1,1,216,0,0.824224," ","integrate(tan(d*x+c)**5*(a+I*a*tan(d*x+c)),x)","- \frac{a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{150 i a e^{8 i c} e^{8 i d x} + 300 i a e^{6 i c} e^{6 i d x} + 400 i a e^{4 i c} e^{4 i d x} + 200 i a e^{2 i c} e^{2 i d x} + 46 i a}{- 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,"-a*log(exp(2*I*d*x) + exp(-2*I*c))/d + (150*I*a*exp(8*I*c)*exp(8*I*d*x) + 300*I*a*exp(6*I*c)*exp(6*I*d*x) + 400*I*a*exp(4*I*c)*exp(4*I*d*x) + 200*I*a*exp(2*I*c)*exp(2*I*d*x) + 46*I*a)/(-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)","B",0
2,1,168,0,0.454257," ","integrate(tan(d*x+c)**4*(a+I*a*tan(d*x+c)),x)","- \frac{i a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{24 i a e^{6 i c} e^{6 i d x} + 36 i a e^{4 i c} e^{4 i d x} + 32 i a e^{2 i c} e^{2 i d x} + 8 i a}{- 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,"-I*a*log(exp(2*I*d*x) + exp(-2*I*c))/d + (24*I*a*exp(6*I*c)*exp(6*I*d*x) + 36*I*a*exp(4*I*c)*exp(4*I*d*x) + 32*I*a*exp(2*I*c)*exp(2*I*d*x) + 8*I*a)/(-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
3,1,136,0,0.405562," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c)),x)","\frac{a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 18 i a e^{4 i c} e^{4 i d x} - 18 i a e^{2 i c} e^{2 i d x} - 8 i a}{- 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,"a*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-18*I*a*exp(4*I*c)*exp(4*I*d*x) - 18*I*a*exp(2*I*c)*exp(2*I*d*x) - 8*I*a)/(-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
4,1,88,0,0.322104," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c)),x)","\frac{i a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 4 a e^{2 i c} e^{2 i d x} - 2 a}{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*a*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-4*a*exp(2*I*c)*exp(2*I*d*x) - 2*a)/(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
5,1,44,0,0.230968," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c)),x)","\frac{2 a}{- d e^{2 i c} e^{2 i d x} - d} - \frac{a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d}"," ",0,"2*a/(-d*exp(2*I*c)*exp(2*I*d*x) - d) - a*log(exp(2*I*d*x) + exp(-2*I*c))/d","A",0
6,1,24,0,0.173846," ","integrate(a+I*a*tan(d*x+c),x)","- \frac{i a \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d}"," ",0,"-I*a*log(exp(2*I*d*x) + exp(-2*I*c))/d","A",0
7,1,20,0,0.187094," ","integrate(cot(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)}}{d}"," ",0,"a*log(exp(2*I*d*x) - exp(-2*I*c))/d","A",0
8,1,46,0,0.265763," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c)),x)","\frac{2 i a}{- d e^{2 i c} e^{2 i d x} + d} + \frac{i a \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d}"," ",0,"2*I*a/(-d*exp(2*I*c)*exp(2*I*d*x) + d) + I*a*log(exp(2*I*d*x) - exp(-2*I*c))/d","A",0
9,1,88,0,0.336712," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c)),x)","- \frac{a \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{4 i a e^{2 i c} e^{2 i d x} - 2 i a}{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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (4*I*a*exp(2*I*c)*exp(2*I*d*x) - 2*I*a)/(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
10,1,128,0,0.385684," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c)),x)","- \frac{i a \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 18 i a e^{4 i c} e^{4 i d x} + 18 i a e^{2 i c} e^{2 i d x} - 8 i a}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-18*I*a*exp(4*I*c)*exp(4*I*d*x) + 18*I*a*exp(2*I*c)*exp(2*I*d*x) - 8*I*a)/(-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
11,1,158,0,0.689846," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c)),x)","\frac{a \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{24 a e^{6 i c} e^{6 i d x} - 36 a e^{4 i c} e^{4 i d x} + 32 a e^{2 i c} e^{2 i d x} - 8 a}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (24*a*exp(6*I*c)*exp(6*I*d*x) - 36*a*exp(4*I*c)*exp(4*I*d*x) + 32*a*exp(2*I*c)*exp(2*I*d*x) - 8*a)/(-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
12,1,206,0,0.577840," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c)),x)","\frac{i a \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 150 i a e^{8 i c} e^{8 i d x} + 300 i a e^{6 i c} e^{6 i d x} - 400 i a e^{4 i c} e^{4 i d x} + 200 i a e^{2 i c} e^{2 i d x} - 46 i a}{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,"I*a*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-150*I*a*exp(8*I*c)*exp(8*I*d*x) + 300*I*a*exp(6*I*c)*exp(6*I*d*x) - 400*I*a*exp(4*I*c)*exp(4*I*d*x) + 200*I*a*exp(2*I*c)*exp(2*I*d*x) - 46*I*a)/(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
13,1,219,0,0.604847," ","integrate(tan(d*x+c)**4*(a+I*a*tan(d*x+c))**2,x)","- \frac{2 i a^{2} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{270 i a^{2} e^{8 i c} e^{8 i d x} + 600 i a^{2} e^{6 i c} e^{6 i d x} + 740 i a^{2} e^{4 i c} e^{4 i d x} + 400 i a^{2} e^{2 i c} e^{2 i d x} + 86 i a^{2}}{- 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,"-2*I*a**2*log(exp(2*I*d*x) + exp(-2*I*c))/d + (270*I*a**2*exp(8*I*c)*exp(8*I*d*x) + 600*I*a**2*exp(6*I*c)*exp(6*I*d*x) + 740*I*a**2*exp(4*I*c)*exp(4*I*d*x) + 400*I*a**2*exp(2*I*c)*exp(2*I*d*x) + 86*I*a**2)/(-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
14,1,172,0,1.406861," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**2,x)","\frac{2 a^{2} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 42 a^{2} e^{6 i c} e^{6 i d x} - 72 a^{2} e^{4 i c} e^{4 i d x} - 58 a^{2} e^{2 i c} e^{2 i d x} - 16 a^{2}}{- 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*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-42*a**2*exp(6*I*c)*exp(6*I*d*x) - 72*a**2*exp(4*I*c)*exp(4*I*d*x) - 58*a**2*exp(2*I*c)*exp(2*I*d*x) - 16*a**2)/(-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
15,1,136,0,0.412511," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**2,x)","\frac{2 i a^{2} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{30 i a^{2} e^{4 i c} e^{4 i d x} + 36 i a^{2} e^{2 i c} e^{2 i d x} + 14 i a^{2}}{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*log(exp(2*I*d*x) + exp(-2*I*c))/d + (30*I*a**2*exp(4*I*c)*exp(4*I*d*x) + 36*I*a**2*exp(2*I*c)*exp(2*I*d*x) + 14*I*a**2)/(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
16,1,97,0,0.363125," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**2,x)","- \frac{2 a^{2} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{6 i a^{2} e^{2 i c} e^{2 i d x} + 4 i a^{2}}{- 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*log(exp(2*I*d*x) + exp(-2*I*c))/d + (6*I*a**2*exp(2*I*c)*exp(2*I*d*x) + 4*I*a**2)/(-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
17,1,53,0,0.253289," ","integrate((a+I*a*tan(d*x+c))**2,x)","\frac{2 i a^{2}}{- d e^{2 i c} e^{2 i d x} - d} - \frac{2 i a^{2} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d}"," ",0,"2*I*a**2/(-d*exp(2*I*c)*exp(2*I*d*x) - d) - 2*I*a**2*log(exp(2*I*d*x) + exp(-2*I*c))/d","A",0
18,1,22,0,0.235672," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**2,x)","\frac{a^{2} \log{\left(e^{4 i d x} - e^{- 4 i c} \right)}}{d}"," ",0,"a**2*log(exp(4*I*d*x) - exp(-4*I*c))/d","A",0
19,1,51,0,0.292702," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**2,x)","\frac{2 i a^{2}}{- d e^{2 i c} e^{2 i d x} + d} + \frac{2 i a^{2} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d}"," ",0,"2*I*a**2/(-d*exp(2*I*c)*exp(2*I*d*x) + d) + 2*I*a**2*log(exp(2*I*d*x) - exp(-2*I*c))/d","A",0
20,1,95,0,0.773965," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**2,x)","- \frac{2 a^{2} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{6 i a^{2} e^{2 i c} e^{2 i d x} - 4 i a^{2}}{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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (6*I*a**2*exp(2*I*c)*exp(2*I*d*x) - 4*I*a**2)/(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
21,1,136,0,0.438696," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**2,x)","- \frac{2 i a^{2} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 30 i a^{2} e^{4 i c} e^{4 i d x} + 36 i a^{2} e^{2 i c} e^{2 i d x} - 14 i a^{2}}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-30*I*a**2*exp(4*I*c)*exp(4*I*d*x) + 36*I*a**2*exp(2*I*c)*exp(2*I*d*x) - 14*I*a**2)/(-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
22,1,168,0,4.500340," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**2,x)","\frac{2 a^{2} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{42 a^{2} e^{6 i c} e^{6 i d x} - 72 a^{2} e^{4 i c} e^{4 i d x} + 58 a^{2} e^{2 i c} e^{2 i d x} - 16 a^{2}}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (42*a**2*exp(6*I*c)*exp(6*I*d*x) - 72*a**2*exp(4*I*c)*exp(4*I*d*x) + 58*a**2*exp(2*I*c)*exp(2*I*d*x) - 16*a**2)/(-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
23,1,218,0,0.631971," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c))**2,x)","\frac{2 i a^{2} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 270 i a^{2} e^{8 i c} e^{8 i d x} + 600 i a^{2} e^{6 i c} e^{6 i d x} - 740 i a^{2} e^{4 i c} e^{4 i d x} + 400 i a^{2} e^{2 i c} e^{2 i d x} - 86 i a^{2}}{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,"2*I*a**2*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-270*I*a**2*exp(8*I*c)*exp(8*I*d*x) + 600*I*a**2*exp(6*I*c)*exp(6*I*d*x) - 740*I*a**2*exp(4*I*c)*exp(4*I*d*x) + 400*I*a**2*exp(2*I*c)*exp(2*I*d*x) - 86*I*a**2)/(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
24,1,226,0,0.765202," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**3,x)","\frac{4 a^{3} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{480 i a^{3} e^{8 i c} e^{8 i d x} + 1170 i a^{3} e^{6 i c} e^{6 i d x} + 1390 i a^{3} e^{4 i c} e^{4 i d x} + 770 i a^{3} e^{2 i c} e^{2 i d x} + 166 i a^{3}}{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*a**3*log(exp(2*I*d*x) + exp(-2*I*c))/d + (480*I*a**3*exp(8*I*c)*exp(8*I*d*x) + 1170*I*a**3*exp(6*I*c)*exp(6*I*d*x) + 1390*I*a**3*exp(4*I*c)*exp(4*I*d*x) + 770*I*a**3*exp(2*I*c)*exp(2*I*d*x) + 166*I*a**3)/(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
25,1,177,0,0.530191," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**3,x)","\frac{4 i a^{3} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 24 i a^{3} e^{6 i c} e^{6 i d x} - 46 i a^{3} e^{4 i c} e^{4 i d x} - 36 i a^{3} e^{2 i c} e^{2 i d x} - 10 i a^{3}}{- d e^{8 i c} e^{8 i d x} - 4 d e^{6 i c} e^{6 i d x} - 6 d e^{4 i c} e^{4 i d x} - 4 d e^{2 i c} e^{2 i d x} - d}"," ",0,"4*I*a**3*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-24*I*a**3*exp(6*I*c)*exp(6*I*d*x) - 46*I*a**3*exp(4*I*c)*exp(4*I*d*x) - 36*I*a**3*exp(2*I*c)*exp(2*I*d*x) - 10*I*a**3)/(-d*exp(8*I*c)*exp(8*I*d*x) - 4*d*exp(6*I*c)*exp(6*I*d*x) - 6*d*exp(4*I*c)*exp(4*I*d*x) - 4*d*exp(2*I*c)*exp(2*I*d*x) - d)","B",0
26,1,143,0,0.421225," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**3,x)","- \frac{4 a^{3} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 48 i a^{3} e^{4 i c} e^{4 i d x} - 66 i a^{3} e^{2 i c} e^{2 i d x} - 26 i a^{3}}{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*a**3*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-48*I*a**3*exp(4*I*c)*exp(4*I*d*x) - 66*I*a**3*exp(2*I*c)*exp(2*I*d*x) - 26*I*a**3)/(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)","A",0
27,1,94,0,0.337121," ","integrate((a+I*a*tan(d*x+c))**3,x)","- \frac{4 i a^{3} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{8 a^{3} e^{2 i c} e^{2 i d x} + 6 a^{3}}{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,"-4*I*a**3*log(exp(2*I*d*x) + exp(-2*I*c))/d + (8*a**3*exp(2*I*c)*exp(2*I*d*x) + 6*a**3)/(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
28,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**3,x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
29,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**3,x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
30,1,95,0,0.467465," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**3,x)","- \frac{4 a^{3} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{8 i a^{3} e^{2 i c} e^{2 i d x} - 6 i a^{3}}{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,"-4*a**3*log(exp(2*I*d*x) - exp(-2*I*c))/d + (8*I*a**3*exp(2*I*c)*exp(2*I*d*x) - 6*I*a**3)/(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
31,1,136,0,0.512111," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**3,x)","- \frac{4 i a^{3} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 48 i a^{3} e^{4 i c} e^{4 i d x} + 66 i a^{3} e^{2 i c} e^{2 i d x} - 26 i a^{3}}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-48*I*a**3*exp(4*I*c)*exp(4*I*d*x) + 66*I*a**3*exp(2*I*c)*exp(2*I*d*x) - 26*I*a**3)/(-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
32,1,165,0,1.161841," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**3,x)","\frac{4 a^{3} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{24 a^{3} e^{6 i c} e^{6 i d x} - 46 a^{3} e^{4 i c} e^{4 i d x} + 36 a^{3} e^{2 i c} e^{2 i d x} - 10 a^{3}}{- d e^{8 i c} e^{8 i d x} + 4 d e^{6 i c} e^{6 i d x} - 6 d e^{4 i c} e^{4 i d x} + 4 d e^{2 i c} e^{2 i d x} - d}"," ",0,"4*a**3*log(exp(2*I*d*x) - exp(-2*I*c))/d + (24*a**3*exp(6*I*c)*exp(6*I*d*x) - 46*a**3*exp(4*I*c)*exp(4*I*d*x) + 36*a**3*exp(2*I*c)*exp(2*I*d*x) - 10*a**3)/(-d*exp(8*I*c)*exp(8*I*d*x) + 4*d*exp(6*I*c)*exp(6*I*d*x) - 6*d*exp(4*I*c)*exp(4*I*d*x) + 4*d*exp(2*I*c)*exp(2*I*d*x) - d)","A",0
33,1,218,0,0.701305," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c))**3,x)","\frac{4 i a^{3} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 480 i a^{3} e^{8 i c} e^{8 i d x} + 1170 i a^{3} e^{6 i c} e^{6 i d x} - 1390 i a^{3} e^{4 i c} e^{4 i d x} + 770 i a^{3} e^{2 i c} e^{2 i d x} - 166 i a^{3}}{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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-480*I*a**3*exp(8*I*c)*exp(8*I*d*x) + 1170*I*a**3*exp(6*I*c)*exp(6*I*d*x) - 1390*I*a**3*exp(4*I*c)*exp(4*I*d*x) + 770*I*a**3*exp(2*I*c)*exp(2*I*d*x) - 166*I*a**3)/(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
34,1,250,0,4.802242," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**4,x)","\frac{8 a^{4} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 1080 a^{4} e^{10 i c} e^{10 i d x} - 3420 a^{4} e^{8 i c} e^{8 i d x} - 5400 a^{4} e^{6 i c} e^{6 i d x} - 4500 a^{4} e^{4 i c} e^{4 i d x} - 1944 a^{4} e^{2 i c} e^{2 i d x} - 344 a^{4}}{- 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*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-1080*a**4*exp(10*I*c)*exp(10*I*d*x) - 3420*a**4*exp(8*I*c)*exp(8*I*d*x) - 5400*a**4*exp(6*I*c)*exp(6*I*d*x) - 4500*a**4*exp(4*I*c)*exp(4*I*d*x) - 1944*a**4*exp(2*I*c)*exp(2*I*d*x) - 344*a**4)/(-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
35,1,218,0,0.638527," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**4,x)","\frac{8 i a^{4} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{840 i a^{4} e^{8 i c} e^{8 i d x} + 2220 i a^{4} e^{6 i c} e^{6 i d x} + 2620 i a^{4} e^{4 i c} e^{4 i d x} + 1460 i a^{4} e^{2 i c} e^{2 i d x} + 316 i a^{4}}{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*log(exp(2*I*d*x) + exp(-2*I*c))/d + (840*I*a**4*exp(8*I*c)*exp(8*I*d*x) + 2220*I*a**4*exp(6*I*c)*exp(6*I*d*x) + 2620*I*a**4*exp(4*I*c)*exp(4*I*d*x) + 1460*I*a**4*exp(2*I*c)*exp(2*I*d*x) + 316*I*a**4)/(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
36,1,185,0,0.879723," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**4,x)","- \frac{8 a^{4} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{- 120 i a^{4} e^{6 i c} e^{6 i d x} - 252 i a^{4} e^{4 i c} e^{4 i d x} - 200 i a^{4} e^{2 i c} e^{2 i d x} - 56 i a^{4}}{3 i d e^{8 i c} e^{8 i d x} + 12 i d e^{6 i c} e^{6 i d x} + 18 i d e^{4 i c} e^{4 i d x} + 12 i d e^{2 i c} e^{2 i d x} + 3 i d}"," ",0,"-8*a**4*log(exp(2*I*d*x) + exp(-2*I*c))/d + (-120*I*a**4*exp(6*I*c)*exp(6*I*d*x) - 252*I*a**4*exp(4*I*c)*exp(4*I*d*x) - 200*I*a**4*exp(2*I*c)*exp(2*I*d*x) - 56*I*a**4)/(3*I*d*exp(8*I*c)*exp(8*I*d*x) + 12*I*d*exp(6*I*c)*exp(6*I*d*x) + 18*I*d*exp(4*I*c)*exp(4*I*d*x) + 12*I*d*exp(2*I*c)*exp(2*I*d*x) + 3*I*d)","B",0
37,1,138,0,0.403241," ","integrate((a+I*a*tan(d*x+c))**4,x)","- \frac{8 i a^{4} \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{d} + \frac{72 i a^{4} e^{4 i c} e^{4 i d x} + 108 i a^{4} e^{2 i c} e^{2 i d x} + 44 i a^{4}}{- 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,"-8*I*a**4*log(exp(2*I*d*x) + exp(-2*I*c))/d + (72*I*a**4*exp(4*I*c)*exp(4*I*d*x) + 108*I*a**4*exp(2*I*c)*exp(2*I*d*x) + 44*I*a**4)/(-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
38,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**4,x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
39,1,51,0,0.360479," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**4,x)","\frac{4 i a^{4}}{- d e^{4 i c} e^{4 i d x} + d} + \frac{4 i a^{4} \log{\left(e^{4 i d x} - e^{- 4 i c} \right)}}{d}"," ",0,"4*I*a**4/(-d*exp(4*I*c)*exp(4*I*d*x) + d) + 4*I*a**4*log(exp(4*I*d*x) - exp(-4*I*c))/d","A",0
40,-2,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**4,x)","\text{Exception raised: NotInvertible}"," ",0,"Exception raised: NotInvertible","F(-2)",0
41,1,136,0,0.513168," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**4,x)","- \frac{8 i a^{4} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 72 i a^{4} e^{4 i c} e^{4 i d x} + 108 i a^{4} e^{2 i c} e^{2 i d x} - 44 i a^{4}}{- 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,"-8*I*a**4*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-72*I*a**4*exp(4*I*c)*exp(4*I*d*x) + 108*I*a**4*exp(2*I*c)*exp(2*I*d*x) - 44*I*a**4)/(-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
42,1,184,0,8.901010," ","integrate(cot(d*x+c)**5*(a+I*a*tan(d*x+c))**4,x)","\frac{8 a^{4} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{120 i a^{4} e^{6 i c} e^{6 i d x} - 252 i a^{4} e^{4 i c} e^{4 i d x} + 200 i a^{4} e^{2 i c} e^{2 i d x} - 56 i a^{4}}{- 3 i d e^{8 i c} e^{8 i d x} + 12 i d e^{6 i c} e^{6 i d x} - 18 i d e^{4 i c} e^{4 i d x} + 12 i d e^{2 i c} e^{2 i d x} - 3 i d}"," ",0,"8*a**4*log(exp(2*I*d*x) - exp(-2*I*c))/d + (120*I*a**4*exp(6*I*c)*exp(6*I*d*x) - 252*I*a**4*exp(4*I*c)*exp(4*I*d*x) + 200*I*a**4*exp(2*I*c)*exp(2*I*d*x) - 56*I*a**4)/(-3*I*d*exp(8*I*c)*exp(8*I*d*x) + 12*I*d*exp(6*I*c)*exp(6*I*d*x) - 18*I*d*exp(4*I*c)*exp(4*I*d*x) + 12*I*d*exp(2*I*c)*exp(2*I*d*x) - 3*I*d)","A",0
43,1,218,0,0.733839," ","integrate(cot(d*x+c)**6*(a+I*a*tan(d*x+c))**4,x)","\frac{8 i a^{4} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 840 i a^{4} e^{8 i c} e^{8 i d x} + 2220 i a^{4} e^{6 i c} e^{6 i d x} - 2620 i a^{4} e^{4 i c} e^{4 i d x} + 1460 i a^{4} e^{2 i c} e^{2 i d x} - 316 i a^{4}}{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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-840*I*a**4*exp(8*I*c)*exp(8*I*d*x) + 2220*I*a**4*exp(6*I*c)*exp(6*I*d*x) - 2620*I*a**4*exp(4*I*c)*exp(4*I*d*x) + 1460*I*a**4*exp(2*I*c)*exp(2*I*d*x) - 316*I*a**4)/(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
44,1,246,0,33.782575," ","integrate(cot(d*x+c)**7*(a+I*a*tan(d*x+c))**4,x)","- \frac{8 a^{4} \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{d} + \frac{- 1080 a^{4} e^{10 i c} e^{10 i d x} + 3420 a^{4} e^{8 i c} e^{8 i d x} - 5400 a^{4} e^{6 i c} e^{6 i d x} + 4500 a^{4} e^{4 i c} e^{4 i d x} - 1944 a^{4} e^{2 i c} e^{2 i d x} + 344 a^{4}}{- 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*log(exp(2*I*d*x) - exp(-2*I*c))/d + (-1080*a**4*exp(10*I*c)*exp(10*I*d*x) + 3420*a**4*exp(8*I*c)*exp(8*I*d*x) - 5400*a**4*exp(6*I*c)*exp(6*I*d*x) + 4500*a**4*exp(4*I*c)*exp(4*I*d*x) - 1944*a**4*exp(2*I*c)*exp(2*I*d*x) + 344*a**4)/(-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
45,1,221,0,0.613794," ","integrate(tan(d*x+c)**6/(a+I*a*tan(d*x+c)),x)","\frac{18 i e^{4 i c} e^{4 i d x} + 20 i e^{2 i c} e^{2 i d x} + 14 i}{- 3 a d e^{8 i c} e^{8 i d x} - 12 a d e^{6 i c} e^{6 i d x} - 18 a d e^{4 i c} e^{4 i d x} - 12 a d e^{2 i c} e^{2 i d x} - 3 a d} + \begin{cases} - \frac{i 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{\left(11 e^{2 i c} - 1\right) e^{- 2 i c}}{2 a} - \frac{11}{2 a}\right) & \text{otherwise} \end{cases} + \frac{11 x}{2 a} + \frac{3 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"(18*I*exp(4*I*c)*exp(4*I*d*x) + 20*I*exp(2*I*c)*exp(2*I*d*x) + 14*I)/(-3*a*d*exp(8*I*c)*exp(8*I*d*x) - 12*a*d*exp(6*I*c)*exp(6*I*d*x) - 18*a*d*exp(4*I*c)*exp(4*I*d*x) - 12*a*d*exp(2*I*c)*exp(2*I*d*x) - 3*a*d) + Piecewise((-I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((11*exp(2*I*c) - 1)*exp(-2*I*c)/(2*a) - 11/(2*a)), True)) + 11*x/(2*a) + 3*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
46,1,211,0,0.768038," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c)),x)","\frac{- 12 i e^{4 i c} e^{4 i d x} - 18 i e^{2 i c} e^{2 i d x} - 14 i}{3 i a d e^{6 i c} e^{6 i d x} + 9 i a d e^{4 i c} e^{4 i d x} + 9 i a d e^{2 i c} e^{2 i d x} + 3 i a d} + \begin{cases} - \frac{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 \left(1 - 9 e^{2 i c}\right) e^{- 2 i c}}{2 a} + \frac{9 i}{2 a}\right) & \text{otherwise} \end{cases} - \frac{9 i x}{2 a} + \frac{2 \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"(-12*I*exp(4*I*c)*exp(4*I*d*x) - 18*I*exp(2*I*c)*exp(2*I*d*x) - 14*I)/(3*I*a*d*exp(6*I*c)*exp(6*I*d*x) + 9*I*a*d*exp(4*I*c)*exp(4*I*d*x) + 9*I*a*d*exp(2*I*c)*exp(2*I*d*x) + 3*I*a*d) + Piecewise((-exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(I*(1 - 9*exp(2*I*c))*exp(-2*I*c)/(2*a) + 9*I/(2*a)), True)) - 9*I*x/(2*a) + 2*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
47,1,139,0,0.437498," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c)),x)","\begin{cases} \frac{i 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{\left(1 - 7 e^{2 i c}\right) e^{- 2 i c}}{2 a} + \frac{7}{2 a}\right) & \text{otherwise} \end{cases} - \frac{2}{i a d e^{4 i c} e^{4 i d x} + 2 i a d e^{2 i c} e^{2 i d x} + i a d} - \frac{7 x}{2 a} - \frac{2 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((1 - 7*exp(2*I*c))*exp(-2*I*c)/(2*a) + 7/(2*a)), True)) - 2/(I*a*d*exp(4*I*c)*exp(4*I*d*x) + 2*I*a*d*exp(2*I*c)*exp(2*I*d*x) + I*a*d) - 7*x/(2*a) - 2*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
48,1,119,0,0.403512," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c)),x)","\begin{cases} \frac{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 \left(1 - 5 e^{2 i c}\right) e^{- 2 i c}}{2 a} - \frac{5 i}{2 a}\right) & \text{otherwise} \end{cases} - \frac{2}{- a d e^{2 i c} e^{2 i d x} - a d} + \frac{5 i x}{2 a} - \frac{\log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-I*(1 - 5*exp(2*I*c))*exp(-2*I*c)/(2*a) - 5*I/(2*a)), True)) - 2/(-a*d*exp(2*I*c)*exp(2*I*d*x) - a*d) + 5*I*x/(2*a) - log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
49,1,90,0,0.336861," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c)),x)","\begin{cases} - \frac{i 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{\left(3 e^{2 i c} - 1\right) e^{- 2 i c}}{2 a} - \frac{3}{2 a}\right) & \text{otherwise} \end{cases} + \frac{3 x}{2 a} + \frac{i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((-I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((3*exp(2*I*c) - 1)*exp(-2*I*c)/(2*a) - 3/(2*a)), True)) + 3*x/(2*a) + I*log(exp(2*I*d*x) + exp(-2*I*c))/(a*d)","A",0
50,1,66,0,0.205399," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c)),x)","\begin{cases} - \frac{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{\left(- i e^{2 i c} + i\right) e^{- 2 i c}}{2 a} + \frac{i}{2 a}\right) & \text{otherwise} \end{cases} - \frac{i x}{2 a}"," ",0,"Piecewise((-exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((-I*exp(2*I*c) + I)*exp(-2*I*c)/(2*a) + I/(2*a)), True)) - I*x/(2*a)","A",0
51,1,61,0,0.165627," ","integrate(1/(a+I*a*tan(d*x+c)),x)","\begin{cases} \frac{i 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{\left(e^{2 i c} + 1\right) e^{- 2 i c}}{2 a} - \frac{1}{2 a}\right) & \text{otherwise} \end{cases} + \frac{x}{2 a}"," ",0,"Piecewise((I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((exp(2*I*c) + 1)*exp(-2*I*c)/(2*a) - 1/(2*a)), True)) + x/(2*a)","A",0
52,1,92,0,0.319535," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c)),x)","\begin{cases} \frac{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 \left(3 e^{2 i c} + 1\right) e^{- 2 i c}}{2 a} + \frac{3 i}{2 a}\right) & \text{otherwise} \end{cases} - \frac{3 i x}{2 a} + \frac{\log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(-I*(3*exp(2*I*c) + 1)*exp(-2*I*c)/(2*a) + 3*I/(2*a)), True)) - 3*I*x/(2*a) + log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
53,1,117,0,0.374758," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c)),x)","\begin{cases} - \frac{i 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{\left(- 5 e^{2 i c} - 1\right) e^{- 2 i c}}{2 a} + \frac{5}{2 a}\right) & \text{otherwise} \end{cases} + \frac{2 i}{- a d e^{2 i c} e^{2 i d x} + a d} - \frac{5 x}{2 a} - \frac{i \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((-I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((-5*exp(2*I*c) - 1)*exp(-2*I*c)/(2*a) + 5/(2*a)), True)) + 2*I/(-a*d*exp(2*I*c)*exp(2*I*d*x) + a*d) - 5*x/(2*a) - I*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
54,1,139,0,0.476416," ","integrate(cot(d*x+c)**3/(a+I*a*tan(d*x+c)),x)","\begin{cases} - \frac{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 \left(7 e^{2 i c} + 1\right) e^{- 2 i c}}{2 a} - \frac{7 i}{2 a}\right) & \text{otherwise} \end{cases} - \frac{2}{- 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} + \frac{7 i x}{2 a} - \frac{2 \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"Piecewise((-exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*(I*(7*exp(2*I*c) + 1)*exp(-2*I*c)/(2*a) - 7*I/(2*a)), True)) - 2/(-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) + 7*I*x/(2*a) - 2*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
55,1,197,0,0.530005," ","integrate(cot(d*x+c)**4/(a+I*a*tan(d*x+c)),x)","\frac{- 12 i e^{4 i c} e^{4 i d x} + 18 i e^{2 i c} e^{2 i d x} - 14 i}{- 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{i 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{\left(9 e^{2 i c} + 1\right) e^{- 2 i c}}{2 a} - \frac{9}{2 a}\right) & \text{otherwise} \end{cases} + \frac{9 x}{2 a} + \frac{2 i \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a d}"," ",0,"(-12*I*exp(4*I*c)*exp(4*I*d*x) + 18*I*exp(2*I*c)*exp(2*I*d*x) - 14*I)/(-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*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((9*exp(2*I*c) + 1)*exp(-2*I*c)/(2*a) - 9/(2*a)), True)) + 9*x/(2*a) + 2*I*log(exp(2*I*d*x) - exp(-2*I*c))/(a*d)","A",0
56,1,267,0,0.673127," ","integrate(tan(d*x+c)**6/(a+I*a*tan(d*x+c))**2,x)","\frac{- 18 i e^{4 i c} e^{4 i d x} - 36 i e^{2 i c} e^{2 i d x} - 26 i}{- 3 a^{2} d e^{6 i c} e^{6 i d x} - 9 a^{2} d e^{4 i c} e^{4 i d x} - 9 a^{2} d e^{2 i c} e^{2 i d x} - 3 a^{2} d} + \begin{cases} \frac{\left(80 i a^{2} d e^{4 i c} e^{- 2 i d x} - 4 i a^{2} d e^{2 i c} 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{\left(- 49 e^{4 i c} + 10 e^{2 i c} - 1\right) e^{- 4 i c}}{4 a^{2}} + \frac{49}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{49 x}{4 a^{2}} - \frac{6 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"(-18*I*exp(4*I*c)*exp(4*I*d*x) - 36*I*exp(2*I*c)*exp(2*I*d*x) - 26*I)/(-3*a**2*d*exp(6*I*c)*exp(6*I*d*x) - 9*a**2*d*exp(4*I*c)*exp(4*I*d*x) - 9*a**2*d*exp(2*I*c)*exp(2*I*d*x) - 3*a**2*d) + Piecewise(((80*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) - 4*I*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*((-49*exp(4*I*c) + 10*exp(2*I*c) - 1)*exp(-4*I*c)/(4*a**2) + 49/(4*a**2)), True)) - 49*x/(4*a**2) - 6*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d)","A",0
57,1,218,0,4.922336," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**2,x)","\frac{- 2 e^{2 i c} e^{2 i d x} - 4}{- 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(16 a^{2} d e^{4 i c} e^{- 2 i d x} - a^{2} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{16 a^{4} d^{2}} & \text{for}\: 16 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(\frac{i \left(31 e^{4 i c} - 8 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} - \frac{31 i}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{31 i x}{4 a^{2}} - \frac{4 \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"(-2*exp(2*I*c)*exp(2*I*d*x) - 4)/(-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(((16*a**2*d*exp(4*I*c)*exp(-2*I*d*x) - a**2*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(16*a**4*d**2), Ne(16*a**4*d**2*exp(6*I*c), 0)), (x*(I*(31*exp(4*I*c) - 8*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) - 31*I/(4*a**2)), True)) + 31*I*x/(4*a**2) - 4*log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d)","A",0
58,1,180,0,0.534161," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(- 48 i a^{2} d e^{4 i c} e^{- 2 i d x} + 4 i a^{2} d e^{2 i c} 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{\left(17 e^{4 i c} - 6 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} - \frac{17}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{2 i}{- a^{2} d e^{2 i c} e^{2 i d x} - a^{2} d} + \frac{17 x}{4 a^{2}} + \frac{2 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"Piecewise(((-48*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + 4*I*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*((17*exp(4*I*c) - 6*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) - 17/(4*a**2)), True)) + 2*I/(-a**2*d*exp(2*I*c)*exp(2*I*d*x) - a**2*d) + 17*x/(4*a**2) + 2*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d)","A",0
59,1,148,0,0.876011," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(- 16 a^{2} d e^{4 i c} e^{- 2 i d x} + 2 a^{2} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{32 a^{4} d^{2}} & \text{for}\: 32 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{i \left(7 e^{4 i c} - 4 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} + \frac{7 i}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{7 i x}{4 a^{2}} + \frac{\log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"Piecewise(((-16*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + 2*a**2*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(32*a**4*d**2), Ne(32*a**4*d**2*exp(6*I*c), 0)), (x*(-I*(7*exp(4*I*c) - 4*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) + 7*I/(4*a**2)), True)) - 7*I*x/(4*a**2) + log(exp(2*I*d*x) + exp(-2*I*c))/(a**2*d)","A",0
60,1,119,0,0.281365," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(16 i a^{2} d e^{4 i c} e^{- 2 i d x} - 4 i a^{2} d e^{2 i c} 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{\left(- e^{4 i c} + 2 e^{2 i c} - 1\right) e^{- 4 i c}}{4 a^{2}} + \frac{1}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x}{4 a^{2}}"," ",0,"Piecewise(((16*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) - 4*I*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*((-exp(4*I*c) + 2*exp(2*I*c) - 1)*exp(-4*I*c)/(4*a**2) + 1/(4*a**2)), True)) - x/(4*a**2)","A",0
61,1,75,0,0.249362," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} - \frac{e^{- 4 i c} e^{- 4 i d x}}{16 a^{2} d} & \text{for}\: 16 a^{2} d e^{4 i c} \neq 0 \\x \left(\frac{\left(- i e^{4 i c} + i\right) e^{- 4 i c}}{4 a^{2}} + \frac{i}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{i x}{4 a^{2}}"," ",0,"Piecewise((-exp(-4*I*c)*exp(-4*I*d*x)/(16*a**2*d), Ne(16*a**2*d*exp(4*I*c), 0)), (x*((-I*exp(4*I*c) + I)*exp(-4*I*c)/(4*a**2) + I/(4*a**2)), True)) - I*x/(4*a**2)","A",0
62,1,119,0,0.246994," ","integrate(1/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(16 i a^{2} d e^{4 i c} e^{- 2 i d x} + 4 i a^{2} d e^{2 i c} 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{\left(e^{4 i c} + 2 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} - \frac{1}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{x}{4 a^{2}}"," ",0,"Piecewise(((16*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + 4*I*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*((exp(4*I*c) + 2*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) - 1/(4*a**2)), True)) + x/(4*a**2)","A",0
63,1,148,0,0.487857," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(16 a^{2} d e^{4 i c} e^{- 2 i d x} + 2 a^{2} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{32 a^{4} d^{2}} & \text{for}\: 32 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(- \frac{i \left(7 e^{4 i c} + 4 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} + \frac{7 i}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{7 i x}{4 a^{2}} + \frac{\log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"Piecewise(((16*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + 2*a**2*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(32*a**4*d**2), Ne(32*a**4*d**2*exp(6*I*c), 0)), (x*(-I*(7*exp(4*I*c) + 4*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) + 7*I/(4*a**2)), True)) - 7*I*x/(4*a**2) + log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d)","A",0
64,1,182,0,0.506016," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**2,x)","\begin{cases} \frac{\left(- 48 i a^{2} d e^{4 i c} e^{- 2 i d x} - 4 i a^{2} d e^{2 i c} 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{\left(- 17 e^{4 i c} - 6 e^{2 i c} - 1\right) e^{- 4 i c}}{4 a^{2}} + \frac{17}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{2 i}{a^{2} d e^{2 i c} e^{2 i d x} - a^{2} d} - \frac{17 x}{4 a^{2}} - \frac{2 i \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"Piecewise(((-48*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) - 4*I*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*((-17*exp(4*I*c) - 6*exp(2*I*c) - 1)*exp(-4*I*c)/(4*a**2) + 17/(4*a**2)), True)) - 2*I/(a**2*d*exp(2*I*c)*exp(2*I*d*x) - a**2*d) - 17*x/(4*a**2) - 2*I*log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d)","A",0
65,1,216,0,1.495844," ","integrate(cot(d*x+c)**3/(a+I*a*tan(d*x+c))**2,x)","\frac{2 e^{2 i c} e^{2 i d x} - 4}{- 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(- 16 a^{2} d e^{4 i c} e^{- 2 i d x} - a^{2} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{16 a^{4} d^{2}} & \text{for}\: 16 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(\frac{i \left(31 e^{4 i c} + 8 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} - \frac{31 i}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{31 i x}{4 a^{2}} - \frac{4 \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{2} d}"," ",0,"(2*exp(2*I*c)*exp(2*I*d*x) - 4)/(-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(((-16*a**2*d*exp(4*I*c)*exp(-2*I*d*x) - a**2*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(16*a**4*d**2), Ne(16*a**4*d**2*exp(6*I*c), 0)), (x*(I*(31*exp(4*I*c) + 8*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) - 31*I/(4*a**2)), True)) + 31*I*x/(4*a**2) - 4*log(exp(2*I*d*x) - exp(-2*I*c))/(a**2*d)","A",0
66,1,264,0,0.771733," ","integrate(tan(d*x+c)**6/(a+I*a*tan(d*x+c))**3,x)","\frac{- 4 e^{2 i c} e^{2 i d x} - 6}{- i a^{3} d e^{4 i c} e^{4 i d x} - 2 i a^{3} d e^{2 i c} e^{2 i d x} - i a^{3} d} + \begin{cases} - \frac{\left(59904 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 6912 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} + 512 i a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(111 e^{6 i c} - 39 e^{4 i c} + 9 e^{2 i c} - 1\right) e^{- 6 i c}}{8 a^{3}} - \frac{111}{8 a^{3}}\right) & \text{otherwise} \end{cases} + \frac{111 x}{8 a^{3}} + \frac{7 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"(-4*exp(2*I*c)*exp(2*I*d*x) - 6)/(-I*a**3*d*exp(4*I*c)*exp(4*I*d*x) - 2*I*a**3*d*exp(2*I*c)*exp(2*I*d*x) - I*a**3*d) + Piecewise((-(59904*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 6912*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) + 512*I*a**6*d**2*exp(6*I*c)*exp(-6*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*exp(6*I*c) - 39*exp(4*I*c) + 9*exp(2*I*c) - 1)*exp(-6*I*c)/(8*a**3) - 111/(8*a**3)), True)) + 111*x/(8*a**3) + 7*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a**3*d)","A",0
67,1,212,0,1.266672," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} \frac{\left(- 35328 a^{6} d^{2} e^{10 i c} e^{- 2 i d x} + 5376 a^{6} d^{2} e^{8 i c} e^{- 4 i d x} - 512 a^{6} d^{2} e^{6 i c} e^{- 6 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 \left(- 49 e^{6 i c} + 23 e^{4 i c} - 7 e^{2 i c} + 1\right) e^{- 6 i c}}{8 a^{3}} + \frac{49 i}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{2}{a^{3} d e^{2 i c} e^{2 i d x} + a^{3} d} - \frac{49 i x}{8 a^{3}} + \frac{3 \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"Piecewise(((-35328*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) + 5376*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) - 512*a**6*d**2*exp(6*I*c)*exp(-6*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*(-49*exp(6*I*c) + 23*exp(4*I*c) - 7*exp(2*I*c) + 1)*exp(-6*I*c)/(8*a**3) + 49*I/(8*a**3)), True)) - 2/(a**3*d*exp(2*I*c)*exp(2*I*d*x) + a**3*d) - 49*I*x/(8*a**3) + 3*log(exp(2*I*d*x) + exp(-2*I*c))/(a**3*d)","A",0
68,1,187,0,0.584262," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(- 16896 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} + 3840 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} - 512 i a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(- 15 e^{6 i c} + 11 e^{4 i c} - 5 e^{2 i c} + 1\right) e^{- 6 i c}}{8 a^{3}} + \frac{15}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{15 x}{8 a^{3}} - \frac{i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"Piecewise((-(-16896*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) + 3840*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) - 512*I*a**6*d**2*exp(6*I*c)*exp(-6*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*exp(6*I*c) + 11*exp(4*I*c) - 5*exp(2*I*c) + 1)*exp(-6*I*c)/(8*a**3) + 15/(8*a**3)), True)) - 15*x/(8*a**3) - I*log(exp(2*I*d*x) + exp(-2*I*c))/(a**3*d)","A",0
69,1,158,0,0.531727," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} \frac{\left(4608 a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 2304 a^{6} d^{2} e^{8 i c} e^{- 4 i d x} + 512 a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(i e^{6 i c} - 3 i e^{4 i c} + 3 i e^{2 i c} - i\right) e^{- 6 i c}}{8 a^{3}} - \frac{i}{8 a^{3}}\right) & \text{otherwise} \end{cases} + \frac{i x}{8 a^{3}}"," ",0,"Piecewise(((4608*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 2304*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) + 512*a**6*d**2*exp(6*I*c)*exp(-6*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*exp(6*I*c) - 3*I*exp(4*I*c) + 3*I*exp(2*I*c) - I)*exp(-6*I*c)/(8*a**3) - I/(8*a**3)), True)) + I*x/(8*a**3)","A",0
70,1,155,0,0.408030," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(- 1536 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 768 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} + 512 i a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(- e^{6 i c} + e^{4 i c} + e^{2 i c} - 1\right) e^{- 6 i c}}{8 a^{3}} + \frac{1}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x}{8 a^{3}}"," ",0,"Piecewise((-(-1536*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 768*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) + 512*I*a**6*d**2*exp(6*I*c)*exp(-6*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*((-exp(6*I*c) + exp(4*I*c) + exp(2*I*c) - 1)*exp(-6*I*c)/(8*a**3) + 1/(8*a**3)), True)) - x/(8*a**3)","A",0
71,1,155,0,0.437707," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} \frac{\left(1536 a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 768 a^{6} d^{2} e^{8 i c} e^{- 4 i d x} - 512 a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(- i e^{6 i c} - i e^{4 i c} + i e^{2 i c} + i\right) e^{- 6 i c}}{8 a^{3}} + \frac{i}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{i x}{8 a^{3}}"," ",0,"Piecewise(((1536*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 768*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) - 512*a**6*d**2*exp(6*I*c)*exp(-6*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*exp(6*I*c) - I*exp(4*I*c) + I*exp(2*I*c) + I)*exp(-6*I*c)/(8*a**3) + I/(8*a**3)), True)) - I*x/(8*a**3)","A",0
72,1,160,0,0.385322," ","integrate(1/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(- 4608 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 2304 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} - 512 i a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(e^{6 i c} + 3 e^{4 i c} + 3 e^{2 i c} + 1\right) e^{- 6 i c}}{8 a^{3}} - \frac{1}{8 a^{3}}\right) & \text{otherwise} \end{cases} + \frac{x}{8 a^{3}}"," ",0,"Piecewise((-(-4608*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 2304*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) - 512*I*a**6*d**2*exp(6*I*c)*exp(-6*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*((exp(6*I*c) + 3*exp(4*I*c) + 3*exp(2*I*c) + 1)*exp(-6*I*c)/(8*a**3) - 1/(8*a**3)), True)) + x/(8*a**3)","A",0
73,1,184,0,0.614595," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} \frac{\left(16896 a^{6} d^{2} e^{10 i c} e^{- 2 i d x} + 3840 a^{6} d^{2} e^{8 i c} e^{- 4 i d x} + 512 a^{6} d^{2} e^{6 i c} e^{- 6 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 \left(15 e^{6 i c} + 11 e^{4 i c} + 5 e^{2 i c} + 1\right) e^{- 6 i c}}{8 a^{3}} + \frac{15 i}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{15 i x}{8 a^{3}} + \frac{\log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"Piecewise(((16896*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) + 3840*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) + 512*a**6*d**2*exp(6*I*c)*exp(-6*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*(15*exp(6*I*c) + 11*exp(4*I*c) + 5*exp(2*I*c) + 1)*exp(-6*I*c)/(8*a**3) + 15*I/(8*a**3)), True)) - 15*I*x/(8*a**3) + log(exp(2*I*d*x) - exp(-2*I*c))/(a**3*d)","A",0
74,1,219,0,0.644033," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**3,x)","\begin{cases} - \frac{\left(35328 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} + 5376 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} + 512 i a^{6} d^{2} e^{6 i c} e^{- 6 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{\left(- 49 e^{6 i c} - 23 e^{4 i c} - 7 e^{2 i c} - 1\right) e^{- 6 i c}}{8 a^{3}} + \frac{49}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{2 i}{a^{3} d e^{2 i c} e^{2 i d x} - a^{3} d} - \frac{49 x}{8 a^{3}} - \frac{3 i \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{3} d}"," ",0,"Piecewise((-(35328*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) + 5376*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) + 512*I*a**6*d**2*exp(6*I*c)*exp(-6*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*exp(6*I*c) - 23*exp(4*I*c) - 7*exp(2*I*c) - 1)*exp(-6*I*c)/(8*a**3) + 49/(8*a**3)), True)) - 2*I/(a**3*d*exp(2*I*c)*exp(2*I*d*x) - a**3*d) - 49*x/(8*a**3) - 3*I*log(exp(2*I*d*x) - exp(-2*I*c))/(a**3*d)","A",0
75,1,250,0,0.858006," ","integrate(tan(d*x+c)**6/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(442368 i a^{12} d^{3} e^{18 i c} e^{- 2 i d x} - 92160 i a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + 16384 i a^{12} d^{3} e^{14 i c} e^{- 6 i d x} - 1536 i a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{196608 a^{16} d^{4}} & \text{for}\: 196608 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(\frac{\left(- 129 e^{8 i c} + 72 e^{6 i c} - 30 e^{4 i c} + 8 e^{2 i c} - 1\right) e^{- 8 i c}}{16 a^{4}} + \frac{129}{16 a^{4}}\right) & \text{otherwise} \end{cases} + \frac{2 i}{a^{4} d e^{2 i c} e^{2 i d x} + a^{4} d} - \frac{129 x}{16 a^{4}} - \frac{4 i \log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"Piecewise(((442368*I*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) - 92160*I*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + 16384*I*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) - 1536*I*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(196608*a**16*d**4), Ne(196608*a**16*d**4*exp(20*I*c), 0)), (x*((-129*exp(8*I*c) + 72*exp(6*I*c) - 30*exp(4*I*c) + 8*exp(2*I*c) - 1)*exp(-8*I*c)/(16*a**4) + 129/(16*a**4)), True)) + 2*I/(a**4*d*exp(2*I*c)*exp(2*I*d*x) + a**4*d) - 129*x/(16*a**4) - 4*I*log(exp(2*I*d*x) + exp(-2*I*c))/(a**4*d)","A",0
76,1,216,0,9.315977," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(106496 a^{12} d^{3} e^{18 i c} e^{- 2 i d x} - 32768 a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + 8192 a^{12} d^{3} e^{14 i c} e^{- 6 i d x} - 1024 a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{131072 a^{16} d^{4}} & \text{for}\: 131072 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(\frac{i \left(31 e^{8 i c} - 26 e^{6 i c} + 16 e^{4 i c} - 6 e^{2 i c} + 1\right) e^{- 8 i c}}{16 a^{4}} - \frac{31 i}{16 a^{4}}\right) & \text{otherwise} \end{cases} + \frac{31 i x}{16 a^{4}} - \frac{\log{\left(e^{2 i d x} + e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"Piecewise(((106496*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) - 32768*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + 8192*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) - 1024*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(131072*a**16*d**4), Ne(131072*a**16*d**4*exp(20*I*c), 0)), (x*(I*(31*exp(8*I*c) - 26*exp(6*I*c) + 16*exp(4*I*c) - 6*exp(2*I*c) + 1)*exp(-8*I*c)/(16*a**4) - 31*I/(16*a**4)), True)) + 31*I*x/(16*a**4) - log(exp(2*I*d*x) + exp(-2*I*c))/(a**4*d)","A",0
77,1,190,0,0.552938," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(- 98304 i a^{12} d^{3} e^{18 i c} e^{- 2 i d x} + 73728 i a^{12} d^{3} e^{16 i c} e^{- 4 i d x} - 32768 i a^{12} d^{3} e^{14 i c} e^{- 6 i d x} + 6144 i a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{786432 a^{16} d^{4}} & \text{for}\: 786432 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(\frac{\left(e^{8 i c} - 4 e^{6 i c} + 6 e^{4 i c} - 4 e^{2 i c} + 1\right) e^{- 8 i c}}{16 a^{4}} - \frac{1}{16 a^{4}}\right) & \text{otherwise} \end{cases} + \frac{x}{16 a^{4}}"," ",0,"Piecewise(((-98304*I*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) + 73728*I*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) - 32768*I*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) + 6144*I*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(786432*a**16*d**4), Ne(786432*a**16*d**4*exp(20*I*c), 0)), (x*((exp(8*I*c) - 4*exp(6*I*c) + 6*exp(4*I*c) - 4*exp(2*I*c) + 1)*exp(-8*I*c)/(16*a**4) - 1/(16*a**4)), True)) + x/(16*a**4)","A",0
78,1,158,0,2.447789," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(6144 a^{8} d^{2} e^{14 i c} e^{- 2 i d x} - 2048 a^{8} d^{2} e^{10 i c} e^{- 6 i d x} + 768 a^{8} d^{2} e^{8 i c} e^{- 8 i d x}\right) e^{- 16 i c}}{98304 a^{12} d^{3}} & \text{for}\: 98304 a^{12} d^{3} e^{16 i c} \neq 0 \\x \left(\frac{\left(i e^{8 i c} - 2 i e^{6 i c} + 2 i e^{2 i c} - i\right) e^{- 8 i c}}{16 a^{4}} - \frac{i}{16 a^{4}}\right) & \text{otherwise} \end{cases} + \frac{i x}{16 a^{4}}"," ",0,"Piecewise(((6144*a**8*d**2*exp(14*I*c)*exp(-2*I*d*x) - 2048*a**8*d**2*exp(10*I*c)*exp(-6*I*d*x) + 768*a**8*d**2*exp(8*I*c)*exp(-8*I*d*x))*exp(-16*I*c)/(98304*a**12*d**3), Ne(98304*a**12*d**3*exp(16*I*c), 0)), (x*((I*exp(8*I*c) - 2*I*exp(6*I*c) + 2*I*exp(2*I*c) - I)*exp(-8*I*c)/(16*a**4) - I/(16*a**4)), True)) + I*x/(16*a**4)","A",0
79,1,119,0,0.387360," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(128 i a^{4} d e^{8 i c} e^{- 4 i d x} - 32 i a^{4} d e^{4 i c} e^{- 8 i d x}\right) e^{- 12 i c}}{4096 a^{8} d^{2}} & \text{for}\: 4096 a^{8} d^{2} e^{12 i c} \neq 0 \\x \left(\frac{\left(- e^{8 i c} + 2 e^{4 i c} - 1\right) e^{- 8 i c}}{16 a^{4}} + \frac{1}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{x}{16 a^{4}}"," ",0,"Piecewise(((128*I*a**4*d*exp(8*I*c)*exp(-4*I*d*x) - 32*I*a**4*d*exp(4*I*c)*exp(-8*I*d*x))*exp(-12*I*c)/(4096*a**8*d**2), Ne(4096*a**8*d**2*exp(12*I*c), 0)), (x*((-exp(8*I*c) + 2*exp(4*I*c) - 1)*exp(-8*I*c)/(16*a**4) + 1/(16*a**4)), True)) - x/(16*a**4)","A",0
80,1,158,0,0.771720," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(6144 a^{8} d^{2} e^{14 i c} e^{- 2 i d x} - 2048 a^{8} d^{2} e^{10 i c} e^{- 6 i d x} - 768 a^{8} d^{2} e^{8 i c} e^{- 8 i d x}\right) e^{- 16 i c}}{98304 a^{12} d^{3}} & \text{for}\: 98304 a^{12} d^{3} e^{16 i c} \neq 0 \\x \left(\frac{\left(- i e^{8 i c} - 2 i e^{6 i c} + 2 i e^{2 i c} + i\right) e^{- 8 i c}}{16 a^{4}} + \frac{i}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{i x}{16 a^{4}}"," ",0,"Piecewise(((6144*a**8*d**2*exp(14*I*c)*exp(-2*I*d*x) - 2048*a**8*d**2*exp(10*I*c)*exp(-6*I*d*x) - 768*a**8*d**2*exp(8*I*c)*exp(-8*I*d*x))*exp(-16*I*c)/(98304*a**12*d**3), Ne(98304*a**12*d**3*exp(16*I*c), 0)), (x*((-I*exp(8*I*c) - 2*I*exp(6*I*c) + 2*I*exp(2*I*c) + I)*exp(-8*I*c)/(16*a**4) + I/(16*a**4)), True)) - I*x/(16*a**4)","A",0
81,1,190,0,0.438227," ","integrate(1/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(98304 i a^{12} d^{3} e^{18 i c} e^{- 2 i d x} + 73728 i a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + 32768 i a^{12} d^{3} e^{14 i c} e^{- 6 i d x} + 6144 i a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{786432 a^{16} d^{4}} & \text{for}\: 786432 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(\frac{\left(e^{8 i c} + 4 e^{6 i c} + 6 e^{4 i c} + 4 e^{2 i c} + 1\right) e^{- 8 i c}}{16 a^{4}} - \frac{1}{16 a^{4}}\right) & \text{otherwise} \end{cases} + \frac{x}{16 a^{4}}"," ",0,"Piecewise(((98304*I*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) + 73728*I*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + 32768*I*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) + 6144*I*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(786432*a**16*d**4), Ne(786432*a**16*d**4*exp(20*I*c), 0)), (x*((exp(8*I*c) + 4*exp(6*I*c) + 6*exp(4*I*c) + 4*exp(2*I*c) + 1)*exp(-8*I*c)/(16*a**4) - 1/(16*a**4)), True)) + x/(16*a**4)","A",0
