 70 A e^{8 i e} + 56 A e^{6 i e} + 28 A e^{4 i e} + 8 A e^{2 i e} + A - i B e^{16 i e} - 6 i B e^{14 i e} - 14 i B e^{12 i e} - 14 i B e^{10 i e} + 14 i B e^{6 i e} + 14 i B e^{4 i e} + 6 i B e^{2 i e} + i B\right) e^{- 6 i e}}{256 a^{3} c^{5}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 28 A - 7 i B\right)}{128 a^{3} c^{5}}"," ",0,"Piecewise(((-7263405479023135948800*I*A*a**21*c**35*f**7*exp(14*I*e)*exp(2*I*f*x) + (34587645138205409280*I*A*a**21*c**35*f**7*exp(6*I*e) - 34587645138205409280*B*a**21*c**35*f**7*exp(6*I*e))*exp(-6*I*f*x) + (415051741658464911360*I*A*a**21*c**35*f**7*exp(8*I*e) - 311288806243848683520*B*a**21*c**35*f**7*exp(8*I*e))*exp(-4*I*f*x) + (2905362191609254379520*I*A*a**21*c**35*f**7*exp(10*I*e) - 1452681095804627189760*B*a**21*c**35*f**7*exp(10*I*e))*exp(-2*I*f*x) + (-2905362191609254379520*I*A*a**21*c**35*f**7*exp(16*I*e) - 726340547902313594880*B*a**21*c**35*f**7*exp(16*I*e))*exp(4*I*f*x) + (-968454063869751459840*I*A*a**21*c**35*f**7*exp(18*I*e) - 484227031934875729920*B*a**21*c**35*f**7*exp(18*I*e))*exp(6*I*f*x) + (-207525870829232455680*I*A*a**21*c**35*f**7*exp(20*I*e) - 155644403121924341760*B*a**21*c**35*f**7*exp(20*I*e))*exp(8*I*f*x) + (-20752587082923245568*I*A*a**21*c**35*f**7*exp(22*I*e) - 20752587082923245568*B*a**21*c**35*f**7*exp(22*I*e))*exp(10*I*f*x))*exp(-12*I*e)/(53126622932283508654080*a**24*c**40*f**8), Ne(53126622932283508654080*a**24*c**40*f**8*exp(12*I*e), 0)), (x*(-(28*A + 7*I*B)/(128*a**3*c**5) + (A*exp(16*I*e) + 8*A*exp(14*I*e) + 28*A*exp(12*I*e) + 56*A*exp(10*I*e) + 70*A*exp(8*I*e) + 56*A*exp(6*I*e) + 28*A*exp(4*I*e) + 8*A*exp(2*I*e) + A - I*B*exp(16*I*e) - 6*I*B*exp(14*I*e) - 14*I*B*exp(12*I*e) - 14*I*B*exp(10*I*e) + 14*I*B*exp(6*I*e) + 14*I*B*exp(4*I*e) + 6*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(256*a**3*c**5)), True)) - x*(-28*A - 7*I*B)/(128*a**3*c**5)","A",0
739,1,750,0,1.681820," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**6,x)","\begin{cases} - \frac{\left(\left(- 6800207735332289107722240 i A a^{24} c^{48} f^{8} e^{6 i e} + 6800207735332289107722240 B a^{24} c^{48} f^{8} e^{6 i e}\right) e^{- 6 i f x} + \left(- 91802804426985902954250240 i A a^{24} c^{48} f^{8} e^{8 i e} + 71402181220989035631083520 B a^{24} c^{48} f^{8} e^{8 i e}\right) e^{- 4 i f x} + \left(- 734422435415887223634001920 i A a^{24} c^{48} f^{8} e^{10 i e} + 408012464119937346463334400 B a^{24} c^{48} f^{8} e^{10 i e}\right) e^{- 2 i f x} + \left(2570478523955605282719006720 i A a^{24} c^{48} f^{8} e^{14 i e} - 285608724883956142524334080 B a^{24} c^{48} f^{8} e^{14 i e}\right) e^{2 i f x} + \left(1285239261977802641359503360 i A a^{24} c^{48} f^{8} e^{16 i e} + 142804362441978071262167040 B a^{24} c^{48} f^{8} e^{16 i e}\right) e^{4 i f x} + \left(571217449767912285048668160 i A a^{24} c^{48} f^{8} e^{18 i e} + 190405816589304095016222720 B a^{24} c^{48} f^{8} e^{18 i e}\right) e^{6 i f x} + \left(183605608853971805908500480 i A a^{24} c^{48} f^{8} e^{20 i e} + 102003116029984336615833600 B a^{24} c^{48} f^{8} e^{20 i e}\right) e^{8 i f x} + \left(36721121770794361181700096 i A a^{24} c^{48} f^{8} e^{22 i e} + 28560872488395614252433408 B a^{24} c^{48} f^{8} e^{22 i e}\right) e^{10 i f x} + \left(3400103867666144553861120 i A a^{24} c^{48} f^{8} e^{24 i e} + 3400103867666144553861120 B a^{24} c^{48} f^{8} e^{24 i e}\right) e^{12 i f x}\right) e^{- 12 i e}}{20890238162940792138922721280 a^{27} c^{54} f^{9}} & \text{for}\: 20890238162940792138922721280 a^{27} c^{54} f^{9} e^{12 i e} \neq 0 \\x \left(- \frac{21 A + 7 i B}{128 a^{3} c^{6}} + \frac{\left(A e^{18 i e} + 9 A e^{16 i e} + 36 A e^{14 i e} + 84 A e^{12 i e} + 126 A e^{10 i e} + 126 A e^{8 i e} + 84 A e^{6 i e} + 36 A e^{4 i e} + 9 A e^{2 i e} + A - i B e^{18 i e} - 7 i B e^{16 i e} - 20 i B e^{14 i e} - 28 i B e^{12 i e} - 14 i B e^{10 i e} + 14 i B e^{8 i e} + 28 i B e^{6 i e} + 20 i B e^{4 i e} + 7 i B e^{2 i e} + i B\right) e^{- 6 i e}}{512 a^{3} c^{6}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- 21 A - 7 i B\right)}{128 a^{3} c^{6}}"," ",0,"Piecewise((-((-6800207735332289107722240*I*A*a**24*c**48*f**8*exp(6*I*e) + 6800207735332289107722240*B*a**24*c**48*f**8*exp(6*I*e))*exp(-6*I*f*x) + (-91802804426985902954250240*I*A*a**24*c**48*f**8*exp(8*I*e) + 71402181220989035631083520*B*a**24*c**48*f**8*exp(8*I*e))*exp(-4*I*f*x) + (-734422435415887223634001920*I*A*a**24*c**48*f**8*exp(10*I*e) + 408012464119937346463334400*B*a**24*c**48*f**8*exp(10*I*e))*exp(-2*I*f*x) + (2570478523955605282719006720*I*A*a**24*c**48*f**8*exp(14*I*e) - 285608724883956142524334080*B*a**24*c**48*f**8*exp(14*I*e))*exp(2*I*f*x) + (1285239261977802641359503360*I*A*a**24*c**48*f**8*exp(16*I*e) + 142804362441978071262167040*B*a**24*c**48*f**8*exp(16*I*e))*exp(4*I*f*x) + (571217449767912285048668160*I*A*a**24*c**48*f**8*exp(18*I*e) + 190405816589304095016222720*B*a**24*c**48*f**8*exp(18*I*e))*exp(6*I*f*x) + (183605608853971805908500480*I*A*a**24*c**48*f**8*exp(20*I*e) + 102003116029984336615833600*B*a**24*c**48*f**8*exp(20*I*e))*exp(8*I*f*x) + (36721121770794361181700096*I*A*a**24*c**48*f**8*exp(22*I*e) + 28560872488395614252433408*B*a**24*c**48*f**8*exp(22*I*e))*exp(10*I*f*x) + (3400103867666144553861120*I*A*a**24*c**48*f**8*exp(24*I*e) + 3400103867666144553861120*B*a**24*c**48*f**8*exp(24*I*e))*exp(12*I*f*x))*exp(-12*I*e)/(20890238162940792138922721280*a**27*c**54*f**9), Ne(20890238162940792138922721280*a**27*c**54*f**9*exp(12*I*e), 0)), (x*(-(21*A + 7*I*B)/(128*a**3*c**6) + (A*exp(18*I*e) + 9*A*exp(16*I*e) + 36*A*exp(14*I*e) + 84*A*exp(12*I*e) + 126*A*exp(10*I*e) + 126*A*exp(8*I*e) + 84*A*exp(6*I*e) + 36*A*exp(4*I*e) + 9*A*exp(2*I*e) + A - I*B*exp(18*I*e) - 7*I*B*exp(16*I*e) - 20*I*B*exp(14*I*e) - 28*I*B*exp(12*I*e) - 14*I*B*exp(10*I*e) + 14*I*B*exp(8*I*e) + 28*I*B*exp(6*I*e) + 20*I*B*exp(4*I*e) + 7*I*B*exp(2*I*e) + I*B)*exp(-6*I*e)/(512*a**3*c**6)), True)) - x*(-21*A - 7*I*B)/(128*a**3*c**6)","A",0