82,1,216,0,1.080103," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(106496 a^{12} d^{3} e^{18 i c} e^{- 2 i d x} + 32768 a^{12} d^{3} e^{16 i c} e^{- 4 i d x} + 8192 a^{12} d^{3} e^{14 i c} e^{- 6 i d x} + 1024 a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{131072 a^{16} d^{4}} & \text{for}\: 131072 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(- \frac{i \left(31 e^{8 i c} + 26 e^{6 i c} + 16 e^{4 i c} + 6 e^{2 i c} + 1\right) e^{- 8 i c}}{16 a^{4}} + \frac{31 i}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{31 i x}{16 a^{4}} + \frac{\log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"Piecewise(((106496*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) + 32768*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) + 8192*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) + 1024*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(131072*a**16*d**4), Ne(131072*a**16*d**4*exp(20*I*c), 0)), (x*(-I*(31*exp(8*I*c) + 26*exp(6*I*c) + 16*exp(4*I*c) + 6*exp(2*I*c) + 1)*exp(-8*I*c)/(16*a**4) + 31*I/(16*a**4)), True)) - 31*I*x/(16*a**4) + log(exp(2*I*d*x) - exp(-2*I*c))/(a**4*d)","A",0
83,1,253,0,0.762327," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**4,x)","\begin{cases} \frac{\left(- 442368 i a^{12} d^{3} e^{18 i c} e^{- 2 i d x} - 92160 i a^{12} d^{3} e^{16 i c} e^{- 4 i d x} - 16384 i a^{12} d^{3} e^{14 i c} e^{- 6 i d x} - 1536 i a^{12} d^{3} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{196608 a^{16} d^{4}} & \text{for}\: 196608 a^{16} d^{4} e^{20 i c} \neq 0 \\x \left(\frac{\left(- 129 e^{8 i c} - 72 e^{6 i c} - 30 e^{4 i c} - 8 e^{2 i c} - 1\right) e^{- 8 i c}}{16 a^{4}} + \frac{129}{16 a^{4}}\right) & \text{otherwise} \end{cases} - \frac{2 i}{a^{4} d e^{2 i c} e^{2 i d x} - a^{4} d} - \frac{129 x}{16 a^{4}} - \frac{4 i \log{\left(e^{2 i d x} - e^{- 2 i c} \right)}}{a^{4} d}"," ",0,"Piecewise(((-442368*I*a**12*d**3*exp(18*I*c)*exp(-2*I*d*x) - 92160*I*a**12*d**3*exp(16*I*c)*exp(-4*I*d*x) - 16384*I*a**12*d**3*exp(14*I*c)*exp(-6*I*d*x) - 1536*I*a**12*d**3*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(196608*a**16*d**4), Ne(196608*a**16*d**4*exp(20*I*c), 0)), (x*((-129*exp(8*I*c) - 72*exp(6*I*c) - 30*exp(4*I*c) - 8*exp(2*I*c) - 1)*exp(-8*I*c)/(16*a**4) + 129/(16*a**4)), True)) - 2*I/(a**4*d*exp(2*I*c)*exp(2*I*d*x) - a**4*d) - 129*x/(16*a**4) - 4*I*log(exp(2*I*d*x) - exp(-2*I*c))/(a**4*d)","A",0
84,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**4,x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**4, x)","F",0
85,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**3,x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**3, x)","F",0
86,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**2,x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**2, x)","F",0
87,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x), x)","F",0
88,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \tan{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(I*a*tan(c + d*x) + a), x)","F",0
89,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x), x)","F",0
90,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x)**2, x)","F",0
91,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x)**3, x)","F",0
92,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**3, x)","F",0
93,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**2, x)","F",0
94,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x), x)","F",0
95,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(3/2), x)","F",0
96,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*cot(c + d*x), x)","F",0
97,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*cot(c + d*x)**2, x)","F",0
98,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*cot(c + d*x)**3, x)","F",0
99,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**(5/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*tan(c + d*x)**3, x)","F",0
100,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(5/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*tan(c + d*x)**2, x)","F",0
101,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(5/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)*tan(c + d*x), x)","F",0
102,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(5/2), x)","F",0
103,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(7/2),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(7/2), x)","F",0
108,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**5/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
109,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**4/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
110,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**3/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
111,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**2/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
112,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{i a \tan{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(I*a*tan(c + d*x) + a), x)","F",0
114,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
115,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)**2/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
116,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{3}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)**3/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
117,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**5/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(cot(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
126,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**5/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)**4/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
128,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
129,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
130,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-5/2), x)","F",0
132,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
133,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(7/2),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-7/2), x)","F",0
135,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(d*tan(e + f*x))**(5/2), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x), x))","F",0
136,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(d*tan(e + f*x))**(3/2), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x), x))","F",0
137,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \sqrt{d \tan{\left(e + f x \right)}}\right)\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*sqrt(d*tan(e + f*x)), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x), x))","F",0
138,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))**(1/2),x)","i a \left(\int \left(- \frac{i}{\sqrt{d \tan{\left(e + f x \right)}}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"I*a*(Integral(-I/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)/sqrt(d*tan(e + f*x)), x))","F",0
139,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))**(3/2),x)","i a \left(\int \left(- \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"I*a*(Integral(-I/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(3/2), x))","F",0
140,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))**(5/2),x)","i a \left(\int \left(- \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"I*a*(Integral(-I/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(5/2), x))","F",0
141,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))**(7/2),x)","i a \left(\int \left(- \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"I*a*(Integral(-I/(d*tan(e + f*x))**(7/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(7/2), x))","F",0
142,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a-I*a*tan(f*x+e)),x)","- i a \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a*(Integral(I*(d*tan(e + f*x))**(5/2), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x), x))","F",0
143,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a-I*a*tan(f*x+e)),x)","- i a \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a*(Integral(I*(d*tan(e + f*x))**(3/2), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x), x))","F",0
144,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a-I*a*tan(f*x+e)),x)","- i a \left(\int i \sqrt{d \tan{\left(e + f x \right)}}\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a*(Integral(I*sqrt(d*tan(e + f*x)), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x), x))","F",0
145,0,0,0,0.000000," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))**(1/2),x)","- i a \left(\int \frac{i}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"-I*a*(Integral(I/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)/sqrt(d*tan(e + f*x)), x))","F",0
146,0,0,0,0.000000," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))**(3/2),x)","- i a \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"-I*a*(Integral(I/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(3/2), x))","F",0
147,0,0,0,0.000000," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))**(5/2),x)","- i a \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"-I*a*(Integral(I/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(5/2), x))","F",0
148,0,0,0,0.000000," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))**(7/2),x)","- i a \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"-I*a*(Integral(I/(d*tan(e + f*x))**(7/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(7/2), x))","F",0
149,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-(d*tan(e + f*x))**(5/2), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x)**2, x) + Integral(-2*I*(d*tan(e + f*x))**(5/2)*tan(e + f*x), x))","F",0
150,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-(d*tan(e + f*x))**(3/2), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x)**2, x) + Integral(-2*I*(d*tan(e + f*x))**(3/2)*tan(e + f*x), x))","F",0
151,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \sqrt{d \tan{\left(e + f x \right)}}\right)\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-sqrt(d*tan(e + f*x)), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-2*I*sqrt(d*tan(e + f*x))*tan(e + f*x), x))","F",0
152,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(d*tan(f*x+e))**(1/2),x)","- a^{2} \left(\int \left(- \frac{1}{\sqrt{d \tan{\left(e + f x \right)}}}\right)\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-1/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)**2/sqrt(d*tan(e + f*x)), x) + Integral(-2*I*tan(e + f*x)/sqrt(d*tan(e + f*x)), x))","F",0
153,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(d*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \left(- \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\right)\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-1/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)**2/(d*tan(e + f*x))**(3/2), x) + Integral(-2*I*tan(e + f*x)/(d*tan(e + f*x))**(3/2), x))","F",0
154,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(d*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \left(- \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\right)\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-1/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)**2/(d*tan(e + f*x))**(5/2), x) + Integral(-2*I*tan(e + f*x)/(d*tan(e + f*x))**(5/2), x))","F",0
155,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(d*tan(f*x+e))**(7/2),x)","- a^{2} \left(\int \left(- \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\right)\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(-1/(d*tan(e + f*x))**(7/2), x) + Integral(tan(e + f*x)**2/(d*tan(e + f*x))**(7/2), x) + Integral(-2*I*tan(e + f*x)/(d*tan(e + f*x))**(7/2), x))","F",0
156,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx + \int \left(- 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(d*tan(e + f*x))**(5/2), x) + Integral(-3*(d*tan(e + f*x))**(5/2)*tan(e + f*x), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x)**3, x) + Integral(-3*I*(d*tan(e + f*x))**(5/2)*tan(e + f*x)**2, x))","F",0
157,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx + \int \left(- 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(d*tan(e + f*x))**(3/2), x) + Integral(-3*(d*tan(e + f*x))**(3/2)*tan(e + f*x), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x)**3, x) + Integral(-3*I*(d*tan(e + f*x))**(3/2)*tan(e + f*x)**2, x))","F",0
158,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \sqrt{d \tan{\left(e + f x \right)}}\, dx + \int \left(- 3 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*sqrt(d*tan(e + f*x)), x) + Integral(-3*sqrt(d*tan(e + f*x))*tan(e + f*x), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-3*I*sqrt(d*tan(e + f*x))*tan(e + f*x)**2, x))","F",0
159,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(d*tan(f*x+e))**(1/2),x)","- i a^{3} \left(\int \frac{i}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/sqrt(d*tan(e + f*x)), x) + Integral(-3*tan(e + f*x)/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)**3/sqrt(d*tan(e + f*x)), x) + Integral(-3*I*tan(e + f*x)**2/sqrt(d*tan(e + f*x)), x))","F",0
160,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(d*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(d*tan(e + f*x))**(3/2), x) + Integral(-3*tan(e + f*x)/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(3/2), x) + Integral(-3*I*tan(e + f*x)**2/(d*tan(e + f*x))**(3/2), x))","F",0
161,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(d*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(d*tan(e + f*x))**(5/2), x) + Integral(-3*tan(e + f*x)/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(5/2), x) + Integral(-3*I*tan(e + f*x)**2/(d*tan(e + f*x))**(5/2), x))","F",0
162,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(d*tan(f*x+e))**(7/2),x)","- i a^{3} \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(d*tan(e + f*x))**(7/2), x) + Integral(-3*tan(e + f*x)/(d*tan(e + f*x))**(7/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(7/2), x) + Integral(-3*I*tan(e + f*x)**2/(d*tan(e + f*x))**(7/2), x))","F",0
163,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(d*tan(f*x+e))**(9/2),x)","- i a^{3} \left(\int \frac{i}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(d*tan(e + f*x))**(9/2), x) + Integral(-3*tan(e + f*x)/(d*tan(e + f*x))**(9/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(9/2), x) + Integral(-3*I*tan(e + f*x)**2/(d*tan(e + f*x))**(9/2), x))","F",0
164,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((d*tan(e + f*x))**(7/2)/(tan(e + f*x) - I), x)/a","F",0
165,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x) - I), x)/a","F",0
166,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x) - I), x)/a","F",0
167,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\sqrt{d \tan{\left(e + f x \right)}}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(sqrt(d*tan(e + f*x))/(tan(e + f*x) - I), x)/a","F",0
168,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - i \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a}"," ",0,"-I*Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x) - I*sqrt(d*tan(e + f*x))), x)/a","F",0
169,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} - i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a}"," ",0,"-I*Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x) - I*(d*tan(e + f*x))**(3/2)), x)/a","F",0
170,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)} - i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx}{a}"," ",0,"-I*Integral(1/((d*tan(e + f*x))**(5/2)*tan(e + f*x) - I*(d*tan(e + f*x))**(5/2)), x)/a","F",0
171,-1,0,0,0.000000," ","integrate((d*tan(f*x+e))**(9/2)/(a+I*a*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((d*tan(e + f*x))**(7/2)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
173,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
174,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
175,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\sqrt{d \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(sqrt(d*tan(e + f*x))/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
176,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 i \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a^{2}}"," ",0,"-Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x)**2 - 2*I*sqrt(d*tan(e + f*x))*tan(e + f*x) - sqrt(d*tan(e + f*x))), x)/a**2","F",0
177,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)} - 2 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} - \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{2}}"," ",0,"-Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x)**2 - 2*I*(d*tan(e + f*x))**(3/2)*tan(e + f*x) - (d*tan(e + f*x))**(3/2)), x)/a**2","F",0
178,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)} - 2 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)} - \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx}{a^{2}}"," ",0,"-Integral(1/((d*tan(e + f*x))**(5/2)*tan(e + f*x)**2 - 2*I*(d*tan(e + f*x))**(5/2)*tan(e + f*x) - (d*tan(e + f*x))**(5/2)), x)/a**2","F",0
179,-1,0,0,0.000000," ","integrate((d*tan(f*x+e))**(9/2)/(a+I*a*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(7/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}{\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}{a^{3}}"," ",0,"I*Integral((d*tan(e + f*x))**(7/2)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x)/a**3","F",0
181,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\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}{a^{3}}"," ",0,"I*Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x)/a**3","F",0
182,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\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}{a^{3}}"," ",0,"I*Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x)/a**3","F",0
183,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\sqrt{d \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}{a^{3}}"," ",0,"I*Integral(sqrt(d*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
184,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 3 i \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 3 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + i \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a^{3}}"," ",0,"I*Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x)**3 - 3*I*sqrt(d*tan(e + f*x))*tan(e + f*x)**2 - 3*sqrt(d*tan(e + f*x))*tan(e + f*x) + I*sqrt(d*tan(e + f*x))), x)/a**3","F",0
185,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)} - 3 i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)} - 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} + i \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{3}}"," ",0,"I*Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x)**3 - 3*I*(d*tan(e + f*x))**(3/2)*tan(e + f*x)**2 - 3*(d*tan(e + f*x))**(3/2)*tan(e + f*x) + I*(d*tan(e + f*x))**(3/2)), x)/a**3","F",0
186,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**(5/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(5/2), x)","F",0
187,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)*tan(d*x+c)**(3/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(3/2), x)","F",0
188,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*sqrt(tan(c + d*x)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/sqrt(tan(c + d*x)), x)","F",0
190,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(3/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(5/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(5/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(7/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(7/2), x)","F",0
193,-1,0,0,0.000000," ","integrate(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
194,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(3/2), x)","F",0
195,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \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((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(tan(c + d*x)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/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}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/sqrt(tan(c + d*x)), x)","F",0
197,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/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}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/tan(c + d*x)**(3/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/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}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/tan(c + d*x)**(5/2), x)","F",0
199,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(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
202,-1,0,0,0.000000," ","integrate(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
203,-1,0,0,0.000000," ","integrate(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
204,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/tan(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)/sqrt(tan(c + d*x)), x)","F",0
205,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/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}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)/tan(c + d*x)**(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/tan(d*x+c)**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(5/2)/tan(c + d*x)**(5/2), x)","F",0
207,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
212,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(3/2)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
213,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
214,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*sqrt(tan(c + d*x))), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(3/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(3/2)), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(5/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(5/2)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(7/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(7/2)), x)","F",0
218,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{\frac{5}{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(tan(c + d*x)**(5/2)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(tan(c + d*x)**(3/2)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
221,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
222,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\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(1/((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(tan(c + d*x))), x)","F",0
223,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(3/2)), x)","F",0
224,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(5/2)), x)","F",0
225,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{\frac{5}{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(tan(c + d*x)**(5/2)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
228,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{\frac{3}{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(tan(c + d*x)**(3/2)/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
229,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\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(sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
230,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(5/2)*sqrt(tan(c + d*x))), x)","F",0
231,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(5/2)*tan(c + d*x)**(3/2)), x)","F",0
232,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(5/2)*tan(c + d*x)**(5/2)), x)","F",0
233,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(10/3)/(a+I*a*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,0,0,0,0.000000," ","integrate(tan(d*x+c)**(8/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{\tan^{\frac{8}{3}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(tan(c + d*x)**(8/3)/(tan(c + d*x) - I), x)/a","F",0
235,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{\tan^{\frac{4}{3}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(tan(c + d*x)**(4/3)/(tan(c + d*x) - I), x)/a","F",0
236,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{\tan^{\frac{2}{3}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(tan(c + d*x)**(2/3)/(tan(c + d*x) - I), x)/a","F",0
237,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\tan^{\frac{4}{3}}{\left(c + d x \right)} - i \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)**(4/3) - I*tan(c + d*x)**(1/3)), x)/a","F",0
238,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\tan^{\frac{8}{3}}{\left(c + d x \right)} - i \tan^{\frac{5}{3}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)**(8/3) - I*tan(c + d*x)**(5/3)), x)/a","F",0
239,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(7/3)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\tan^{\frac{10}{3}}{\left(c + d x \right)} - i \tan^{\frac{7}{3}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)**(10/3) - I*tan(c + d*x)**(7/3)), x)/a","F",0
240,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(14/3)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(10/3)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(8/3)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{\tan^{\frac{4}{3}}{\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(tan(c + d*x)**(4/3)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x)/a**2","F",0
244,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{\tan^{\frac{2}{3}}{\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(tan(c + d*x)**(2/3)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x)/a**2","F",0
245,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/3)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{1}{\tan^{\frac{7}{3}}{\left(c + d x \right)} - 2 i \tan^{\frac{4}{3}}{\left(c + d x \right)} - \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"-Integral(1/(tan(c + d*x)**(7/3) - 2*I*tan(c + d*x)**(4/3) - tan(c + d*x)**(1/3)), x)/a**2","F",0
246,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/3)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{1}{\tan^{\frac{11}{3}}{\left(c + d x \right)} - 2 i \tan^{\frac{8}{3}}{\left(c + d x \right)} - \tan^{\frac{5}{3}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"-Integral(1/(tan(c + d*x)**(11/3) - 2*I*tan(c + d*x)**(8/3) - tan(c + d*x)**(5/3)), x)/a**2","F",0
247,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(7/3)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{1}{\tan^{\frac{13}{3}}{\left(c + d x \right)} - 2 i \tan^{\frac{10}{3}}{\left(c + d x \right)} - \tan^{\frac{7}{3}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"-Integral(1/(tan(c + d*x)**(13/3) - 2*I*tan(c + d*x)**(10/3) - tan(c + d*x)**(7/3)), x)/a**2","F",0
248,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{4}{3}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(4/3), x)","F",0
249,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{2}{3}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(2/3), x)","F",0
250,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt[3]{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(1/3), x)","F",0
251,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/3),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(1/3), x)","F",0
252,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(2/3),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\tan^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(2/3), x)","F",0
253,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(4/3),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\tan^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/tan(c + d*x)**(4/3), x)","F",0
254,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)*(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)*(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt[3]{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(1/3), x)","F",0
257,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/tan(d*x+c)**(1/3),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}{\sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/tan(c + d*x)**(1/3), x)","F",0
258,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/tan(d*x+c)**(2/3),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}{\tan^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/tan(c + d*x)**(2/3), x)","F",0
259,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/tan(d*x+c)**(4/3),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}}}{\tan^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/tan(c + d*x)**(4/3), x)","F",0
260,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{4}{3}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(4/3)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
261,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{2}{3}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(2/3)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
262,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt[3]{\tan{\left(c + d x \right)}}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(1/3)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
263,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/3),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(1/3)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(2/3),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(2/3)), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/2)/tan(d*x+c)**(4/3),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*tan(c + d*x)**(4/3)), x)","F",0
266,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{\frac{4}{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(tan(c + d*x)**(4/3)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{\frac{2}{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(tan(c + d*x)**(2/3)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
268,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\sqrt[3]{\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(tan(c + d*x)**(1/3)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(1/3)), x)","F",0
270,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(2/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(2/3)), x)","F",0
271,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(4/3)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \tan^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*tan(c + d*x)**(4/3)), x)","F",0
272,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*tan(c + d*x)**3, x)","F",0
273,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*tan(c + d*x)**2, x)","F",0
274,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*tan(c + d*x), x)","F",0
275,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \tan{\left(c + d x \right)} + a}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(1/3), x)","F",0
276,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*cot(c + d*x), x)","F",0
277,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*cot(c + d*x)**2, x)","F",0
278,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(1/3)*cot(c + d*x)**3, x)","F",0
279,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(2/3),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(2/3), x)","F",0
280,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(4/3)*tan(c + d*x)**3, x)","F",0
281,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(4/3)*tan(c + d*x)**2, x)","F",0
282,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(4/3)*tan(c + d*x), x)","F",0
283,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(4/3), x)","F",0
284,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(4/3)*cot(c + d*x), x)","F",0
285,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**(4/3),x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(4/3)*cot(c + d*x)**2, x)","F",0
286,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+I*a*tan(d*x+c))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/3),x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{5}{3}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(5/3), x)","F",0
288,0,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\tan^{m}{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**m/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
289,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
290,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
291,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
292,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
293,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\tan{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
294,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{i a \tan{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-1/3), x)","F",0
295,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\cot{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
296,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**(1/3),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\sqrt[3]{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(1/3), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(2/3),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-2/3), x)","F",0
298,0,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\tan^{m}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(c + d*x)**m/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
299,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
300,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
301,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(c + d*x)**3/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
302,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
303,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\tan{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(tan(c + d*x)/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-4/3), x)","F",0
305,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\cot{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(cot(c + d*x)/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
306,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+I*a*tan(d*x+c))**(4/3),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(cot(c + d*x)**2/(I*a*(tan(c + d*x) - I))**(4/3), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))**(5/3),x)","\int \frac{1}{\left(i a \tan{\left(c + d x \right)} + a\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**(-5/3), x)","F",0
308,0,0,0,0.000000," ","integrate((e*tan(d*x+c))**m*(a+I*a*tan(d*x+c)),x)","i a \left(\int \left(- i \left(e \tan{\left(c + d x \right)}\right)^{m}\right)\, dx + \int \left(e \tan{\left(c + d x \right)}\right)^{m} \tan{\left(c + d x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(e*tan(c + d*x))**m, x) + Integral((e*tan(c + d*x))**m*tan(c + d*x), x))","F",0
309,0,0,0,0.000000," ","integrate((e*tan(d*x+c))**m*(a-I*a*tan(d*x+c)),x)","- i a \left(\int i \left(e \tan{\left(c + d x \right)}\right)^{m}\, dx + \int \left(e \tan{\left(c + d x \right)}\right)^{m} \tan{\left(c + d x \right)}\, dx\right)"," ",0,"-I*a*(Integral(I*(e*tan(c + d*x))**m, x) + Integral((e*tan(c + d*x))**m*tan(c + d*x), x))","F",0
310,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**4,x)","a^{4} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{n}\, dx + \int \left(- 6 \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{4}{\left(e + f x \right)}\, dx + \int 4 i \left(d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\, dx + \int \left(- 4 i \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"a**4*(Integral((d*tan(e + f*x))**n, x) + Integral(-6*(d*tan(e + f*x))**n*tan(e + f*x)**2, x) + Integral((d*tan(e + f*x))**n*tan(e + f*x)**4, x) + Integral(4*I*(d*tan(e + f*x))**n*tan(e + f*x), x) + Integral(-4*I*(d*tan(e + f*x))**n*tan(e + f*x)**3, x))","F",0
311,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{n}\, dx + \int \left(- 3 \left(d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(d*tan(e + f*x))**n, x) + Integral(-3*(d*tan(e + f*x))**n*tan(e + f*x), x) + Integral((d*tan(e + f*x))**n*tan(e + f*x)**3, x) + Integral(-3*I*(d*tan(e + f*x))**n*tan(e + f*x)**2, x))","F",0
312,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \left(d \tan{\left(e + f x \right)}\right)^{n}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-(d*tan(e + f*x))**n, x) + Integral((d*tan(e + f*x))**n*tan(e + f*x)**2, x) + Integral(-2*I*(d*tan(e + f*x))**n*tan(e + f*x), x))","F",0
313,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \left(d \tan{\left(e + f x \right)}\right)^{n}\right)\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(d*tan(e + f*x))**n, x) + Integral((d*tan(e + f*x))**n*tan(e + f*x), x))","F",0
314,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((d*tan(e + f*x))**n/(tan(e + f*x) - I), x)/a","F",0
315,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((d*tan(e + f*x))**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
316,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\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}{a^{3}}"," ",0,"I*Integral((d*tan(e + f*x))**n/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x)/a**3","F",0
317,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**4,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\tan^{4}{\left(e + f x \right)} - 4 i \tan^{3}{\left(e + f x \right)} - 6 \tan^{2}{\left(e + f x \right)} + 4 i \tan{\left(e + f x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral((d*tan(e + f*x))**n/(tan(e + f*x)**4 - 4*I*tan(e + f*x)**3 - 6*tan(e + f*x)**2 + 4*I*tan(e + f*x) + 1), x)/a**4","F",0
318,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a-I*a*tan(f*x+e)),x)","- i a \left(\int i \left(d \tan{\left(e + f x \right)}\right)^{n}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a*(Integral(I*(d*tan(e + f*x))**n, x) + Integral((d*tan(e + f*x))**n*tan(e + f*x), x))","F",0
319,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a-I*a*tan(f*x+e)),x)","\frac{i \int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\tan{\left(e + f x \right)} + i}\, dx}{a}"," ",0,"I*Integral((d*tan(e + f*x))**n/(tan(e + f*x) + I), x)/a","F",0
320,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**(3/2),x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
321,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**(1/2),x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
322,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((d*tan(e + f*x))**n/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
323,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*tan(e + f*x))**n/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
324,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+I*a*tan(f*x+e))**m,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(I*a*(tan(e + f*x) - I))**m, x)","F",0
325,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \tan^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*tan(c + d*x)**4, x)","F",0
326,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*tan(c + d*x)**3, x)","F",0
327,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*tan(c + d*x)**2, x)","F",0
328,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*tan(c + d*x), x)","F",0
329,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**m,x)","\int \left(i a \tan{\left(c + d x \right)} + a\right)^{m}\, dx"," ",0,"Integral((I*a*tan(c + d*x) + a)**m, x)","F",0
330,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*cot(c + d*x), x)","F",0
331,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*cot(c + d*x)**2, x)","F",0
332,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*tan(c + d*x)**(3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**m,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m*sqrt(tan(c + d*x)), x)","F",0
334,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**m/tan(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m/sqrt(tan(c + d*x)), x)","F",0
335,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**m/tan(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{m}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**m/tan(c + d*x)**(3/2), x)","F",0
336,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+a*tan(f*x+e)),x)","a \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral((d*tan(e + f*x))**(5/2), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x), x))","F",0
337,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+a*tan(f*x+e)),x)","a \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral((d*tan(e + f*x))**(3/2), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x), x))","F",0
338,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+a*tan(f*x+e)),x)","a \left(\int \sqrt{d \tan{\left(e + f x \right)}}\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral(sqrt(d*tan(e + f*x)), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x), x))","F",0
339,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))**(1/2),x)","a \left(\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"a*(Integral(1/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)/sqrt(d*tan(e + f*x)), x))","F",0
340,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))**(3/2),x)","a \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a*(Integral((d*tan(e + f*x))**(-3/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(3/2), x))","F",0
341,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))**(5/2),x)","a \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a*(Integral((d*tan(e + f*x))**(-5/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(5/2), x))","F",0
342,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))**(7/2),x)","a \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{\tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"a*(Integral((d*tan(e + f*x))**(-7/2), x) + Integral(tan(e + f*x)/(d*tan(e + f*x))**(7/2), x))","F",0
343,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+a*tan(f*x+e))**2,x)","a^{2} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx + \int 2 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral((d*tan(e + f*x))**(5/2), x) + Integral(2*(d*tan(e + f*x))**(5/2)*tan(e + f*x), x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x)**2, x))","F",0
344,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+a*tan(f*x+e))**2,x)","a^{2} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx + \int 2 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral((d*tan(e + f*x))**(3/2), x) + Integral(2*(d*tan(e + f*x))**(3/2)*tan(e + f*x), x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x)**2, x))","F",0
345,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+a*tan(f*x+e))**2,x)","a^{2} \left(\int \sqrt{d \tan{\left(e + f x \right)}}\, dx + \int 2 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"a**2*(Integral(sqrt(d*tan(e + f*x)), x) + Integral(2*sqrt(d*tan(e + f*x))*tan(e + f*x), x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x)**2, x))","F",0
346,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**2/(d*tan(f*x+e))**(1/2),x)","a^{2} \left(\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{2 \tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(1/sqrt(d*tan(e + f*x)), x) + Integral(2*tan(e + f*x)/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)**2/sqrt(d*tan(e + f*x)), x))","F",0
347,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**2/(d*tan(f*x+e))**(3/2),x)","a^{2} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{2 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a**2*(Integral((d*tan(e + f*x))**(-3/2), x) + Integral(2*tan(e + f*x)/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)**2/(d*tan(e + f*x))**(3/2), x))","F",0
348,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**2/(d*tan(f*x+e))**(5/2),x)","a^{2} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{2 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a**2*(Integral((d*tan(e + f*x))**(-5/2), x) + Integral(2*tan(e + f*x)/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)**2/(d*tan(e + f*x))**(5/2), x))","F",0
349,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(7/2)*(a+a*tan(f*x+e))**3,x)","a^{3} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}} \tan{\left(e + f x \right)}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}} \tan^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(7/2), x) + Integral(3*(d*tan(e + f*x))**(7/2)*tan(e + f*x), x) + Integral(3*(d*tan(e + f*x))**(7/2)*tan(e + f*x)**2, x) + Integral((d*tan(e + f*x))**(7/2)*tan(e + f*x)**3, x))","F",0
350,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)*(a+a*tan(f*x+e))**3,x)","a^{3} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(5/2), x) + Integral(3*(d*tan(e + f*x))**(5/2)*tan(e + f*x), x) + Integral(3*(d*tan(e + f*x))**(5/2)*tan(e + f*x)**2, x) + Integral((d*tan(e + f*x))**(5/2)*tan(e + f*x)**3, x))","F",0
351,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)*(a+a*tan(f*x+e))**3,x)","a^{3} \left(\int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx + \int 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(3/2), x) + Integral(3*(d*tan(e + f*x))**(3/2)*tan(e + f*x), x) + Integral(3*(d*tan(e + f*x))**(3/2)*tan(e + f*x)**2, x) + Integral((d*tan(e + f*x))**(3/2)*tan(e + f*x)**3, x))","F",0
352,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)*(a+a*tan(f*x+e))**3,x)","a^{3} \left(\int \sqrt{d \tan{\left(e + f x \right)}}\, dx + \int 3 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int 3 \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \sqrt{d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx\right)"," ",0,"a**3*(Integral(sqrt(d*tan(e + f*x)), x) + Integral(3*sqrt(d*tan(e + f*x))*tan(e + f*x), x) + Integral(3*sqrt(d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(sqrt(d*tan(e + f*x))*tan(e + f*x)**3, x))","F",0
353,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**3/(d*tan(f*x+e))**(1/2),x)","a^{3} \left(\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{3 \tan{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{3 \tan^{2}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(1/sqrt(d*tan(e + f*x)), x) + Integral(3*tan(e + f*x)/sqrt(d*tan(e + f*x)), x) + Integral(3*tan(e + f*x)**2/sqrt(d*tan(e + f*x)), x) + Integral(tan(e + f*x)**3/sqrt(d*tan(e + f*x)), x))","F",0
354,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**3/(d*tan(f*x+e))**(3/2),x)","a^{3} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{3 \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(-3/2), x) + Integral(3*tan(e + f*x)/(d*tan(e + f*x))**(3/2), x) + Integral(3*tan(e + f*x)**2/(d*tan(e + f*x))**(3/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(3/2), x))","F",0
355,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**3/(d*tan(f*x+e))**(5/2),x)","a^{3} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{3 \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(-5/2), x) + Integral(3*tan(e + f*x)/(d*tan(e + f*x))**(5/2), x) + Integral(3*tan(e + f*x)**2/(d*tan(e + f*x))**(5/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(5/2), x))","F",0
356,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**3/(d*tan(f*x+e))**(7/2),x)","a^{3} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{3 \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(-7/2), x) + Integral(3*tan(e + f*x)/(d*tan(e + f*x))**(7/2), x) + Integral(3*tan(e + f*x)**2/(d*tan(e + f*x))**(7/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(7/2), x))","F",0
357,0,0,0,0.000000," ","integrate((a+a*tan(f*x+e))**3/(d*tan(f*x+e))**(9/2),x)","a^{3} \left(\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{3 \tan{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{3 \tan^{2}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}\, dx\right)"," ",0,"a**3*(Integral((d*tan(e + f*x))**(-9/2), x) + Integral(3*tan(e + f*x)/(d*tan(e + f*x))**(9/2), x) + Integral(3*tan(e + f*x)**2/(d*tan(e + f*x))**(9/2), x) + Integral(tan(e + f*x)**3/(d*tan(e + f*x))**(9/2), x))","F",0
358,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\tan{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x) + 1), x)/a","F",0
359,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\tan{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x) + 1), x)/a","F",0
360,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{\sqrt{d \tan{\left(e + f x \right)}}}{\tan{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(d*tan(e + f*x))/(tan(e + f*x) + 1), x)/a","F",0
361,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a}"," ",0,"Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x) + sqrt(d*tan(e + f*x))), x)/a","F",0
362,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a}"," ",0,"Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x) + (d*tan(e + f*x))**(3/2)), x)/a","F",0
363,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e)),x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx}{a}"," ",0,"Integral(1/((d*tan(e + f*x))**(5/2)*tan(e + f*x) + (d*tan(e + f*x))**(5/2)), x)/a","F",0
364,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\tan^{2}{\left(e + f x \right)} + 2 \tan{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x)**2 + 2*tan(e + f*x) + 1), x)/a**2","F",0
365,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\tan^{2}{\left(e + f x \right)} + 2 \tan{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x)**2 + 2*tan(e + f*x) + 1), x)/a**2","F",0
366,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{\sqrt{d \tan{\left(e + f x \right)}}}{\tan^{2}{\left(e + f x \right)} + 2 \tan{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sqrt(d*tan(e + f*x))/(tan(e + f*x)**2 + 2*tan(e + f*x) + 1), x)/a**2","F",0
367,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} + 2 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a^{2}}"," ",0,"Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x)**2 + 2*sqrt(d*tan(e + f*x))*tan(e + f*x) + sqrt(d*tan(e + f*x))), x)/a**2","F",0
368,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)} + 2 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{2}}"," ",0,"Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x)**2 + 2*(d*tan(e + f*x))**(3/2)*tan(e + f*x) + (d*tan(e + f*x))**(3/2)), x)/a**2","F",0
369,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e))**2,x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)} + 2 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx}{a^{2}}"," ",0,"Integral(1/((d*tan(e + f*x))**(5/2)*tan(e + f*x)**2 + 2*(d*tan(e + f*x))**(5/2)*tan(e + f*x) + (d*tan(e + f*x))**(5/2)), x)/a**2","F",0
370,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(9/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{9}{2}}}{\tan^{3}{\left(e + f x \right)} + 3 \tan^{2}{\left(e + f x \right)} + 3 \tan{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((d*tan(e + f*x))**(9/2)/(tan(e + f*x)**3 + 3*tan(e + f*x)**2 + 3*tan(e + f*x) + 1), x)/a**3","F",0
371,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(7/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}{\tan^{3}{\left(e + f x \right)} + 3 \tan^{2}{\left(e + f x \right)} + 3 \tan{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((d*tan(e + f*x))**(7/2)/(tan(e + f*x)**3 + 3*tan(e + f*x)**2 + 3*tan(e + f*x) + 1), x)/a**3","F",0
372,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\tan^{3}{\left(e + f x \right)} + 3 \tan^{2}{\left(e + f x \right)} + 3 \tan{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((d*tan(e + f*x))**(5/2)/(tan(e + f*x)**3 + 3*tan(e + f*x)**2 + 3*tan(e + f*x) + 1), x)/a**3","F",0
373,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\tan^{3}{\left(e + f x \right)} + 3 \tan^{2}{\left(e + f x \right)} + 3 \tan{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((d*tan(e + f*x))**(3/2)/(tan(e + f*x)**3 + 3*tan(e + f*x)**2 + 3*tan(e + f*x) + 1), x)/a**3","F",0
374,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{\sqrt{d \tan{\left(e + f x \right)}}}{\tan^{3}{\left(e + f x \right)} + 3 \tan^{2}{\left(e + f x \right)} + 3 \tan{\left(e + f x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sqrt(d*tan(e + f*x))/(tan(e + f*x)**3 + 3*tan(e + f*x)**2 + 3*tan(e + f*x) + 1), x)/a**3","F",0
375,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(1/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{1}{\sqrt{d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} + 3 \sqrt{d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} + 3 \sqrt{d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + \sqrt{d \tan{\left(e + f x \right)}}}\, dx}{a^{3}}"," ",0,"Integral(1/(sqrt(d*tan(e + f*x))*tan(e + f*x)**3 + 3*sqrt(d*tan(e + f*x))*tan(e + f*x)**2 + 3*sqrt(d*tan(e + f*x))*tan(e + f*x) + sqrt(d*tan(e + f*x))), x)/a**3","F",0
376,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(3/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)} + 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)} + 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{3}}"," ",0,"Integral(1/((d*tan(e + f*x))**(3/2)*tan(e + f*x)**3 + 3*(d*tan(e + f*x))**(3/2)*tan(e + f*x)**2 + 3*(d*tan(e + f*x))**(3/2)*tan(e + f*x) + (d*tan(e + f*x))**(3/2)), x)/a**3","F",0
377,0,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))**(5/2)/(a+a*tan(f*x+e))**3,x)","\frac{\int \frac{1}{\left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{3}{\left(e + f x \right)} + 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan^{2}{\left(e + f x \right)} + 3 \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \tan{\left(e + f x \right)} + \left(d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx}{a^{3}}"," ",0,"Integral(1/((d*tan(e + f*x))**(5/2)*tan(e + f*x)**3 + 3*(d*tan(e + f*x))**(5/2)*tan(e + f*x)**2 + 3*(d*tan(e + f*x))**(5/2)*tan(e + f*x) + (d*tan(e + f*x))**(5/2)), x)/a**3","F",0
378,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2)*tan(f*x+e)**5,x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*tan(e + f*x)**5, x)","F",0
379,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2)*tan(f*x+e)**3,x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*tan(e + f*x)**3, x)","F",0
380,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2)*tan(f*x+e),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*tan(e + f*x), x)","F",0
381,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*cot(e + f*x), x)","F",0
382,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*cot(e + f*x)**3, x)","F",0
383,0,0,0,0.000000," ","integrate(cot(f*x+e)**5*(1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \cot^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*cot(e + f*x)**5, x)","F",0
384,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2)*tan(f*x+e)**4,x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*tan(e + f*x)**4, x)","F",0
385,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2)*tan(f*x+e)**2,x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*tan(e + f*x)**2, x)","F",0
386,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1), x)","F",0
387,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*cot(e + f*x)**2, x)","F",0
388,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(1+tan(f*x+e))**(1/2),x)","\int \sqrt{\tan{\left(e + f x \right)} + 1} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(tan(e + f*x) + 1)*cot(e + f*x)**4, x)","F",0
389,0,0,0,0.000000," ","integrate(tan(f*x+e)**5*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*tan(e + f*x)**5, x)","F",0
390,0,0,0,0.000000," ","integrate(tan(f*x+e)**3*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*tan(e + f*x)**3, x)","F",0
391,0,0,0,0.000000," ","integrate(tan(f*x+e)*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*tan(e + f*x), x)","F",0
392,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*cot(e + f*x), x)","F",0
393,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*cot(e + f*x)**3, x)","F",0
394,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5*(1+tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,0,0,0,0.000000," ","integrate(tan(f*x+e)**4*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*tan(e + f*x)**4, x)","F",0
396,0,0,0,0.000000," ","integrate(tan(f*x+e)**2*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*tan(e + f*x)**2, x)","F",0
397,0,0,0,0.000000," ","integrate((1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*cot(e + f*x)**2, x)","F",0
399,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(1+tan(f*x+e))**(3/2),x)","\int \left(\tan{\left(e + f x \right)} + 1\right)^{\frac{3}{2}} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((tan(e + f*x) + 1)**(3/2)*cot(e + f*x)**4, x)","F",0
400,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(1+tan(f*x+e))**(1/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(tan(e + f*x)**5/sqrt(tan(e + f*x) + 1), x)","F",0
401,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(1+tan(f*x+e))**(1/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(tan(e + f*x)**3/sqrt(tan(e + f*x) + 1), x)","F",0
402,0,0,0,0.000000," ","integrate(tan(f*x+e)/(1+tan(f*x+e))**(1/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(tan(e + f*x)/sqrt(tan(e + f*x) + 1), x)","F",0
403,0,0,0,0.000000," ","integrate(cot(f*x+e)/(1+tan(f*x+e))**(1/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(cot(e + f*x)/sqrt(tan(e + f*x) + 1), x)","F",0
404,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(1+tan(f*x+e))**(1/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(cot(e + f*x)**3/sqrt(tan(e + f*x) + 1), x)","F",0
405,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(1+tan(f*x+e))**(1/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(cot(e + f*x)**5/sqrt(tan(e + f*x) + 1), x)","F",0
406,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(1+tan(f*x+e))**(1/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(tan(e + f*x)**4/sqrt(tan(e + f*x) + 1), x)","F",0
407,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(1+tan(f*x+e))**(1/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(tan(e + f*x)**2/sqrt(tan(e + f*x) + 1), x)","F",0
408,0,0,0,0.000000," ","integrate(1/(1+tan(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(1/sqrt(tan(e + f*x) + 1), x)","F",0
409,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(1+tan(f*x+e))**(1/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(cot(e + f*x)**2/sqrt(tan(e + f*x) + 1), x)","F",0
410,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(1+tan(f*x+e))**(1/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\sqrt{\tan{\left(e + f x \right)} + 1}}\, dx"," ",0,"Integral(cot(e + f*x)**4/sqrt(tan(e + f*x) + 1), x)","F",0
411,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+a*tan(f*x+e))**m,x)","\int \left(a \left(\tan{\left(e + f x \right)} + 1\right)\right)^{m} \left(d \tan{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*(tan(e + f*x) + 1))**m*(d*tan(e + f*x))**n, x)","F",0
412,1,97,0,0.593331," ","integrate(tan(d*x+c)**5*(a+b*tan(d*x+c)),x)","\begin{cases} \frac{a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{a \tan^{2}{\left(c + d x \right)}}{2 d} - b x + \frac{b \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{b \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{b \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \tan^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(tan(c + d*x)**2 + 1)/(2*d) + a*tan(c + d*x)**4/(4*d) - a*tan(c + d*x)**2/(2*d) - b*x + b*tan(c + d*x)**5/(5*d) - b*tan(c + d*x)**3/(3*d) + b*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))*tan(c)**5, True))","A",0
413,1,83,0,0.427307," ","integrate(tan(d*x+c)**4*(a+b*tan(d*x+c)),x)","\begin{cases} a x + \frac{a \tan^{3}{\left(c + d x \right)}}{3 d} - \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^{4}{\left(c + d x \right)}}{4 d} - \frac{b \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \tan^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x + a*tan(c + d*x)**3/(3*d) - a*tan(c + d*x)/d + b*log(tan(c + d*x)**2 + 1)/(2*d) + b*tan(c + d*x)**4/(4*d) - b*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))*tan(c)**4, True))","A",0
414,1,70,0,0.309707," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c)),x)","\begin{cases} - \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} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \tan^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-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, Ne(d, 0)), (x*(a + b*tan(c))*tan(c)**3, True))","A",0
415,1,56,0,0.206854," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c)),x)","\begin{cases} - 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} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-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), Ne(d, 0)), (x*(a + b*tan(c))*tan(c)**2, True))","A",0
416,1,41,0,0.166138," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c)),x)","\begin{cases} \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} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(tan(c + d*x)**2 + 1)/(2*d) - b*x + b*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))*tan(c), True))","A",0
417,1,24,0,0.119352," ","integrate(a+b*tan(d*x+c),x)","a x + b \left(\begin{cases} \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\x \tan{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*tan(c), True))","A",0
418,1,42,0,0.293425," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c)),x)","\begin{cases} - \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 & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*log(tan(c + d*x)**2 + 1)/(2*d) + a*log(tan(c + d*x))/d + b*x, Ne(d, 0)), (x*(a + b*tan(c))*cot(c), True))","A",0
419,1,66,0,0.649017," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right) \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} a x & \text{for}\: c = - d x \\- 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} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))*cot(c)**2, Eq(d, 0)), (zoo*a*x, Eq(c, -d*x)), (-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, True))","A",0
420,1,83,0,0.995682," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} 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) \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*cot(c)**3, 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)), True))","A",0
421,1,97,0,1.532492," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} 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) \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*cot(c)**4, 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), True))","A",0
422,1,110,0,2.103926," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} 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) \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*cot(c)**5, 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), True))","A",0
423,1,124,0,3.491589," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} 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) \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- a x - \frac{a}{d \tan{\left(c + d x \right)}} + \frac{a}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{a}{5 d \tan^{5}{\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)}} - \frac{b}{4 d \tan^{4}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*cot(c)**6, Eq(d, 0)), (-a*x - a/(d*tan(c + d*x)) + a/(3*d*tan(c + d*x)**3) - a/(5*d*tan(c + d*x)**5) - 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/(4*d*tan(c + d*x)**4), True))","A",0
424,1,139,0,0.705210," ","integrate(tan(d*x+c)**4*(a+b*tan(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{a^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \tan{\left(c + d x \right)}}{d} + \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{a b \tan^{4}{\left(c + d x \right)}}{2 d} - \frac{a b \tan^{2}{\left(c + d x \right)}}{d} - b^{2} x + \frac{b^{2} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \tan^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + a**2*tan(c + d*x)**3/(3*d) - a**2*tan(c + d*x)/d + a*b*log(tan(c + d*x)**2 + 1)/d + a*b*tan(c + d*x)**4/(2*d) - a*b*tan(c + d*x)**2/d - b**2*x + b**2*tan(c + d*x)**5/(5*d) - b**2*tan(c + d*x)**3/(3*d) + b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**2*tan(c)**4, True))","A",0
425,1,134,0,0.508214," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + 2 a b x + \frac{2 a b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{2 a b \tan{\left(c + d x \right)}}{d} + \frac{b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{2} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{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)^{2} \tan^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*log(tan(c + d*x)**2 + 1)/(2*d) + a**2*tan(c + d*x)**2/(2*d) + 2*a*b*x + 2*a*b*tan(c + d*x)**3/(3*d) - 2*a*b*tan(c + d*x)/d + b**2*log(tan(c + d*x)**2 + 1)/(2*d) + b**2*tan(c + d*x)**4/(4*d) - b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**2*tan(c)**3, True))","A",0
426,1,94,0,0.349664," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**2,x)","\begin{cases} - a^{2} x + \frac{a^{2} \tan{\left(c + d x \right)}}{d} - \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{a b \tan^{2}{\left(c + d x \right)}}{d} + b^{2} x + \frac{b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x + a**2*tan(c + d*x)/d - a*b*log(tan(c + d*x)**2 + 1)/d + a*b*tan(c + d*x)**2/d + b**2*x + b**2*tan(c + d*x)**3/(3*d) - b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**2*tan(c)**2, True))","A",0
427,1,85,0,0.249161," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 2 a b x + \frac{2 a b \tan{\left(c + d x \right)}}{d} - \frac{b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{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)^{2} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*log(tan(c + d*x)**2 + 1)/(2*d) - 2*a*b*x + 2*a*b*tan(c + d*x)/d - b**2*log(tan(c + d*x)**2 + 1)/(2*d) + b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**2*tan(c), True))","A",0
428,1,48,0,0.183152," ","integrate((a+b*tan(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - b^{2} x + \frac{b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + a*b*log(tan(c + d*x)**2 + 1)/d - b**2*x + b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**2, True))","A",0
429,1,70,0,0.421375," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 2 a b x + \frac{b^{2} \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)^{2} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*log(tan(c + d*x)**2 + 1)/(2*d) + a**2*log(tan(c + d*x))/d + 2*a*b*x + b**2*log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**2*cot(c), True))","A",0
430,1,83,0,0.832115," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} a^{2} x & \text{for}\: c = - d x \\- a^{2} x - \frac{a^{2}}{d \tan{\left(c + d x \right)}} - \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + b^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))**2*cot(c)**2, Eq(d, 0)), (zoo*a**2*x, Eq(c, -d*x)), (-a**2*x - a**2/(d*tan(c + d*x)) - a*b*log(tan(c + d*x)**2 + 1)/d + 2*a*b*log(tan(c + d*x))/d + b**2*x, True))","A",0
431,1,131,0,1.280319," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} 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)^{2} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - 2 a b x - \frac{2 a b}{d \tan{\left(c + d x \right)}} - \frac{b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*cot(c)**3, Eq(d, 0)), (a**2*log(tan(c + d*x)**2 + 1)/(2*d) - a**2*log(tan(c + d*x))/d - a**2/(2*d*tan(c + d*x)**2) - 2*a*b*x - 2*a*b/(d*tan(c + d*x)) - b**2*log(tan(c + d*x)**2 + 1)/(2*d) + b**2*log(tan(c + d*x))/d, True))","A",0
432,1,126,0,1.923317," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} 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)^{2} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\a^{2} x + \frac{a^{2}}{d \tan{\left(c + d x \right)}} - \frac{a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{2 a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{a b}{d \tan^{2}{\left(c + d x \right)}} - b^{2} x - \frac{b^{2}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*cot(c)**4, Eq(d, 0)), (a**2*x + a**2/(d*tan(c + d*x)) - a**2/(3*d*tan(c + d*x)**3) + a*b*log(tan(c + d*x)**2 + 1)/d - 2*a*b*log(tan(c + d*x))/d - a*b/(d*tan(c + d*x)**2) - b**2*x - b**2/(d*tan(c + d*x)), True))","A",0
433,1,178,0,2.630045," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} 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)^{2} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{a^{2}}{4 d \tan^{4}{\left(c + d x \right)}} + 2 a b x + \frac{2 a b}{d \tan{\left(c + d x \right)}} - \frac{2 a b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*cot(c)**5, Eq(d, 0)), (-a**2*log(tan(c + d*x)**2 + 1)/(2*d) + a**2*log(tan(c + d*x))/d + a**2/(2*d*tan(c + d*x)**2) - a**2/(4*d*tan(c + d*x)**4) + 2*a*b*x + 2*a*b/(d*tan(c + d*x)) - 2*a*b/(3*d*tan(c + d*x)**3) + b**2*log(tan(c + d*x)**2 + 1)/(2*d) - b**2*log(tan(c + d*x))/d - b**2/(2*d*tan(c + d*x)**2), True))","A",0
434,1,172,0,4.858628," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} 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)^{2} \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- a^{2} x - \frac{a^{2}}{d \tan{\left(c + d x \right)}} + \frac{a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{a^{2}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{a b}{d \tan^{2}{\left(c + d x \right)}} - \frac{a b}{2 d \tan^{4}{\left(c + d x \right)}} + b^{2} x + \frac{b^{2}}{d \tan{\left(c + d x \right)}} - \frac{b^{2}}{3 d \tan^{3}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*cot(c)**6, Eq(d, 0)), (-a**2*x - a**2/(d*tan(c + d*x)) + a**2/(3*d*tan(c + d*x)**3) - a**2/(5*d*tan(c + d*x)**5) - a*b*log(tan(c + d*x)**2 + 1)/d + 2*a*b*log(tan(c + d*x))/d + a*b/(d*tan(c + d*x)**2) - a*b/(2*d*tan(c + d*x)**4) + b**2*x + b**2/(d*tan(c + d*x)) - b**2/(3*d*tan(c + d*x)**3), True))","A",0
435,1,194,0,0.763447," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**3,x)","\begin{cases} - \frac{a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{3} \tan^{2}{\left(c + d x \right)}}{2 d} + 3 a^{2} b x + \frac{a^{2} b \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 a^{2} b \tan{\left(c + d x \right)}}{d} + \frac{3 a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a b^{2} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{3 a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} - b^{3} x + \frac{b^{3} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \tan^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*log(tan(c + d*x)**2 + 1)/(2*d) + a**3*tan(c + d*x)**2/(2*d) + 3*a**2*b*x + a**2*b*tan(c + d*x)**3/d - 3*a**2*b*tan(c + d*x)/d + 3*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a*b**2*tan(c + d*x)**4/(4*d) - 3*a*b**2*tan(c + d*x)**2/(2*d) - b**3*x + b**3*tan(c + d*x)**5/(5*d) - b**3*tan(c + d*x)**3/(3*d) + b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**3*tan(c)**3, True))","A",0
436,1,160,0,0.529470," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**3,x)","\begin{cases} - a^{3} x + \frac{a^{3} \tan{\left(c + d x \right)}}{d} - \frac{3 a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a^{2} b \tan^{2}{\left(c + d x \right)}}{2 d} + 3 a b^{2} x + \frac{a b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 a b^{2} \tan{\left(c + d x \right)}}{d} + \frac{b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{3} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{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)^{3} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*x + a**3*tan(c + d*x)/d - 3*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a**2*b*tan(c + d*x)**2/(2*d) + 3*a*b**2*x + a*b**2*tan(c + d*x)**3/d - 3*a*b**2*tan(c + d*x)/d + b**3*log(tan(c + d*x)**2 + 1)/(2*d) + b**3*tan(c + d*x)**4/(4*d) - b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**3*tan(c)**2, True))","A",0
437,1,128,0,0.378207," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 a^{2} b x + \frac{3 a^{2} b \tan{\left(c + d x \right)}}{d} - \frac{3 a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + b^{3} x + \frac{b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*log(tan(c + d*x)**2 + 1)/(2*d) - 3*a**2*b*x + 3*a**2*b*tan(c + d*x)/d - 3*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a*b**2*tan(c + d*x)**2/(2*d) + b**3*x + b**3*tan(c + d*x)**3/(3*d) - b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**3*tan(c), True))","A",0
438,1,94,0,0.248056," ","integrate((a+b*tan(d*x+c))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 a b^{2} x + \frac{3 a b^{2} \tan{\left(c + d x \right)}}{d} - \frac{b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{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)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*a*b**2*x + 3*a*b**2*tan(c + d*x)/d - b**3*log(tan(c + d*x)**2 + 1)/(2*d) + b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**3, True))","A",0
439,1,92,0,0.677059," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**3,x)","\begin{cases} - \frac{a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 a^{2} b x + \frac{3 a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - b^{3} x + \frac{b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*log(tan(c + d*x)**2 + 1)/(2*d) + a**3*log(tan(c + d*x))/d + 3*a**2*b*x + 3*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - b**3*x + b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**3*cot(c), True))","A",0
440,1,112,0,1.230077," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**3,x)","\begin{cases} \tilde{\infty} a^{3} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} a^{3} x & \text{for}\: c = - d x \\- a^{3} x - \frac{a^{3}}{d \tan{\left(c + d x \right)}} - \frac{3 a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 a b^{2} x + \frac{b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**3*x, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))**3*cot(c)**2, Eq(d, 0)), (zoo*a**3*x, Eq(c, -d*x)), (-a**3*x - a**3/(d*tan(c + d*x)) - 3*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a**2*b*log(tan(c + d*x))/d + 3*a*b**2*x + b**3*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
441,1,146,0,1.787300," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**3,x)","\begin{cases} \tilde{\infty} 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)^{3} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - 3 a^{2} b x - \frac{3 a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{3 a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + b^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*cot(c)**3, Eq(d, 0)), (a**3*log(tan(c + d*x)**2 + 1)/(2*d) - a**3*log(tan(c + d*x))/d - a**3/(2*d*tan(c + d*x)**2) - 3*a**2*b*x - 3*a**2*b/(d*tan(c + d*x)) - 3*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a*b**2*log(tan(c + d*x))/d + b**3*x, True))","A",0
442,1,177,0,2.492240," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**3,x)","\begin{cases} \tilde{\infty} 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)^{3} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\a^{3} x + \frac{a^{3}}{d \tan{\left(c + d x \right)}} - \frac{a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - 3 a b^{2} x - \frac{3 a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*cot(c)**4, Eq(d, 0)), (a**3*x + a**3/(d*tan(c + d*x)) - a**3/(3*d*tan(c + d*x)**3) + 3*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*a**2*b*log(tan(c + d*x))/d - 3*a**2*b/(2*d*tan(c + d*x)**2) - 3*a*b**2*x - 3*a*b**2/(d*tan(c + d*x)) - b**3*log(tan(c + d*x)**2 + 1)/(2*d) + b**3*log(tan(c + d*x))/d, True))","A",0
443,1,207,0,4.691552," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**3,x)","\begin{cases} \tilde{\infty} 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)^{3} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{a^{3}}{4 d \tan^{4}{\left(c + d x \right)}} + 3 a^{2} b x + \frac{3 a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{a^{2} b}{d \tan^{3}{\left(c + d x \right)}} + \frac{3 a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 a b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - b^{3} x - \frac{b^{3}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*cot(c)**5, Eq(d, 0)), (-a**3*log(tan(c + d*x)**2 + 1)/(2*d) + a**3*log(tan(c + d*x))/d + a**3/(2*d*tan(c + d*x)**2) - a**3/(4*d*tan(c + d*x)**4) + 3*a**2*b*x + 3*a**2*b/(d*tan(c + d*x)) - a**2*b/(d*tan(c + d*x)**3) + 3*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - 3*a*b**2*log(tan(c + d*x))/d - 3*a*b**2/(2*d*tan(c + d*x)**2) - b**3*x - b**3/(d*tan(c + d*x)), True))","A",0
444,1,241,0,6.167918," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**3,x)","\begin{cases} \tilde{\infty} 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)^{3} \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- a^{3} x - \frac{a^{3}}{d \tan{\left(c + d x \right)}} + \frac{a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{a^{3}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{3 a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{3 a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{3 a^{2} b}{4 d \tan^{4}{\left(c + d x \right)}} + 3 a b^{2} x + \frac{3 a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{a b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{b^{3}}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**3*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*cot(c)**6, Eq(d, 0)), (-a**3*x - a**3/(d*tan(c + d*x)) + a**3/(3*d*tan(c + d*x)**3) - a**3/(5*d*tan(c + d*x)**5) - 3*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*a**2*b*log(tan(c + d*x))/d + 3*a**2*b/(2*d*tan(c + d*x)**2) - 3*a**2*b/(4*d*tan(c + d*x)**4) + 3*a*b**2*x + 3*a*b**2/(d*tan(c + d*x)) - a*b**2/(d*tan(c + d*x)**3) + b**3*log(tan(c + d*x)**2 + 1)/(2*d) - b**3*log(tan(c + d*x))/d - b**3/(2*d*tan(c + d*x)**2), True))","A",0
445,1,277,0,1.129340," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**4,x)","\begin{cases} - \frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{4} \tan^{2}{\left(c + d x \right)}}{2 d} + 4 a^{3} b x + \frac{4 a^{3} b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a^{3} b \tan{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 a^{2} b^{2} \tan^{4}{\left(c + d x \right)}}{2 d} - \frac{3 a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{d} - 4 a b^{3} x + \frac{4 a b^{3} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{4 a b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} \tan{\left(c + d x \right)}}{d} - \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{4} \tan^{6}{\left(c + d x \right)}}{6 d} - \frac{b^{4} \tan^{4}{\left(c + d x \right)}}{4 d} + \frac{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)^{4} \tan^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*log(tan(c + d*x)**2 + 1)/(2*d) + a**4*tan(c + d*x)**2/(2*d) + 4*a**3*b*x + 4*a**3*b*tan(c + d*x)**3/(3*d) - 4*a**3*b*tan(c + d*x)/d + 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 3*a**2*b**2*tan(c + d*x)**4/(2*d) - 3*a**2*b**2*tan(c + d*x)**2/d - 4*a*b**3*x + 4*a*b**3*tan(c + d*x)**5/(5*d) - 4*a*b**3*tan(c + d*x)**3/(3*d) + 4*a*b**3*tan(c + d*x)/d - b**4*log(tan(c + d*x)**2 + 1)/(2*d) + b**4*tan(c + d*x)**6/(6*d) - b**4*tan(c + d*x)**4/(4*d) + b**4*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**4*tan(c)**3, True))","A",0
446,1,214,0,0.812758," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**4,x)","\begin{cases} - a^{4} x + \frac{a^{4} \tan{\left(c + d x \right)}}{d} - \frac{2 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 a^{3} b \tan^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} x + \frac{2 a^{2} b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{6 a^{2} b^{2} \tan{\left(c + d x \right)}}{d} + \frac{2 a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{a b^{3} \tan^{4}{\left(c + d x \right)}}{d} - \frac{2 a b^{3} \tan^{2}{\left(c + d x \right)}}{d} - b^{4} x + \frac{b^{4} \tan^{5}{\left(c + d x \right)}}{5 d} - \frac{b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{4} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{4} \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*x + a**4*tan(c + d*x)/d - 2*a**3*b*log(tan(c + d*x)**2 + 1)/d + 2*a**3*b*tan(c + d*x)**2/d + 6*a**2*b**2*x + 2*a**2*b**2*tan(c + d*x)**3/d - 6*a**2*b**2*tan(c + d*x)/d + 2*a*b**3*log(tan(c + d*x)**2 + 1)/d + a*b**3*tan(c + d*x)**4/d - 2*a*b**3*tan(c + d*x)**2/d - b**4*x + b**4*tan(c + d*x)**5/(5*d) - b**4*tan(c + d*x)**3/(3*d) + b**4*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**4*tan(c)**2, True))","A",0
447,1,187,0,0.564240," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 4 a^{3} b x + \frac{4 a^{3} b \tan{\left(c + d x \right)}}{d} - \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{d} + 4 a b^{3} x + \frac{4 a b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a b^{3} \tan{\left(c + d x \right)}}{d} + \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{4} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{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)^{4} \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*log(tan(c + d*x)**2 + 1)/(2*d) - 4*a**3*b*x + 4*a**3*b*tan(c + d*x)/d - 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 3*a**2*b**2*tan(c + d*x)**2/d + 4*a*b**3*x + 4*a*b**3*tan(c + d*x)**3/(3*d) - 4*a*b**3*tan(c + d*x)/d + b**4*log(tan(c + d*x)**2 + 1)/(2*d) + b**4*tan(c + d*x)**4/(4*d) - b**4*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**4*tan(c), True))","A",0
448,1,131,0,0.393853," ","integrate((a+b*tan(d*x+c))**4,x)","\begin{cases} a^{4} x + \frac{2 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 6 a^{2} b^{2} x + \frac{6 a^{2} b^{2} \tan{\left(c + d x \right)}}{d} - \frac{2 a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 a b^{3} \tan^{2}{\left(c + d x \right)}}{d} + b^{4} x + \frac{b^{4} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{b^{4} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 2*a**3*b*log(tan(c + d*x)**2 + 1)/d - 6*a**2*b**2*x + 6*a**2*b**2*tan(c + d*x)/d - 2*a*b**3*log(tan(c + d*x)**2 + 1)/d + 2*a*b**3*tan(c + d*x)**2/d + b**4*x + b**4*tan(c + d*x)**3/(3*d) - b**4*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**4, True))","A",0
449,1,133,0,1.102164," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**4,x)","\begin{cases} - \frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 a^{3} b x + \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - 4 a b^{3} x + \frac{4 a b^{3} \tan{\left(c + d x \right)}}{d} - \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{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)^{4} \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*log(tan(c + d*x)**2 + 1)/(2*d) + a**4*log(tan(c + d*x))/d + 4*a**3*b*x + 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 4*a*b**3*x + 4*a*b**3*tan(c + d*x)/d - b**4*log(tan(c + d*x)**2 + 1)/(2*d) + b**4*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**4*cot(c), True))","A",0
450,1,131,0,1.828014," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} a^{4} x & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right)^{4} \cot^{2}{\left(c \right)} & \text{for}\: d = 0 \\\tilde{\infty} a^{4} x & \text{for}\: c = - d x \\- a^{4} x - \frac{a^{4}}{d \tan{\left(c + d x \right)}} - \frac{2 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 6 a^{2} b^{2} x + \frac{2 a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - b^{4} x + \frac{b^{4} \tan{\left(c + d x \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))**4*cot(c)**2, Eq(d, 0)), (zoo*a**4*x, Eq(c, -d*x)), (-a**4*x - a**4/(d*tan(c + d*x)) - 2*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*a**3*b*log(tan(c + d*x))/d + 6*a**2*b**2*x + 2*a*b**3*log(tan(c + d*x)**2 + 1)/d - b**4*x + b**4*tan(c + d*x)/d, True))","A",0
451,1,170,0,2.408030," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} 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)^{4} \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - 4 a^{3} b x - \frac{4 a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{6 a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 4 a b^{3} x + \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**4*cot(c)**3, Eq(d, 0)), (a**4*log(tan(c + d*x)**2 + 1)/(2*d) - a**4*log(tan(c + d*x))/d - a**4/(2*d*tan(c + d*x)**2) - 4*a**3*b*x - 4*a**3*b/(d*tan(c + d*x)) - 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 6*a**2*b**2*log(tan(c + d*x))/d + 4*a*b**3*x + b**4*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
452,1,187,0,4.434203," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} 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)^{4} \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\a^{4} x + \frac{a^{4}}{d \tan{\left(c + d x \right)}} - \frac{a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{2 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - 6 a^{2} b^{2} x - \frac{6 a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + b^{4} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**4*cot(c)**4, Eq(d, 0)), (a**4*x + a**4/(d*tan(c + d*x)) - a**4/(3*d*tan(c + d*x)**3) + 2*a**3*b*log(tan(c + d*x)**2 + 1)/d - 4*a**3*b*log(tan(c + d*x))/d - 2*a**3*b/(d*tan(c + d*x)**2) - 6*a**2*b**2*x - 6*a**2*b**2/(d*tan(c + d*x)) - 2*a*b**3*log(tan(c + d*x)**2 + 1)/d + 4*a*b**3*log(tan(c + d*x))/d + b**4*x, True))","A",0
453,1,252,0,5.827164," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} 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)^{4} \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{a^{4}}{4 d \tan^{4}{\left(c + d x \right)}} + 4 a^{3} b x + \frac{4 a^{3} b}{d \tan{\left(c + d x \right)}} - \frac{4 a^{3} b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{6 a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 a^{2} b^{2}}{d \tan^{2}{\left(c + d x \right)}} - 4 a b^{3} x - \frac{4 a b^{3}}{d \tan{\left(c + d x \right)}} - \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**4*cot(c)**5, Eq(d, 0)), (-a**4*log(tan(c + d*x)**2 + 1)/(2*d) + a**4*log(tan(c + d*x))/d + a**4/(2*d*tan(c + d*x)**2) - a**4/(4*d*tan(c + d*x)**4) + 4*a**3*b*x + 4*a**3*b/(d*tan(c + d*x)) - 4*a**3*b/(3*d*tan(c + d*x)**3) + 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d - 6*a**2*b**2*log(tan(c + d*x))/d - 3*a**2*b**2/(d*tan(c + d*x)**2) - 4*a*b**3*x - 4*a*b**3/(d*tan(c + d*x)) - b**4*log(tan(c + d*x)**2 + 1)/(2*d) + b**4*log(tan(c + d*x))/d, True))","A",0
454,1,265,0,9.333114," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} 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)^{4} \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- a^{4} x - \frac{a^{4}}{d \tan{\left(c + d x \right)}} + \frac{a^{4}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{a^{4}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{2 a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{2 a^{3} b}{d \tan^{2}{\left(c + d x \right)}} - \frac{a^{3} b}{d \tan^{4}{\left(c + d x \right)}} + 6 a^{2} b^{2} x + \frac{6 a^{2} b^{2}}{d \tan{\left(c + d x \right)}} - \frac{2 a^{2} b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{2 a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{4 a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{2 a b^{3}}{d \tan^{2}{\left(c + d x \right)}} - b^{4} x - \frac{b^{4}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**4*cot(c)**6, Eq(d, 0)), (-a**4*x - a**4/(d*tan(c + d*x)) + a**4/(3*d*tan(c + d*x)**3) - a**4/(5*d*tan(c + d*x)**5) - 2*a**3*b*log(tan(c + d*x)**2 + 1)/d + 4*a**3*b*log(tan(c + d*x))/d + 2*a**3*b/(d*tan(c + d*x)**2) - a**3*b/(d*tan(c + d*x)**4) + 6*a**2*b**2*x + 6*a**2*b**2/(d*tan(c + d*x)) - 2*a**2*b**2/(d*tan(c + d*x)**3) + 2*a*b**3*log(tan(c + d*x)**2 + 1)/d - 4*a*b**3*log(tan(c + d*x))/d - 2*a*b**3/(d*tan(c + d*x)**2) - b**4*x - b**4/(d*tan(c + d*x)), True))","A",0
455,1,340,0,12.043461," ","integrate(cot(d*x+c)**7*(a+b*tan(d*x+c))**4,x)","\begin{cases} \tilde{\infty} 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)^{4} \cot^{7}{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{a^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{a^{4}}{2 d \tan^{2}{\left(c + d x \right)}} + \frac{a^{4}}{4 d \tan^{4}{\left(c + d x \right)}} - \frac{a^{4}}{6 d \tan^{6}{\left(c + d x \right)}} - 4 a^{3} b x - \frac{4 a^{3} b}{d \tan{\left(c + d x \right)}} + \frac{4 a^{3} b}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{4 a^{3} b}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{3 a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{6 a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{3 a^{2} b^{2}}{d \tan^{2}{\left(c + d x \right)}} - \frac{3 a^{2} b^{2}}{2 d \tan^{4}{\left(c + d x \right)}} + 4 a b^{3} x + \frac{4 a b^{3}}{d \tan{\left(c + d x \right)}} - \frac{4 a b^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{b^{4}}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**4*x, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**4*cot(c)**7, Eq(d, 0)), (a**4*log(tan(c + d*x)**2 + 1)/(2*d) - a**4*log(tan(c + d*x))/d - a**4/(2*d*tan(c + d*x)**2) + a**4/(4*d*tan(c + d*x)**4) - a**4/(6*d*tan(c + d*x)**6) - 4*a**3*b*x - 4*a**3*b/(d*tan(c + d*x)) + 4*a**3*b/(3*d*tan(c + d*x)**3) - 4*a**3*b/(5*d*tan(c + d*x)**5) - 3*a**2*b**2*log(tan(c + d*x)**2 + 1)/d + 6*a**2*b**2*log(tan(c + d*x))/d + 3*a**2*b**2/(d*tan(c + d*x)**2) - 3*a**2*b**2/(2*d*tan(c + d*x)**4) + 4*a*b**3*x + 4*a*b**3/(d*tan(c + d*x)) - 4*a*b**3/(3*d*tan(c + d*x)**3) + b**4*log(tan(c + d*x)**2 + 1)/(2*d) - b**4*log(tan(c + d*x))/d - b**4/(2*d*tan(c + d*x)**2), True))","A",0
456,1,944,0,3.544182," ","integrate(tan(d*x+c)**6/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \tan^{5}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{30 d x \tan{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{30 i d x}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{18 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{18 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{3 i \tan^{5}{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{\tan^{4}{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{8 i \tan^{3}{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{12 \tan^{2}{\left(c + d x \right)}}{12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{30}{12 i b d \tan{\left(c + d x \right)} + 12 b d} & \text{for}\: a = - i b \\- \frac{30 d x \tan{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{30 i d x}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{18 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{18 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{3 i \tan^{5}{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} - \frac{\tan^{4}{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{8 i \tan^{3}{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{12 \tan^{2}{\left(c + d x \right)}}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} + \frac{30}{- 12 i b d \tan{\left(c + d x \right)} + 12 b d} & \text{for}\: a = i b \\\frac{- x + \frac{\tan^{5}{\left(c + d x \right)}}{5 d} - \frac{\tan^{3}{\left(c + d x \right)}}{3 d} + \frac{\tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{6}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{12 a^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} - \frac{12 a^{5} b \tan{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} + \frac{6 a^{4} b^{2} \tan^{2}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} - \frac{4 a^{3} b^{3} \tan^{3}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} + \frac{3 a^{2} b^{4} \tan^{4}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} - \frac{12 a b^{5} d x}{12 a^{2} b^{5} d + 12 b^{7} d} - \frac{4 a b^{5} \tan^{3}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} + \frac{12 a b^{5} \tan{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} + \frac{6 b^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} + \frac{3 b^{6} \tan^{4}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} - \frac{6 b^{6} \tan^{2}{\left(c + d x \right)}}{12 a^{2} b^{5} d + 12 b^{7} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c)**5, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-30*d*x*tan(c + d*x)/(12*I*b*d*tan(c + d*x) + 12*b*d) + 30*I*d*x/(12*I*b*d*tan(c + d*x) + 12*b*d) + 18*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(12*I*b*d*tan(c + d*x) + 12*b*d) + 18*log(tan(c + d*x)**2 + 1)/(12*I*b*d*tan(c + d*x) + 12*b*d) + 3*I*tan(c + d*x)**5/(12*I*b*d*tan(c + d*x) + 12*b*d) - tan(c + d*x)**4/(12*I*b*d*tan(c + d*x) + 12*b*d) - 8*I*tan(c + d*x)**3/(12*I*b*d*tan(c + d*x) + 12*b*d) + 12*tan(c + d*x)**2/(12*I*b*d*tan(c + d*x) + 12*b*d) + 30/(12*I*b*d*tan(c + d*x) + 12*b*d), Eq(a, -I*b)), (-30*d*x*tan(c + d*x)/(-12*I*b*d*tan(c + d*x) + 12*b*d) - 30*I*d*x/(-12*I*b*d*tan(c + d*x) + 12*b*d) - 18*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-12*I*b*d*tan(c + d*x) + 12*b*d) + 18*log(tan(c + d*x)**2 + 1)/(-12*I*b*d*tan(c + d*x) + 12*b*d) - 3*I*tan(c + d*x)**5/(-12*I*b*d*tan(c + d*x) + 12*b*d) - tan(c + d*x)**4/(-12*I*b*d*tan(c + d*x) + 12*b*d) + 8*I*tan(c + d*x)**3/(-12*I*b*d*tan(c + d*x) + 12*b*d) + 12*tan(c + d*x)**2/(-12*I*b*d*tan(c + d*x) + 12*b*d) + 30/(-12*I*b*d*tan(c + d*x) + 12*b*d), Eq(a, I*b)), ((-x + tan(c + d*x)**5/(5*d) - tan(c + d*x)**3/(3*d) + tan(c + d*x)/d)/a, Eq(b, 0)), (x*tan(c)**6/(a + b*tan(c)), Eq(d, 0)), (12*a**6*log(a/b + tan(c + d*x))/(12*a**2*b**5*d + 12*b**7*d) - 12*a**5*b*tan(c + d*x)/(12*a**2*b**5*d + 12*b**7*d) + 6*a**4*b**2*tan(c + d*x)**2/(12*a**2*b**5*d + 12*b**7*d) - 4*a**3*b**3*tan(c + d*x)**3/(12*a**2*b**5*d + 12*b**7*d) + 3*a**2*b**4*tan(c + d*x)**4/(12*a**2*b**5*d + 12*b**7*d) - 12*a*b**5*d*x/(12*a**2*b**5*d + 12*b**7*d) - 4*a*b**5*tan(c + d*x)**3/(12*a**2*b**5*d + 12*b**7*d) + 12*a*b**5*tan(c + d*x)/(12*a**2*b**5*d + 12*b**7*d) + 6*b**6*log(tan(c + d*x)**2 + 1)/(12*a**2*b**5*d + 12*b**7*d) + 3*b**6*tan(c + d*x)**4/(12*a**2*b**5*d + 12*b**7*d) - 6*b**6*tan(c + d*x)**2/(12*a**2*b**5*d + 12*b**7*d), True))","A",0
457,1,835,0,2.340045," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \tan^{4}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{4}{\left(c + d x \right)}}{4 d} - \frac{\tan^{2}{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\- \frac{15 d x \tan{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} + \frac{15 i d x}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} + \frac{6 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} + \frac{6 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} - \frac{2 \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} - \frac{i \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} + \frac{9 \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} + \frac{15}{- 6 b d \tan{\left(c + d x \right)} + 6 i b d} & \text{for}\: a = - i b \\- \frac{15 d x \tan{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} - \frac{15 i d x}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} - \frac{6 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} + \frac{6 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} - \frac{2 \tan^{4}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} + \frac{i \tan^{3}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} + \frac{9 \tan^{2}{\left(c + d x \right)}}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} + \frac{15}{- 6 b d \tan{\left(c + d x \right)} - 6 i b d} & \text{for}\: a = i b \\\frac{x \tan^{5}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{6 a^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} + \frac{6 a^{4} b \tan{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} - \frac{3 a^{3} b^{2} \tan^{2}{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} + \frac{2 a^{2} b^{3} \tan^{3}{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} + \frac{3 a b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} - \frac{3 a b^{4} \tan^{2}{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} + \frac{6 b^{5} d x}{6 a^{2} b^{4} d + 6 b^{6} d} + \frac{2 b^{5} \tan^{3}{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} - \frac{6 b^{5} \tan{\left(c + d x \right)}}{6 a^{2} b^{4} d + 6 b^{6} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c)**4, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**4/(4*d) - tan(c + d*x)**2/(2*d))/a, Eq(b, 0)), (-15*d*x*tan(c + d*x)/(-6*b*d*tan(c + d*x) + 6*I*b*d) + 15*I*d*x/(-6*b*d*tan(c + d*x) + 6*I*b*d) + 6*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-6*b*d*tan(c + d*x) + 6*I*b*d) + 6*log(tan(c + d*x)**2 + 1)/(-6*b*d*tan(c + d*x) + 6*I*b*d) - 2*tan(c + d*x)**4/(-6*b*d*tan(c + d*x) + 6*I*b*d) - I*tan(c + d*x)**3/(-6*b*d*tan(c + d*x) + 6*I*b*d) + 9*tan(c + d*x)**2/(-6*b*d*tan(c + d*x) + 6*I*b*d) + 15/(-6*b*d*tan(c + d*x) + 6*I*b*d), Eq(a, -I*b)), (-15*d*x*tan(c + d*x)/(-6*b*d*tan(c + d*x) - 6*I*b*d) - 15*I*d*x/(-6*b*d*tan(c + d*x) - 6*I*b*d) - 6*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-6*b*d*tan(c + d*x) - 6*I*b*d) + 6*log(tan(c + d*x)**2 + 1)/(-6*b*d*tan(c + d*x) - 6*I*b*d) - 2*tan(c + d*x)**4/(-6*b*d*tan(c + d*x) - 6*I*b*d) + I*tan(c + d*x)**3/(-6*b*d*tan(c + d*x) - 6*I*b*d) + 9*tan(c + d*x)**2/(-6*b*d*tan(c + d*x) - 6*I*b*d) + 15/(-6*b*d*tan(c + d*x) - 6*I*b*d), Eq(a, I*b)), (x*tan(c)**5/(a + b*tan(c)), Eq(d, 0)), (-6*a**5*log(a/b + tan(c + d*x))/(6*a**2*b**4*d + 6*b**6*d) + 6*a**4*b*tan(c + d*x)/(6*a**2*b**4*d + 6*b**6*d) - 3*a**3*b**2*tan(c + d*x)**2/(6*a**2*b**4*d + 6*b**6*d) + 2*a**2*b**3*tan(c + d*x)**3/(6*a**2*b**4*d + 6*b**6*d) + 3*a*b**4*log(tan(c + d*x)**2 + 1)/(6*a**2*b**4*d + 6*b**6*d) - 3*a*b**4*tan(c + d*x)**2/(6*a**2*b**4*d + 6*b**6*d) + 6*b**5*d*x/(6*a**2*b**4*d + 6*b**6*d) + 2*b**5*tan(c + d*x)**3/(6*a**2*b**4*d + 6*b**6*d) - 6*b**5*tan(c + d*x)/(6*a**2*b**4*d + 6*b**6*d), True))","A",0
458,1,673,0,1.828305," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \tan^{3}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{3 d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i \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 \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 \tan^{3}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{\tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\\frac{3 d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i \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 \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 \tan^{3}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{\tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{x + \frac{\tan^{3}{\left(c + d x \right)}}{3 d} - \frac{\tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{4}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 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 a^{3} b \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 a b^{3} d x}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 a b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{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^{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*tan(c)**3, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (3*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*tan(c + d*x)**3/(2*I*b*d*tan(c + d*x) + 2*b*d) - tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (3*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*tan(c + d*x)**3/(-2*I*b*d*tan(c + d*x) + 2*b*d) - tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), ((x + tan(c + d*x)**3/(3*d) - tan(c + d*x)/d)/a, Eq(b, 0)), (x*tan(c)**4/(a + b*tan(c)), Eq(d, 0)), (2*a**4*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) - 2*a**3*b*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + a**2*b**2*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d) + 2*a*b**3*d*x/(2*a**2*b**3*d + 2*b**5*d) - 2*a*b**3*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - b**4*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) + b**4*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d), True))","A",0