740,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","i a \left(\int \left(- i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- 2 A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx + \int \left(- i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*A*c**3*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-2*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-2*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x))","F",0
741,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","i a \left(\int \left(- i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*c**2*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x))","F",0
742,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","i a \left(\int \left(- i A c \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x))","F",0
743,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x)","i a \left(\int \left(- i A \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- i B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-I*B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x))","F",0
744,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","i a \left(\int \left(- \frac{i A}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{i B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(A*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(B*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-I*B*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x))","F",0
745,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","i a \left(\int \left(- \frac{i A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan^{2}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{i B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**2/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-I*B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
746,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","i a \left(\int \left(- \frac{i A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan^{2}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{i B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**2/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-I*B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
747,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","i a \left(\int \left(- \frac{i A}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan^{2}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{i B \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*A/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**2/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-I*B*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
748,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","- a^{2} \left(\int \left(- A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- 2 A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\right)\, dx + \int i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int 2 i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\, dx + \int i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int 2 i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx + \int i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{6}{\left(e + f x \right)}\, dx\right)"," ",0,"-a**2*(Integral(-A*c**3*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x) + Integral(I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(2*I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x) + Integral(I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(2*I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**6, x))","F",0
749,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- 2 A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x))","F",0
750,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \left(- A c \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*c*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x))","F",0
751,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e)),x)","- a^{2} \left(\int \left(- A \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 2 i A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 i B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-2*I*A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*I*B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x))","F",0
752,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","- a^{2} \left(\int \left(- \frac{A}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{3}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{2 i A \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \left(- \frac{2 i B \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(A*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-B*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(B*tan(e + f*x)**3/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*I*A*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*I*B*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x))","F",0
753,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \left(- \frac{A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{2}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{3}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{2 i A \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \left(- \frac{2 i B \tan^{2}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**2/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**3/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*A*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*B*tan(e + f*x)**2/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