459,1,564,0,1.335480," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \tan^{2}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{3 d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 i d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i \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{\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 \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\\frac{3 d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 i d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i \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{\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 \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{3}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{- \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{2}{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 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 a^{2} b \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{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^{3} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 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*tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (3*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - 3*I*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) - I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - 2*tan(c + d*x)**2/(-2*b*d*tan(c + d*x) + 2*I*b*d) - 3/(-2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (3*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) + 3*I*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) + I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - 2*tan(c + d*x)**2/(-2*b*d*tan(c + d*x) - 2*I*b*d) - 3/(-2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, I*b)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**2/(2*d))/a, Eq(b, 0)), (x*tan(c)**3/(a + b*tan(c)), Eq(d, 0)), (-2*a**3*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) + 2*a**2*b*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d) - a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*b**3*d*x/(2*a**2*b**2*d + 2*b**4*d) + 2*b**3*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d), True))","A",0
460,1,405,0,1.051651," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i \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{\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{1}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\- \frac{d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i \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{\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{1}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{- x + \frac{\tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 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 a b d x}{2 a^{2} b d + 2 b^{3} d} + \frac{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*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + 1/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (-d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 1/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), ((-x + tan(c + d*x)/d)/a, Eq(b, 0)), (x*tan(c)**2/(a + b*tan(c)), Eq(d, 0)), (2*a**2*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) - 2*a*b*d*x/(2*a**2*b*d + 2*b**3*d) + b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d), True))","A",0
461,1,260,0,0.884803," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{1}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\- \frac{d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{1}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{x \tan{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a d} & \text{for}\: b = 0 \\- \frac{2 a \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 b d x}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) + 1/(-2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (-d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) + 1/(-2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, I*b)), (x*tan(c)/(a + b*tan(c)), Eq(d, 0)), (log(tan(c + d*x)**2 + 1)/(2*a*d), Eq(b, 0)), (-2*a*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) + a*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*b*d*x/(2*a**2*d + 2*b**2*d), True))","A",0
462,1,246,0,0.873570," ","integrate(1/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} - \frac{i d x}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} + \frac{1}{- 2 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = - i b \\\frac{d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} - 2 b d} + \frac{i d x}{2 i b d \tan{\left(c + d x \right)} - 2 b d} + \frac{1}{2 i b d \tan{\left(c + d x \right)} - 2 b d} & \text{for}\: a = i b \\\frac{x}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{x}{a} & \text{for}\: b = 0 \\\frac{2 a d x}{2 a^{2} d + 2 b^{2} d} + \frac{2 b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{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*x/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) - 2*b*d) - I*d*x/(-2*I*b*d*tan(c + d*x) - 2*b*d) + 1/(-2*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, -I*b)), (d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) - 2*b*d) + I*d*x/(2*I*b*d*tan(c + d*x) - 2*b*d) + 1/(2*I*b*d*tan(c + d*x) - 2*b*d), Eq(a, I*b)), (x/(a + b*tan(c)), Eq(d, 0)), (x/a, Eq(b, 0)), (2*a*d*x/(2*a**2*d + 2*b**2*d) + 2*b*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) - b*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d), True))","A",0
463,1,626,0,1.857162," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \cot{\left(c \right)}}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- x - \frac{1}{d \tan{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i \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{\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 \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 \log{\left(\tan{\left(c + d x \right)} \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{1}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\\frac{d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i \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{\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 \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 \log{\left(\tan{\left(c + d x \right)} \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{1}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{x \cot{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{- \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}}{a} & \text{for}\: b = 0 \\- \frac{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^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{2 a b d x}{2 a^{3} d + 2 a b^{2} d} - \frac{2 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^{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*x*cot(c)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x - 1/(d*tan(c + d*x)))/b, Eq(a, 0)), (d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*I*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*log(tan(c + d*x))/(2*b*d*tan(c + d*x) - 2*I*b*d) + 1/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) - log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) - 2*I*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + 2*log(tan(c + d*x))/(2*b*d*tan(c + d*x) + 2*I*b*d) + 1/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), (x*cot(c)/(a + b*tan(c)), Eq(d, 0)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + log(tan(c + d*x))/d)/a, Eq(b, 0)), (-a**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d) + 2*a**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - 2*a*b*d*x/(2*a**3*d + 2*a*b**2*d) - 2*b**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*b**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d), True))","A",0
464,1,1080,0,3.304945," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{- x - \frac{\cot{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{\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)}}}{b} & \text{for}\: a = 0 \\- \frac{3 i 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 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{\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 \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 \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 \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 \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}{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 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 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{\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 \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 \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 \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 \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}{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} x}{a} & \text{for}\: c = - d x \\\frac{x \cot^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 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^{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^{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^{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 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^{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^{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*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((-x - cot(c + d*x)/d)/a, Eq(b, 0)), ((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*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 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*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*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*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*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)), Eq(a, -I*b)), (3*I*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 3*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 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*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*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*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*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)), Eq(a, I*b)), (zoo*x/a, Eq(c, -d*x)), (x*cot(c)**2/(a + b*tan(c)), Eq(d, 0)), (-2*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**3/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 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**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*b**2/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*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**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
465,1,1352,0,5.158734," ","integrate(cot(d*x+c)**3/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{x + \frac{1}{d \tan{\left(c + d x \right)}} - \frac{1}{3 d \tan^{3}{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{3 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 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 \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 \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 \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 \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 \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 \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{1}{- 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 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 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 \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 \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 \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 \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 \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 \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{1}{- 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} x}{a} & \text{for}\: c = - d x \\\frac{x \cot^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\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)}}}{a} & \text{for}\: b = 0 \\\frac{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^{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^{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^{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^{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^{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 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^{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^{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*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((x + 1/(d*tan(c + d*x)) - 1/(3*d*tan(c + d*x)**3))/b, Eq(a, 0)), (3*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*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*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*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*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*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*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 1/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2), Eq(a, -I*b)), (3*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*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*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*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*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*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*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 1/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2), Eq(a, I*b)), (zoo*x/a, Eq(c, -d*x)), (x*cot(c)**3/(a + b*tan(c)), Eq(d, 0)), ((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)), (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**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**4/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*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**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**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*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**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**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
466,1,1550,0,7.901867," ","integrate(cot(d*x+c)**4/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{x - \frac{\cot^{3}{\left(c + d x \right)}}{3 d} + \frac{\cot{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{- \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)}} - \frac{1}{4 d \tan^{4}{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{15 i 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 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 \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 \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 \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 \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 \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 \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 \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}{- 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 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 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 \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 \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 \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 \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 \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 \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 \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}{- 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} x}{a} & \text{for}\: c = - d x \\\frac{x \cot^{4}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{6 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^{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^{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^{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^{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^{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^{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^{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 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 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 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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((x - cot(c + d*x)**3/(3*d) + cot(c + d*x)/d)/a, Eq(b, 0)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + log(tan(c + d*x))/d + 1/(2*d*tan(c + d*x)**2) - 1/(4*d*tan(c + d*x)**4))/b, Eq(a, 0)), (-15*I*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*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*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*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*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*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*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - 9*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) - I*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3) + 2/(-6*b*d*tan(c + d*x)**4 + 6*I*b*d*tan(c + d*x)**3), Eq(a, -I*b)), (15*I*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*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*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*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*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*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*tan(c + d*x)**3/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) - 9*tan(c + d*x)**2/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + I*tan(c + d*x)/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3) + 2/(-6*b*d*tan(c + d*x)**4 - 6*I*b*d*tan(c + d*x)**3), Eq(a, I*b)), (zoo*x/a, Eq(c, -d*x)), (x*cot(c)**4/(a + b*tan(c)), Eq(d, 0)), (6*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**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**5/(6*a**6*d*tan(c + d*x)**3 + 6*a**4*b**2*d*tan(c + d*x)**3) - 3*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**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**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**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**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*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*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*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), True))","A",0
467,1,3320,0,4.803162," ","integrate(tan(d*x+c)**6/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \tan^{4}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- x + \frac{\tan^{5}{\left(c + d x \right)}}{5 d} - \frac{\tan^{3}{\left(c + d x \right)}}{3 d} + \frac{\tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{75 i d x \tan^{2}{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} - \frac{150 d x \tan{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{75 i d x}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} - \frac{36 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{72 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{36 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} - \frac{4 i \tan^{5}{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{4 \tan^{4}{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{28 i \tan^{3}{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{153 i \tan{\left(c + d x \right)}}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} + \frac{114}{- 12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} + 12 i b^{2} d} & \text{for}\: a = - i b \\\frac{75 i d x \tan^{2}{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{150 d x \tan{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{75 i d x}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{36 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{72 i \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} + \frac{36 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} + \frac{4 i \tan^{5}{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} + \frac{4 \tan^{4}{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{28 i \tan^{3}{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} - \frac{153 i \tan{\left(c + d x \right)}}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} + \frac{114}{12 i b^{2} d \tan^{2}{\left(c + d x \right)} - 24 b^{2} d \tan{\left(c + d x \right)} - 12 i b^{2} d} & \text{for}\: a = i b \\\frac{x \tan^{6}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{12 a^{8} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{12 a^{8}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{12 a^{7} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{18 a^{6} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{6 a^{6} b^{2} \tan^{2}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{18 a^{6} b^{2}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{18 a^{5} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{2 a^{5} b^{3} \tan^{3}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{a^{4} b^{4} \tan^{4}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{9 a^{4} b^{4} \tan^{2}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{3 a^{4} b^{4}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{3 a^{3} b^{5} d x}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{4 a^{3} b^{5} \tan^{3}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{3 a^{2} b^{6} d x \tan{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{3 a^{2} b^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{2 a^{2} b^{6} \tan^{4}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{3 a^{2} b^{6}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{3 a b^{7} d x}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{3 a b^{7} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{2 a b^{7} \tan^{3}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{3 b^{8} d x \tan{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} + \frac{b^{8} \tan^{4}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} - \frac{3 b^{8} \tan^{2}{\left(c + d x \right)}}{3 a^{5} b^{5} d + 3 a^{4} b^{6} d \tan{\left(c + d x \right)} + 6 a^{3} b^{7} d + 6 a^{2} b^{8} d \tan{\left(c + d x \right)} + 3 a b^{9} d + 3 b^{10} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c)**4, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x + tan(c + d*x)**5/(5*d) - tan(c + d*x)**3/(3*d) + tan(c + d*x)/d)/a**2, Eq(b, 0)), (-75*I*d*x*tan(c + d*x)**2/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) - 150*d*x*tan(c + d*x)/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 75*I*d*x/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) - 36*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 72*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 36*log(tan(c + d*x)**2 + 1)/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) - 4*I*tan(c + d*x)**5/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 4*tan(c + d*x)**4/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 28*I*tan(c + d*x)**3/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 153*I*tan(c + d*x)/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d) + 114/(-12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) + 12*I*b**2*d), Eq(a, -I*b)), (75*I*d*x*tan(c + d*x)**2/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 150*d*x*tan(c + d*x)/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 75*I*d*x/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 36*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 72*I*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) + 36*log(tan(c + d*x)**2 + 1)/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) + 4*I*tan(c + d*x)**5/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) + 4*tan(c + d*x)**4/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 28*I*tan(c + d*x)**3/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) - 153*I*tan(c + d*x)/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d) + 114/(12*I*b**2*d*tan(c + d*x)**2 - 24*b**2*d*tan(c + d*x) - 12*I*b**2*d), Eq(a, I*b)), (x*tan(c)**6/(a + b*tan(c))**2, Eq(d, 0)), (-12*a**8*log(a/b + tan(c + d*x))/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 12*a**8/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 12*a**7*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 18*a**6*b**2*log(a/b + tan(c + d*x))/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 6*a**6*b**2*tan(c + d*x)**2/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 18*a**6*b**2/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 18*a**5*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 2*a**5*b**3*tan(c + d*x)**3/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + a**4*b**4*tan(c + d*x)**4/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 9*a**4*b**4*tan(c + d*x)**2/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 3*a**4*b**4/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 3*a**3*b**5*d*x/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 4*a**3*b**5*tan(c + d*x)**3/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 3*a**2*b**6*d*x*tan(c + d*x)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 3*a**2*b**6*log(tan(c + d*x)**2 + 1)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 2*a**2*b**6*tan(c + d*x)**4/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 3*a**2*b**6/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 3*a*b**7*d*x/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 3*a*b**7*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 2*a*b**7*tan(c + d*x)**3/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + 3*b**8*d*x*tan(c + d*x)/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) + b**8*tan(c + d*x)**4/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)) - 3*b**8*tan(c + d*x)**2/(3*a**5*b**5*d + 3*a**4*b**6*d*tan(c + d*x) + 6*a**3*b**7*d + 6*a**2*b**8*d*tan(c + d*x) + 3*a*b**9*d + 3*b**10*d*tan(c + d*x)), True))","A",0
468,1,2837,0,3.359492," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \tan^{3}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{15 i 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{30 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{15 i 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{8 \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{16 i \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{8 \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{2 \tan^{4}{\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 \tan^{3}{\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{29 i \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{22}{- 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{15 i 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{30 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{15 i 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{8 \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{16 i \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{8 \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{2 \tan^{4}{\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 \tan^{3}{\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{29 i \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{22}{- 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{\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{4}{\left(c + d x \right)}}{4 d} - \frac{\tan^{2}{\left(c + d x \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \tan^{5}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{6 a^{7} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{6 a^{7}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{6 a^{6} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{10 a^{5} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} - \frac{3 a^{5} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{10 a^{5} b^{2}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{10 a^{4} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{a^{4} b^{3} \tan^{3}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{a^{3} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} - \frac{6 a^{3} b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{4 a^{3} b^{4}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{4 a^{2} b^{5} d x}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{a^{2} b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{2 a^{2} b^{5} \tan^{3}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{4 a b^{6} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} - \frac{a b^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} - \frac{3 a b^{6} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} - \frac{b^{7} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} + \frac{b^{7} \tan^{3}{\left(c + d x \right)}}{2 a^{5} b^{4} d + 2 a^{4} b^{5} d \tan{\left(c + d x \right)} + 4 a^{3} b^{6} d + 4 a^{2} b^{7} d \tan{\left(c + d x \right)} + 2 a b^{8} d + 2 b^{9} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c)**3, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (15*I*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) + 30*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) - 15*I*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 8*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) - 16*I*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) - 8*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) - 2*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 4*I*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 29*I*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) - 22/(-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)), (-15*I*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) + 30*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) + 15*I*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 8*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) + 16*I*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) - 8*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) - 2*tan(c + d*x)**4/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*I*tan(c + d*x)**3/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 29*I*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) - 22/(-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)), ((log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**4/(4*d) - tan(c + d*x)**2/(2*d))/a**2, Eq(b, 0)), (x*tan(c)**5/(a + b*tan(c))**2, Eq(d, 0)), (6*a**7*log(a/b + tan(c + d*x))/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 6*a**7/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 6*a**6*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 10*a**5*b**2*log(a/b + tan(c + d*x))/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) - 3*a**5*b**2*tan(c + d*x)**2/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 10*a**5*b**2/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 10*a**4*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + a**4*b**3*tan(c + d*x)**3/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + a**3*b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) - 6*a**3*b**4*tan(c + d*x)**2/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 4*a**3*b**4/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 4*a**2*b**5*d*x/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + a**2*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 2*a**2*b**5*tan(c + d*x)**3/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + 4*a*b**6*d*x*tan(c + d*x)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) - a*b**6*log(tan(c + d*x)**2 + 1)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) - 3*a*b**6*tan(c + d*x)**2/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) - b**7*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)) + b**7*tan(c + d*x)**3/(2*a**5*b**4*d + 2*a**4*b**5*d*tan(c + d*x) + 4*a**3*b**6*d + 4*a**2*b**7*d*tan(c + d*x) + 2*a*b**8*d + 2*b**9*d*tan(c + d*x)), True))","A",0
469,1,2346,0,2.638322," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \tan^{2}{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{x + \frac{\tan^{3}{\left(c + d x \right)}}{3 d} - \frac{\tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\\frac{9 i 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 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 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 \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 \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 \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 \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 \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}{- 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{9 i 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 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 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 \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 \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 \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 \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 \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}{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 \tan^{4}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 a^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{2 a^{6}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{2 a^{5} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{4 a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} + \frac{a^{4} b^{2} \tan^{2}{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{3 a^{4} b^{2}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} + \frac{a^{3} b^{3} d x}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{4 a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} + \frac{a^{2} b^{4} d x \tan{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{a^{2} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} + \frac{2 a^{2} b^{4} \tan^{2}{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{a^{2} b^{4}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{a b^{5} d x}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{a b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} - \frac{b^{6} d x \tan{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} + \frac{b^{6} \tan^{2}{\left(c + d x \right)}}{a^{5} b^{3} d + a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d + 2 a^{2} b^{6} d \tan{\left(c + d x \right)} + a b^{7} d + b^{8} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((x + tan(c + d*x)**3/(3*d) - tan(c + d*x)/d)/a**2, Eq(b, 0)), (9*I*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*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*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*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*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*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*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*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/(-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)), (-9*I*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*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*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*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*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*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*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*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/(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*tan(c)**4/(a + b*tan(c))**2, Eq(d, 0)), (-2*a**6*log(a/b + tan(c + d*x))/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - 2*a**6/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - 2*a**5*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - 4*a**4*b**2*log(a/b + tan(c + d*x))/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) + a**4*b**2*tan(c + d*x)**2/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - 3*a**4*b**2/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) + a**3*b**3*d*x/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - 4*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) + a**2*b**4*d*x*tan(c + d*x)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - a**2*b**4*log(tan(c + d*x)**2 + 1)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) + 2*a**2*b**4*tan(c + d*x)**2/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - a**2*b**4/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - a*b**5*d*x/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - a*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) - b**6*d*x*tan(c + d*x)/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)) + b**6*tan(c + d*x)**2/(a**5*b**3*d + a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d + 2*a**2*b**6*d*tan(c + d*x) + a*b**7*d + b**8*d*tan(c + d*x)), True))","A",0
470,1,1992,0,2.082696," ","integrate(tan(d*x+c)**3/(a+b*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{- \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{2}{\left(c + d x \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\\frac{3 i 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 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 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 \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 \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 \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 \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}{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 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 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 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 \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 \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 \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 \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}{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 \tan^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 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 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 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 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{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 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 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 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{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 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{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^{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*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**2/(2*d))/a**2, Eq(b, 0)), (3*I*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*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*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*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*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*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*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/(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*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*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*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*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*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*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*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/(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*tan(c)**3/(a + b*tan(c))**2, Eq(d, 0)), (2*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*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*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*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)) - 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*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*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*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)) - 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*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)) + 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**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
471,1,1314,0,1.658154," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{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 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{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 \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}{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{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 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{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 \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}{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 + \frac{\tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \tan^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{a^{4}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} - \frac{a^{3} b d x}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} - \frac{a^{2} b^{2} d x \tan{\left(c + d x \right)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} - \frac{2 a^{2} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} + \frac{a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} - \frac{a^{2} b^{2}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} + \frac{a b^{3} d x}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} 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)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} + \frac{a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} + \frac{b^{4} d x \tan{\left(c + d x \right)}}{a^{5} b d + a^{4} b^{2} d \tan{\left(c + d x \right)} + 2 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + a b^{5} d + b^{6} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (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*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) - 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*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/(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)), (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*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) - 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*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/(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 + tan(c + d*x)/d)/a**2, Eq(b, 0)), (x*tan(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (-a**4/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) - a**3*b*d*x/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) - a**2*b**2*d*x*tan(c + d*x)/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) - 2*a**2*b**2*log(a/b + tan(c + d*x))/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) + a**2*b**2*log(tan(c + d*x)**2 + 1)/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) - a**2*b**2/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) + a*b**3*d*x/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) - 2*a*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) + a*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)) + b**4*d*x*tan(c + d*x)/(a**5*b*d + a**4*b**2*d*tan(c + d*x) + 2*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + a*b**5*d + b**6*d*tan(c + d*x)), True))","A",0
472,1,1482,0,1.702413," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{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{2 i 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{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{\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} & \text{for}\: a = - i b \\- \frac{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{2 i 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{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{\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} & \text{for}\: a = i b \\\frac{x \tan{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d} & \text{for}\: b = 0 \\- \frac{2 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{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 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 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 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{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 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 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{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 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^{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^{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/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-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) + 2*I*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) + 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) - 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), Eq(a, -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) - 2*I*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) + 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) - 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), Eq(a, I*b)), (x*tan(c)/(a + b*tan(c))**2, Eq(d, 0)), (log(tan(c + d*x)**2 + 1)/(2*a**2*d), Eq(b, 0)), (-2*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)) + 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*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*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*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)) + 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*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*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)) - 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*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**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**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
473,1,1260,0,1.581183," ","integrate(1/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{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 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{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{\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}{- 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{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 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{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{\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}{- 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)^{2}} & \text{for}\: d = 0 \\\frac{x}{a^{2}} & \text{for}\: b = 0 \\\frac{a^{3} d x}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} + \frac{a^{2} b d x \tan{\left(c + d x \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} + \frac{2 a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{a^{2} b}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{a b^{2} d x}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} + \frac{2 a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{b^{3} d x \tan{\left(c + d x \right)}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} - \frac{b^{3}}{a^{5} d + a^{4} b d \tan{\left(c + d x \right)} + 2 a^{3} b^{2} d + 2 a^{2} b^{3} d \tan{\left(c + d x \right)} + a b^{4} d + b^{5} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (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*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) - d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 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/(-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)), (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*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) - d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 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/(-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))**2, Eq(d, 0)), (x/a**2, Eq(b, 0)), (a**3*d*x/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) + a**2*b*d*x*tan(c + d*x)/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) + 2*a**2*b*log(a/b + tan(c + d*x))/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - a**2*b*log(tan(c + d*x)**2 + 1)/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - a**2*b/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - a*b**2*d*x/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) + 2*a*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - a*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - b**3*d*x*tan(c + d*x)/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)) - b**3/(a**5*d + a**4*b*d*tan(c + d*x) + 2*a**3*b**2*d + 2*a**2*b**3*d*tan(c + d*x) + a*b**4*d + b**5*d*tan(c + d*x)), True))","A",0
474,1,2927,0,3.901920," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \cot{\left(c \right)}}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- \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}}{a^{2}} & \text{for}\: b = 0 \\\frac{\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)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 i 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 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 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 \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 \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 \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 \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 \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 \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 \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}{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 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 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 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 \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 \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 \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 \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 \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 \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 \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}{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 \cot{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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 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 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 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 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 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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cot(c)/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + log(tan(c + d*x))/d)/a**2, Eq(b, 0)), ((log(tan(c + d*x)**2 + 1)/(2*d) - log(tan(c + d*x))/d - 1/(2*d*tan(c + d*x)**2))/b**2, Eq(a, 0)), (3*I*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*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*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*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*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*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*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*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*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*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/(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*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*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*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*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*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*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*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*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*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*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/(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*cot(c)/(a + b*tan(c))**2, Eq(d, 0)), (-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**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**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**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**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**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**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**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**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**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**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**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**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*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*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*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*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*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)), True))","A",0
475,1,4070,0,5.308398," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{x + \frac{1}{d \tan{\left(c + d x \right)}} - \frac{1}{3 d \tan^{3}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{9 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 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 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 \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 \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 \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 \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 \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 \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 \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 \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}{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 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 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 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 \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 \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 \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 \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 \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 \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 \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 \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}{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} x}{a^{2}} & \text{for}\: c = - d x \\\frac{x \cot^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{- x - \frac{\cot{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{a^{6} d x \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{a^{6}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{a^{5} b d x \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{a^{5} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 a^{5} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{a^{5} b \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{a^{4} b^{2} d x \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{a^{4} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 a^{4} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 a^{4} b^{2}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{a^{3} b^{3} d x \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 a^{3} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{3 a^{3} b^{3} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 a^{2} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{a^{2} b^{4}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\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)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\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)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 a b^{5} \tan{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 b^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 b^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{a^{8} d \tan{\left(c + d x \right)} + a^{7} b d \tan^{2}{\left(c + d x \right)} + 2 a^{6} b^{2} d \tan{\left(c + d x \right)} + 2 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + a^{4} b^{4} d \tan{\left(c + d x \right)} + a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((x + 1/(d*tan(c + d*x)) - 1/(3*d*tan(c + d*x)**3))/b**2, Eq(a, 0)), (9*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*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*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*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*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*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*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*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*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*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*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/(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*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*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*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*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*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*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*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*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*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*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*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/(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*x/a**2, Eq(c, -d*x)), (x*cot(c)**2/(a + b*tan(c))**2, Eq(d, 0)), ((-x - cot(c + d*x)/d)/a**2, Eq(b, 0)), (-a**6*d*x*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - a**6/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - a**5*b*d*x*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + a**5*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*a**5*b*log(tan(c + d*x))*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - a**5*b*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + a**4*b**2*d*x*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + a**4*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*a**4*b**2*log(tan(c + d*x))*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*a**4*b**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + a**3*b**3*d*x*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + 4*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 4*a**3*b**3*log(tan(c + d*x))*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 3*a**3*b**3*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + 4*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 4*a**2*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - a**2*b**4/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + 2*a*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*a*b**5*log(tan(c + d*x))*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*a*b**5*tan(c + d*x)/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) + 2*b**6*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2) - 2*b**6*log(tan(c + d*x))*tan(c + d*x)**2/(a**8*d*tan(c + d*x) + a**7*b*d*tan(c + d*x)**2 + 2*a**6*b**2*d*tan(c + d*x) + 2*a**5*b**3*d*tan(c + d*x)**2 + a**4*b**4*d*tan(c + d*x) + a**3*b**5*d*tan(c + d*x)**2), True))","A",0
476,1,5222,0,7.299497," ","integrate(cot(d*x+c)**3/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{- \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)}} - \frac{1}{4 d \tan^{4}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{15 i 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 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 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 \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 \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 \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 \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 \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 \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 \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 \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 \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}{- 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 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 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 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 \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 \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 \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 \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 \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 \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 \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 \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 \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}{- 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} x}{a^{2}} & \text{for}\: c = - d x \\\frac{x \cot^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{\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)}}}{a^{2}} & \text{for}\: b = 0 \\\frac{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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^{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 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 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 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 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 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)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((-log(tan(c + d*x)**2 + 1)/(2*d) + log(tan(c + d*x))/d + 1/(2*d*tan(c + d*x)**2) - 1/(4*d*tan(c + d*x)**4))/b**2, Eq(a, 0)), (15*I*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*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*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*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*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*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*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*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*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*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*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*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/(-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*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*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*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*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*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*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*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*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*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*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*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*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/(-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*x/a**2, Eq(c, -d*x)), (x*cot(c)**3/(a + b*tan(c))**2, Eq(d, 0)), ((log(tan(c + d*x)**2 + 1)/(2*d) - log(tan(c + d*x))/d - 1/(2*d*tan(c + d*x)**2))/a**2, Eq(b, 0)), (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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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*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*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*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*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*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), True))","A",0
477,-2,0,0,0.000000," ","integrate(tan(d*x+c)**6/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
478,-2,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
479,-2,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
480,-2,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
481,-2,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
482,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
483,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
484,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
485,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
486,-2,0,0,0.000000," ","integrate(tan(d*x+c)**6/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
487,-2,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
488,-2,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
489,-2,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
490,-2,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
491,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
492,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
493,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
494,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
495,1,46,0,0.349876," ","integrate(1/(3+5*tan(d*x+c)),x)","\begin{cases} \frac{3 x}{34} + \frac{5 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)}}{34 d} - \frac{5 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{68 d} & \text{for}\: d \neq 0 \\\frac{x}{5 \tan{\left(c \right)} + 3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x/34 + 5*log(tan(c + d*x) + 3/5)/(34*d) - 5*log(tan(c + d*x)**2 + 1)/(68*d), Ne(d, 0)), (x/(5*tan(c) + 3), True))","A",0
496,1,190,0,0.560768," ","integrate(1/(3+5*tan(d*x+c))**2,x)","\begin{cases} - \frac{80 d x \tan{\left(c + d x \right)}}{5780 d \tan{\left(c + d x \right)} + 3468 d} - \frac{48 d x}{5780 d \tan{\left(c + d x \right)} + 3468 d} + \frac{150 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan{\left(c + d x \right)}}{5780 d \tan{\left(c + d x \right)} + 3468 d} + \frac{90 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)}}{5780 d \tan{\left(c + d x \right)} + 3468 d} - \frac{75 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{5780 d \tan{\left(c + d x \right)} + 3468 d} - \frac{45 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{5780 d \tan{\left(c + d x \right)} + 3468 d} - \frac{170}{5780 d \tan{\left(c + d x \right)} + 3468 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(5 \tan{\left(c \right)} + 3\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-80*d*x*tan(c + d*x)/(5780*d*tan(c + d*x) + 3468*d) - 48*d*x/(5780*d*tan(c + d*x) + 3468*d) + 150*log(tan(c + d*x) + 3/5)*tan(c + d*x)/(5780*d*tan(c + d*x) + 3468*d) + 90*log(tan(c + d*x) + 3/5)/(5780*d*tan(c + d*x) + 3468*d) - 75*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(5780*d*tan(c + d*x) + 3468*d) - 45*log(tan(c + d*x)**2 + 1)/(5780*d*tan(c + d*x) + 3468*d) - 170/(5780*d*tan(c + d*x) + 3468*d), Ne(d, 0)), (x/(5*tan(c) + 3)**2, True))","A",0
497,1,442,0,0.808300," ","integrate(1/(3+5*tan(d*x+c))**3,x)","\begin{cases} - \frac{4950 d x \tan^{2}{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{5940 d x \tan{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{1782 d x}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} + \frac{250 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan^{2}{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} + \frac{300 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} + \frac{90 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{125 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{150 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{45 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{5100 \tan{\left(c + d x \right)}}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} - \frac{5950}{982600 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 353736 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(5 \tan{\left(c \right)} + 3\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4950*d*x*tan(c + d*x)**2/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 5940*d*x*tan(c + d*x)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 1782*d*x/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) + 250*log(tan(c + d*x) + 3/5)*tan(c + d*x)**2/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) + 300*log(tan(c + d*x) + 3/5)*tan(c + d*x)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) + 90*log(tan(c + d*x) + 3/5)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 125*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 150*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 45*log(tan(c + d*x)**2 + 1)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 5100*tan(c + d*x)/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d) - 5950/(982600*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 353736*d), Ne(d, 0)), (x/(5*tan(c) + 3)**3, True))","A",0
498,1,790,0,1.131900," ","integrate(1/(3+5*tan(d*x+c))**4,x)","\begin{cases} - \frac{60375 d x \tan^{3}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{108675 d x \tan^{2}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{65205 d x \tan{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{13041 d x}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{90000 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan^{3}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{162000 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan^{2}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{97200 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)} \tan{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{19440 \log{\left(\tan{\left(c + d x \right)} + \frac{3}{5} \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} + \frac{45000 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} + \frac{81000 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} + \frac{48600 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} + \frac{9720 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{6375 \tan^{2}{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{72675 \tan{\left(c + d x \right)}}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} - \frac{90440}{125281500 d \tan^{3}{\left(c + d x \right)} + 225506700 d \tan^{2}{\left(c + d x \right)} + 135304020 d \tan{\left(c + d x \right)} + 27060804 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(5 \tan{\left(c \right)} + 3\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60375*d*x*tan(c + d*x)**3/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 108675*d*x*tan(c + d*x)**2/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 65205*d*x*tan(c + d*x)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 13041*d*x/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 90000*log(tan(c + d*x) + 3/5)*tan(c + d*x)**3/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 162000*log(tan(c + d*x) + 3/5)*tan(c + d*x)**2/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 97200*log(tan(c + d*x) + 3/5)*tan(c + d*x)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 19440*log(tan(c + d*x) + 3/5)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) + 45000*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) + 81000*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) + 48600*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) + 9720*log(tan(c + d*x)**2 + 1)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 6375*tan(c + d*x)**2/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 72675*tan(c + d*x)/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d) - 90440/(125281500*d*tan(c + d*x)**3 + 225506700*d*tan(c + d*x)**2 + 135304020*d*tan(c + d*x) + 27060804*d), Ne(d, 0)), (x/(5*tan(c) + 3)**4, True))","A",0
499,1,46,0,0.348611," ","integrate(1/(5+3*tan(d*x+c)),x)","\begin{cases} \frac{5 x}{34} + \frac{3 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)}}{34 d} - \frac{3 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{68 d} & \text{for}\: d \neq 0 \\\frac{x}{3 \tan{\left(c \right)} + 5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*x/34 + 3*log(tan(c + d*x) + 5/3)/(34*d) - 3*log(tan(c + d*x)**2 + 1)/(68*d), Ne(d, 0)), (x/(3*tan(c) + 5), True))","A",0
500,1,190,0,0.549872," ","integrate(1/(5+3*tan(d*x+c))**2,x)","\begin{cases} \frac{48 d x \tan{\left(c + d x \right)}}{3468 d \tan{\left(c + d x \right)} + 5780 d} + \frac{80 d x}{3468 d \tan{\left(c + d x \right)} + 5780 d} + \frac{90 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan{\left(c + d x \right)}}{3468 d \tan{\left(c + d x \right)} + 5780 d} + \frac{150 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)}}{3468 d \tan{\left(c + d x \right)} + 5780 d} - \frac{45 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{3468 d \tan{\left(c + d x \right)} + 5780 d} - \frac{75 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{3468 d \tan{\left(c + d x \right)} + 5780 d} - \frac{102}{3468 d \tan{\left(c + d x \right)} + 5780 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(3 \tan{\left(c \right)} + 5\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((48*d*x*tan(c + d*x)/(3468*d*tan(c + d*x) + 5780*d) + 80*d*x/(3468*d*tan(c + d*x) + 5780*d) + 90*log(tan(c + d*x) + 5/3)*tan(c + d*x)/(3468*d*tan(c + d*x) + 5780*d) + 150*log(tan(c + d*x) + 5/3)/(3468*d*tan(c + d*x) + 5780*d) - 45*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(3468*d*tan(c + d*x) + 5780*d) - 75*log(tan(c + d*x)**2 + 1)/(3468*d*tan(c + d*x) + 5780*d) - 102/(3468*d*tan(c + d*x) + 5780*d), Ne(d, 0)), (x/(3*tan(c) + 5)**2, True))","A",0
501,1,442,0,0.793377," ","integrate(1/(5+3*tan(d*x+c))**3,x)","\begin{cases} - \frac{90 d x \tan^{2}{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{300 d x \tan{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{250 d x}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} + \frac{1782 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan^{2}{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} + \frac{5940 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} + \frac{4950 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{891 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{2970 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{2475 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{3060 \tan{\left(c + d x \right)}}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} - \frac{6834}{353736 d \tan^{2}{\left(c + d x \right)} + 1179120 d \tan{\left(c + d x \right)} + 982600 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(3 \tan{\left(c \right)} + 5\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-90*d*x*tan(c + d*x)**2/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 300*d*x*tan(c + d*x)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 250*d*x/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) + 1782*log(tan(c + d*x) + 5/3)*tan(c + d*x)**2/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) + 5940*log(tan(c + d*x) + 5/3)*tan(c + d*x)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) + 4950*log(tan(c + d*x) + 5/3)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 891*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 2970*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 2475*log(tan(c + d*x)**2 + 1)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 3060*tan(c + d*x)/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d) - 6834/(353736*d*tan(c + d*x)**2 + 1179120*d*tan(c + d*x) + 982600*d), Ne(d, 0)), (x/(3*tan(c) + 5)**3, True))","A",0
502,1,790,0,1.143571," ","integrate(1/(5+3*tan(d*x+c))**4,x)","\begin{cases} - \frac{4347 d x \tan^{3}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{21735 d x \tan^{2}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{36225 d x \tan{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{20125 d x}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} + \frac{6480 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan^{3}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} + \frac{32400 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan^{2}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} + \frac{54000 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)} \tan{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} + \frac{30000 \log{\left(\tan{\left(c + d x \right)} + \frac{5}{3} \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{3240 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{16200 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{27000 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{15000 \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{15147 \tan^{2}{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{63495 \tan{\left(c + d x \right)}}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} - \frac{73576}{9020268 d \tan^{3}{\left(c + d x \right)} + 45101340 d \tan^{2}{\left(c + d x \right)} + 75168900 d \tan{\left(c + d x \right)} + 41760500 d} & \text{for}\: d \neq 0 \\\frac{x}{\left(3 \tan{\left(c \right)} + 5\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4347*d*x*tan(c + d*x)**3/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 21735*d*x*tan(c + d*x)**2/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 36225*d*x*tan(c + d*x)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 20125*d*x/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) + 6480*log(tan(c + d*x) + 5/3)*tan(c + d*x)**3/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) + 32400*log(tan(c + d*x) + 5/3)*tan(c + d*x)**2/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) + 54000*log(tan(c + d*x) + 5/3)*tan(c + d*x)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) + 30000*log(tan(c + d*x) + 5/3)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 3240*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 16200*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 27000*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 15000*log(tan(c + d*x)**2 + 1)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 15147*tan(c + d*x)**2/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 63495*tan(c + d*x)/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d) - 73576/(9020268*d*tan(c + d*x)**3 + 45101340*d*tan(c + d*x)**2 + 75168900*d*tan(c + d*x) + 41760500*d), Ne(d, 0)), (x/(3*tan(c) + 5)**4, True))","A",0
503,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**4,x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**4, x)","F",0
504,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**3,x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**3, x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c)**2,x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**2, x)","F",0
506,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)*tan(d*x+c),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x), x)","F",0
507,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x)), x)","F",0
508,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*cot(c + d*x), x)","F",0
509,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**2, x)","F",0
510,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**3, x)","F",0
511,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(a+b*tan(d*x+c))**(3/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**4, x)","F",0
512,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**(3/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**3, x)","F",0
513,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*tan(c + d*x)**2, x)","F",0
514,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*tan(c + d*x), x)","F",0
515,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(3/2), x)","F",0
516,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*cot(c + d*x), x)","F",0
517,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*cot(c + d*x)**2, x)","F",0
518,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*cot(c + d*x)**3, x)","F",0
519,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**(5/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \tan^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(5/2)*tan(c + d*x)**3, x)","F",0
520,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**(5/2),x)","\int \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))**(5/2)*tan(c + d*x)**2, x)","F",0
521,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**(5/2),x)","\int \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))**(5/2)*tan(c + d*x), x)","F",0
522,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(5/2), x)","F",0
523,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**(5/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(5/2)*cot(c + d*x), x)","F",0
524,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(7/2),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(7/2), x)","F",0
528,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**5/sqrt(a + b*tan(c + d*x)), x)","F",0
529,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**4/sqrt(a + b*tan(c + d*x)), x)","F",0
530,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**3/sqrt(a + b*tan(c + d*x)), x)","F",0
531,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**2/sqrt(a + b*tan(c + d*x)), x)","F",0
532,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
533,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*tan(c + d*x)), x)","F",0
534,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)/sqrt(a + b*tan(c + d*x)), x)","F",0
535,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**2/sqrt(a + b*tan(c + d*x)), x)","F",0
536,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{3}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**3/sqrt(a + b*tan(c + d*x)), x)","F",0
537,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**5/(a + b*tan(c + d*x))**(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(a + b*tan(c + d*x))**(3/2), x)","F",0
539,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**3/(a + b*tan(c + d*x))**(3/2), x)","F",0
540,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**2/(a + b*tan(c + d*x))**(3/2), x)","F",0
541,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)/(a + b*tan(c + d*x))**(3/2), x)","F",0
542,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-3/2), x)","F",0
543,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)/(a + b*tan(c + d*x))**(3/2), x)","F",0
544,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**2/(a + b*tan(c + d*x))**(3/2), x)","F",0
545,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\cot^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**3/(a + b*tan(c + d*x))**(3/2), x)","F",0
546,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**5/(a + b*tan(c + d*x))**(5/2), x)","F",0
547,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(a + b*tan(c + d*x))**(5/2), x)","F",0
548,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**3/(a + b*tan(c + d*x))**(5/2), x)","F",0
549,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**2/(a + b*tan(c + d*x))**(5/2), x)","F",0
550,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)/(a + b*tan(c + d*x))**(5/2), x)","F",0
551,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-5/2), x)","F",0
552,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)/(a + b*tan(c + d*x))**(5/2), x)","F",0
553,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**2/(a + b*tan(c + d*x))**(5/2), x)","F",0
554,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-7/2), x)","F",0
555,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c)),x)","\int \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))*tan(c + d*x)**(5/2), x)","F",0
556,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c)),x)","\int \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))*tan(c + d*x)**(3/2), x)","F",0
557,0,0,0,0.000000," ","integrate(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{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{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(tan(c + d*x)), x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)**(3/2),x)","\int \frac{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))/tan(c + d*x)**(3/2), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)**(5/2),x)","\int \frac{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))/tan(c + d*x)**(5/2), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)**(7/2),x)","\int \frac{a + b \tan{\left(c + d x \right)}}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))/tan(c + d*x)**(7/2), x)","F",0
562,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**2,x)","\int \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))**2*tan(c + d*x)**(5/2), x)","F",0
563,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**2,x)","\int \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))**2*tan(c + d*x)**(3/2), x)","F",0
564,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**2,x)","\int \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))**2*sqrt(tan(c + d*x)), x)","F",0
565,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/tan(d*x+c)**(1/2),x)","\int \frac{\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))**2/sqrt(tan(c + d*x)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/tan(d*x+c)**(3/2),x)","\int \frac{\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))**2/tan(c + d*x)**(3/2), x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/tan(d*x+c)**(5/2),x)","\int \frac{\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))**2/tan(c + d*x)**(5/2), x)","F",0
568,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/tan(d*x+c)**(7/2),x)","\int \frac{\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))**2/tan(c + d*x)**(7/2), x)","F",0
569,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**3,x)","\int \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))**3*tan(c + d*x)**(5/2), x)","F",0
570,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**3,x)","\int \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))**3*tan(c + d*x)**(3/2), x)","F",0
571,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**3,x)","\int \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))**3*sqrt(tan(c + d*x)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(1/2),x)","\int \frac{\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))**3/sqrt(tan(c + d*x)), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(3/2),x)","\int \frac{\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))**3/tan(c + d*x)**(3/2), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(5/2),x)","\int \frac{\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))**3/tan(c + d*x)**(5/2), x)","F",0
575,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(7/2),x)","\int \frac{\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))**3/tan(c + d*x)**(7/2), x)","F",0
576,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(9/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\tan^{\frac{9}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**3/tan(c + d*x)**(9/2), x)","F",0
577,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/tan(d*x+c)**(11/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\tan^{\frac{11}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**3/tan(c + d*x)**(11/2), x)","F",0
578,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)**(1/2),x)","\int \frac{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(tan(c + d*x)), x)","F",0
579,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(-tan(d*x+c))**(1/2),x)","\int \frac{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(-tan(c + d*x)), x)","F",0
580,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(e*tan(d*x+c))**(1/2),x)","\int \frac{a + b \tan{\left(c + d x \right)}}{\sqrt{e \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))/sqrt(e*tan(c + d*x)), x)","F",0
581,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(-e*tan(d*x+c))**(1/2),x)","\int \frac{a + b \tan{\left(c + d x \right)}}{\sqrt{- e \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))/sqrt(-e*tan(c + d*x)), x)","F",0
582,0,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)/(a+b*tan(d*x+c)),x)","\int \frac{\tan^{\frac{9}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(9/2)/(a + b*tan(c + d*x)), x)","F",0
583,0,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+b*tan(d*x+c)),x)","\int \frac{\tan^{\frac{7}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(7/2)/(a + b*tan(c + d*x)), x)","F",0
584,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x)), x)","F",0
585,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x)), x)","F",0
586,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x)), x)","F",0
587,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
588,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*tan(c + d*x)**(3/2)), x)","F",0
589,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*tan(c + d*x)**(5/2)), x)","F",0
590,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(7/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*tan(c + d*x)**(7/2)), x)","F",0
591,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**2, x)","F",0
594,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**2, x)","F",0
595,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**2, x)","F",0
596,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*sqrt(tan(c + d*x))), x)","F",0
597,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*tan(c + d*x)**(3/2)), x)","F",0
598,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*tan(c + d*x)**(5/2)), x)","F",0
599,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(11/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,0,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\tan^{\frac{7}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(tan(c + d*x)**(7/2)/(a + b*tan(c + d*x))**3, x)","F",0
602,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**3, x)","F",0
603,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**3, x)","F",0
604,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**3, x)","F",0
605,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**3*sqrt(tan(c + d*x))), x)","F",0
606,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**3*tan(c + d*x)**(3/2)), x)","F",0
607,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**3*tan(c + d*x)**(5/2)), x)","F",0
608,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{5}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(5/2), x)","F",0
609,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(3/2), x)","F",0
610,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x)), x)","F",0
611,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/sqrt(tan(c + d*x)), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(3/2), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(5/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(5/2), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(7/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/tan(c + d*x)**(7/2), x)","F",0
615,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*tan(c + d*x)**(3/2), x)","F",0
617,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*sqrt(tan(c + d*x)), x)","F",0
618,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/tan(d*x+c)**(1/2),x)","\int \frac{\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))**(3/2)/sqrt(tan(c + d*x)), x)","F",0
619,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/tan(d*x+c)**(3/2),x)","\int \frac{\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))**(3/2)/tan(c + d*x)**(3/2), x)","F",0
620,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/tan(d*x+c)**(5/2),x)","\int \frac{\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))**(3/2)/tan(c + d*x)**(5/2), x)","F",0
621,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(1/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(5/2)/sqrt(tan(c + d*x)), x)","F",0
627,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(3/2),x)","\int \frac{\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))**(5/2)/tan(c + d*x)**(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(5/2),x)","\int \frac{\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))**(5/2)/tan(c + d*x)**(5/2), x)","F",0
629,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/tan(d*x+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
634,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**(3/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
635,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
636,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
637,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(3/2)), x)","F",0
638,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(5/2)), x)","F",0
639,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(7/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{7}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(7/2)), x)","F",0
640,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(7/2)/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{\frac{5}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**(3/2), x)","F",0
642,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\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(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**(3/2), x)","F",0
643,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**(3/2)*sqrt(tan(c + d*x))), x)","F",0
645,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\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(1/((a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**(3/2)), x)","F",0
646,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\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(1/((a + b*tan(c + d*x))**(3/2)*tan(c + d*x)**(5/2)), x)","F",0
647,-1,0,0,0.000000," ","integrate(tan(d*x+c)**(9/2)/(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(tan(d*x+c)**(7/2)/(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(tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)**(5/2)/(a + b*tan(c + d*x))**(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\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(tan(c + d*x)**(3/2)/(a + b*tan(c + d*x))**(5/2), x)","F",0
651,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/(a + b*tan(c + d*x))**(5/2), x)","F",0
652,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**(5/2)*sqrt(tan(c + d*x))), x)","F",0
653,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{1}{\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(1/((a + b*tan(c + d*x))**(5/2)*tan(c + d*x)**(3/2)), x)","F",0
654,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{1}{\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(1/((a + b*tan(c + d*x))**(5/2)*tan(c + d*x)**(5/2)), x)","F",0
655,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(2+3*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 \tan{\left(c + d x \right)} + 2} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3*tan(c + d*x) + 2)*sqrt(tan(c + d*x))), x)","F",0
656,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(-2+3*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{3 \tan{\left(c + d x \right)} - 2} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3*tan(c + d*x) - 2)*sqrt(tan(c + d*x))), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(2-3*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{2 - 3 \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2 - 3*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(-2-3*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{- 3 \tan{\left(c + d x \right)} - 2} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-3*tan(c + d*x) - 2)*sqrt(tan(c + d*x))), x)","F",0
659,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(3+2*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{2 \tan{\left(c + d x \right)} + 3} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2*tan(c + d*x) + 3)*sqrt(tan(c + d*x))), x)","F",0
660,0,0,0,0.000000," ","integrate(1/(3-2*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{3 - 2 \tan{\left(c + d x \right)}} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(3 - 2*tan(c + d*x))*sqrt(tan(c + d*x))), x)","F",0
661,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/2)/(-3+2*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{2 \tan{\left(c + d x \right)} - 3} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(2*tan(c + d*x) - 3)*sqrt(tan(c + d*x))), x)","F",0
662,0,0,0,0.000000," ","integrate(1/(-3-2*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/2),x)","\int \frac{1}{\sqrt{- 2 \tan{\left(c + d x \right)} - 3} \sqrt{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(-2*tan(c + d*x) - 3)*sqrt(tan(c + d*x))), x)","F",0
663,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(2+3*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{3 \tan{\left(c + d x \right)} + 2}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(3*tan(c + d*x) + 2), x)","F",0
664,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(-2+3*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{3 \tan{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(3*tan(c + d*x) - 2), x)","F",0
665,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(2-3*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{2 - 3 \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(2 - 3*tan(c + d*x)), x)","F",0
666,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(-2-3*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{- 3 \tan{\left(c + d x \right)} - 2}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(-3*tan(c + d*x) - 2), x)","F",0
667,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(3+2*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{2 \tan{\left(c + d x \right)} + 3}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(2*tan(c + d*x) + 3), x)","F",0
668,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(3-2*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{3 - 2 \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(3 - 2*tan(c + d*x)), x)","F",0
669,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(-3+2*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{2 \tan{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(2*tan(c + d*x) - 3), x)","F",0
670,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)/(-3-2*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\tan{\left(c + d x \right)}}}{\sqrt{- 2 \tan{\left(c + d x \right)} - 3}}\, dx"," ",0,"Integral(sqrt(tan(c + d*x))/sqrt(-2*tan(c + d*x) - 3), x)","F",0
671,0,0,0,0.000000," ","integrate(tan(d*x+c)**(5/3)/(a+b*tan(d*x+c)),x)","\int \frac{\tan^{\frac{5}{3}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(5/3)/(a + b*tan(c + d*x)), x)","F",0
672,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)/(a+b*tan(d*x+c)),x)","\int \frac{\sqrt[3]{\tan{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**(1/3)/(a + b*tan(c + d*x)), x)","F",0
673,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(1/3)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*tan(c + d*x)**(1/3)), x)","F",0
674,0,0,0,0.000000," ","integrate(1/tan(d*x+c)**(5/3)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \tan^{\frac{5}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*tan(c + d*x)**(5/3)), x)","F",0
675,0,0,0,0.000000," ","integrate(tan(d*x+c)**(4/3)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{4}{3}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**(4/3)/sqrt(a + b*tan(c + d*x)), x)","F",0
676,0,0,0,0.000000," ","integrate(tan(d*x+c)**(2/3)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{\frac{2}{3}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**(2/3)/sqrt(a + b*tan(c + d*x)), x)","F",0