754,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \left(- \frac{A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{2}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{3}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{2 i A \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \left(- \frac{2 i B \tan^{2}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**2/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**3/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*A*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*B*tan(e + f*x)**2/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
755,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","- a^{2} \left(\int \left(- \frac{A}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{2}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{B \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{3}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{2 i A \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \left(- \frac{2 i B \tan^{2}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-A/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**2/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-B*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**3/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*A*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-2*I*B*tan(e + f*x)**2/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
756,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","- i a^{3} \left(\int i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int 3 i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int 3 i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx + \int i A c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{6}{\left(e + f x \right)}\, dx + \int i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int 3 i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int 3 i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\, dx + \int i B c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{7}{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*c**3*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(3*I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(3*I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(I*A*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**6, x) + Integral(I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(3*I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(3*I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x) + Integral(I*B*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**7, x))","F",0
757,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{6}{\left(e + f x \right)}\right)\, dx + \int 2 i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx + \int i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int 2 i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*c**2*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-2*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**6, x) + Integral(2*I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(2*I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x))","F",0
758,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int i A c \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- 2 A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int \left(- i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*c*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-2*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-2*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x))","F",0
759,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e)),x)","- i a^{3} \left(\int i A \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- 3 A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx + \int \left(- 3 i A \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int i B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\, dx + \int \left(- 3 i B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-3*B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x) + Integral(-3*I*A*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(I*B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-3*I*B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x))","F",0
760,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","- i a^{3} \left(\int \frac{i A}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 A \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{3}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 B \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{4}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i A \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{i B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i B \tan^{3}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*A*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(A*tan(e + f*x)**3/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*B*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(B*tan(e + f*x)**4/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*I*A*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(I*B*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*I*B*tan(e + f*x)**3/sqrt(-I*c*tan(e + f*x) + c), x))","F",0
761,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int \frac{i A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 A \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{3}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 B \tan^{2}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{4}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i A \tan^{2}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{i B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i B \tan^{3}{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*A*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**3/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*B*tan(e + f*x)**2/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**4/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*A*tan(e + f*x)**2/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(I*B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*B*tan(e + f*x)**3/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
762,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int \frac{i A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 A \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{3}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 B \tan^{2}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{4}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i A \tan^{2}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{i B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i B \tan^{3}{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*A*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**3/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*B*tan(e + f*x)**2/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**4/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*A*tan(e + f*x)**2/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(I*B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*B*tan(e + f*x)**3/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**2*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
763,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","- i a^{3} \left(\int \frac{i A}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 A \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{A \tan^{3}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 B \tan^{2}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{B \tan^{4}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i A \tan^{2}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{i B \tan{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i B \tan^{3}{\left(e + f x \right)}}{i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 i c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + c^{3} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*A/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*A*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(A*tan(e + f*x)**3/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*B*tan(e + f*x)**2/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)**4/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*A*tan(e + f*x)**2/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(I*B*tan(e + f*x)/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(-3*I*B*tan(e + f*x)**3/(I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*I*c**3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + c**3*sqrt(-I*c*tan(e + f*x) + c)), x))","F",0
764,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx + \int \left(- \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx + \int \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx + \int \left(- \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx + \int \left(- \frac{2 i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx + \int \left(- \frac{2 i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx\right)}{a}"," ",0,"-I*(Integral(A*c**2*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x) - I), x) + Integral(B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3/(tan(e + f*x) - I), x) + Integral(-2*I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x) + Integral(-2*I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x) - I), x))/a","F",0
766,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{A c \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx + \int \left(- \frac{i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx + \int \left(- \frac{i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\right)\, dx\right)}{a}"," ",0,"-I*(Integral(A*c*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x) + Integral(B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x) - I), x))/a","F",0
767,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{A \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(A*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
768,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{A}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - i \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - i \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a}"," ",0,"-I*(Integral(A/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - I*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - I*sqrt(-I*c*tan(e + f*x) + c)), x))/a","F",0
769,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","- \frac{i \left(\int \frac{A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - i c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - i c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a}"," ",0,"-I*(Integral(A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - I*c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - I*c*sqrt(-I*c*tan(e + f*x) + c)), x))/a","F",0
770,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","- \frac{i \left(\int \frac{A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a}"," ",0,"-I*(Integral(A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - I*c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - I*c**2*sqrt(-I*c*tan(e + f*x) + c)), x))/a","F",0
771,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(9/2)/(a+I*a*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
773,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \left(- \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx + \int \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \left(- \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx + \int \left(- \frac{2 i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx + \int \left(- \frac{2 i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx}{a^{2}}"," ",0,"-(Integral(A*c**2*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-2*I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-2*I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