677,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/3)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt[3]{\tan{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**(1/3)/sqrt(a + b*tan(c + d*x)), x)","F",0
678,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(1/3),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt[3]{\tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(1/3)), x)","F",0
679,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(2/3),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{2}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(2/3)), x)","F",0
680,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(1/2)/tan(d*x+c)**(4/3),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \tan^{\frac{4}{3}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**(4/3)), x)","F",0
681,0,0,0,0.000000," ","integrate(tan(f*x+e)**4*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*tan(e + f*x)**4, x)","F",0
682,0,0,0,0.000000," ","integrate(tan(f*x+e)**3*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*tan(e + f*x)**3, x)","F",0
683,0,0,0,0.000000," ","integrate(tan(f*x+e)**2*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*tan(e + f*x)**2, x)","F",0
684,0,0,0,0.000000," ","integrate(tan(f*x+e)*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*tan(e + f*x), x)","F",0
685,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3), x)","F",0
686,0,0,0,0.000000," ","integrate(cot(f*x+e)*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*cot(e + f*x), x)","F",0
687,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(c+d*tan(f*x+e))**(1/3),x)","\int \sqrt[3]{c + d \tan{\left(e + f x \right)}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(1/3)*cot(e + f*x)**2, x)","F",0
688,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/3),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{3}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(5/3), x)","F",0
689,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(4/3),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(4/3), x)","F",0
690,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(2/3),x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(2/3), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/3),x)","\int \sqrt[3]{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(1/3), x)","F",0
692,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-1/3), x)","F",0
693,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(2/3),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-2/3), x)","F",0
694,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(4/3),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-4/3), x)","F",0
695,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))**(5/3),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**(-5/3), x)","F",0
696,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+b*tan(f*x+e))**4,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{4}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*tan(e + f*x))**4, x)","F",0
697,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+b*tan(f*x+e))**3,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*tan(e + f*x))**3, x)","F",0
698,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+b*tan(f*x+e))**2,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*tan(e + f*x))**2, x)","F",0
699,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+b*tan(f*x+e)),x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*tan(e + f*x)), x)","F",0
700,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((d*tan(e + f*x))**n/(a + b*tan(e + f*x)), x)","F",0
701,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{n}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((d*tan(e + f*x))**n/(a + b*tan(e + f*x))**2, x)","F",0
702,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*tan(c + d*x)**m, x)","F",0
703,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*tan(c + d*x)**m, x)","F",0
704,0,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\tan^{m}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**m/sqrt(a + b*tan(c + d*x)), x)","F",0
705,0,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\tan^{m}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(c + d*x)**m/(a + b*tan(c + d*x))**(3/2), x)","F",0
706,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**n*(a+b*tan(f*x+e))**m,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*tan(e + f*x))**m, x)","F",0
707,0,0,0,0.000000," ","integrate(tan(d*x+c)**4*(a+b*tan(d*x+c))**n,x)","\int \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))**n*tan(c + d*x)**4, x)","F",0
708,0,0,0,0.000000," ","integrate(tan(d*x+c)**3*(a+b*tan(d*x+c))**n,x)","\int \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))**n*tan(c + d*x)**3, x)","F",0
709,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(a+b*tan(d*x+c))**n,x)","\int \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))**n*tan(c + d*x)**2, x)","F",0
710,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**n,x)","\int \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))**n*tan(c + d*x), x)","F",0
711,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n,x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**n, x)","F",0
712,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**n,x)","\int \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))**n*cot(c + d*x), x)","F",0
713,0,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**n,x)","\int \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))**n*cot(c + d*x)**2, x)","F",0
714,0,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**n,x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{n} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**n*cot(c + d*x)**3, x)","F",0
715,0,0,0,0.000000," ","integrate(tan(d*x+c)**(3/2)*(a+b*tan(d*x+c))**n,x)","\int \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))**n*tan(c + d*x)**(3/2), x)","F",0
716,0,0,0,0.000000," ","integrate(tan(d*x+c)**(1/2)*(a+b*tan(d*x+c))**n,x)","\int \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))**n*sqrt(tan(c + d*x)), x)","F",0
717,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n/tan(d*x+c)**(1/2),x)","\int \frac{\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))**n/sqrt(tan(c + d*x)), x)","F",0
718,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n/tan(d*x+c)**(3/2),x)","\int \frac{\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))**n/tan(c + d*x)**(3/2), x)","F",0
719,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c)),x)","i a \left(\int \left(- i \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*cot(c + d*x)**(3/2), x) + Integral(tan(c + d*x)*cot(c + d*x)**(3/2), x))","F",0
721,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c)),x)","i a \left(\int \left(- i \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx\right)"," ",0,"I*a*(Integral(-I*sqrt(cot(c + d*x)), x) + Integral(tan(c + d*x)*sqrt(cot(c + d*x)), x))","F",0
722,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)**(1/2),x)","i a \left(\int \left(- \frac{i}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{\tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"I*a*(Integral(-I/sqrt(cot(c + d*x)), x) + Integral(tan(c + d*x)/sqrt(cot(c + d*x)), x))","F",0
723,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)**(3/2),x)","i a \left(\int \left(- \frac{i}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \frac{\tan{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx\right)"," ",0,"I*a*(Integral(-I/cot(c + d*x)**(3/2), x) + Integral(tan(c + d*x)/cot(c + d*x)**(3/2), x))","F",0
724,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**2,x)","- a^{2} \left(\int \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 2 i \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \left(- \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(c + d*x)**2*cot(c + d*x)**(3/2), x) + Integral(-2*I*tan(c + d*x)*cot(c + d*x)**(3/2), x) + Integral(-cot(c + d*x)**(3/2), x))","F",0
727,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**2,x)","- a^{2} \left(\int \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 2 i \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int \left(- \sqrt{\cot{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(c + d*x)**2*sqrt(cot(c + d*x)), x) + Integral(-2*I*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(-sqrt(cot(c + d*x)), x))","F",0
728,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2/cot(d*x+c)**(1/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{2 i \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \left(- \frac{1}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(c + d*x)**2/sqrt(cot(c + d*x)), x) + Integral(-2*I*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(-1/sqrt(cot(c + d*x)), x))","F",0
729,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**2/cot(d*x+c)**(3/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx + \int \left(- \frac{2 i \tan{\left(c + d x \right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx + \int \left(- \frac{1}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(c + d*x)**2/cot(c + d*x)**(3/2), x) + Integral(-2*I*tan(c + d*x)/cot(c + d*x)**(3/2), x) + Integral(-1/cot(c + d*x)**(3/2), x))","F",0
730,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**3,x)","- i a^{3} \left(\int i \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx + \int \tan^{3}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx + \int \left(- 3 i \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*cot(c + d*x)**(3/2), x) + Integral(-3*tan(c + d*x)*cot(c + d*x)**(3/2), x) + Integral(tan(c + d*x)**3*cot(c + d*x)**(3/2), x) + Integral(-3*I*tan(c + d*x)**2*cot(c + d*x)**(3/2), x))","F",0
733,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**3,x)","- i a^{3} \left(\int i \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 \tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx + \int \tan^{3}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\, dx + \int \left(- 3 i \tan^{2}{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*sqrt(cot(c + d*x)), x) + Integral(-3*tan(c + d*x)*sqrt(cot(c + d*x)), x) + Integral(tan(c + d*x)**3*sqrt(cot(c + d*x)), x) + Integral(-3*I*tan(c + d*x)**2*sqrt(cot(c + d*x)), x))","F",0
734,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**3/cot(d*x+c)**(1/2),x)","- i a^{3} \left(\int \frac{i}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 \tan{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{\tan^{3}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(c + d x \right)}}{\sqrt{\cot{\left(c + d x \right)}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/sqrt(cot(c + d*x)), x) + Integral(-3*tan(c + d*x)/sqrt(cot(c + d*x)), x) + Integral(tan(c + d*x)**3/sqrt(cot(c + d*x)), x) + Integral(-3*I*tan(c + d*x)**2/sqrt(cot(c + d*x)), x))","F",0
735,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\tan{\left(c + d x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(cot(c + d*x)**(3/2)/(tan(c + d*x) - I), x)/a","F",0
736,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\tan{\left(c + d x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(sqrt(cot(c + d*x))/(tan(c + d*x) - I), x)/a","F",0
737,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\tan{\left(c + d x \right)} \sqrt{\cot{\left(c + d x \right)}} - i \sqrt{\cot{\left(c + d x \right)}}}\, dx}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)*sqrt(cot(c + d*x)) - I*sqrt(cot(c + d*x))), x)/a","F",0
738,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\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}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)*cot(c + d*x)**(3/2) - I*cot(c + d*x)**(3/2)), x)/a","F",0
739,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c)),x)","- \frac{i \int \frac{1}{\tan{\left(c + d x \right)} \cot^{\frac{5}{2}}{\left(c + d x \right)} - i \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx}{a}"," ",0,"-I*Integral(1/(tan(c + d*x)*cot(c + d*x)**(5/2) - I*cot(c + d*x)**(5/2)), x)/a","F",0
740,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{\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(cot(c + d*x)**(3/2)/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x)/a**2","F",0
741,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{\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(sqrt(cot(c + d*x))/(tan(c + d*x)**2 - 2*I*tan(c + d*x) - 1), x)/a**2","F",0
742,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{1}{\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(1/(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
743,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**2,x)","- \frac{\int \frac{1}{\tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - 2 i \tan{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"-Integral(1/(tan(c + d*x)**2*cot(c + d*x)**(3/2) - 2*I*tan(c + d*x)*cot(c + d*x)**(3/2) - cot(c + d*x)**(3/2)), x)/a**2","F",0
744,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**3,x)","\frac{i \int \frac{\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}{a^{3}}"," ",0,"I*Integral(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
747,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**3,x)","\frac{i \int \frac{1}{\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}{a^{3}}"," ",0,"I*Integral(1/(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
748,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**3,x)","\frac{i \int \frac{1}{\tan^{3}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - 3 i \tan^{2}{\left(c + d x \right)} \cot^{\frac{3}{2}}{\left(c + d x \right)} - 3 \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}{a^{3}}"," ",0,"I*Integral(1/(tan(c + d*x)**3*cot(c + d*x)**(3/2) - 3*I*tan(c + d*x)**2*cot(c + d*x)**(3/2) - 3*tan(c + d*x)*cot(c + d*x)**(3/2) + I*cot(c + d*x)**(3/2)), x)/a**3","F",0
749,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
753,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x)**(3/2), x)","F",0
754,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))*sqrt(cot(c + d*x)), x)","F",0
755,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/cot(d*x+c)**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/sqrt(cot(c + d*x)), x)","F",0
756,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(1/2)/cot(d*x+c)**(3/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(c + d*x) - I))/cot(c + d*x)**(3/2), x)","F",0
757,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate(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
760,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**(3/2),x)","\int \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((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(cot(c + d*x)), x)","F",0
761,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(3/2)/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}}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**(3/2)/sqrt(cot(c + d*x)), x)","F",0
762,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(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
765,-1,0,0,0.000000," ","integrate(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
766,-1,0,0,0.000000," ","integrate(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
767,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**(5/2)/cot(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
768,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
770,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/sqrt(I*a*(tan(c + d*x) - I)), x)","F",0
771,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*sqrt(cot(c + d*x))), x)","F",0
772,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x)**(3/2)), x)","F",0
773,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(c + d x \right)} - i\right)} \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(c + d*x) - I))*cot(c + d*x)**(5/2)), x)","F",0
774,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
775,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\cot^{\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(cot(c + d*x)**(3/2)/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
776,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{\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(sqrt(cot(c + d*x))/(I*a*(tan(c + d*x) - I))**(3/2), x)","F",0
777,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\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(1/((I*a*(tan(c + d*x) - I))**(3/2)*sqrt(cot(c + d*x))), x)","F",0
778,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{3}{2}} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(3/2)*cot(c + d*x)**(3/2)), x)","F",0
779,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
781,-1,0,0,0.000000," ","integrate(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
782,-1,0,0,0.000000," ","integrate(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
783,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{\sqrt{\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(sqrt(cot(c + d*x))/(I*a*(tan(c + d*x) - I))**(5/2), x)","F",0
784,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{\frac{5}{2}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((I*a*(tan(c + d*x) - I))**(5/2)*sqrt(cot(c + d*x))), x)","F",0
785,-1,0,0,0.000000," ","integrate(1/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
786,-1,0,0,0.000000," ","integrate(1/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
787,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+I*a*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
788,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \left(d \cot{\left(e + f x \right)}\right)^{n}\, dx + \int \left(- 3 \left(d \cot{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx + \int \left(d \cot{\left(e + f x \right)}\right)^{n} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(d \cot{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(d*cot(e + f*x))**n, x) + Integral(-3*(d*cot(e + f*x))**n*tan(e + f*x), x) + Integral((d*cot(e + f*x))**n*tan(e + f*x)**3, x) + Integral(-3*I*(d*cot(e + f*x))**n*tan(e + f*x)**2, x))","F",0
789,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \left(d \cot{\left(e + f x \right)}\right)^{n}\right)\, dx + \int \left(d \cot{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(d \cot{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-(d*cot(e + f*x))**n, x) + Integral((d*cot(e + f*x))**n*tan(e + f*x)**2, x) + Integral(-2*I*(d*cot(e + f*x))**n*tan(e + f*x), x))","F",0
790,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \left(d \cot{\left(e + f x \right)}\right)^{n}\right)\, dx + \int \left(d \cot{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(d*cot(e + f*x))**n, x) + Integral((d*cot(e + f*x))**n*tan(e + f*x), x))","F",0
791,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(d \cot{\left(e + f x \right)}\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((d*cot(e + f*x))**n/(tan(e + f*x) - I), x)/a","F",0
792,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(d \cot{\left(e + f x \right)}\right)^{n}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((d*cot(e + f*x))**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
793,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+I*a*tan(f*x+e))**m,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*(I*a*(tan(e + f*x) - I))**m, x)","F",0
794,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+I*a*tan(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
795,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+I*a*tan(d*x+c))**n,x)","\int \left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n*sqrt(cot(c + d*x)), x)","F",0
796,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n/cot(d*x+c)**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n/sqrt(cot(c + d*x)), x)","F",0
797,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))**n/cot(d*x+c)**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(c + d x \right)} - i\right)\right)^{n}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((I*a*(tan(c + d*x) - I))**n/cot(c + d*x)**(3/2), x)","F",0
798,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,0,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c)),x)","\int \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))*cot(c + d*x)**(5/2), x)","F",0
800,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c)),x)","\int \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))*cot(c + d*x)**(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c)),x)","\int \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))*sqrt(cot(c + d*x)), x)","F",0
802,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)**(1/2),x)","\int \frac{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(cot(c + d*x)), x)","F",0
803,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)**(3/2),x)","\int \frac{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))/cot(c + d*x)**(3/2), x)","F",0
804,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)**(5/2),x)","\int \frac{a + b \tan{\left(c + d x \right)}}{\cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))/cot(c + d*x)**(5/2), x)","F",0
805,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**2,x)","\int \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))**2*cot(c + d*x)**(3/2), x)","F",0
809,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**2,x)","\int \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))**2*sqrt(cot(c + d*x)), x)","F",0
810,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/cot(d*x+c)**(1/2),x)","\int \frac{\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))**2/sqrt(cot(c + d*x)), x)","F",0
811,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/cot(d*x+c)**(3/2),x)","\int \frac{\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))**2/cot(c + d*x)**(3/2), x)","F",0
812,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**2/cot(d*x+c)**(5/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}{\cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**2/cot(c + d*x)**(5/2), x)","F",0
813,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**3,x)","\int \left(a + b \tan{\left(c + d x \right)}\right)^{3} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**3*cot(c + d*x)**(3/2), x)","F",0
817,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**3,x)","\int \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))**3*sqrt(cot(c + d*x)), x)","F",0
818,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/cot(d*x+c)**(1/2),x)","\int \frac{\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))**3/sqrt(cot(c + d*x)), x)","F",0
819,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**3/cot(d*x+c)**(3/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**3/cot(c + d*x)**(3/2), x)","F",0
820,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/(a + b*tan(c + d*x)), x)","F",0
822,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{a + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/(a + b*tan(c + d*x)), x)","F",0
823,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*sqrt(cot(c + d*x))), x)","F",0
824,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*cot(c + d*x)**(3/2)), x)","F",0
825,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c)),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right) \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))*cot(c + d*x)**(5/2)), x)","F",0
826,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
827,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/(a + b*tan(c + d*x))**2, x)","F",0
828,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**2, x)","F",0
829,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*sqrt(cot(c + d*x))), x)","F",0
830,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*cot(c + d*x)**(3/2)), x)","F",0
831,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{2} \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**2*cot(c + d*x)**(5/2)), x)","F",0
832,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/(a + b*tan(c + d*x))**3, x)","F",0
835,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**3, x)","F",0
836,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**3*sqrt(cot(c + d*x))), x)","F",0
837,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{3} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**3*cot(c + d*x)**(3/2)), x)","F",0
838,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \cot^{\frac{3}{2}}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**(3/2), x)","F",0
843,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(1/2),x)","\int \sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\cot{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))*sqrt(cot(c + d*x)), x)","F",0
844,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/cot(d*x+c)**(1/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/sqrt(cot(c + d*x)), x)","F",0
845,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(1/2)/cot(d*x+c)**(3/2),x)","\int \frac{\sqrt{a + b \tan{\left(c + d x \right)}}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x))/cot(c + d*x)**(3/2), x)","F",0
846,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(3/2),x)","\int \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))**(3/2)*sqrt(cot(c + d*x)), x)","F",0
851,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/cot(d*x+c)**(1/2),x)","\int \frac{\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))**(3/2)/sqrt(cot(c + d*x)), x)","F",0
852,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(3/2)/cot(d*x+c)**(3/2),x)","\int \frac{\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))**(3/2)/cot(c + d*x)**(3/2), x)","F",0
853,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(11/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(9/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(7/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/cot(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**(5/2)/cot(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/sqrt(a + b*tan(c + d*x)), x)","F",0
863,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/sqrt(a + b*tan(c + d*x)), x)","F",0
864,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*sqrt(cot(c + d*x))), x)","F",0
865,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**(3/2)), x)","F",0
866,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(c + d x \right)}} \cot^{\frac{5}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(c + d*x))*cot(c + d*x)**(5/2)), x)","F",0
867,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,0,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\cot^{\frac{3}{2}}{\left(c + d x \right)}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**(3/2)/(a + b*tan(c + d*x))**(3/2), x)","F",0
869,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**(3/2), x)","F",0
870,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{3}{2}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**(3/2)*sqrt(cot(c + d*x))), x)","F",0
871,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(3/2),x)","\int \frac{1}{\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(1/((a + b*tan(c + d*x))**(3/2)*cot(c + d*x)**(3/2)), x)","F",0
872,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(7/2)/(a+b*tan(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{\sqrt{\cot{\left(c + d x \right)}}}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(cot(c + d*x))/(a + b*tan(c + d*x))**(5/2), x)","F",0
877,0,0,0,0.000000," ","integrate(1/cot(d*x+c)**(1/2)/(a+b*tan(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(c + d x \right)}\right)^{\frac{5}{2}} \sqrt{\cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(c + d*x))**(5/2)*sqrt(cot(c + d*x))), x)","F",0
878,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(3/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)**(5/2)/(a+b*tan(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+b*tan(f*x+e))**3,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*(a + b*tan(e + f*x))**3, x)","F",0
881,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+b*tan(f*x+e))**2,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*(a + b*tan(e + f*x))**2, x)","F",0
882,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+b*tan(f*x+e)),x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((d*cot(e + f*x))**n*(a + b*tan(e + f*x)), x)","F",0
883,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n/(a+b*tan(f*x+e)),x)","\int \frac{\left(d \cot{\left(e + f x \right)}\right)^{n}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((d*cot(e + f*x))**n/(a + b*tan(e + f*x)), x)","F",0
884,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(d \cot{\left(e + f x \right)}\right)^{n}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((d*cot(e + f*x))**n/(a + b*tan(e + f*x))**2, x)","F",0
885,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*(a+b*tan(f*x+e))**m,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*(a + b*tan(e + f*x))**m, x)","F",0
886,-1,0,0,0.000000," ","integrate(cot(d*x+c)**(3/2)*(a+b*tan(d*x+c))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,0,0,0,0.000000," ","integrate(cot(d*x+c)**(1/2)*(a+b*tan(d*x+c))**n,x)","\int \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))**n*sqrt(cot(c + d*x)), x)","F",0
888,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n/cot(d*x+c)**(1/2),x)","\int \frac{\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))**n/sqrt(cot(c + d*x)), x)","F",0
889,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))**n/cot(d*x+c)**(3/2),x)","\int \frac{\left(a + b \tan{\left(c + d x \right)}\right)^{n}}{\cot^{\frac{3}{2}}{\left(c + d x \right)}}\, dx"," ",0,"Integral((a + b*tan(c + d*x))**n/cot(c + d*x)**(3/2), x)","F",0
890,1,114,0,0.321973," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e)),x)","\frac{24 i a^{3} c e^{4 i e} e^{4 i f x} + 24 i a^{3} c e^{2 i e} e^{2 i f x} + 8 i a^{3} c}{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,"(24*I*a**3*c*exp(4*I*e)*exp(4*I*f*x) + 24*I*a**3*c*exp(2*I*e)*exp(2*I*f*x) + 8*I*a**3*c)/(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
891,1,68,0,0.247145," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e)),x)","\frac{4 i a^{2} c e^{2 i e} e^{2 i f x} + 2 i a^{2} c}{f e^{4 i e} e^{4 i f x} + 2 f e^{2 i e} e^{2 i f x} + f}"," ",0,"(4*I*a**2*c*exp(2*I*e)*exp(2*I*f*x) + 2*I*a**2*c)/(f*exp(4*I*e)*exp(4*I*f*x) + 2*f*exp(2*I*e)*exp(2*I*f*x) + f)","B",0
892,1,27,0,0.168379," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x)","- \frac{2 i a c}{- f e^{2 i e} e^{2 i f x} - f}"," ",0,"-2*I*a*c/(-f*exp(2*I*e)*exp(2*I*f*x) - f)","C",0
893,1,44,0,0.170593," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\begin{cases} \frac{i c e^{- 2 i e} e^{- 2 i f x}}{2 a f} & \text{for}\: 2 a f e^{2 i e} \neq 0 \\\frac{c x e^{- 2 i e}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*c*exp(-2*I*e)*exp(-2*I*f*x)/(2*a*f), Ne(2*a*f*exp(2*I*e), 0)), (c*x*exp(-2*I*e)/a, True))","A",0
894,1,102,0,0.278333," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(8 i a^{2} c f e^{4 i e} e^{- 2 i f x} + 4 i a^{2} c f e^{2 i e} e^{- 4 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(c e^{2 i e} + c\right) e^{- 4 i e}}{2 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((8*I*a**2*c*f*exp(4*I*e)*exp(-2*I*f*x) + 4*I*a**2*c*f*exp(2*I*e)*exp(-4*I*f*x))*exp(-6*I*e)/(32*a**4*f**2), Ne(32*a**4*f**2*exp(6*I*e), 0)), (x*(c*exp(2*I*e) + c)*exp(-4*I*e)/(2*a**2), True))","A",0
895,1,146,0,0.348414," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(- 192 i a^{6} c f^{2} e^{10 i e} e^{- 2 i f x} - 192 i a^{6} c f^{2} e^{8 i e} e^{- 4 i f x} - 64 i a^{6} c f^{2} e^{6 i e} e^{- 6 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(c e^{4 i e} + 2 c e^{2 i e} + c\right) e^{- 6 i e}}{4 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-192*I*a**6*c*f**2*exp(10*I*e)*exp(-2*I*f*x) - 192*I*a**6*c*f**2*exp(8*I*e)*exp(-4*I*f*x) - 64*I*a**6*c*f**2*exp(6*I*e)*exp(-6*I*f*x))*exp(-12*I*e)/(1536*a**9*f**3), Ne(1536*a**9*f**3*exp(12*I*e), 0)), (x*(c*exp(4*I*e) + 2*c*exp(2*I*e) + c)*exp(-6*I*e)/(4*a**3), True))","A",0
896,1,185,0,0.576920," ","integrate((a+I*a*tan(f*x+e))**4*(c-I*c*tan(f*x+e))**2,x)","\frac{- 80 i a^{4} c^{2} e^{6 i e} e^{6 i f x} - 80 i a^{4} c^{2} e^{4 i e} e^{4 i f x} - 40 i a^{4} c^{2} e^{2 i e} e^{2 i f x} - 8 i a^{4} c^{2}}{- 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,"(-80*I*a**4*c**2*exp(6*I*e)*exp(6*I*f*x) - 80*I*a**4*c**2*exp(4*I*e)*exp(4*I*f*x) - 40*I*a**4*c**2*exp(2*I*e)*exp(2*I*f*x) - 8*I*a**4*c**2)/(-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
897,1,143,0,0.475610," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**2,x)","\frac{24 a^{3} c^{2} e^{4 i e} e^{4 i f x} + 16 a^{3} c^{2} e^{2 i e} e^{2 i f x} + 4 a^{3} c^{2}}{- 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,"(24*a**3*c**2*exp(4*I*e)*exp(4*I*f*x) + 16*a**3*c**2*exp(2*I*e)*exp(2*I*f*x) + 4*a**3*c**2)/(-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
898,1,99,0,0.324666," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**2,x)","\frac{12 a^{2} c^{2} e^{2 i e} e^{2 i f x} + 4 a^{2} c^{2}}{- 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,"(12*a**2*c**2*exp(2*I*e)*exp(2*I*f*x) + 4*a**2*c**2)/(-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)","C",0
899,1,49,0,0.235147," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**2,x)","- \frac{2 a c^{2}}{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*a*c**2/(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)","B",0
900,1,100,0,0.332689," ","integrate((c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e)),x)","\begin{cases} \frac{i c^{2} 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 c^{2}}{a} + \frac{\left(- 2 c^{2} e^{2 i e} + 2 c^{2}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{2 c^{2} x}{a} - \frac{i c^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f}"," ",0,"Piecewise((I*c**2*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(2*c**2/a + (-2*c**2*exp(2*I*e) + 2*c**2)*exp(-2*I*e)/a), True)) - 2*c**2*x/a - I*c**2*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f)","A",0
901,1,53,0,0.235845," ","integrate((c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{i c^{2} e^{- 4 i e} e^{- 4 i f x}}{4 a^{2} f} & \text{for}\: 4 a^{2} f e^{4 i e} \neq 0 \\\frac{c^{2} x e^{- 4 i e}}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*c**2*exp(-4*I*e)*exp(-4*I*f*x)/(4*a**2*f), Ne(4*a**2*f*exp(4*I*e), 0)), (c**2*x*exp(-4*I*e)/a**2, True))","A",0
902,1,109,0,0.373041," ","integrate((c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(12 i a^{3} c^{2} f e^{6 i e} e^{- 4 i f x} + 8 i a^{3} c^{2} f e^{4 i e} e^{- 6 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(c^{2} e^{2 i e} + c^{2}\right) e^{- 6 i e}}{2 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((12*I*a**3*c**2*f*exp(6*I*e)*exp(-4*I*f*x) + 8*I*a**3*c**2*f*exp(4*I*e)*exp(-6*I*f*x))*exp(-10*I*e)/(96*a**6*f**2), Ne(96*a**6*f**2*exp(10*I*e), 0)), (x*(c**2*exp(2*I*e) + c**2)*exp(-6*I*e)/(2*a**3), True))","A",0
903,1,156,0,0.473717," ","integrate((c-I*c*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**4,x)","\begin{cases} - \frac{\left(- 384 i a^{8} c^{2} f^{2} e^{14 i e} e^{- 4 i f x} - 512 i a^{8} c^{2} f^{2} e^{12 i e} e^{- 6 i f x} - 192 i a^{8} c^{2} f^{2} e^{10 i e} e^{- 8 i f x}\right) e^{- 18 i e}}{6144 a^{12} f^{3}} & \text{for}\: 6144 a^{12} f^{3} e^{18 i e} \neq 0 \\\frac{x \left(c^{2} e^{4 i e} + 2 c^{2} e^{2 i e} + c^{2}\right) e^{- 8 i e}}{4 a^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-384*I*a**8*c**2*f**2*exp(14*I*e)*exp(-4*I*f*x) - 512*I*a**8*c**2*f**2*exp(12*I*e)*exp(-6*I*f*x) - 192*I*a**8*c**2*f**2*exp(10*I*e)*exp(-8*I*f*x))*exp(-18*I*e)/(6144*a**12*f**3), Ne(6144*a**12*f**3*exp(18*I*e), 0)), (x*(c**2*exp(4*I*e) + 2*c**2*exp(2*I*e) + c**2)*exp(-8*I*e)/(4*a**4), True))","A",0
904,1,248,0,0.869683," ","integrate((a+I*a*tan(f*x+e))**5*(c-I*c*tan(f*x+e))**3,x)","\frac{- 4480 i a^{5} c^{3} e^{8 i e} e^{8 i f x} - 4480 i a^{5} c^{3} e^{6 i e} e^{6 i f x} - 2688 i a^{5} c^{3} e^{4 i e} e^{4 i f x} - 896 i a^{5} c^{3} e^{2 i e} e^{2 i f x} - 128 i a^{5} c^{3}}{- 105 f e^{14 i e} e^{14 i f x} - 735 f e^{12 i e} e^{12 i f x} - 2205 f e^{10 i e} e^{10 i f x} - 3675 f e^{8 i e} e^{8 i f x} - 3675 f e^{6 i e} e^{6 i f x} - 2205 f e^{4 i e} e^{4 i f x} - 735 f e^{2 i e} e^{2 i f x} - 105 f}"," ",0,"(-4480*I*a**5*c**3*exp(8*I*e)*exp(8*I*f*x) - 4480*I*a**5*c**3*exp(6*I*e)*exp(6*I*f*x) - 2688*I*a**5*c**3*exp(4*I*e)*exp(4*I*f*x) - 896*I*a**5*c**3*exp(2*I*e)*exp(2*I*f*x) - 128*I*a**5*c**3)/(-105*f*exp(14*I*e)*exp(14*I*f*x) - 735*f*exp(12*I*e)*exp(12*I*f*x) - 2205*f*exp(10*I*e)*exp(10*I*f*x) - 3675*f*exp(8*I*e)*exp(8*I*f*x) - 3675*f*exp(6*I*e)*exp(6*I*f*x) - 2205*f*exp(4*I*e)*exp(4*I*f*x) - 735*f*exp(2*I*e)*exp(2*I*f*x) - 105*f)","B",0
905,1,207,0,0.719078," ","integrate((a+I*a*tan(f*x+e))**4*(c-I*c*tan(f*x+e))**3,x)","\frac{320 a^{4} c^{3} e^{6 i e} e^{6 i f x} + 240 a^{4} c^{3} e^{4 i e} e^{4 i f x} + 96 a^{4} c^{3} e^{2 i e} e^{2 i f x} + 16 a^{4} c^{3}}{- 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,"(320*a**4*c**3*exp(6*I*e)*exp(6*I*f*x) + 240*a**4*c**3*exp(4*I*e)*exp(4*I*f*x) + 96*a**4*c**3*exp(2*I*e)*exp(2*I*f*x) + 16*a**4*c**3)/(-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
906,1,156,0,0.515490," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**3,x)","\frac{160 i a^{3} c^{3} e^{4 i e} e^{4 i f x} + 80 i a^{3} c^{3} e^{2 i e} e^{2 i f x} + 16 i a^{3} c^{3}}{15 f e^{10 i e} e^{10 i f x} + 75 f e^{8 i e} e^{8 i f x} + 150 f e^{6 i e} e^{6 i f x} + 150 f e^{4 i e} e^{4 i f x} + 75 f e^{2 i e} e^{2 i f x} + 15 f}"," ",0,"(160*I*a**3*c**3*exp(4*I*e)*exp(4*I*f*x) + 80*I*a**3*c**3*exp(2*I*e)*exp(2*I*f*x) + 16*I*a**3*c**3)/(15*f*exp(10*I*e)*exp(10*I*f*x) + 75*f*exp(8*I*e)*exp(8*I*f*x) + 150*f*exp(6*I*e)*exp(6*I*f*x) + 150*f*exp(4*I*e)*exp(4*I*f*x) + 75*f*exp(2*I*e)*exp(2*I*f*x) + 15*f)","C",0
907,1,119,0,0.457311," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**3,x)","\frac{- 16 a^{2} c^{3} e^{2 i e} e^{2 i f x} - 4 a^{2} c^{3}}{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**2*c**3*exp(2*I*e)*exp(2*I*f*x) - 4*a**2*c**3)/(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
908,1,70,0,0.304187," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**3,x)","- \frac{8 i a c^{3}}{- 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,"-8*I*a*c**3/(-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
909,1,134,0,0.412196," ","integrate((c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e)),x)","- \frac{2 i c^{3}}{- a f e^{2 i e} e^{2 i f x} - a f} + \begin{cases} \frac{2 i c^{3} 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 c^{3}}{a} + \frac{\left(- 8 c^{3} e^{2 i e} + 4 c^{3}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{8 c^{3} x}{a} - \frac{4 i c^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f}"," ",0,"-2*I*c**3/(-a*f*exp(2*I*e)*exp(2*I*f*x) - a*f) + Piecewise((2*I*c**3*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(8*c**3/a + (-8*c**3*exp(2*I*e) + 4*c**3)*exp(-2*I*e)/a), True)) - 8*c**3*x/a - 4*I*c**3*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f)","A",0
910,1,168,0,0.498607," ","integrate((c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(- 2 i a^{2} c^{3} f e^{4 i e} e^{- 2 i f x} + i a^{2} c^{3} f e^{2 i e} e^{- 4 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 c^{3}}{a^{2}} + \frac{\left(2 c^{3} e^{4 i e} - 2 c^{3} e^{2 i e} + 2 c^{3}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases} + \frac{2 c^{3} x}{a^{2}} + \frac{i c^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f}"," ",0,"Piecewise(((-2*I*a**2*c**3*f*exp(4*I*e)*exp(-2*I*f*x) + I*a**2*c**3*f*exp(2*I*e)*exp(-4*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*c**3/a**2 + (2*c**3*exp(4*I*e) - 2*c**3*exp(2*I*e) + 2*c**3)*exp(-4*I*e)/a**2), True)) + 2*c**3*x/a**2 + I*c**3*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f)","A",0
911,1,53,0,0.320355," ","integrate((c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} \frac{i c^{3} e^{- 6 i e} e^{- 6 i f x}}{6 a^{3} f} & \text{for}\: 6 a^{3} f e^{6 i e} \neq 0 \\\frac{c^{3} x e^{- 6 i e}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*c**3*exp(-6*I*e)*exp(-6*I*f*x)/(6*a**3*f), Ne(6*a**3*f*exp(6*I*e), 0)), (c**3*x*exp(-6*I*e)/a**3, True))","A",0
912,1,109,0,0.507379," ","integrate((c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**4,x)","\begin{cases} \frac{\left(16 i a^{4} c^{3} f e^{8 i e} e^{- 6 i f x} + 12 i a^{4} c^{3} f e^{6 i e} e^{- 8 i f x}\right) e^{- 14 i e}}{192 a^{8} f^{2}} & \text{for}\: 192 a^{8} f^{2} e^{14 i e} \neq 0 \\\frac{x \left(c^{3} e^{2 i e} + c^{3}\right) e^{- 8 i e}}{2 a^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((16*I*a**4*c**3*f*exp(8*I*e)*exp(-6*I*f*x) + 12*I*a**4*c**3*f*exp(6*I*e)*exp(-8*I*f*x))*exp(-14*I*e)/(192*a**8*f**2), Ne(192*a**8*f**2*exp(14*I*e), 0)), (x*(c**3*exp(2*I*e) + c**3)*exp(-8*I*e)/(2*a**4), True))","A",0
913,1,156,0,0.593874," ","integrate((c-I*c*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**5,x)","\begin{cases} - \frac{\left(- 640 i a^{10} c^{3} f^{2} e^{18 i e} e^{- 6 i f x} - 960 i a^{10} c^{3} f^{2} e^{16 i e} e^{- 8 i f x} - 384 i a^{10} c^{3} f^{2} e^{14 i e} e^{- 10 i f x}\right) e^{- 24 i e}}{15360 a^{15} f^{3}} & \text{for}\: 15360 a^{15} f^{3} e^{24 i e} \neq 0 \\\frac{x \left(c^{3} e^{4 i e} + 2 c^{3} e^{2 i e} + c^{3}\right) e^{- 10 i e}}{4 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-640*I*a**10*c**3*f**2*exp(18*I*e)*exp(-6*I*f*x) - 960*I*a**10*c**3*f**2*exp(16*I*e)*exp(-8*I*f*x) - 384*I*a**10*c**3*f**2*exp(14*I*e)*exp(-10*I*f*x))*exp(-24*I*e)/(15360*a**15*f**3), Ne(15360*a**15*f**3*exp(24*I*e), 0)), (x*(c**3*exp(4*I*e) + 2*c**3*exp(2*I*e) + c**3)*exp(-10*I*e)/(4*a**5), True))","A",0
914,1,272,0,1.050332," ","integrate((a+I*a*tan(f*x+e))**5*(c-I*c*tan(f*x+e))**4,x)","\frac{- 2240 a^{5} c^{4} e^{8 i e} e^{8 i f x} - 1792 a^{5} c^{4} e^{6 i e} e^{6 i f x} - 896 a^{5} c^{4} e^{4 i e} e^{4 i f x} - 256 a^{5} c^{4} e^{2 i e} e^{2 i f x} - 32 a^{5} c^{4}}{35 i f e^{16 i e} e^{16 i f x} + 280 i f e^{14 i e} e^{14 i f x} + 980 i f e^{12 i e} e^{12 i f x} + 1960 i f e^{10 i e} e^{10 i f x} + 2450 i f e^{8 i e} e^{8 i f x} + 1960 i f e^{6 i e} e^{6 i f x} + 980 i f e^{4 i e} e^{4 i f x} + 280 i f e^{2 i e} e^{2 i f x} + 35 i f}"," ",0,"(-2240*a**5*c**4*exp(8*I*e)*exp(8*I*f*x) - 1792*a**5*c**4*exp(6*I*e)*exp(6*I*f*x) - 896*a**5*c**4*exp(4*I*e)*exp(4*I*f*x) - 256*a**5*c**4*exp(2*I*e)*exp(2*I*f*x) - 32*a**5*c**4)/(35*I*f*exp(16*I*e)*exp(16*I*f*x) + 280*I*f*exp(14*I*e)*exp(14*I*f*x) + 980*I*f*exp(12*I*e)*exp(12*I*f*x) + 1960*I*f*exp(10*I*e)*exp(10*I*f*x) + 2450*I*f*exp(8*I*e)*exp(8*I*f*x) + 1960*I*f*exp(6*I*e)*exp(6*I*f*x) + 980*I*f*exp(4*I*e)*exp(4*I*f*x) + 280*I*f*exp(2*I*e)*exp(2*I*f*x) + 35*I*f)","B",0
915,1,219,0,0.748829," ","integrate((a+I*a*tan(f*x+e))**4*(c-I*c*tan(f*x+e))**4,x)","\frac{1120 i a^{4} c^{4} e^{6 i e} e^{6 i f x} + 672 i a^{4} c^{4} e^{4 i e} e^{4 i f x} + 224 i a^{4} c^{4} e^{2 i e} e^{2 i f x} + 32 i a^{4} c^{4}}{35 f e^{14 i e} e^{14 i f x} + 245 f e^{12 i e} e^{12 i f x} + 735 f e^{10 i e} e^{10 i f x} + 1225 f e^{8 i e} e^{8 i f x} + 1225 f e^{6 i e} e^{6 i f x} + 735 f e^{4 i e} e^{4 i f x} + 245 f e^{2 i e} e^{2 i f x} + 35 f}"," ",0,"(1120*I*a**4*c**4*exp(6*I*e)*exp(6*I*f*x) + 672*I*a**4*c**4*exp(4*I*e)*exp(4*I*f*x) + 224*I*a**4*c**4*exp(2*I*e)*exp(2*I*f*x) + 32*I*a**4*c**4)/(35*f*exp(14*I*e)*exp(14*I*f*x) + 245*f*exp(12*I*e)*exp(12*I*f*x) + 735*f*exp(10*I*e)*exp(10*I*f*x) + 1225*f*exp(8*I*e)*exp(8*I*f*x) + 1225*f*exp(6*I*e)*exp(6*I*f*x) + 735*f*exp(4*I*e)*exp(4*I*f*x) + 245*f*exp(2*I*e)*exp(2*I*f*x) + 35*f)","C",0
916,1,184,0,0.710575," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**4,x)","\frac{- 240 a^{3} c^{4} e^{4 i e} e^{4 i f x} - 96 a^{3} c^{4} e^{2 i e} e^{2 i f x} - 16 a^{3} c^{4}}{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**3*c**4*exp(4*I*e)*exp(4*I*f*x) - 96*a**3*c**4*exp(2*I*e)*exp(2*I*f*x) - 16*a**3*c**4)/(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
917,1,139,0,0.542028," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**4,x)","\frac{40 a^{2} c^{4} e^{2 i e} e^{2 i f x} + 8 a^{2} c^{4}}{- 5 i f e^{10 i e} e^{10 i f x} - 25 i f e^{8 i e} e^{8 i f x} - 50 i f e^{6 i e} e^{6 i f x} - 50 i f e^{4 i e} e^{4 i f x} - 25 i f e^{2 i e} e^{2 i f x} - 5 i f}"," ",0,"(40*a**2*c**4*exp(2*I*e)*exp(2*I*f*x) + 8*a**2*c**4)/(-5*I*f*exp(10*I*e)*exp(10*I*f*x) - 25*I*f*exp(8*I*e)*exp(8*I*f*x) - 50*I*f*exp(6*I*e)*exp(6*I*f*x) - 50*I*f*exp(4*I*e)*exp(4*I*f*x) - 25*I*f*exp(2*I*e)*exp(2*I*f*x) - 5*I*f)","B",0
918,1,90,0,0.385875," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**4,x)","\frac{4 a c^{4}}{- i f e^{8 i e} e^{8 i f x} - 4 i f e^{6 i e} e^{6 i f x} - 6 i f e^{4 i e} e^{4 i f x} - 4 i f e^{2 i e} e^{2 i f x} - i f}"," ",0,"4*a*c**4/(-I*f*exp(8*I*e)*exp(8*I*f*x) - 4*I*f*exp(6*I*e)*exp(6*I*f*x) - 6*I*f*exp(4*I*e)*exp(4*I*f*x) - 4*I*f*exp(2*I*e)*exp(2*I*f*x) - I*f)","B",0
919,1,175,0,0.498566," ","integrate((c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e)),x)","\frac{8 i c^{4} e^{2 i e} e^{2 i f x} + 10 i c^{4}}{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{4 i c^{4} 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 c^{4}}{a} + \frac{\left(- 24 c^{4} e^{2 i e} + 8 c^{4}\right) e^{- 2 i e}}{a}\right) & \text{otherwise} \end{cases} - \frac{24 c^{4} x}{a} - \frac{12 i c^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f}"," ",0,"(8*I*c**4*exp(2*I*e)*exp(2*I*f*x) + 10*I*c**4)/(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((4*I*c**4*exp(-2*I*e)*exp(-2*I*f*x)/(a*f), Ne(a*f*exp(2*I*e), 0)), (x*(24*c**4/a + (-24*c**4*exp(2*I*e) + 8*c**4)*exp(-2*I*e)/a), True)) - 24*c**4*x/a - 12*I*c**4*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f)","A",0
920,1,201,0,0.587122," ","integrate((c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**2,x)","\frac{2 i c^{4}}{- a^{2} f e^{2 i e} e^{2 i f x} - a^{2} f} + \begin{cases} \frac{\left(- 4 i a^{2} c^{4} f e^{4 i e} e^{- 2 i f x} + i a^{2} c^{4} f e^{2 i e} e^{- 4 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 c^{4}}{a^{2}} + \frac{\left(12 c^{4} e^{4 i e} - 8 c^{4} e^{2 i e} + 4 c^{4}\right) e^{- 4 i e}}{a^{2}}\right) & \text{otherwise} \end{cases} + \frac{12 c^{4} x}{a^{2}} + \frac{6 i c^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f}"," ",0,"2*I*c**4/(-a**2*f*exp(2*I*e)*exp(2*I*f*x) - a**2*f) + Piecewise(((-4*I*a**2*c**4*f*exp(4*I*e)*exp(-2*I*f*x) + I*a**2*c**4*f*exp(2*I*e)*exp(-4*I*f*x))*exp(-6*I*e)/(a**4*f**2), Ne(a**4*f**2*exp(6*I*e), 0)), (x*(-12*c**4/a**2 + (12*c**4*exp(4*I*e) - 8*c**4*exp(2*I*e) + 4*c**4)*exp(-4*I*e)/a**2), True)) + 12*c**4*x/a**2 + 6*I*c**4*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f)","A",0
921,1,216,0,0.646798," ","integrate((c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(- 6 i a^{6} c^{4} f^{2} e^{10 i e} e^{- 2 i f x} + 3 i a^{6} c^{4} f^{2} e^{8 i e} e^{- 4 i f x} - 2 i a^{6} c^{4} f^{2} e^{6 i e} e^{- 6 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 c^{4}}{a^{3}} + \frac{\left(- 2 c^{4} e^{6 i e} + 2 c^{4} e^{4 i e} - 2 c^{4} e^{2 i e} + 2 c^{4}\right) e^{- 6 i e}}{a^{3}}\right) & \text{otherwise} \end{cases} - \frac{2 c^{4} x}{a^{3}} - \frac{i c^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{3} f}"," ",0,"Piecewise((-(-6*I*a**6*c**4*f**2*exp(10*I*e)*exp(-2*I*f*x) + 3*I*a**6*c**4*f**2*exp(8*I*e)*exp(-4*I*f*x) - 2*I*a**6*c**4*f**2*exp(6*I*e)*exp(-6*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*c**4/a**3 + (-2*c**4*exp(6*I*e) + 2*c**4*exp(4*I*e) - 2*c**4*exp(2*I*e) + 2*c**4)*exp(-6*I*e)/a**3), True)) - 2*c**4*x/a**3 - I*c**4*log(exp(2*I*f*x) + exp(-2*I*e))/(a**3*f)","A",0
922,1,53,0,0.432393," ","integrate((c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**4,x)","\begin{cases} \frac{i c^{4} e^{- 8 i e} e^{- 8 i f x}}{8 a^{4} f} & \text{for}\: 8 a^{4} f e^{8 i e} \neq 0 \\\frac{c^{4} x e^{- 8 i e}}{a^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*c**4*exp(-8*I*e)*exp(-8*I*f*x)/(8*a**4*f), Ne(8*a**4*f*exp(8*I*e), 0)), (c**4*x*exp(-8*I*e)/a**4, True))","A",0
923,1,109,0,0.622865," ","integrate((c-I*c*tan(f*x+e))**4/(a+I*a*tan(f*x+e))**5,x)","\begin{cases} \frac{\left(20 i a^{5} c^{4} f e^{10 i e} e^{- 8 i f x} + 16 i a^{5} c^{4} f e^{8 i e} e^{- 10 i f x}\right) e^{- 18 i e}}{320 a^{10} f^{2}} & \text{for}\: 320 a^{10} f^{2} e^{18 i e} \neq 0 \\\frac{x \left(c^{4} e^{2 i e} + c^{4}\right) e^{- 10 i e}}{2 a^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((20*I*a**5*c**4*f*exp(10*I*e)*exp(-8*I*f*x) + 16*I*a**5*c**4*f*exp(8*I*e)*exp(-10*I*f*x))*exp(-18*I*e)/(320*a**10*f**2), Ne(320*a**10*f**2*exp(18*I*e), 0)), (x*(c**4*exp(2*I*e) + c**4)*exp(-10*I*e)/(2*a**5), True))","A",0
924,1,146,0,0.463212," ","integrate((a+I*a*tan(f*x+e))**4/(c-I*c*tan(f*x+e)),x)","\frac{12 i a^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \frac{- 12 a^{4} e^{2 i e} e^{2 i f x} - 10 a^{4}}{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{4 i a^{4} e^{2 i e} e^{2 i f x}}{c f} & \text{for}\: c f \neq 0 \\\frac{8 a^{4} x e^{2 i e}}{c} & \text{otherwise} \end{cases}"," ",0,"12*I*a**4*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + (-12*a**4*exp(2*I*e)*exp(2*I*f*x) - 10*a**4)/(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((-4*I*a**4*exp(2*I*e)*exp(2*I*f*x)/(c*f), Ne(c*f, 0)), (8*a**4*x*exp(2*I*e)/c, True))","A",0
925,1,102,0,0.391635," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e)),x)","- \frac{2 i a^{3}}{- c f e^{2 i e} e^{2 i f x} - c f} + \frac{4 i a^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \begin{cases} - \frac{2 i a^{3} e^{2 i e} e^{2 i f x}}{c f} & \text{for}\: c f \neq 0 \\\frac{4 a^{3} x e^{2 i e}}{c} & \text{otherwise} \end{cases}"," ",0,"-2*I*a**3/(-c*f*exp(2*I*e)*exp(2*I*f*x) - c*f) + 4*I*a**3*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + Piecewise((-2*I*a**3*exp(2*I*e)*exp(2*I*f*x)/(c*f), Ne(c*f, 0)), (4*a**3*x*exp(2*I*e)/c, True))","A",0