774,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{A c \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \left(- \frac{i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx + \int \left(- \frac{i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\right)\, dx}{a^{2}}"," ",0,"-(Integral(A*c*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
775,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{A \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-(Integral(A*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
776,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{A}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 2 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx}{a^{2}}"," ",0,"-(Integral(A/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 2*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - sqrt(-I*c*tan(e + f*x) + c)), x))/a**2","F",0
777,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(3/2),x)","- \frac{\int \frac{A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} - c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx}{a^{2}}"," ",0,"-(Integral(A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) - c*sqrt(-I*c*tan(e + f*x) + c)), x))/a**2","F",0
778,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(5/2),x)","- \frac{\int \frac{A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx}{a^{2}}"," ",0,"-(Integral(A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)), x))/a**2","F",0
779,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(9/2)/(a+I*a*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \left(- \frac{A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx + \int \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \left(- \frac{B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx + \int \left(- \frac{2 i A c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx + \int \left(- \frac{2 i B c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*c**2*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-2*I*A*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-2*I*B*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x))/a**3","F",0
782,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{A c \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \frac{B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \left(- \frac{i A c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx + \int \left(- \frac{i B c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\right)\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*c*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-I*A*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(-I*B*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x))/a**3","F",0
783,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{A \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx + \int \frac{B \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}}{\tan^{3}{\left(e + f x \right)} - 3 i \tan^{2}{\left(e + f x \right)} - 3 \tan{\left(e + f x \right)} + i}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(B*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x))/a**3","F",0
784,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{A}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 3 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - 3 \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 3*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - 3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*sqrt(-I*c*tan(e + f*x) + c)), x))/a**3","F",0
785,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(3/2),x)","\frac{i \left(\int \frac{A}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} - 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i c \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*c*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 - 2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*c*sqrt(-I*c*tan(e + f*x) + c)), x))/a**3","F",0
786,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(5/2),x)","\frac{i \left(\int \frac{A}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)} + i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} + 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \frac{B \tan{\left(e + f x \right)}}{- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)} + i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)} - 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)} + 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)} - c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)} + i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx\right)}{a^{3}}"," ",0,"I*(Integral(A/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5 + I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 + 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*c**2*sqrt(-I*c*tan(e + f*x) + c)), x) + Integral(B*tan(e + f*x)/(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5 + I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4 - 2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3 + 2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2 - c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x) + I*c**2*sqrt(-I*c*tan(e + f*x) + c)), x))/a**3","F",0
787,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
788,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
789,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","\int \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(3/2)*(A + B*tan(e + f*x)), x)","F",0
790,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)),x)","\int \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)} \left(A + B \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*sqrt(-I*c*(tan(e + f*x) + I))*(A + B*tan(e + f*x)), x)","F",0
791,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(A + B*tan(e + f*x))/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
792,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