926,1,68,0,0.323898," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e)),x)","\frac{i a^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c f} + \begin{cases} - \frac{i a^{2} e^{2 i e} e^{2 i f x}}{c f} & \text{for}\: c f \neq 0 \\\frac{2 a^{2} x e^{2 i e}}{c} & \text{otherwise} \end{cases}"," ",0,"I*a**2*log(exp(2*I*f*x) + exp(-2*I*e))/(c*f) + Piecewise((-I*a**2*exp(2*I*e)*exp(2*I*f*x)/(c*f), Ne(c*f, 0)), (2*a**2*x*exp(2*I*e)/c, True))","A",0
927,1,39,0,0.170550," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\begin{cases} - \frac{i a e^{2 i e} e^{2 i f x}}{2 c f} & \text{for}\: 2 c f \neq 0 \\\frac{a x e^{2 i e}}{c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a*exp(2*I*e)*exp(2*I*f*x)/(2*c*f), Ne(2*c*f, 0)), (a*x*exp(2*I*e)/c, True))","A",0
928,1,119,0,0.258762," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x)","\begin{cases} \frac{\left(- 8 i a c f e^{4 i e} e^{2 i f x} + 8 i a c f 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{\left(e^{4 i e} + 2 e^{2 i e} + 1\right) e^{- 2 i e}}{4 a c} - \frac{1}{2 a c}\right) & \text{otherwise} \end{cases} + \frac{x}{2 a c}"," ",0,"Piecewise(((-8*I*a*c*f*exp(4*I*e)*exp(2*I*f*x) + 8*I*a*c*f*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*((exp(4*I*e) + 2*exp(2*I*e) + 1)*exp(-2*I*e)/(4*a*c) - 1/(2*a*c)), True)) + x/(2*a*c)","A",0
929,1,182,0,0.356349," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e)),x)","\begin{cases} - \frac{\left(512 i a^{4} c^{2} f^{2} e^{8 i e} e^{2 i f x} - 1536 i a^{4} c^{2} f^{2} e^{4 i e} e^{- 2 i f x} - 256 i a^{4} c^{2} f^{2} e^{2 i e} e^{- 4 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{\left(e^{6 i e} + 3 e^{4 i e} + 3 e^{2 i e} + 1\right) e^{- 4 i e}}{8 a^{2} c} - \frac{3}{8 a^{2} c}\right) & \text{otherwise} \end{cases} + \frac{3 x}{8 a^{2} c}"," ",0,"Piecewise((-(512*I*a**4*c**2*f**2*exp(8*I*e)*exp(2*I*f*x) - 1536*I*a**4*c**2*f**2*exp(4*I*e)*exp(-2*I*f*x) - 256*I*a**4*c**2*f**2*exp(2*I*e)*exp(-4*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*((exp(6*I*e) + 3*exp(4*I*e) + 3*exp(2*I*e) + 1)*exp(-4*I*e)/(8*a**2*c) - 3/(8*a**2*c)), True)) + 3*x/(8*a**2*c)","A",0
930,1,216,0,0.442170," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e)),x)","\begin{cases} \frac{\left(- 24576 i a^{9} c^{3} f^{3} e^{14 i e} e^{2 i f x} + 147456 i a^{9} c^{3} f^{3} e^{10 i e} e^{- 2 i f x} + 49152 i a^{9} c^{3} f^{3} e^{8 i e} e^{- 4 i f x} + 8192 i a^{9} c^{3} f^{3} e^{6 i e} e^{- 6 i f x}\right) e^{- 12 i e}}{786432 a^{12} c^{4} f^{4}} & \text{for}\: 786432 a^{12} c^{4} f^{4} e^{12 i e} \neq 0 \\x \left(\frac{\left(e^{8 i e} + 4 e^{6 i e} + 6 e^{4 i e} + 4 e^{2 i e} + 1\right) e^{- 6 i e}}{16 a^{3} c} - \frac{1}{4 a^{3} c}\right) & \text{otherwise} \end{cases} + \frac{x}{4 a^{3} c}"," ",0,"Piecewise(((-24576*I*a**9*c**3*f**3*exp(14*I*e)*exp(2*I*f*x) + 147456*I*a**9*c**3*f**3*exp(10*I*e)*exp(-2*I*f*x) + 49152*I*a**9*c**3*f**3*exp(8*I*e)*exp(-4*I*f*x) + 8192*I*a**9*c**3*f**3*exp(6*I*e)*exp(-6*I*f*x))*exp(-12*I*e)/(786432*a**12*c**4*f**4), Ne(786432*a**12*c**4*f**4*exp(12*I*e), 0)), (x*((exp(8*I*e) + 4*exp(6*I*e) + 6*exp(4*I*e) + 4*exp(2*I*e) + 1)*exp(-6*I*e)/(16*a**3*c) - 1/(4*a**3*c)), True)) + x/(4*a**3*c)","A",0
931,1,156,0,0.525178," ","integrate((a+I*a*tan(f*x+e))**4/(c-I*c*tan(f*x+e))**2,x)","\frac{2 i a^{4}}{- c^{2} f e^{2 i e} e^{2 i f x} - c^{2} f} - \frac{6 i a^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{2} f} + \begin{cases} \frac{- i a^{4} c^{2} f e^{4 i e} e^{4 i f x} + 4 i a^{4} c^{2} f e^{2 i e} e^{2 i f x}}{c^{4} f^{2}} & \text{for}\: c^{4} f^{2} \neq 0 \\\frac{x \left(4 a^{4} e^{4 i e} - 8 a^{4} e^{2 i e}\right)}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"2*I*a**4/(-c**2*f*exp(2*I*e)*exp(2*I*f*x) - c**2*f) - 6*I*a**4*log(exp(2*I*f*x) + exp(-2*I*e))/(c**2*f) + Piecewise(((-I*a**4*c**2*f*exp(4*I*e)*exp(4*I*f*x) + 4*I*a**4*c**2*f*exp(2*I*e)*exp(2*I*f*x))/(c**4*f**2), Ne(c**4*f**2, 0)), (x*(4*a**4*exp(4*I*e) - 8*a**4*exp(2*I*e))/c**2, True))","A",0
932,1,124,0,0.441227," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**2,x)","- \frac{i a^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{2} f} + \begin{cases} \frac{- i a^{3} c^{2} f e^{4 i e} e^{4 i f x} + 2 i a^{3} c^{2} f e^{2 i e} e^{2 i f x}}{2 c^{4} f^{2}} & \text{for}\: 2 c^{4} f^{2} \neq 0 \\\frac{x \left(2 a^{3} e^{4 i e} - 2 a^{3} e^{2 i e}\right)}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"-I*a**3*log(exp(2*I*f*x) + exp(-2*I*e))/(c**2*f) + Piecewise(((-I*a**3*c**2*f*exp(4*I*e)*exp(4*I*f*x) + 2*I*a**3*c**2*f*exp(2*I*e)*exp(2*I*f*x))/(2*c**4*f**2), Ne(2*c**4*f**2, 0)), (x*(2*a**3*exp(4*I*e) - 2*a**3*exp(2*I*e))/c**2, True))","A",0
933,1,48,0,0.232336," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} - \frac{i a^{2} e^{4 i e} e^{4 i f x}}{4 c^{2} f} & \text{for}\: 4 c^{2} f \neq 0 \\\frac{a^{2} x e^{4 i e}}{c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**2*exp(4*I*e)*exp(4*I*f*x)/(4*c**2*f), Ne(4*c**2*f, 0)), (a**2*x*exp(4*I*e)/c**2, True))","A",0
934,1,90,0,0.259361," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} \frac{- 4 i a c^{2} f e^{4 i e} e^{4 i f x} - 8 i a c^{2} f e^{2 i e} e^{2 i f x}}{32 c^{4} f^{2}} & \text{for}\: 32 c^{4} f^{2} \neq 0 \\\frac{x \left(a e^{4 i e} + a e^{2 i e}\right)}{2 c^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-4*I*a*c**2*f*exp(4*I*e)*exp(4*I*f*x) - 8*I*a*c**2*f*exp(2*I*e)*exp(2*I*f*x))/(32*c**4*f**2), Ne(32*c**4*f**2, 0)), (x*(a*exp(4*I*e) + a*exp(2*I*e))/(2*c**2), True))","A",0
935,1,175,0,0.352758," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} - \frac{\left(256 i a^{2} c^{4} f^{2} e^{6 i e} e^{4 i f x} + 1536 i a^{2} c^{4} f^{2} e^{4 i e} e^{2 i f x} - 512 i a^{2} c^{4} f^{2} e^{- 2 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{\left(e^{6 i e} + 3 e^{4 i e} + 3 e^{2 i e} + 1\right) e^{- 2 i e}}{8 a c^{2}} - \frac{3}{8 a c^{2}}\right) & \text{otherwise} \end{cases} + \frac{3 x}{8 a c^{2}}"," ",0,"Piecewise((-(256*I*a**2*c**4*f**2*exp(6*I*e)*exp(4*I*f*x) + 1536*I*a**2*c**4*f**2*exp(4*I*e)*exp(2*I*f*x) - 512*I*a**2*c**4*f**2*exp(-2*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*((exp(6*I*e) + 3*exp(4*I*e) + 3*exp(2*I*e) + 1)*exp(-2*I*e)/(8*a*c**2) - 3/(8*a*c**2)), True)) + 3*x/(8*a*c**2)","A",0
936,1,223,0,0.420103," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(- 4096 i a^{6} c^{6} f^{3} e^{10 i e} e^{4 i f x} - 32768 i a^{6} c^{6} f^{3} e^{8 i e} e^{2 i f x} + 32768 i a^{6} c^{6} f^{3} e^{4 i e} e^{- 2 i f x} + 4096 i a^{6} c^{6} f^{3} e^{2 i e} e^{- 4 i f x}\right) e^{- 6 i e}}{262144 a^{8} c^{8} f^{4}} & \text{for}\: 262144 a^{8} c^{8} f^{4} e^{6 i e} \neq 0 \\x \left(\frac{\left(e^{8 i e} + 4 e^{6 i e} + 6 e^{4 i e} + 4 e^{2 i e} + 1\right) e^{- 4 i e}}{16 a^{2} c^{2}} - \frac{3}{8 a^{2} c^{2}}\right) & \text{otherwise} \end{cases} + \frac{3 x}{8 a^{2} c^{2}}"," ",0,"Piecewise(((-4096*I*a**6*c**6*f**3*exp(10*I*e)*exp(4*I*f*x) - 32768*I*a**6*c**6*f**3*exp(8*I*e)*exp(2*I*f*x) + 32768*I*a**6*c**6*f**3*exp(4*I*e)*exp(-2*I*f*x) + 4096*I*a**6*c**6*f**3*exp(2*I*e)*exp(-4*I*f*x))*exp(-6*I*e)/(262144*a**8*c**8*f**4), Ne(262144*a**8*c**8*f**4*exp(6*I*e), 0)), (x*((exp(8*I*e) + 4*exp(6*I*e) + 6*exp(4*I*e) + 4*exp(2*I*e) + 1)*exp(-4*I*e)/(16*a**2*c**2) - 3/(8*a**2*c**2)), True)) + 3*x/(8*a**2*c**2)","A",0
937,1,262,0,0.576120," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**2,x)","\begin{cases} - \frac{\left(50331648 i a^{12} c^{8} f^{4} e^{16 i e} e^{4 i f x} + 503316480 i a^{12} c^{8} f^{4} e^{14 i e} e^{2 i f x} - 1006632960 i a^{12} c^{8} f^{4} e^{10 i e} e^{- 2 i f x} - 251658240 i a^{12} c^{8} f^{4} e^{8 i e} e^{- 4 i f x} - 33554432 i a^{12} c^{8} f^{4} e^{6 i e} e^{- 6 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{\left(e^{10 i e} + 5 e^{8 i e} + 10 e^{6 i e} + 10 e^{4 i e} + 5 e^{2 i e} + 1\right) e^{- 6 i e}}{32 a^{3} c^{2}} - \frac{5}{16 a^{3} c^{2}}\right) & \text{otherwise} \end{cases} + \frac{5 x}{16 a^{3} c^{2}}"," ",0,"Piecewise((-(50331648*I*a**12*c**8*f**4*exp(16*I*e)*exp(4*I*f*x) + 503316480*I*a**12*c**8*f**4*exp(14*I*e)*exp(2*I*f*x) - 1006632960*I*a**12*c**8*f**4*exp(10*I*e)*exp(-2*I*f*x) - 251658240*I*a**12*c**8*f**4*exp(8*I*e)*exp(-4*I*f*x) - 33554432*I*a**12*c**8*f**4*exp(6*I*e)*exp(-6*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*((exp(10*I*e) + 5*exp(8*I*e) + 10*exp(6*I*e) + 10*exp(4*I*e) + 5*exp(2*I*e) + 1)*exp(-6*I*e)/(32*a**3*c**2) - 5/(16*a**3*c**2)), True)) + 5*x/(16*a**3*c**2)","A",0
938,1,253,0,0.793473," ","integrate((a+I*a*tan(f*x+e))**6/(c-I*c*tan(f*x+e))**3,x)","\frac{40 i a^{6} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{3} f} + \frac{- 20 a^{6} e^{2 i e} e^{2 i f x} - 18 a^{6}}{i c^{3} f e^{4 i e} e^{4 i f x} + 2 i c^{3} f e^{2 i e} e^{2 i f x} + i c^{3} f} + \begin{cases} - \frac{4 i a^{6} c^{6} f^{2} e^{6 i e} e^{6 i f x} - 18 i a^{6} c^{6} f^{2} e^{4 i e} e^{4 i f x} + 72 i a^{6} c^{6} f^{2} e^{2 i e} e^{2 i f x}}{3 c^{9} f^{3}} & \text{for}\: 3 c^{9} f^{3} \neq 0 \\\frac{x \left(8 a^{6} e^{6 i e} - 24 a^{6} e^{4 i e} + 48 a^{6} e^{2 i e}\right)}{c^{3}} & \text{otherwise} \end{cases}"," ",0,"40*I*a**6*log(exp(2*I*f*x) + exp(-2*I*e))/(c**3*f) + (-20*a**6*exp(2*I*e)*exp(2*I*f*x) - 18*a**6)/(I*c**3*f*exp(4*I*e)*exp(4*I*f*x) + 2*I*c**3*f*exp(2*I*e)*exp(2*I*f*x) + I*c**3*f) + Piecewise((-(4*I*a**6*c**6*f**2*exp(6*I*e)*exp(6*I*f*x) - 18*I*a**6*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + 72*I*a**6*c**6*f**2*exp(2*I*e)*exp(2*I*f*x))/(3*c**9*f**3), Ne(3*c**9*f**3, 0)), (x*(8*a**6*exp(6*I*e) - 24*a**6*exp(4*I*e) + 48*a**6*exp(2*I*e))/c**3, True))","A",0
939,1,207,0,0.692345," ","integrate((a+I*a*tan(f*x+e))**5/(c-I*c*tan(f*x+e))**3,x)","- \frac{2 i a^{5}}{- c^{3} f e^{2 i e} e^{2 i f x} - c^{3} f} + \frac{8 i a^{5} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{3} f} + \begin{cases} - \frac{2 i a^{5} c^{6} f^{2} e^{6 i e} e^{6 i f x} - 6 i a^{5} c^{6} f^{2} e^{4 i e} e^{4 i f x} + 18 i a^{5} c^{6} f^{2} e^{2 i e} e^{2 i f x}}{3 c^{9} f^{3}} & \text{for}\: 3 c^{9} f^{3} \neq 0 \\\frac{x \left(4 a^{5} e^{6 i e} - 8 a^{5} e^{4 i e} + 12 a^{5} e^{2 i e}\right)}{c^{3}} & \text{otherwise} \end{cases}"," ",0,"-2*I*a**5/(-c**3*f*exp(2*I*e)*exp(2*I*f*x) - c**3*f) + 8*I*a**5*log(exp(2*I*f*x) + exp(-2*I*e))/(c**3*f) + Piecewise((-(2*I*a**5*c**6*f**2*exp(6*I*e)*exp(6*I*f*x) - 6*I*a**5*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + 18*I*a**5*c**6*f**2*exp(2*I*e)*exp(2*I*f*x))/(3*c**9*f**3), Ne(3*c**9*f**3, 0)), (x*(4*a**5*exp(6*I*e) - 8*a**5*exp(4*I*e) + 12*a**5*exp(2*I*e))/c**3, True))","A",0
940,1,172,0,0.599227," ","integrate((a+I*a*tan(f*x+e))**4/(c-I*c*tan(f*x+e))**3,x)","\frac{i a^{4} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{3} f} + \begin{cases} - \frac{2 i a^{4} c^{6} f^{2} e^{6 i e} e^{6 i f x} - 3 i a^{4} c^{6} f^{2} e^{4 i e} e^{4 i f x} + 6 i a^{4} c^{6} f^{2} e^{2 i e} e^{2 i f x}}{6 c^{9} f^{3}} & \text{for}\: 6 c^{9} f^{3} \neq 0 \\\frac{x \left(2 a^{4} e^{6 i e} - 2 a^{4} e^{4 i e} + 2 a^{4} e^{2 i e}\right)}{c^{3}} & \text{otherwise} \end{cases}"," ",0,"I*a**4*log(exp(2*I*f*x) + exp(-2*I*e))/(c**3*f) + Piecewise((-(2*I*a**4*c**6*f**2*exp(6*I*e)*exp(6*I*f*x) - 3*I*a**4*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + 6*I*a**4*c**6*f**2*exp(2*I*e)*exp(2*I*f*x))/(6*c**9*f**3), Ne(6*c**9*f**3, 0)), (x*(2*a**4*exp(6*I*e) - 2*a**4*exp(4*I*e) + 2*a**4*exp(2*I*e))/c**3, True))","A",0
941,1,48,0,0.321247," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} - \frac{i a^{3} e^{6 i e} e^{6 i f x}}{6 c^{3} f} & \text{for}\: 6 c^{3} f \neq 0 \\\frac{a^{3} x e^{6 i e}}{c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**3*exp(6*I*e)*exp(6*I*f*x)/(6*c**3*f), Ne(6*c**3*f, 0)), (a**3*x*exp(6*I*e)/c**3, True))","A",0
942,1,97,0,0.352458," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} \frac{- 8 i a^{2} c^{3} f e^{6 i e} e^{6 i f x} - 12 i a^{2} c^{3} f e^{4 i e} e^{4 i f x}}{96 c^{6} f^{2}} & \text{for}\: 96 c^{6} f^{2} \neq 0 \\\frac{x \left(a^{2} e^{6 i e} + a^{2} e^{4 i e}\right)}{2 c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-8*I*a**2*c**3*f*exp(6*I*e)*exp(6*I*f*x) - 12*I*a**2*c**3*f*exp(4*I*e)*exp(4*I*f*x))/(96*c**6*f**2), Ne(96*c**6*f**2, 0)), (x*(a**2*exp(6*I*e) + a**2*exp(4*I*e))/(2*c**3), True))","A",0
943,1,131,0,0.333071," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} - \frac{64 i a c^{6} f^{2} e^{6 i e} e^{6 i f x} + 192 i a c^{6} f^{2} e^{4 i e} e^{4 i f x} + 192 i a c^{6} f^{2} e^{2 i e} e^{2 i f x}}{1536 c^{9} f^{3}} & \text{for}\: 1536 c^{9} f^{3} \neq 0 \\\frac{x \left(a e^{6 i e} + 2 a e^{4 i e} + a e^{2 i e}\right)}{4 c^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(64*I*a*c**6*f**2*exp(6*I*e)*exp(6*I*f*x) + 192*I*a*c**6*f**2*exp(4*I*e)*exp(4*I*f*x) + 192*I*a*c**6*f**2*exp(2*I*e)*exp(2*I*f*x))/(1536*c**9*f**3), Ne(1536*c**9*f**3, 0)), (x*(a*exp(6*I*e) + 2*a*exp(4*I*e) + a*exp(2*I*e))/(4*c**3), True))","A",0
944,1,209,0,0.419340," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(- 8192 i a^{3} c^{9} f^{3} e^{8 i e} e^{6 i f x} - 49152 i a^{3} c^{9} f^{3} e^{6 i e} e^{4 i f x} - 147456 i a^{3} c^{9} f^{3} e^{4 i e} e^{2 i f x} + 24576 i a^{3} c^{9} f^{3} e^{- 2 i f x}\right) e^{- 2 i e}}{786432 a^{4} c^{12} f^{4}} & \text{for}\: 786432 a^{4} c^{12} f^{4} e^{2 i e} \neq 0 \\x \left(\frac{\left(e^{8 i e} + 4 e^{6 i e} + 6 e^{4 i e} + 4 e^{2 i e} + 1\right) e^{- 2 i e}}{16 a c^{3}} - \frac{1}{4 a c^{3}}\right) & \text{otherwise} \end{cases} + \frac{x}{4 a c^{3}}"," ",0,"Piecewise(((-8192*I*a**3*c**9*f**3*exp(8*I*e)*exp(6*I*f*x) - 49152*I*a**3*c**9*f**3*exp(6*I*e)*exp(4*I*f*x) - 147456*I*a**3*c**9*f**3*exp(4*I*e)*exp(2*I*f*x) + 24576*I*a**3*c**9*f**3*exp(-2*I*f*x))*exp(-2*I*e)/(786432*a**4*c**12*f**4), Ne(786432*a**4*c**12*f**4*exp(2*I*e), 0)), (x*((exp(8*I*e) + 4*exp(6*I*e) + 6*exp(4*I*e) + 4*exp(2*I*e) + 1)*exp(-2*I*e)/(16*a*c**3) - 1/(4*a*c**3)), True)) + x/(4*a*c**3)","A",0
945,1,262,0,0.564990," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(33554432 i a^{8} c^{12} f^{4} e^{12 i e} e^{6 i f x} + 251658240 i a^{8} c^{12} f^{4} e^{10 i e} e^{4 i f x} + 1006632960 i a^{8} c^{12} f^{4} e^{8 i e} e^{2 i f x} - 503316480 i a^{8} c^{12} f^{4} e^{4 i e} e^{- 2 i f x} - 50331648 i a^{8} c^{12} f^{4} e^{2 i e} e^{- 4 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{\left(e^{10 i e} + 5 e^{8 i e} + 10 e^{6 i e} + 10 e^{4 i e} + 5 e^{2 i e} + 1\right) e^{- 4 i e}}{32 a^{2} c^{3}} - \frac{5}{16 a^{2} c^{3}}\right) & \text{otherwise} \end{cases} + \frac{5 x}{16 a^{2} c^{3}}"," ",0,"Piecewise((-(33554432*I*a**8*c**12*f**4*exp(12*I*e)*exp(6*I*f*x) + 251658240*I*a**8*c**12*f**4*exp(10*I*e)*exp(4*I*f*x) + 1006632960*I*a**8*c**12*f**4*exp(8*I*e)*exp(2*I*f*x) - 503316480*I*a**8*c**12*f**4*exp(4*I*e)*exp(-2*I*f*x) - 50331648*I*a**8*c**12*f**4*exp(2*I*e)*exp(-4*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*((exp(10*I*e) + 5*exp(8*I*e) + 10*exp(6*I*e) + 10*exp(4*I*e) + 5*exp(2*I*e) + 1)*exp(-4*I*e)/(32*a**2*c**3) - 5/(16*a**2*c**3)), True)) + 5*x/(16*a**2*c**3)","A",0
946,1,298,0,0.600550," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**3,x)","\begin{cases} \frac{\left(- 103079215104 i a^{15} c^{15} f^{5} e^{18 i e} e^{6 i f x} - 927712935936 i a^{15} c^{15} f^{5} e^{16 i e} e^{4 i f x} - 4638564679680 i a^{15} c^{15} f^{5} e^{14 i e} e^{2 i f x} + 4638564679680 i a^{15} c^{15} f^{5} e^{10 i e} e^{- 2 i f x} + 927712935936 i a^{15} c^{15} f^{5} e^{8 i e} e^{- 4 i f x} + 103079215104 i a^{15} c^{15} f^{5} e^{6 i e} 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{\left(e^{12 i e} + 6 e^{10 i e} + 15 e^{8 i e} + 20 e^{6 i e} + 15 e^{4 i e} + 6 e^{2 i e} + 1\right) e^{- 6 i e}}{64 a^{3} c^{3}} - \frac{5}{16 a^{3} c^{3}}\right) & \text{otherwise} \end{cases} + \frac{5 x}{16 a^{3} c^{3}}"," ",0,"Piecewise(((-103079215104*I*a**15*c**15*f**5*exp(18*I*e)*exp(6*I*f*x) - 927712935936*I*a**15*c**15*f**5*exp(16*I*e)*exp(4*I*f*x) - 4638564679680*I*a**15*c**15*f**5*exp(14*I*e)*exp(2*I*f*x) + 4638564679680*I*a**15*c**15*f**5*exp(10*I*e)*exp(-2*I*f*x) + 927712935936*I*a**15*c**15*f**5*exp(8*I*e)*exp(-4*I*f*x) + 103079215104*I*a**15*c**15*f**5*exp(6*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*((exp(12*I*e) + 6*exp(10*I*e) + 15*exp(8*I*e) + 20*exp(6*I*e) + 15*exp(4*I*e) + 6*exp(2*I*e) + 1)*exp(-6*I*e)/(64*a**3*c**3) - 5/(16*a**3*c**3)), True)) + 5*x/(16*a**3*c**3)","A",0
947,1,246,0,0.893330," ","integrate((a+I*a*tan(f*x+e))**6/(c-I*c*tan(f*x+e))**4,x)","\frac{2 i a^{6}}{- c^{4} f e^{2 i e} e^{2 i f x} - c^{4} f} - \frac{10 i a^{6} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{4} f} + \begin{cases} \frac{- 3 i a^{6} c^{12} f^{3} e^{8 i e} e^{8 i f x} + 8 i a^{6} c^{12} f^{3} e^{6 i e} e^{6 i f x} - 18 i a^{6} c^{12} f^{3} e^{4 i e} e^{4 i f x} + 48 i a^{6} c^{12} f^{3} e^{2 i e} e^{2 i f x}}{6 c^{16} f^{4}} & \text{for}\: 6 c^{16} f^{4} \neq 0 \\\frac{x \left(4 a^{6} e^{8 i e} - 8 a^{6} e^{6 i e} + 12 a^{6} e^{4 i e} - 16 a^{6} e^{2 i e}\right)}{c^{4}} & \text{otherwise} \end{cases}"," ",0,"2*I*a**6/(-c**4*f*exp(2*I*e)*exp(2*I*f*x) - c**4*f) - 10*I*a**6*log(exp(2*I*f*x) + exp(-2*I*e))/(c**4*f) + Piecewise(((-3*I*a**6*c**12*f**3*exp(8*I*e)*exp(8*I*f*x) + 8*I*a**6*c**12*f**3*exp(6*I*e)*exp(6*I*f*x) - 18*I*a**6*c**12*f**3*exp(4*I*e)*exp(4*I*f*x) + 48*I*a**6*c**12*f**3*exp(2*I*e)*exp(2*I*f*x))/(6*c**16*f**4), Ne(6*c**16*f**4, 0)), (x*(4*a**6*exp(8*I*e) - 8*a**6*exp(6*I*e) + 12*a**6*exp(4*I*e) - 16*a**6*exp(2*I*e))/c**4, True))","A",0
948,1,211,0,0.766071," ","integrate((a+I*a*tan(f*x+e))**5/(c-I*c*tan(f*x+e))**4,x)","- \frac{i a^{5} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{c^{4} f} + \begin{cases} \frac{- 6 i a^{5} c^{12} f^{3} e^{8 i e} e^{8 i f x} + 8 i a^{5} c^{12} f^{3} e^{6 i e} e^{6 i f x} - 12 i a^{5} c^{12} f^{3} e^{4 i e} e^{4 i f x} + 24 i a^{5} c^{12} f^{3} e^{2 i e} e^{2 i f x}}{24 c^{16} f^{4}} & \text{for}\: 24 c^{16} f^{4} \neq 0 \\\frac{x \left(2 a^{5} e^{8 i e} - 2 a^{5} e^{6 i e} + 2 a^{5} e^{4 i e} - 2 a^{5} e^{2 i e}\right)}{c^{4}} & \text{otherwise} \end{cases}"," ",0,"-I*a**5*log(exp(2*I*f*x) + exp(-2*I*e))/(c**4*f) + Piecewise(((-6*I*a**5*c**12*f**3*exp(8*I*e)*exp(8*I*f*x) + 8*I*a**5*c**12*f**3*exp(6*I*e)*exp(6*I*f*x) - 12*I*a**5*c**12*f**3*exp(4*I*e)*exp(4*I*f*x) + 24*I*a**5*c**12*f**3*exp(2*I*e)*exp(2*I*f*x))/(24*c**16*f**4), Ne(24*c**16*f**4, 0)), (x*(2*a**5*exp(8*I*e) - 2*a**5*exp(6*I*e) + 2*a**5*exp(4*I*e) - 2*a**5*exp(2*I*e))/c**4, True))","A",0
949,1,48,0,0.428659," ","integrate((a+I*a*tan(f*x+e))**4/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{i a^{4} e^{8 i e} e^{8 i f x}}{8 c^{4} f} & \text{for}\: 8 c^{4} f \neq 0 \\\frac{a^{4} x e^{8 i e}}{c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*a**4*exp(8*I*e)*exp(8*I*f*x)/(8*c**4*f), Ne(8*c**4*f, 0)), (a**4*x*exp(8*I*e)/c**4, True))","A",0
950,1,97,0,0.475898," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{- 12 i a^{3} c^{4} f e^{8 i e} e^{8 i f x} - 16 i a^{3} c^{4} f e^{6 i e} e^{6 i f x}}{192 c^{8} f^{2}} & \text{for}\: 192 c^{8} f^{2} \neq 0 \\\frac{x \left(a^{3} e^{8 i e} + a^{3} e^{6 i e}\right)}{2 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-12*I*a**3*c**4*f*exp(8*I*e)*exp(8*I*f*x) - 16*I*a**3*c**4*f*exp(6*I*e)*exp(6*I*f*x))/(192*c**8*f**2), Ne(192*c**8*f**2, 0)), (x*(a**3*exp(8*I*e) + a**3*exp(6*I*e))/(2*c**4), True))","A",0
951,1,141,0,0.440231," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{192 i a^{2} c^{8} f^{2} e^{8 i e} e^{8 i f x} + 512 i a^{2} c^{8} f^{2} e^{6 i e} e^{6 i f x} + 384 i a^{2} c^{8} f^{2} e^{4 i e} e^{4 i f x}}{6144 c^{12} f^{3}} & \text{for}\: 6144 c^{12} f^{3} \neq 0 \\\frac{x \left(a^{2} e^{8 i e} + 2 a^{2} e^{6 i e} + a^{2} e^{4 i e}\right)}{4 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(192*I*a**2*c**8*f**2*exp(8*I*e)*exp(8*I*f*x) + 512*I*a**2*c**8*f**2*exp(6*I*e)*exp(6*I*f*x) + 384*I*a**2*c**8*f**2*exp(4*I*e)*exp(4*I*f*x))/(6144*c**12*f**3), Ne(6144*c**12*f**3, 0)), (x*(a**2*exp(8*I*e) + 2*a**2*exp(6*I*e) + a**2*exp(4*I*e))/(4*c**4), True))","A",0
952,1,168,0,0.410102," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{- 8192 i a c^{12} f^{3} e^{8 i e} e^{8 i f x} - 32768 i a c^{12} f^{3} e^{6 i e} e^{6 i f x} - 49152 i a c^{12} f^{3} e^{4 i e} e^{4 i f x} - 32768 i a c^{12} f^{3} e^{2 i e} e^{2 i f x}}{524288 c^{16} f^{4}} & \text{for}\: 524288 c^{16} f^{4} \neq 0 \\\frac{x \left(a e^{8 i e} + 3 a e^{6 i e} + 3 a e^{4 i e} + a e^{2 i e}\right)}{8 c^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-8192*I*a*c**12*f**3*exp(8*I*e)*exp(8*I*f*x) - 32768*I*a*c**12*f**3*exp(6*I*e)*exp(6*I*f*x) - 49152*I*a*c**12*f**3*exp(4*I*e)*exp(4*I*f*x) - 32768*I*a*c**12*f**3*exp(2*I*e)*exp(2*I*f*x))/(524288*c**16*f**4), Ne(524288*c**16*f**4, 0)), (x*(a*exp(8*I*e) + 3*a*exp(6*I*e) + 3*a*exp(4*I*e) + a*exp(2*I*e))/(8*c**4), True))","B",0
953,1,250,0,0.511430," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{\left(25165824 i a^{4} c^{16} f^{4} e^{10 i e} e^{8 i f x} + 167772160 i a^{4} c^{16} f^{4} e^{8 i e} e^{6 i f x} + 503316480 i a^{4} c^{16} f^{4} e^{6 i e} e^{4 i f x} + 1006632960 i a^{4} c^{16} f^{4} e^{4 i e} e^{2 i f x} - 100663296 i a^{4} c^{16} f^{4} e^{- 2 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{\left(e^{10 i e} + 5 e^{8 i e} + 10 e^{6 i e} + 10 e^{4 i e} + 5 e^{2 i e} + 1\right) e^{- 2 i e}}{32 a c^{4}} - \frac{5}{32 a c^{4}}\right) & \text{otherwise} \end{cases} + \frac{5 x}{32 a c^{4}}"," ",0,"Piecewise((-(25165824*I*a**4*c**16*f**4*exp(10*I*e)*exp(8*I*f*x) + 167772160*I*a**4*c**16*f**4*exp(8*I*e)*exp(6*I*f*x) + 503316480*I*a**4*c**16*f**4*exp(6*I*e)*exp(4*I*f*x) + 1006632960*I*a**4*c**16*f**4*exp(4*I*e)*exp(2*I*f*x) - 100663296*I*a**4*c**16*f**4*exp(-2*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*((exp(10*I*e) + 5*exp(8*I*e) + 10*exp(6*I*e) + 10*exp(4*I*e) + 5*exp(2*I*e) + 1)*exp(-2*I*e)/(32*a*c**4) - 5/(32*a*c**4)), True)) + 5*x/(32*a*c**4)","A",0
954,1,298,0,0.662701," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} \frac{\left(- 8589934592 i a^{10} c^{20} f^{5} e^{14 i e} e^{8 i f x} - 68719476736 i a^{10} c^{20} f^{5} e^{12 i e} e^{6 i f x} - 257698037760 i a^{10} c^{20} f^{5} e^{10 i e} e^{4 i f x} - 687194767360 i a^{10} c^{20} f^{5} e^{8 i e} e^{2 i f x} + 206158430208 i a^{10} c^{20} f^{5} e^{4 i e} e^{- 2 i f x} + 17179869184 i a^{10} c^{20} f^{5} e^{2 i e} e^{- 4 i f x}\right) e^{- 6 i e}}{4398046511104 a^{12} c^{24} f^{6}} & \text{for}\: 4398046511104 a^{12} c^{24} f^{6} e^{6 i e} \neq 0 \\x \left(\frac{\left(e^{12 i e} + 6 e^{10 i e} + 15 e^{8 i e} + 20 e^{6 i e} + 15 e^{4 i e} + 6 e^{2 i e} + 1\right) e^{- 4 i e}}{64 a^{2} c^{4}} - \frac{15}{64 a^{2} c^{4}}\right) & \text{otherwise} \end{cases} + \frac{15 x}{64 a^{2} c^{4}}"," ",0,"Piecewise(((-8589934592*I*a**10*c**20*f**5*exp(14*I*e)*exp(8*I*f*x) - 68719476736*I*a**10*c**20*f**5*exp(12*I*e)*exp(6*I*f*x) - 257698037760*I*a**10*c**20*f**5*exp(10*I*e)*exp(4*I*f*x) - 687194767360*I*a**10*c**20*f**5*exp(8*I*e)*exp(2*I*f*x) + 206158430208*I*a**10*c**20*f**5*exp(4*I*e)*exp(-2*I*f*x) + 17179869184*I*a**10*c**20*f**5*exp(2*I*e)*exp(-4*I*f*x))*exp(-6*I*e)/(4398046511104*a**12*c**24*f**6), Ne(4398046511104*a**12*c**24*f**6*exp(6*I*e), 0)), (x*((exp(12*I*e) + 6*exp(10*I*e) + 15*exp(8*I*e) + 20*exp(6*I*e) + 15*exp(4*I*e) + 6*exp(2*I*e) + 1)*exp(-4*I*e)/(64*a**2*c**4) - 15/(64*a**2*c**4)), True)) + 15*x/(64*a**2*c**4)","A",0
955,1,337,0,0.766826," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**4,x)","\begin{cases} - \frac{\left(10133099161583616 i a^{18} c^{24} f^{6} e^{20 i e} e^{8 i f x} + 94575592174780416 i a^{18} c^{24} f^{6} e^{18 i e} e^{6 i f x} + 425590164786511872 i a^{18} c^{24} f^{6} e^{16 i e} e^{4 i f x} + 1418633882621706240 i a^{18} c^{24} f^{6} e^{14 i e} e^{2 i f x} - 851180329573023744 i a^{18} c^{24} f^{6} e^{10 i e} e^{- 2 i f x} - 141863388262170624 i a^{18} c^{24} f^{6} e^{8 i e} e^{- 4 i f x} - 13510798882111488 i a^{18} c^{24} f^{6} e^{6 i e} e^{- 6 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{\left(e^{14 i e} + 7 e^{12 i e} + 21 e^{10 i e} + 35 e^{8 i e} + 35 e^{6 i e} + 21 e^{4 i e} + 7 e^{2 i e} + 1\right) e^{- 6 i e}}{128 a^{3} c^{4}} - \frac{35}{128 a^{3} c^{4}}\right) & \text{otherwise} \end{cases} + \frac{35 x}{128 a^{3} c^{4}}"," ",0,"Piecewise((-(10133099161583616*I*a**18*c**24*f**6*exp(20*I*e)*exp(8*I*f*x) + 94575592174780416*I*a**18*c**24*f**6*exp(18*I*e)*exp(6*I*f*x) + 425590164786511872*I*a**18*c**24*f**6*exp(16*I*e)*exp(4*I*f*x) + 1418633882621706240*I*a**18*c**24*f**6*exp(14*I*e)*exp(2*I*f*x) - 851180329573023744*I*a**18*c**24*f**6*exp(10*I*e)*exp(-2*I*f*x) - 141863388262170624*I*a**18*c**24*f**6*exp(8*I*e)*exp(-4*I*f*x) - 13510798882111488*I*a**18*c**24*f**6*exp(6*I*e)*exp(-6*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*((exp(14*I*e) + 7*exp(12*I*e) + 21*exp(10*I*e) + 35*exp(8*I*e) + 35*exp(6*I*e) + 21*exp(4*I*e) + 7*exp(2*I*e) + 1)*exp(-6*I*e)/(128*a**3*c**4) - 35/(128*a**3*c**4)), True)) + 35*x/(128*a**3*c**4)","A",0
956,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- 3 \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-3*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x))","F",0
957,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx\right)"," ",0,"-a**2*(Integral(sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-2*I*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-sqrt(-I*c*tan(e + f*x) + c), x))","F",0
958,1,42,0,2.984450," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e)),x)","\begin{cases} \frac{2 i a \sqrt{- i c \tan{\left(e + f x \right)} + c}}{f} & \text{for}\: f \neq 0 \\x \left(i a \tan{\left(e \right)} + a\right) \sqrt{- i c \tan{\left(e \right)} + c} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a*sqrt(-I*c*tan(e + f*x) + c)/f, Ne(f, 0)), (x*(I*a*tan(e) + a)*sqrt(-I*c*tan(e) + c), True))","A",0
959,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x)/a","F",0
960,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\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}{a^{2}}"," ",0,"-Integral(sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
961,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\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}{a^{3}}"," ",0,"I*Integral(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)/a**3","F",0
962,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int i c \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*c*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x))","F",0
963,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \left(- c \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- i c \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-c*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x))","F",0
964,1,44,0,3.144955," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**(3/2),x)","\begin{cases} \frac{2 i a \left(- i c \tan{\left(e + f x \right)} + c\right)^{\frac{3}{2}}}{3 f} & \text{for}\: f \neq 0 \\x \left(i a \tan{\left(e \right)} + a\right) \left(- i c \tan{\left(e \right)} + c\right)^{\frac{3}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a*(-I*c*tan(e + f*x) + c)**(3/2)/(3*f), Ne(f, 0)), (x*(I*a*tan(e) + a)*(-I*c*tan(e) + c)**(3/2), True))","A",0
965,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{c \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx + \int \left(- \frac{i 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\right)}{a}"," ",0,"-I*(Integral(c*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x) + Integral(-I*c*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
966,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{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 \left(- \frac{i 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}{a^{2}}"," ",0,"-(Integral(c*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-I*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))/a**2","F",0
967,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{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 \left(- \frac{i 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\right)}{a^{3}}"," ",0,"I*(Integral(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(-I*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))/a**3","F",0
968,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}\, dx + \int \left(- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{5}{\left(e + f x \right)}\right)\, dx + \int 2 i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\, dx + \int i c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\, dx\right)"," ",0,"-I*a**3*(Integral(I*c**2*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x), x) + Integral(-2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**3, x) + Integral(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**5, x) + Integral(2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x))","F",0
969,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \left(- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}\right)\, dx + \int \left(- 2 c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int \left(- c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c} \tan^{4}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-c**2*sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2, x) + Integral(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**4, x))","F",0
970,1,44,0,8.231747," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**(5/2),x)","\begin{cases} \frac{2 i a \left(- i c \tan{\left(e + f x \right)} + c\right)^{\frac{5}{2}}}{5 f} & \text{for}\: f \neq 0 \\x \left(i a \tan{\left(e \right)} + a\right) \left(- i c \tan{\left(e \right)} + c\right)^{\frac{5}{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*I*a*(-I*c*tan(e + f*x) + c)**(5/2)/(5*f), Ne(f, 0)), (x*(I*a*tan(e) + a)*(-I*c*tan(e) + c)**(5/2), True))","A",0
971,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{c^{2} \sqrt{- i c \tan{\left(e + f x \right)} + c}}{\tan{\left(e + f x \right)} - i}\, dx + \int \left(- \frac{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 \left(- \frac{2 i 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\right)}{a}"," ",0,"-I*(Integral(c**2*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x) - I), x) + Integral(-c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)**2/(tan(e + f*x) - I), x) + Integral(-2*I*c**2*sqrt(-I*c*tan(e + f*x) + c)*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
972,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{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{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 \left(- \frac{2 i 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}{a^{2}}"," ",0,"-(Integral(c**2*sqrt(-I*c*tan(e + f*x) + c)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(-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(-2*I*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))/a**2","F",0
973,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{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{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 \left(- \frac{2 i 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\right)}{a^{3}}"," ",0,"I*(Integral(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(-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(-2*I*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))/a**3","F",0
974,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(1/2),x)","- i a^{3} \left(\int \frac{i}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(tan(e + f*x)**3/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-3*I*tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x))","F",0
975,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(1/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx + \int \left(- \frac{1}{\sqrt{- i c \tan{\left(e + f x \right)} + c}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(e + f*x)**2/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-2*I*tan(e + f*x)/sqrt(-I*c*tan(e + f*x) + c), x) + Integral(-1/sqrt(-I*c*tan(e + f*x) + c), x))","F",0
976,1,44,0,2.574406," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(1/2),x)","\begin{cases} - \frac{2 i a}{f \sqrt{- i c \tan{\left(e + f x \right)} + c}} & \text{for}\: f \neq 0 \\\frac{x \left(i a \tan{\left(e \right)} + a\right)}{\sqrt{- i c \tan{\left(e \right)} + c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*a/(f*sqrt(-I*c*tan(e + f*x) + c)), Ne(f, 0)), (x*(I*a*tan(e) + a)/sqrt(-I*c*tan(e) + c), True))","A",0
977,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{1}{\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}{a}"," ",0,"-I*Integral(1/(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
978,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{1}{\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(1/(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
979,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{1}{\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}{a^{3}}"," ",0,"I*Integral(1/(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
980,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int \frac{i}{- 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 \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{\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 i \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,"-I*a**3*(Integral(I/(-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*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(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*I*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
981,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \frac{\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{2 i \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{1}{- 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(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(-2*I*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(-1/(-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
982,1,46,0,24.298172," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","\begin{cases} - \frac{2 i a}{3 f \left(- i c \tan{\left(e + f x \right)} + c\right)^{\frac{3}{2}}} & \text{for}\: f \neq 0 \\\frac{x \left(i a \tan{\left(e \right)} + a\right)}{\left(- i c \tan{\left(e \right)} + c\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*a/(3*f*(-I*c*tan(e + f*x) + c)**(3/2)), Ne(f, 0)), (x*(I*a*tan(e) + a)/(-I*c*tan(e) + c)**(3/2), True))","A",0
983,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(3/2),x)","- \frac{i \int \frac{1}{- 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}{a}"," ",0,"-I*Integral(1/(-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
984,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(3/2),x)","- \frac{\int \frac{1}{- 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(1/(-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
985,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(3/2),x)","\frac{i \int \frac{1}{- 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}{a^{3}}"," ",0,"I*Integral(1/(-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
986,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int \frac{i}{- 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 \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{\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 i \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,"-I*a**3*(Integral(I/(-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*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(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*I*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
987,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \frac{\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{2 i \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{1}{- 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(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(-2*I*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(-1/(-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
988,1,46,0,13.268633," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","\begin{cases} - \frac{2 i a}{5 f \left(- i c \tan{\left(e + f x \right)} + c\right)^{\frac{5}{2}}} & \text{for}\: f \neq 0 \\\frac{x \left(i a \tan{\left(e \right)} + a\right)}{\left(- i c \tan{\left(e \right)} + c\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*I*a/(5*f*(-I*c*tan(e + f*x) + c)**(5/2)), Ne(f, 0)), (x*(I*a*tan(e) + a)/(-I*c*tan(e) + c)**(5/2), True))","A",0
989,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))**(5/2),x)","- \frac{i \int \frac{1}{- 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}{a}"," ",0,"-I*Integral(1/(-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
990,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c-I*c*tan(f*x+e))**(5/2),x)","- \frac{\int \frac{1}{- 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(1/(-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
991,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c-I*c*tan(f*x+e))**(5/2),x)","\frac{i \int \frac{1}{- 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}{a^{3}}"," ",0,"I*Integral(1/(-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
992,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(5/2),x)","\int \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((I*a*(tan(e + f*x) - I))**(5/2)*sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
993,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(3/2),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)}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
994,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(1/2),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)}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
995,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(-I*c*(tan(e + f*x) + I))/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
996,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(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(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))/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
997,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(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(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))/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
998,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
999,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1000,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(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}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1001,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(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}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1002,0,0,0,0.000000," ","integrate((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}}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((-I*c*(tan(e + f*x) + I))**(3/2)/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
1003,0,0,0,0.000000," ","integrate((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(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)/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
1004,0,0,0,0.000000," ","integrate((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(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)/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
1005,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1006,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1007,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1008,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1009,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(c-I*c*tan(f*x+e))**(5/2),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{5}{2}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
1010,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(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{5}{2}}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((-I*c*(tan(e + f*x) + I))**(5/2)/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
1011,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(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{5}{2}}}{\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))**(5/2)/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
1012,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(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{5}{2}}}{\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))**(5/2)/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
1013,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1014,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1015,-1,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1016,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)/(c-I*c*tan(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1017,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(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}}}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
1018,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(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}}}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
1019,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(1/2),x)","\int \frac{\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(sqrt(I*a*(tan(e + f*x) - I))/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
1020,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{1}{\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(1/(sqrt(I*a*(tan(e + f*x) - I))*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
1021,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
1022,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(5/2)*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
1023,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(7/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{7}{2}} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(7/2)*sqrt(-I*c*(tan(e + f*x) + I))), x)","F",0
1024,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(9/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1025,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(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(- 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)/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1027,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(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(- 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)/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1028,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(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(- 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))/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1029,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
1030,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(3/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
1031,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(5/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(5/2)*(-I*c*(tan(e + f*x) + I))**(3/2)), x)","F",0
1032,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(7/2)/(c-I*c*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(11/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1034,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(9/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1035,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(7/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(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(- 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)/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
1037,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(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(- 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)/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
1038,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(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(- 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))/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
1039,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(1/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{1}{\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(1/(sqrt(I*a*(tan(e + f*x) - I))*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
1040,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(3/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(3/2)*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
1041,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(5/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\int \frac{1}{\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(1/((I*a*(tan(e + f*x) - I))**(5/2)*(-I*c*(tan(e + f*x) + I))**(5/2)), x)","F",0
1042,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(7/2)/(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1043,1,2244,0,6.522599," ","integrate((a+I*a*tan(f*x+e))**4*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \left(i a \tan{\left(e \right)} + a\right)^{4} \left(- i c \tan{\left(e \right)} + c\right)^{n} & \text{for}\: f = 0 \\\frac{6 a^{4} f x \tan^{3}{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} + \frac{18 i a^{4} f x \tan^{2}{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{18 a^{4} f x \tan{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{6 i a^{4} f x}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} + \frac{3 i a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{3}{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{9 a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{9 i a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} + \frac{3 a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{36 a^{4} \tan^{2}{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} - \frac{36 i a^{4} \tan{\left(e + f x \right)}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} + \frac{16 a^{4}}{- 6 c^{3} f \tan^{3}{\left(e + f x \right)} - 18 i c^{3} f \tan^{2}{\left(e + f x \right)} + 18 c^{3} f \tan{\left(e + f x \right)} + 6 i c^{3} f} & \text{for}\: n = -3 \\\frac{6 i a^{4} f x \tan^{2}{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{12 a^{4} f x \tan{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{6 i a^{4} f x}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{3 a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{6 i a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} + \frac{3 a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{i a^{4} \tan^{3}{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} - \frac{15 i a^{4} \tan{\left(e + f x \right)}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} + \frac{10 a^{4}}{i c^{2} f \tan^{2}{\left(e + f x \right)} - 2 c^{2} f \tan{\left(e + f x \right)} - i c^{2} f} & \text{for}\: n = -2 \\\frac{24 i a^{4} f x \tan{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{24 a^{4} f x}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{12 a^{4} \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{12 i a^{4} \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{a^{4} \tan^{3}{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{9 i a^{4} \tan^{2}{\left(e + f x \right)}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} - \frac{26 i a^{4}}{- 2 i c f \tan{\left(e + f x \right)} + 2 c f} & \text{for}\: n = -1 \\8 a^{4} x + \frac{4 i a^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{a^{4} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 i a^{4} \tan^{2}{\left(e + f x \right)}}{f} - \frac{7 a^{4} \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\\frac{a^{4} 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{3 i a^{4} 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{3 a^{4} 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^{4} 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{3 a^{4} 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{15 i a^{4} 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{21 a^{4} 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{9 i a^{4} 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 a^{4} 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{12 i a^{4} 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{42 a^{4} 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{32 i a^{4} 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{48 i a^{4} \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*(I*a*tan(e) + a)**4*(-I*c*tan(e) + c)**n, Eq(f, 0)), (6*a**4*f*x*tan(e + f*x)**3/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) + 18*I*a**4*f*x*tan(e + f*x)**2/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 18*a**4*f*x*tan(e + f*x)/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 6*I*a**4*f*x/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) + 3*I*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**3/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 9*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 9*I*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) + 3*a**4*log(tan(e + f*x)**2 + 1)/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 36*a**4*tan(e + f*x)**2/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) - 36*I*a**4*tan(e + f*x)/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f) + 16*a**4/(-6*c**3*f*tan(e + f*x)**3 - 18*I*c**3*f*tan(e + f*x)**2 + 18*c**3*f*tan(e + f*x) + 6*I*c**3*f), Eq(n, -3)), (6*I*a**4*f*x*tan(e + f*x)**2/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - 12*a**4*f*x*tan(e + f*x)/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - 6*I*a**4*f*x/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - 3*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - 6*I*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) + 3*a**4*log(tan(e + f*x)**2 + 1)/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - I*a**4*tan(e + f*x)**3/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) - 15*I*a**4*tan(e + f*x)/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f) + 10*a**4/(I*c**2*f*tan(e + f*x)**2 - 2*c**2*f*tan(e + f*x) - I*c**2*f), Eq(n, -2)), (24*I*a**4*f*x*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 24*a**4*f*x/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 12*a**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 12*I*a**4*log(tan(e + f*x)**2 + 1)/(-2*I*c*f*tan(e + f*x) + 2*c*f) + a**4*tan(e + f*x)**3/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 9*I*a**4*tan(e + f*x)**2/(-2*I*c*f*tan(e + f*x) + 2*c*f) - 26*I*a**4/(-2*I*c*f*tan(e + f*x) + 2*c*f), Eq(n, -1)), (8*a**4*x + 4*I*a**4*log(tan(e + f*x)**2 + 1)/f + a**4*tan(e + f*x)**3/(3*f) - 2*I*a**4*tan(e + f*x)**2/f - 7*a**4*tan(e + f*x)/f, Eq(n, 0)), (a**4*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) - 3*I*a**4*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) - 3*a**4*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**4*n**3*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 3*a**4*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) - 15*I*a**4*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) - 21*a**4*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) + 9*I*a**4*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*a**4*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) - 12*I*a**4*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) - 42*a**4*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) + 32*I*a**4*n*(-I*c*tan(e + f*x) + c)**n/(f*n**4 + 6*f*n**3 + 11*f*n**2 + 6*f*n) + 48*I*a**4*(-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