793,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
794,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
795,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(3/2)*(A + B*tan(e + f*x)), x)","F",0
798,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)} \left(A + B \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(-I*c*(tan(e + f*x) + I))*(A + B*tan(e + f*x)), x)","F",0
799,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(A + B*tan(e + f*x))/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
800,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
802,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)*(A + B*tan(e + f*x))/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
810,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
811,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)*(A + B*tan(e + f*x))/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
812,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
826,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((-I*c*(tan(e + f*x) + I))**(3/2)*(A + B*tan(e + f*x))/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
832,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(-I*c*(tan(e + f*x) + I))*(A + B*tan(e + f*x))/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
833,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(1/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/(sqrt(I*a*(tan(e + f*x) - I))*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
834,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
835,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
836,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-I*c*(tan(e + f*x) + I))**(3/2)*(A + B*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
839,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-I*c*(tan(e + f*x) + I))*(A + B*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
840,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
841,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(3/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
842,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(3/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
843,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(9/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
846,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{\left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-I*c*(tan(e + f*x) + I))**(3/2)*(A + B*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
847,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)} \left(A + B \tan{\left(e + f x \right)}\right)}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(-I*c*(tan(e + f*x) + I))*(A + B*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
848,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(5/2)*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
849,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(5/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(5/2)*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
850,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))**(5/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))/((I*a*(tan(e + f*x) - I))**(5/2)*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
851,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**n,x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(- i c \left(\tan{\left(e + f x \right)} + i\right)\right)^{n} \left(A + B \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(-I*c*(tan(e + f*x) + I))**n*(A + B*tan(e + f*x)), x)","F",0
852,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1+m)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))**(-1-m),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
853,1,66,0,1.468854," ","integrate((c-I*c*tan(f*x+e))**n*(-I*(2+n)+(-2+n)*tan(f*x+e))/(tan(f*x+e)-I)**2,x)","\begin{cases} \frac{\left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f \tan^{2}{\left(e + f x \right)} - 2 i f \tan{\left(e + f x \right)} - f} & \text{for}\: f \neq 0 \\\frac{x \left(\left(n - 2\right) \tan{\left(e \right)} - i \left(n + 2\right)\right) \left(- i c \tan{\left(e \right)} + c\right)^{n}}{\left(\tan{\left(e \right)} - i\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-I*c*tan(e + f*x) + c)**n/(f*tan(e + f*x)**2 - 2*I*f*tan(e + f*x) - f), Ne(f, 0)), (x*((n - 2)*tan(e) - I*(n + 2))*(-I*c*tan(e) + c)**n/(tan(e) - I)**2, True))","A",0
854,1,298,0,0.548844," ","integrate((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(\left(16 i A a^{2} c f e^{4 i e} + 16 i B a^{2} d f e^{4 i e}\right) e^{- 2 i f x} + \left(4 i A a^{2} c f e^{2 i e} - 4 A a^{2} d f e^{2 i e} - 4 B a^{2} c f e^{2 i e} - 4 i B a^{2} d f e^{2 i e}\right) e^{- 4 i f x}\right) e^{- 6 i e}}{64 a^{4} f^{2}} & \text{for}\: 64 a^{4} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{A c - i A d - i B c - B d}{4 a^{2}} + \frac{\left(A c e^{4 i e} + 2 A c e^{2 i e} + A c - i A d e^{4 i e} + i A d - i B c e^{4 i e} + i B c - B d e^{4 i e} + 2 B d e^{2 i e} - B d\right) e^{- 4 i e}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- A c + i A d + i B c + B d\right)}{4 a^{2}}"," ",0,"Piecewise((((16*I*A*a**2*c*f*exp(4*I*e) + 16*I*B*a**2*d*f*exp(4*I*e))*exp(-2*I*f*x) + (4*I*A*a**2*c*f*exp(2*I*e) - 4*A*a**2*d*f*exp(2*I*e) - 4*B*a**2*c*f*exp(2*I*e) - 4*I*B*a**2*d*f*exp(2*I*e))*exp(-4*I*f*x))*exp(-6*I*e)/(64*a**4*f**2), Ne(64*a**4*f**2*exp(6*I*e), 0)), (x*(-(A*c - I*A*d - I*B*c - B*d)/(4*a**2) + (A*c*exp(4*I*e) + 2*A*c*exp(2*I*e) + A*c - I*A*d*exp(4*I*e) + I*A*d - I*B*c*exp(4*I*e) + I*B*c - B*d*exp(4*I*e) + 2*B*d*exp(2*I*e) - B*d)*exp(-4*I*e)/(4*a**2)), True)) - x*(-A*c + I*A*d + I*B*c + B*d)/(4*a**2)","A",0
855,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\left(A + B \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x))*(c + d*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