1044,1,993,0,2.894306," ","integrate((a+I*a*tan(f*x+e))**3*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \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{2 i a^{3} f x \tan^{2}{\left(e + f x \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} + \frac{4 a^{3} f x \tan{\left(e + f x \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} + \frac{2 i a^{3} f x}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} + \frac{a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} + \frac{2 i a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} - \frac{a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} + \frac{8 i a^{3} \tan{\left(e + f x \right)}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} - \frac{4 a^{3}}{- 2 i c^{2} f \tan^{2}{\left(e + f x \right)} + 4 c^{2} f \tan{\left(e + f x \right)} + 2 i c^{2} f} & \text{for}\: n = -2 \\- \frac{4 a^{3} f x \tan{\left(e + f x \right)}}{c f \tan{\left(e + f x \right)} + i c f} - \frac{4 i a^{3} f x}{c f \tan{\left(e + f x \right)} + i c f} - \frac{2 i a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c f \tan{\left(e + f x \right)} + i c f} + \frac{2 a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c f \tan{\left(e + f x \right)} + i c f} + \frac{a^{3} \tan^{2}{\left(e + f x \right)}}{c f \tan{\left(e + f x \right)} + i c f} + \frac{5 a^{3}}{c f \tan{\left(e + f x \right)} + i c f} & \text{for}\: n = -1 \\4 a^{3} x + \frac{2 i a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{i a^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{3 a^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\- \frac{i 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^{3} + 3 f n^{2} + 2 f n} - \frac{2 a^{3} 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^{3} 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{i a^{3} 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{6 a^{3} 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{5 i a^{3} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{3} + 3 f n^{2} + 2 f n} + \frac{8 i a^{3} \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*(I*a*tan(e) + a)**3*(-I*c*tan(e) + c)**n, Eq(f, 0)), (-2*I*a**3*f*x*tan(e + f*x)**2/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) + 4*a**3*f*x*tan(e + f*x)/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) + 2*I*a**3*f*x/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) + a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) + 2*I*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) - a**3*log(tan(e + f*x)**2 + 1)/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) + 8*I*a**3*tan(e + f*x)/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f) - 4*a**3/(-2*I*c**2*f*tan(e + f*x)**2 + 4*c**2*f*tan(e + f*x) + 2*I*c**2*f), Eq(n, -2)), (-4*a**3*f*x*tan(e + f*x)/(c*f*tan(e + f*x) + I*c*f) - 4*I*a**3*f*x/(c*f*tan(e + f*x) + I*c*f) - 2*I*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c*f*tan(e + f*x) + I*c*f) + 2*a**3*log(tan(e + f*x)**2 + 1)/(c*f*tan(e + f*x) + I*c*f) + a**3*tan(e + f*x)**2/(c*f*tan(e + f*x) + I*c*f) + 5*a**3/(c*f*tan(e + f*x) + I*c*f), Eq(n, -1)), (4*a**3*x + 2*I*a**3*log(tan(e + f*x)**2 + 1)/f - I*a**3*tan(e + f*x)**2/(2*f) - 3*a**3*tan(e + f*x)/f, Eq(n, 0)), (-I*a**3*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) - 2*a**3*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**3*n**2*(-I*c*tan(e + f*x) + c)**n/(f*n**3 + 3*f*n**2 + 2*f*n) - I*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)**2/(f*n**3 + 3*f*n**2 + 2*f*n) - 6*a**3*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**3 + 3*f*n**2 + 2*f*n) + 5*I*a**3*n*(-I*c*tan(e + f*x) + c)**n/(f*n**3 + 3*f*n**2 + 2*f*n) + 8*I*a**3*(-I*c*tan(e + f*x) + c)**n/(f*n**3 + 3*f*n**2 + 2*f*n), True))","A",0
1045,1,320,0,1.315481," ","integrate((a+I*a*tan(f*x+e))**2*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \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^{2} f x \tan{\left(e + f x \right)}}{- 2 c f \tan{\left(e + f x \right)} - 2 i c f} + \frac{2 i a^{2} f x}{- 2 c f \tan{\left(e + f x \right)} - 2 i c f} + \frac{i a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 c f \tan{\left(e + f x \right)} - 2 i c f} - \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 c f \tan{\left(e + f x \right)} - 2 i c f} - \frac{4 a^{2}}{- 2 c f \tan{\left(e + f x \right)} - 2 i c f} & \text{for}\: n = -1 \\2 a^{2} x + \frac{i a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{a^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: n = 0 \\- \frac{a^{2} 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{i a^{2} n \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{2} + f n} + \frac{2 i a^{2} \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n^{2} + f n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(I*a*tan(e) + a)**2*(-I*c*tan(e) + c)**n, Eq(f, 0)), (2*a**2*f*x*tan(e + f*x)/(-2*c*f*tan(e + f*x) - 2*I*c*f) + 2*I*a**2*f*x/(-2*c*f*tan(e + f*x) - 2*I*c*f) + I*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*c*f*tan(e + f*x) - 2*I*c*f) - a**2*log(tan(e + f*x)**2 + 1)/(-2*c*f*tan(e + f*x) - 2*I*c*f) - 4*a**2/(-2*c*f*tan(e + f*x) - 2*I*c*f), Eq(n, -1)), (2*a**2*x + I*a**2*log(tan(e + f*x)**2 + 1)/f - a**2*tan(e + f*x)/f, Eq(n, 0)), (-a**2*n*(-I*c*tan(e + f*x) + c)**n*tan(e + f*x)/(f*n**2 + f*n) + I*a**2*n*(-I*c*tan(e + f*x) + c)**n/(f*n**2 + f*n) + 2*I*a**2*(-I*c*tan(e + f*x) + c)**n/(f*n**2 + f*n), True))","A",0
1046,1,70,0,0.470392," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))**n,x)","\begin{cases} x \left(i a \tan{\left(e \right)} + a\right) & \text{for}\: f = 0 \wedge n = 0 \\x \left(i a \tan{\left(e \right)} + a\right) \left(- i c \tan{\left(e \right)} + c\right)^{n} & \text{for}\: f = 0 \\a x + \frac{i a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} & \text{for}\: n = 0 \\\frac{i a \left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{f n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(I*a*tan(e) + a), Eq(f, 0) & Eq(n, 0)), (x*(I*a*tan(e) + a)*(-I*c*tan(e) + c)**n, Eq(f, 0)), (a*x + I*a*log(tan(e + f*x)**2 + 1)/(2*f), Eq(n, 0)), (I*a*(-I*c*tan(e + f*x) + c)**n/(f*n), True))","A",0
1047,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(- i c \tan{\left(e + f x \right)} + c\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((-I*c*tan(e + f*x) + c)**n/(tan(e + f*x) - I), x)/a","F",0
1048,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\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}{a^{2}}"," ",0,"-Integral((-I*c*tan(e + f*x) + c)**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
1049,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\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}{a^{3}}"," ",0,"I*Integral((-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)/a**3","F",0
1050,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(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}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(-I*c*(tan(e + f*x) + I))**n, x)","F",0
1051,1,2244,0,6.373924," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**4,x)","\begin{cases} x \left(i a \tan{\left(e \right)} + a\right)^{m} \left(- i c \tan{\left(e \right)} + c\right)^{4} & \text{for}\: f = 0 \\\frac{6 c^{4} f x \tan^{3}{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} - \frac{18 i c^{4} f x \tan^{2}{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} - \frac{18 c^{4} f x \tan{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} + \frac{6 i c^{4} f x}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} - \frac{3 i c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{3}{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} - \frac{9 c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} + \frac{9 i c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} + \frac{3 c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} - \frac{36 c^{4} \tan^{2}{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} + \frac{36 i c^{4} \tan{\left(e + f x \right)}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} + \frac{16 c^{4}}{- 6 a^{3} f \tan^{3}{\left(e + f x \right)} + 18 i a^{3} f \tan^{2}{\left(e + f x \right)} + 18 a^{3} f \tan{\left(e + f x \right)} - 6 i a^{3} f} & \text{for}\: m = -3 \\- \frac{6 i c^{4} f x \tan^{2}{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} - \frac{12 c^{4} f x \tan{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{6 i c^{4} f x}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} - \frac{3 c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{6 i c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{3 c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{i c^{4} \tan^{3}{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{15 i c^{4} \tan{\left(e + f x \right)}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} + \frac{10 c^{4}}{- i a^{2} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} f \tan{\left(e + f x \right)} + i a^{2} f} & \text{for}\: m = -2 \\- \frac{24 i c^{4} f x \tan{\left(e + f x \right)}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} - \frac{24 c^{4} f x}{2 i a f \tan{\left(e + f x \right)} + 2 a f} - \frac{12 c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} + \frac{12 i c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} + \frac{c^{4} \tan^{3}{\left(e + f x \right)}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} + \frac{9 i c^{4} \tan^{2}{\left(e + f x \right)}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} + \frac{26 i c^{4}}{2 i a f \tan{\left(e + f x \right)} + 2 a f} & \text{for}\: m = -1 \\8 c^{4} x - \frac{4 i c^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{c^{4} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{2 i c^{4} \tan^{2}{\left(e + f x \right)}}{f} - \frac{7 c^{4} \tan{\left(e + f x \right)}}{f} & \text{for}\: m = 0 \\\frac{c^{4} m^{3} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{3}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} + \frac{3 i c^{4} m^{3} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{2}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{3 c^{4} m^{3} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{i c^{4} m^{3} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} + \frac{3 c^{4} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{3}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} + \frac{15 i c^{4} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{2}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{21 c^{4} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{9 i c^{4} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} + \frac{2 c^{4} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{3}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} + \frac{12 i c^{4} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{2}{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{42 c^{4} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{32 i c^{4} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} - \frac{48 i c^{4} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 6 f m^{3} + 11 f m^{2} + 6 f m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(I*a*tan(e) + a)**m*(-I*c*tan(e) + c)**4, Eq(f, 0)), (6*c**4*f*x*tan(e + f*x)**3/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) - 18*I*c**4*f*x*tan(e + f*x)**2/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) - 18*c**4*f*x*tan(e + f*x)/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) + 6*I*c**4*f*x/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) - 3*I*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**3/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) - 9*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) + 9*I*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) + 3*c**4*log(tan(e + f*x)**2 + 1)/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) - 36*c**4*tan(e + f*x)**2/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) + 36*I*c**4*tan(e + f*x)/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f) + 16*c**4/(-6*a**3*f*tan(e + f*x)**3 + 18*I*a**3*f*tan(e + f*x)**2 + 18*a**3*f*tan(e + f*x) - 6*I*a**3*f), Eq(m, -3)), (-6*I*c**4*f*x*tan(e + f*x)**2/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) - 12*c**4*f*x*tan(e + f*x)/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + 6*I*c**4*f*x/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) - 3*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + 6*I*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + 3*c**4*log(tan(e + f*x)**2 + 1)/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + I*c**4*tan(e + f*x)**3/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + 15*I*c**4*tan(e + f*x)/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f) + 10*c**4/(-I*a**2*f*tan(e + f*x)**2 - 2*a**2*f*tan(e + f*x) + I*a**2*f), Eq(m, -2)), (-24*I*c**4*f*x*tan(e + f*x)/(2*I*a*f*tan(e + f*x) + 2*a*f) - 24*c**4*f*x/(2*I*a*f*tan(e + f*x) + 2*a*f) - 12*c**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*a*f*tan(e + f*x) + 2*a*f) + 12*I*c**4*log(tan(e + f*x)**2 + 1)/(2*I*a*f*tan(e + f*x) + 2*a*f) + c**4*tan(e + f*x)**3/(2*I*a*f*tan(e + f*x) + 2*a*f) + 9*I*c**4*tan(e + f*x)**2/(2*I*a*f*tan(e + f*x) + 2*a*f) + 26*I*c**4/(2*I*a*f*tan(e + f*x) + 2*a*f), Eq(m, -1)), (8*c**4*x - 4*I*c**4*log(tan(e + f*x)**2 + 1)/f + c**4*tan(e + f*x)**3/(3*f) + 2*I*c**4*tan(e + f*x)**2/f - 7*c**4*tan(e + f*x)/f, Eq(m, 0)), (c**4*m**3*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**3/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) + 3*I*c**4*m**3*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**2/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 3*c**4*m**3*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - I*c**4*m**3*(I*a*tan(e + f*x) + a)**m/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) + 3*c**4*m**2*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**3/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) + 15*I*c**4*m**2*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**2/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 21*c**4*m**2*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 9*I*c**4*m**2*(I*a*tan(e + f*x) + a)**m/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) + 2*c**4*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**3/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) + 12*I*c**4*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**2/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 42*c**4*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 32*I*c**4*m*(I*a*tan(e + f*x) + a)**m/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m) - 48*I*c**4*(I*a*tan(e + f*x) + a)**m/(f*m**4 + 6*f*m**3 + 11*f*m**2 + 6*f*m), True))","A",0
1052,1,993,0,2.806443," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**3,x)","\begin{cases} x \left(i a \tan{\left(e \right)} + a\right)^{m} \left(- i c \tan{\left(e \right)} + c\right)^{3} & \text{for}\: f = 0 \\\frac{2 i c^{3} f x \tan^{2}{\left(e + f x \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} + \frac{4 c^{3} f x \tan{\left(e + f x \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} - \frac{2 i c^{3} f x}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} + \frac{c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} - \frac{2 i c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} - \frac{c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} - \frac{8 i c^{3} \tan{\left(e + f x \right)}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} - \frac{4 c^{3}}{2 i a^{2} f \tan^{2}{\left(e + f x \right)} + 4 a^{2} f \tan{\left(e + f x \right)} - 2 i a^{2} f} & \text{for}\: m = -2 \\- \frac{4 c^{3} f x \tan{\left(e + f x \right)}}{a f \tan{\left(e + f x \right)} - i a f} + \frac{4 i c^{3} f x}{a f \tan{\left(e + f x \right)} - i a f} + \frac{2 i c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{a f \tan{\left(e + f x \right)} - i a f} + \frac{2 c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{a f \tan{\left(e + f x \right)} - i a f} + \frac{c^{3} \tan^{2}{\left(e + f x \right)}}{a f \tan{\left(e + f x \right)} - i a f} + \frac{5 c^{3}}{a f \tan{\left(e + f x \right)} - i a f} & \text{for}\: m = -1 \\4 c^{3} x - \frac{2 i c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{i c^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{3 c^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: m = 0 \\\frac{i c^{3} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{2}{\left(e + f x \right)}}{f m^{3} + 3 f m^{2} + 2 f m} - \frac{2 c^{3} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{3} + 3 f m^{2} + 2 f m} - \frac{i c^{3} m^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 3 f m^{2} + 2 f m} + \frac{i c^{3} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan^{2}{\left(e + f x \right)}}{f m^{3} + 3 f m^{2} + 2 f m} - \frac{6 c^{3} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{3} + 3 f m^{2} + 2 f m} - \frac{5 i c^{3} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 3 f m^{2} + 2 f m} - \frac{8 i c^{3} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 3 f m^{2} + 2 f m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(I*a*tan(e) + a)**m*(-I*c*tan(e) + c)**3, Eq(f, 0)), (2*I*c**3*f*x*tan(e + f*x)**2/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) + 4*c**3*f*x*tan(e + f*x)/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) - 2*I*c**3*f*x/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) + c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) - 2*I*c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) - c**3*log(tan(e + f*x)**2 + 1)/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) - 8*I*c**3*tan(e + f*x)/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f) - 4*c**3/(2*I*a**2*f*tan(e + f*x)**2 + 4*a**2*f*tan(e + f*x) - 2*I*a**2*f), Eq(m, -2)), (-4*c**3*f*x*tan(e + f*x)/(a*f*tan(e + f*x) - I*a*f) + 4*I*c**3*f*x/(a*f*tan(e + f*x) - I*a*f) + 2*I*c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(a*f*tan(e + f*x) - I*a*f) + 2*c**3*log(tan(e + f*x)**2 + 1)/(a*f*tan(e + f*x) - I*a*f) + c**3*tan(e + f*x)**2/(a*f*tan(e + f*x) - I*a*f) + 5*c**3/(a*f*tan(e + f*x) - I*a*f), Eq(m, -1)), (4*c**3*x - 2*I*c**3*log(tan(e + f*x)**2 + 1)/f + I*c**3*tan(e + f*x)**2/(2*f) - 3*c**3*tan(e + f*x)/f, Eq(m, 0)), (I*c**3*m**2*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**2/(f*m**3 + 3*f*m**2 + 2*f*m) - 2*c**3*m**2*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**3 + 3*f*m**2 + 2*f*m) - I*c**3*m**2*(I*a*tan(e + f*x) + a)**m/(f*m**3 + 3*f*m**2 + 2*f*m) + I*c**3*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)**2/(f*m**3 + 3*f*m**2 + 2*f*m) - 6*c**3*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**3 + 3*f*m**2 + 2*f*m) - 5*I*c**3*m*(I*a*tan(e + f*x) + a)**m/(f*m**3 + 3*f*m**2 + 2*f*m) - 8*I*c**3*(I*a*tan(e + f*x) + a)**m/(f*m**3 + 3*f*m**2 + 2*f*m), True))","A",0
1053,1,313,0,1.218613," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**2,x)","\begin{cases} x \left(i a \tan{\left(e \right)} + a\right)^{m} \left(- i c \tan{\left(e \right)} + c\right)^{2} & \text{for}\: f = 0 \\\frac{2 c^{2} f x \tan{\left(e + f x \right)}}{- 2 a f \tan{\left(e + f x \right)} + 2 i a f} - \frac{2 i c^{2} f x}{- 2 a f \tan{\left(e + f x \right)} + 2 i a f} - \frac{i c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 a f \tan{\left(e + f x \right)} + 2 i a f} - \frac{c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 a f \tan{\left(e + f x \right)} + 2 i a f} - \frac{4 c^{2}}{- 2 a f \tan{\left(e + f x \right)} + 2 i a f} & \text{for}\: m = -1 \\2 c^{2} x - \frac{i c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{c^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: m = 0 \\- \frac{c^{2} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m} \tan{\left(e + f x \right)}}{f m^{2} + f m} - \frac{i c^{2} m \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + f m} - \frac{2 i c^{2} \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + f m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(I*a*tan(e) + a)**m*(-I*c*tan(e) + c)**2, Eq(f, 0)), (2*c**2*f*x*tan(e + f*x)/(-2*a*f*tan(e + f*x) + 2*I*a*f) - 2*I*c**2*f*x/(-2*a*f*tan(e + f*x) + 2*I*a*f) - I*c**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*a*f*tan(e + f*x) + 2*I*a*f) - c**2*log(tan(e + f*x)**2 + 1)/(-2*a*f*tan(e + f*x) + 2*I*a*f) - 4*c**2/(-2*a*f*tan(e + f*x) + 2*I*a*f), Eq(m, -1)), (2*c**2*x - I*c**2*log(tan(e + f*x)**2 + 1)/f - c**2*tan(e + f*x)/f, Eq(m, 0)), (-c**2*m*(I*a*tan(e + f*x) + a)**m*tan(e + f*x)/(f*m**2 + f*m) - I*c**2*m*(I*a*tan(e + f*x) + a)**m/(f*m**2 + f*m) - 2*I*c**2*(I*a*tan(e + f*x) + a)**m/(f*m**2 + f*m), True))","A",0
1054,1,71,0,0.471334," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e)),x)","\begin{cases} x \left(- i c \tan{\left(e \right)} + c\right) & \text{for}\: f = 0 \wedge m = 0 \\x \left(i a \tan{\left(e \right)} + a\right)^{m} \left(- i c \tan{\left(e \right)} + c\right) & \text{for}\: f = 0 \\c x - \frac{i c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} & \text{for}\: m = 0 \\- \frac{i c \left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{f m} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(-I*c*tan(e) + c), Eq(f, 0) & Eq(m, 0)), (x*(I*a*tan(e) + a)**m*(-I*c*tan(e) + c), Eq(f, 0)), (c*x - I*c*log(tan(e + f*x)**2 + 1)/(2*f), Eq(m, 0)), (-I*c*(I*a*tan(e + f*x) + a)**m/(f*m), True))","A",0
1055,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c-I*c*tan(f*x+e)),x)","\frac{i \int \frac{\left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{\tan{\left(e + f x \right)} + i}\, dx}{c}"," ",0,"I*Integral((I*a*tan(e + f*x) + a)**m/(tan(e + f*x) + I), x)/c","F",0
1056,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c-I*c*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{\tan^{2}{\left(e + f x \right)} + 2 i \tan{\left(e + f x \right)} - 1}\, dx}{c^{2}}"," ",0,"-Integral((I*a*tan(e + f*x) + a)**m/(tan(e + f*x)**2 + 2*I*tan(e + f*x) - 1), x)/c**2","F",0
1057,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c-I*c*tan(f*x+e))**3,x)","- \frac{i \int \frac{\left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{\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}{c^{3}}"," ",0,"-I*Integral((I*a*tan(e + f*x) + a)**m/(tan(e + f*x)**3 + 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) - I), x)/c**3","F",0
1058,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c-I*c*tan(f*x+e))**4,x)","\frac{\int \frac{\left(i a \tan{\left(e + f x \right)} + a\right)^{m}}{\tan^{4}{\left(e + f x \right)} + 4 i \tan^{3}{\left(e + f x \right)} - 6 \tan^{2}{\left(e + f x \right)} - 4 i \tan{\left(e + f x \right)} + 1}\, dx}{c^{4}}"," ",0,"Integral((I*a*tan(e + f*x) + a)**m/(tan(e + f*x)**4 + 4*I*tan(e + f*x)**3 - 6*tan(e + f*x)**2 - 4*I*tan(e + f*x) + 1), x)/c**4","F",0
1059,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1060,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**(3/2),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)^{\frac{3}{2}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1061,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c-I*c*tan(f*x+e))**(1/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
1062,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(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)^{m}}{\sqrt{- i c \left(\tan{\left(e + f x \right)} + i\right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/sqrt(-I*c*(tan(e + f*x) + I)), x)","F",0
1063,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(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)^{m}}{\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))**m/(-I*c*(tan(e + f*x) + I))**(3/2), x)","F",0
1064,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(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)^{m}}{\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))**m/(-I*c*(tan(e + f*x) + I))**(5/2), x)","F",0
1065,1,187,0,0.736144," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e)),x)","- \frac{4 i a^{3} \left(c - i d\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{18 a^{3} c - 26 i a^{3} d + \left(42 a^{3} c e^{2 i e} - 66 i a^{3} d e^{2 i e}\right) e^{2 i f x} + \left(24 a^{3} c e^{4 i e} - 48 i a^{3} d 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*(c - I*d)*log(exp(2*I*f*x) + exp(-2*I*e))/f + (18*a**3*c - 26*I*a**3*d + (42*a**3*c*exp(2*I*e) - 66*I*a**3*d*exp(2*I*e))*exp(2*I*f*x) + (24*a**3*c*exp(4*I*e) - 48*I*a**3*d*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
1066,1,128,0,0.601728," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e)),x)","- \frac{2 i a^{2} \left(c - i d\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{- 2 a^{2} c + 4 i a^{2} d + \left(- 2 a^{2} c e^{2 i e} + 6 i a^{2} d 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*(c - I*d)*log(exp(2*I*f*x) + exp(-2*I*e))/f + (-2*a**2*c + 4*I*a**2*d + (-2*a**2*c*exp(2*I*e) + 6*I*a**2*d*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
1067,1,53,0,0.412165," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x)","\frac{2 a d}{- f e^{2 i e} e^{2 i f x} - f} - \frac{i a \left(c - i d\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f}"," ",0,"2*a*d/(-f*exp(2*I*e)*exp(2*I*f*x) - f) - I*a*(c - I*d)*log(exp(2*I*f*x) + exp(-2*I*e))/f","A",0
1068,1,90,0,0.262881," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x)","\begin{cases} - \frac{\left(- i c + d\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{c - i d}{2 a} + \frac{\left(c e^{2 i e} + c - i d e^{2 i e} + i d\right) e^{- 2 i e}}{2 a}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c + i d\right)}{2 a}"," ",0,"Piecewise((-(-I*c + d)*exp(-2*I*e)*exp(-2*I*f*x)/(4*a*f), Ne(4*a*f*exp(2*I*e), 0)), (x*(-(c - I*d)/(2*a) + (c*exp(2*I*e) + c - I*d*exp(2*I*e) + I*d)*exp(-2*I*e)/(2*a)), True)) - x*(-c + I*d)/(2*a)","A",0
1069,1,163,0,0.367889," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(16 i a^{2} c f e^{4 i e} e^{- 2 i f x} + \left(4 i a^{2} c f e^{2 i e} - 4 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{c - i d}{4 a^{2}} + \frac{\left(c e^{4 i e} + 2 c e^{2 i e} + c - i d e^{4 i e} + i d\right) e^{- 4 i e}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c + i d\right)}{4 a^{2}}"," ",0,"Piecewise(((16*I*a**2*c*f*exp(4*I*e)*exp(-2*I*f*x) + (4*I*a**2*c*f*exp(2*I*e) - 4*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*(-(c - I*d)/(4*a**2) + (c*exp(4*I*e) + 2*c*exp(2*I*e) + c - I*d*exp(4*I*e) + I*d)*exp(-4*I*e)/(4*a**2)), True)) - x*(-c + I*d)/(4*a**2)","A",0
1070,1,264,0,0.522120," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(\left(- 512 i a^{6} c f^{2} e^{6 i e} + 512 a^{6} d f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(- 2304 i a^{6} c f^{2} e^{8 i e} + 768 a^{6} d f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 4608 i a^{6} c f^{2} e^{10 i e} - 1536 a^{6} d 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{c - i d}{8 a^{3}} + \frac{\left(c e^{6 i e} + 3 c e^{4 i e} + 3 c e^{2 i e} + c - i d e^{6 i e} - i d e^{4 i e} + i d e^{2 i e} + i d\right) e^{- 6 i e}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c + i d\right)}{8 a^{3}}"," ",0,"Piecewise((-((-512*I*a**6*c*f**2*exp(6*I*e) + 512*a**6*d*f**2*exp(6*I*e))*exp(-6*I*f*x) + (-2304*I*a**6*c*f**2*exp(8*I*e) + 768*a**6*d*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-4608*I*a**6*c*f**2*exp(10*I*e) - 1536*a**6*d*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*(-(c - I*d)/(8*a**3) + (c*exp(6*I*e) + 3*c*exp(4*I*e) + 3*c*exp(2*I*e) + c - I*d*exp(6*I*e) - I*d*exp(4*I*e) + I*d*exp(2*I*e) + I*d)*exp(-6*I*e)/(8*a**3)), True)) - x*(-c + I*d)/(8*a**3)","A",0
1071,1,314,0,1.126725," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e))**2,x)","- \frac{4 i a^{3} \left(c - i d\right)^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{18 i a^{3} c^{2} + 52 a^{3} c d - 30 i a^{3} d^{2} + \left(60 i a^{3} c^{2} e^{2 i e} + 184 a^{3} c d e^{2 i e} - 108 i a^{3} d^{2} e^{2 i e}\right) e^{2 i f x} + \left(66 i a^{3} c^{2} e^{4 i e} + 228 a^{3} c d e^{4 i e} - 138 i a^{3} d^{2} e^{4 i e}\right) e^{4 i f x} + \left(24 i a^{3} c^{2} e^{6 i e} + 96 a^{3} c d e^{6 i e} - 72 i a^{3} d^{2} 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,"-4*I*a**3*(c - I*d)**2*log(exp(2*I*f*x) + exp(-2*I*e))/f + (18*I*a**3*c**2 + 52*a**3*c*d - 30*I*a**3*d**2 + (60*I*a**3*c**2*exp(2*I*e) + 184*a**3*c*d*exp(2*I*e) - 108*I*a**3*d**2*exp(2*I*e))*exp(2*I*f*x) + (66*I*a**3*c**2*exp(4*I*e) + 228*a**3*c*d*exp(4*I*e) - 138*I*a**3*d**2*exp(4*I*e))*exp(4*I*f*x) + (24*I*a**3*c**2*exp(6*I*e) + 96*a**3*c*d*exp(6*I*e) - 72*I*a**3*d**2*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
1072,1,236,0,0.855619," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e))**2,x)","- \frac{2 i a^{2} \left(c - i d\right)^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{- 6 i a^{2} c^{2} - 24 a^{2} c d + 14 i a^{2} d^{2} + \left(- 12 i a^{2} c^{2} e^{2 i e} - 60 a^{2} c d e^{2 i e} + 36 i a^{2} d^{2} e^{2 i e}\right) e^{2 i f x} + \left(- 6 i a^{2} c^{2} e^{4 i e} - 36 a^{2} c d e^{4 i e} + 30 i a^{2} d^{2} e^{4 i e}\right) e^{4 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,"-2*I*a**2*(c - I*d)**2*log(exp(2*I*f*x) + exp(-2*I*e))/f + (-6*I*a**2*c**2 - 24*a**2*c*d + 14*I*a**2*d**2 + (-12*I*a**2*c**2*exp(2*I*e) - 60*a**2*c*d*exp(2*I*e) + 36*I*a**2*d**2*exp(2*I*e))*exp(2*I*f*x) + (-6*I*a**2*c**2*exp(4*I*e) - 36*a**2*c*d*exp(4*I*e) + 30*I*a**2*d**2*exp(4*I*e))*exp(4*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
1073,1,126,0,0.668979," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))**2,x)","- \frac{i a \left(c - i d\right)^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{- 4 i a c d - 2 a d^{2} + \left(- 4 i a c d e^{2 i e} - 4 a d^{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,"-I*a*(c - I*d)**2*log(exp(2*I*f*x) + exp(-2*I*e))/f + (-4*I*a*c*d - 2*a*d**2 + (-4*I*a*c*d*exp(2*I*e) - 4*a*d**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
1074,1,173,0,0.528899," ","integrate((c+d*tan(f*x+e))**2/(a+I*a*tan(f*x+e)),x)","\begin{cases} - \frac{\left(- i c^{2} + 2 c d + i d^{2}\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{c^{2} - 2 i c d + 3 d^{2}}{2 a} + \frac{\left(c^{2} e^{2 i e} + c^{2} - 2 i c d e^{2 i e} + 2 i c d + 3 d^{2} e^{2 i e} - d^{2}\right) e^{- 2 i e}}{2 a}\right) & \text{otherwise} \end{cases} + \frac{i d^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} - \frac{x \left(- c^{2} + 2 i c d - 3 d^{2}\right)}{2 a}"," ",0,"Piecewise((-(-I*c**2 + 2*c*d + I*d**2)*exp(-2*I*e)*exp(-2*I*f*x)/(4*a*f), Ne(4*a*f*exp(2*I*e), 0)), (x*(-(c**2 - 2*I*c*d + 3*d**2)/(2*a) + (c**2*exp(2*I*e) + c**2 - 2*I*c*d*exp(2*I*e) + 2*I*c*d + 3*d**2*exp(2*I*e) - d**2)*exp(-2*I*e)/(2*a)), True)) + I*d**2*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) - x*(-c**2 + 2*I*c*d - 3*d**2)/(2*a)","A",0
1075,1,260,0,0.481629," ","integrate((c+d*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(\left(16 i a^{2} c^{2} f e^{4 i e} + 16 i a^{2} d^{2} f e^{4 i e}\right) e^{- 2 i f x} + \left(4 i a^{2} c^{2} f e^{2 i e} - 8 a^{2} c d f e^{2 i e} - 4 i a^{2} d^{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{c^{2} - 2 i c d - d^{2}}{4 a^{2}} + \frac{\left(c^{2} e^{4 i e} + 2 c^{2} e^{2 i e} + c^{2} - 2 i c d e^{4 i e} + 2 i c d - d^{2} e^{4 i e} + 2 d^{2} e^{2 i e} - d^{2}\right) e^{- 4 i e}}{4 a^{2}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c^{2} + 2 i c d + d^{2}\right)}{4 a^{2}}"," ",0,"Piecewise((((16*I*a**2*c**2*f*exp(4*I*e) + 16*I*a**2*d**2*f*exp(4*I*e))*exp(-2*I*f*x) + (4*I*a**2*c**2*f*exp(2*I*e) - 8*a**2*c*d*f*exp(2*I*e) - 4*I*a**2*d**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*(-(c**2 - 2*I*c*d - d**2)/(4*a**2) + (c**2*exp(4*I*e) + 2*c**2*exp(2*I*e) + c**2 - 2*I*c*d*exp(4*I*e) + 2*I*c*d - d**2*exp(4*I*e) + 2*d**2*exp(2*I*e) - d**2)*exp(-4*I*e)/(4*a**2)), True)) - x*(-c**2 + 2*I*c*d + d**2)/(4*a**2)","A",0
1076,1,406,0,0.864932," ","integrate((c+d*tan(f*x+e))**2/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(\left(- 512 i a^{6} c^{2} f^{2} e^{6 i e} + 1024 a^{6} c d f^{2} e^{6 i e} + 512 i a^{6} d^{2} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(- 2304 i a^{6} c^{2} f^{2} e^{8 i e} + 1536 a^{6} c d f^{2} e^{8 i e} - 768 i a^{6} d^{2} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 4608 i a^{6} c^{2} f^{2} e^{10 i e} - 3072 a^{6} c d f^{2} e^{10 i e} - 1536 i a^{6} d^{2} 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{c^{2} - 2 i c d - d^{2}}{8 a^{3}} + \frac{\left(c^{2} e^{6 i e} + 3 c^{2} e^{4 i e} + 3 c^{2} e^{2 i e} + c^{2} - 2 i c d e^{6 i e} - 2 i c d e^{4 i e} + 2 i c d e^{2 i e} + 2 i c d - d^{2} e^{6 i e} + d^{2} e^{4 i e} + d^{2} e^{2 i e} - d^{2}\right) e^{- 6 i e}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c^{2} + 2 i c d + d^{2}\right)}{8 a^{3}}"," ",0,"Piecewise((-((-512*I*a**6*c**2*f**2*exp(6*I*e) + 1024*a**6*c*d*f**2*exp(6*I*e) + 512*I*a**6*d**2*f**2*exp(6*I*e))*exp(-6*I*f*x) + (-2304*I*a**6*c**2*f**2*exp(8*I*e) + 1536*a**6*c*d*f**2*exp(8*I*e) - 768*I*a**6*d**2*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-4608*I*a**6*c**2*f**2*exp(10*I*e) - 3072*a**6*c*d*f**2*exp(10*I*e) - 1536*I*a**6*d**2*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*(-(c**2 - 2*I*c*d - d**2)/(8*a**3) + (c**2*exp(6*I*e) + 3*c**2*exp(4*I*e) + 3*c**2*exp(2*I*e) + c**2 - 2*I*c*d*exp(6*I*e) - 2*I*c*d*exp(4*I*e) + 2*I*c*d*exp(2*I*e) + 2*I*c*d - d**2*exp(6*I*e) + d**2*exp(4*I*e) + d**2*exp(2*I*e) - d**2)*exp(-6*I*e)/(8*a**3)), True)) - x*(-c**2 + 2*I*c*d + d**2)/(8*a**3)","A",0
1077,1,486,0,1.604942," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e))**3,x)","- \frac{4 i a^{3} \left(c - i d\right)^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{90 a^{3} c^{3} - 390 i a^{3} c^{2} d - 450 a^{3} c d^{2} + 166 i a^{3} d^{3} + \left(390 a^{3} c^{3} e^{2 i e} - 1770 i a^{3} c^{2} d e^{2 i e} - 2070 a^{3} c d^{2} e^{2 i e} + 770 i a^{3} d^{3} e^{2 i e}\right) e^{2 i f x} + \left(630 a^{3} c^{3} e^{4 i e} - 3090 i a^{3} c^{2} d e^{4 i e} - 3690 a^{3} c d^{2} e^{4 i e} + 1390 i a^{3} d^{3} e^{4 i e}\right) e^{4 i f x} + \left(450 a^{3} c^{3} e^{6 i e} - 2430 i a^{3} c^{2} d e^{6 i e} - 3150 a^{3} c d^{2} e^{6 i e} + 1170 i a^{3} d^{3} e^{6 i e}\right) e^{6 i f x} + \left(120 a^{3} c^{3} e^{8 i e} - 720 i a^{3} c^{2} d e^{8 i e} - 1080 a^{3} c d^{2} e^{8 i e} + 480 i a^{3} d^{3} e^{8 i e}\right) e^{8 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,"-4*I*a**3*(c - I*d)**3*log(exp(2*I*f*x) + exp(-2*I*e))/f + (90*a**3*c**3 - 390*I*a**3*c**2*d - 450*a**3*c*d**2 + 166*I*a**3*d**3 + (390*a**3*c**3*exp(2*I*e) - 1770*I*a**3*c**2*d*exp(2*I*e) - 2070*a**3*c*d**2*exp(2*I*e) + 770*I*a**3*d**3*exp(2*I*e))*exp(2*I*f*x) + (630*a**3*c**3*exp(4*I*e) - 3090*I*a**3*c**2*d*exp(4*I*e) - 3690*a**3*c*d**2*exp(4*I*e) + 1390*I*a**3*d**3*exp(4*I*e))*exp(4*I*f*x) + (450*a**3*c**3*exp(6*I*e) - 2430*I*a**3*c**2*d*exp(6*I*e) - 3150*a**3*c*d**2*exp(6*I*e) + 1170*I*a**3*d**3*exp(6*I*e))*exp(6*I*f*x) + (120*a**3*c**3*exp(8*I*e) - 720*I*a**3*c**2*d*exp(8*I*e) - 1080*a**3*c*d**2*exp(8*I*e) + 480*I*a**3*d**3*exp(8*I*e))*exp(8*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
1078,1,389,0,1.352021," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e))**3,x)","- \frac{2 i a^{2} \left(c - i d\right)^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{6 a^{2} c^{3} - 36 i a^{2} c^{2} d - 42 a^{2} c d^{2} + 16 i a^{2} d^{3} + \left(18 a^{2} c^{3} e^{2 i e} - 126 i a^{2} c^{2} d e^{2 i e} - 150 a^{2} c d^{2} e^{2 i e} + 58 i a^{2} d^{3} e^{2 i e}\right) e^{2 i f x} + \left(18 a^{2} c^{3} e^{4 i e} - 144 i a^{2} c^{2} d e^{4 i e} - 198 a^{2} c d^{2} e^{4 i e} + 72 i a^{2} d^{3} e^{4 i e}\right) e^{4 i f x} + \left(6 a^{2} c^{3} e^{6 i e} - 54 i a^{2} c^{2} d e^{6 i e} - 90 a^{2} c d^{2} e^{6 i e} + 42 i a^{2} d^{3} e^{6 i e}\right) e^{6 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,"-2*I*a**2*(c - I*d)**3*log(exp(2*I*f*x) + exp(-2*I*e))/f + (6*a**2*c**3 - 36*I*a**2*c**2*d - 42*a**2*c*d**2 + 16*I*a**2*d**3 + (18*a**2*c**3*exp(2*I*e) - 126*I*a**2*c**2*d*exp(2*I*e) - 150*a**2*c*d**2*exp(2*I*e) + 58*I*a**2*d**3*exp(2*I*e))*exp(2*I*f*x) + (18*a**2*c**3*exp(4*I*e) - 144*I*a**2*c**2*d*exp(4*I*e) - 198*a**2*c*d**2*exp(4*I*e) + 72*I*a**2*d**3*exp(4*I*e))*exp(4*I*f*x) + (6*a**2*c**3*exp(6*I*e) - 54*I*a**2*c**2*d*exp(6*I*e) - 90*a**2*c*d**2*exp(6*I*e) + 42*I*a**2*d**3*exp(6*I*e))*exp(6*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
1079,1,236,0,0.984686," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))**3,x)","- \frac{i a \left(c - i d\right)^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{f} + \frac{18 i a c^{2} d + 18 a c d^{2} - 8 i a d^{3} + \left(36 i a c^{2} d e^{2 i e} + 54 a c d^{2} e^{2 i e} - 18 i a d^{3} e^{2 i e}\right) e^{2 i f x} + \left(18 i a c^{2} d e^{4 i e} + 36 a c d^{2} e^{4 i e} - 18 i a d^{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,"-I*a*(c - I*d)**3*log(exp(2*I*f*x) + exp(-2*I*e))/f + (18*I*a*c**2*d + 18*a*c*d**2 - 8*I*a*d**3 + (36*I*a*c**2*d*exp(2*I*e) + 54*a*c*d**2*exp(2*I*e) - 18*I*a*d**3*exp(2*I*e))*exp(2*I*f*x) + (18*I*a*c**2*d*exp(4*I*e) + 36*a*c*d**2*exp(4*I*e) - 18*I*a*d**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
1080,1,267,0,0.864200," ","integrate((c+d*tan(f*x+e))**3/(a+I*a*tan(f*x+e)),x)","- \frac{2 d^{3}}{- a f e^{2 i e} e^{2 i f x} - a f} + \begin{cases} - \frac{\left(- i c^{3} + 3 c^{2} d + 3 i c d^{2} - d^{3}\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{c^{3} - 3 i c^{2} d + 9 c d^{2} + 5 i d^{3}}{2 a} + \frac{i \left(- i c^{3} e^{2 i e} - i c^{3} - 3 c^{2} d e^{2 i e} + 3 c^{2} d - 9 i c d^{2} e^{2 i e} + 3 i c d^{2} + 5 d^{3} e^{2 i e} - d^{3}\right) e^{- 2 i e}}{2 a}\right) & \text{otherwise} \end{cases} + \frac{i d^{2} \left(3 c + i d\right) \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a f} - \frac{x \left(- c^{3} + 3 i c^{2} d - 9 c d^{2} - 5 i d^{3}\right)}{2 a}"," ",0,"-2*d**3/(-a*f*exp(2*I*e)*exp(2*I*f*x) - a*f) + Piecewise((-(-I*c**3 + 3*c**2*d + 3*I*c*d**2 - d**3)*exp(-2*I*e)*exp(-2*I*f*x)/(4*a*f), Ne(4*a*f*exp(2*I*e), 0)), (x*(-(c**3 - 3*I*c**2*d + 9*c*d**2 + 5*I*d**3)/(2*a) + I*(-I*c**3*exp(2*I*e) - I*c**3 - 3*c**2*d*exp(2*I*e) + 3*c**2*d - 9*I*c*d**2*exp(2*I*e) + 3*I*c*d**2 + 5*d**3*exp(2*I*e) - d**3)*exp(-2*I*e)/(2*a)), True)) + I*d**2*(3*c + I*d)*log(exp(2*I*f*x) + exp(-2*I*e))/(a*f) - x*(-c**3 + 3*I*c**2*d - 9*c*d**2 - 5*I*d**3)/(2*a)","A",0
1081,1,398,0,1.068988," ","integrate((c+d*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**2,x)","\begin{cases} \frac{\left(\left(16 i a^{2} c^{3} f e^{4 i e} + 48 i a^{2} c d^{2} f e^{4 i e} - 32 a^{2} d^{3} f e^{4 i e}\right) e^{- 2 i f x} + \left(4 i a^{2} c^{3} f e^{2 i e} - 12 a^{2} c^{2} d f e^{2 i e} - 12 i a^{2} c d^{2} f e^{2 i e} + 4 a^{2} d^{3} 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{c^{3} - 3 i c^{2} d - 3 c d^{2} - 7 i d^{3}}{4 a^{2}} + \frac{i \left(- i c^{3} e^{4 i e} - 2 i c^{3} e^{2 i e} - i c^{3} - 3 c^{2} d e^{4 i e} + 3 c^{2} d + 3 i c d^{2} e^{4 i e} - 6 i c d^{2} e^{2 i e} + 3 i c d^{2} - 7 d^{3} e^{4 i e} + 4 d^{3} e^{2 i e} - d^{3}\right) e^{- 4 i e}}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{d^{3} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{a^{2} f} - \frac{x \left(- c^{3} + 3 i c^{2} d + 3 c d^{2} + 7 i d^{3}\right)}{4 a^{2}}"," ",0,"Piecewise((((16*I*a**2*c**3*f*exp(4*I*e) + 48*I*a**2*c*d**2*f*exp(4*I*e) - 32*a**2*d**3*f*exp(4*I*e))*exp(-2*I*f*x) + (4*I*a**2*c**3*f*exp(2*I*e) - 12*a**2*c**2*d*f*exp(2*I*e) - 12*I*a**2*c*d**2*f*exp(2*I*e) + 4*a**2*d**3*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*(-(c**3 - 3*I*c**2*d - 3*c*d**2 - 7*I*d**3)/(4*a**2) + I*(-I*c**3*exp(4*I*e) - 2*I*c**3*exp(2*I*e) - I*c**3 - 3*c**2*d*exp(4*I*e) + 3*c**2*d + 3*I*c*d**2*exp(4*I*e) - 6*I*c*d**2*exp(2*I*e) + 3*I*c*d**2 - 7*d**3*exp(4*I*e) + 4*d**3*exp(2*I*e) - d**3)*exp(-4*I*e)/(4*a**2)), True)) + d**3*log(exp(2*I*f*x) + exp(-2*I*e))/(a**2*f) - x*(-c**3 + 3*I*c**2*d + 3*c*d**2 + 7*I*d**3)/(4*a**2)","A",0
1082,1,558,0,0.956583," ","integrate((c+d*tan(f*x+e))**3/(a+I*a*tan(f*x+e))**3,x)","\begin{cases} - \frac{\left(\left(- 512 i a^{6} c^{3} f^{2} e^{6 i e} + 1536 a^{6} c^{2} d f^{2} e^{6 i e} + 1536 i a^{6} c d^{2} f^{2} e^{6 i e} - 512 a^{6} d^{3} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(- 2304 i a^{6} c^{3} f^{2} e^{8 i e} + 2304 a^{6} c^{2} d f^{2} e^{8 i e} - 2304 i a^{6} c d^{2} f^{2} e^{8 i e} + 2304 a^{6} d^{3} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(- 4608 i a^{6} c^{3} f^{2} e^{10 i e} - 4608 a^{6} c^{2} d f^{2} e^{10 i e} - 4608 i a^{6} c d^{2} f^{2} e^{10 i e} - 4608 a^{6} d^{3} 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{c^{3} - 3 i c^{2} d - 3 c d^{2} + i d^{3}}{8 a^{3}} + \frac{\left(c^{3} e^{6 i e} + 3 c^{3} e^{4 i e} + 3 c^{3} e^{2 i e} + c^{3} - 3 i c^{2} d e^{6 i e} - 3 i c^{2} d e^{4 i e} + 3 i c^{2} d e^{2 i e} + 3 i c^{2} d - 3 c d^{2} e^{6 i e} + 3 c d^{2} e^{4 i e} + 3 c d^{2} e^{2 i e} - 3 c d^{2} + i d^{3} e^{6 i e} - 3 i d^{3} e^{4 i e} + 3 i d^{3} e^{2 i e} - i d^{3}\right) e^{- 6 i e}}{8 a^{3}}\right) & \text{otherwise} \end{cases} - \frac{x \left(- c^{3} + 3 i c^{2} d + 3 c d^{2} - i d^{3}\right)}{8 a^{3}}"," ",0,"Piecewise((-((-512*I*a**6*c**3*f**2*exp(6*I*e) + 1536*a**6*c**2*d*f**2*exp(6*I*e) + 1536*I*a**6*c*d**2*f**2*exp(6*I*e) - 512*a**6*d**3*f**2*exp(6*I*e))*exp(-6*I*f*x) + (-2304*I*a**6*c**3*f**2*exp(8*I*e) + 2304*a**6*c**2*d*f**2*exp(8*I*e) - 2304*I*a**6*c*d**2*f**2*exp(8*I*e) + 2304*a**6*d**3*f**2*exp(8*I*e))*exp(-4*I*f*x) + (-4608*I*a**6*c**3*f**2*exp(10*I*e) - 4608*a**6*c**2*d*f**2*exp(10*I*e) - 4608*I*a**6*c*d**2*f**2*exp(10*I*e) - 4608*a**6*d**3*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*(-(c**3 - 3*I*c**2*d - 3*c*d**2 + I*d**3)/(8*a**3) + (c**3*exp(6*I*e) + 3*c**3*exp(4*I*e) + 3*c**3*exp(2*I*e) + c**3 - 3*I*c**2*d*exp(6*I*e) - 3*I*c**2*d*exp(4*I*e) + 3*I*c**2*d*exp(2*I*e) + 3*I*c**2*d - 3*c*d**2*exp(6*I*e) + 3*c*d**2*exp(4*I*e) + 3*c*d**2*exp(2*I*e) - 3*c*d**2 + I*d**3*exp(6*I*e) - 3*I*d**3*exp(4*I*e) + 3*I*d**3*exp(2*I*e) - I*d**3)*exp(-6*I*e)/(8*a**3)), True)) - x*(-c**3 + 3*I*c**2*d + 3*c*d**2 - I*d**3)/(8*a**3)","A",0
1083,1,262,0,19.134037," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)","- \frac{2 a^{3}}{- d f e^{2 i e} e^{2 i f x} - d f} - \frac{i a^{3} \left(c + 3 i d\right) \log{\left(e^{2 i f x} + \frac{- a^{3} c^{2} - 3 i a^{3} c d + 2 a^{3} d^{2} + i a^{3} d \left(c + 3 i d\right)}{- a^{3} c^{2} e^{2 i e} - 2 i a^{3} c d e^{2 i e} - a^{3} d^{2} e^{2 i e}} \right)}}{d^{2} f} + \frac{i a^{3} \left(c + i d\right)^{2} \log{\left(e^{2 i f x} + \frac{- a^{3} c^{2} - 3 i a^{3} c d + 2 a^{3} d^{2} - \frac{i a^{3} d \left(c + i d\right)^{2}}{c - i d}}{- a^{3} c^{2} e^{2 i e} - 2 i a^{3} c d e^{2 i e} - a^{3} d^{2} e^{2 i e}} \right)}}{d^{2} f \left(c - i d\right)}"," ",0,"-2*a**3/(-d*f*exp(2*I*e)*exp(2*I*f*x) - d*f) - I*a**3*(c + 3*I*d)*log(exp(2*I*f*x) + (-a**3*c**2 - 3*I*a**3*c*d + 2*a**3*d**2 + I*a**3*d*(c + 3*I*d))/(-a**3*c**2*exp(2*I*e) - 2*I*a**3*c*d*exp(2*I*e) - a**3*d**2*exp(2*I*e)))/(d**2*f) + I*a**3*(c + I*d)**2*log(exp(2*I*f*x) + (-a**3*c**2 - 3*I*a**3*c*d + 2*a**3*d**2 - I*a**3*d*(c + I*d)**2/(c - I*d))/(-a**3*c**2*exp(2*I*e) - 2*I*a**3*c*d*exp(2*I*e) - a**3*d**2*exp(2*I*e)))/(d**2*f*(c - I*d))","B",0
1084,1,92,0,8.534733," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)","\frac{a^{2} \log{\left(e^{2 i f x} + e^{- 2 i e} \right)}}{d f} - \frac{a^{2} \left(c + i d\right) \log{\left(e^{2 i f x} + \frac{\left(a^{2} c + i a^{2} d + \frac{i a^{2} d \left(c + i d\right)}{c - i d}\right) e^{- 2 i e}}{a^{2} c} \right)}}{d f \left(c - i d\right)}"," ",0,"a**2*log(exp(2*I*f*x) + exp(-2*I*e))/(d*f) - a**2*(c + I*d)*log(exp(2*I*f*x) + (a**2*c + I*a**2*d + I*a**2*d*(c + I*d)/(c - I*d))*exp(-2*I*e)/(a**2*c))/(d*f*(c - I*d))","A",0
1085,1,46,0,1.593733," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x)","- \frac{i a \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)}"," ",0,"-I*a*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d))","A",0
1086,1,253,0,5.016238," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x)","\frac{x \left(- c - 3 i d\right)}{- 2 a c^{2} - 4 i a c d + 2 a d^{2}} + \begin{cases} \frac{i e^{- 2 i f x}}{4 a c f e^{2 i e} + 4 i a d f e^{2 i e}} & \text{for}\: 4 a c f e^{2 i e} + 4 i a d f e^{2 i e} \neq 0 \\x \left(- \frac{- c - 3 i d}{- 2 a c^{2} - 4 i a c d + 2 a d^{2}} + \frac{- i c e^{2 i e} - i c + 3 d e^{2 i e} + d}{- 2 i a c^{2} e^{2 i e} + 4 a c d e^{2 i e} + 2 i a d^{2} e^{2 i e}}\right) & \text{otherwise} \end{cases} + \frac{i d^{2} \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{a f \left(c - i d\right) \left(c + i d\right)^{2}}"," ",0,"x*(-c - 3*I*d)/(-2*a*c**2 - 4*I*a*c*d + 2*a*d**2) + Piecewise((I*exp(-2*I*f*x)/(4*a*c*f*exp(2*I*e) + 4*I*a*d*f*exp(2*I*e)), Ne(4*a*c*f*exp(2*I*e) + 4*I*a*d*f*exp(2*I*e), 0)), (x*(-(-c - 3*I*d)/(-2*a*c**2 - 4*I*a*c*d + 2*a*d**2) + (-I*c*exp(2*I*e) - I*c + 3*d*exp(2*I*e) + d)/(-2*I*a*c**2*exp(2*I*e) + 4*a*c*d*exp(2*I*e) + 2*I*a*d**2*exp(2*I*e))), True)) + I*d**2*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(a*f*(c - I*d)*(c + I*d)**2)","A",0
1087,1,614,0,12.534389," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)","\frac{x \left(- c^{2} - 4 i c d + 7 d^{2}\right)}{- 4 a^{2} c^{3} - 12 i a^{2} c^{2} d + 12 a^{2} c d^{2} + 4 i a^{2} d^{3}} + \begin{cases} \frac{\left(4 i a^{2} c^{2} f e^{2 i e} - 8 a^{2} c d f e^{2 i e} - 4 i a^{2} d^{2} f e^{2 i e}\right) e^{- 4 i f x} + \left(16 i a^{2} c^{2} f e^{4 i e} - 48 a^{2} c d f e^{4 i e} - 32 i a^{2} d^{2} f e^{4 i e}\right) e^{- 2 i f x}}{64 a^{4} c^{3} f^{2} e^{6 i e} + 192 i a^{4} c^{2} d f^{2} e^{6 i e} - 192 a^{4} c d^{2} f^{2} e^{6 i e} - 64 i a^{4} d^{3} f^{2} e^{6 i e}} & \text{for}\: 64 a^{4} c^{3} f^{2} e^{6 i e} + 192 i a^{4} c^{2} d f^{2} e^{6 i e} - 192 a^{4} c d^{2} f^{2} e^{6 i e} - 64 i a^{4} d^{3} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{i c^{2} - 4 c d - 7 i d^{2}}{4 i a^{2} c^{3} - 12 a^{2} c^{2} d - 12 i a^{2} c d^{2} + 4 a^{2} d^{3}} + \frac{- c^{2} e^{4 i e} - 2 c^{2} e^{2 i e} - c^{2} - 4 i c d e^{4 i e} - 6 i c d e^{2 i e} - 2 i c d + 7 d^{2} e^{4 i e} + 4 d^{2} e^{2 i e} + d^{2}}{- 4 a^{2} c^{3} e^{4 i e} - 12 i a^{2} c^{2} d e^{4 i e} + 12 a^{2} c d^{2} e^{4 i e} + 4 i a^{2} d^{3} e^{4 i e}}\right) & \text{otherwise} \end{cases} - \frac{d^{3} \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{a^{2} f \left(c - i d\right) \left(c + i d\right)^{3}}"," ",0,"x*(-c**2 - 4*I*c*d + 7*d**2)/(-4*a**2*c**3 - 12*I*a**2*c**2*d + 12*a**2*c*d**2 + 4*I*a**2*d**3) + Piecewise((((4*I*a**2*c**2*f*exp(2*I*e) - 8*a**2*c*d*f*exp(2*I*e) - 4*I*a**2*d**2*f*exp(2*I*e))*exp(-4*I*f*x) + (16*I*a**2*c**2*f*exp(4*I*e) - 48*a**2*c*d*f*exp(4*I*e) - 32*I*a**2*d**2*f*exp(4*I*e))*exp(-2*I*f*x))/(64*a**4*c**3*f**2*exp(6*I*e) + 192*I*a**4*c**2*d*f**2*exp(6*I*e) - 192*a**4*c*d**2*f**2*exp(6*I*e) - 64*I*a**4*d**3*f**2*exp(6*I*e)), Ne(64*a**4*c**3*f**2*exp(6*I*e) + 192*I*a**4*c**2*d*f**2*exp(6*I*e) - 192*a**4*c*d**2*f**2*exp(6*I*e) - 64*I*a**4*d**3*f**2*exp(6*I*e), 0)), (x*(-(I*c**2 - 4*c*d - 7*I*d**2)/(4*I*a**2*c**3 - 12*a**2*c**2*d - 12*I*a**2*c*d**2 + 4*a**2*d**3) + (-c**2*exp(4*I*e) - 2*c**2*exp(2*I*e) - c**2 - 4*I*c*d*exp(4*I*e) - 6*I*c*d*exp(2*I*e) - 2*I*c*d + 7*d**2*exp(4*I*e) + 4*d**2*exp(2*I*e) + d**2)/(-4*a**2*c**3*exp(4*I*e) - 12*I*a**2*c**2*d*exp(4*I*e) + 12*a**2*c*d**2*exp(4*I*e) + 4*I*a**2*d**3*exp(4*I*e))), True)) - d**3*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(a**2*f*(c - I*d)*(c + I*d)**3)","A",0
1088,1,1195,0,34.611478," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)","\frac{x \left(- c^{3} - 5 i c^{2} d + 11 c d^{2} + 15 i d^{3}\right)}{- 8 a^{3} c^{4} - 32 i a^{3} c^{3} d + 48 a^{3} c^{2} d^{2} + 32 i a^{3} c d^{3} - 8 a^{3} d^{4}} + \begin{cases} \frac{\left(512 a^{6} c^{5} f^{2} e^{6 i e} + 2560 i a^{6} c^{4} d f^{2} e^{6 i e} - 5120 a^{6} c^{3} d^{2} f^{2} e^{6 i e} - 5120 i a^{6} c^{2} d^{3} f^{2} e^{6 i e} + 2560 a^{6} c d^{4} f^{2} e^{6 i e} + 512 i a^{6} d^{5} f^{2} e^{6 i e}\right) e^{- 6 i f x} + \left(2304 a^{6} c^{5} f^{2} e^{8 i e} + 13056 i a^{6} c^{4} d f^{2} e^{8 i e} - 29184 a^{6} c^{3} d^{2} f^{2} e^{8 i e} - 32256 i a^{6} c^{2} d^{3} f^{2} e^{8 i e} + 17664 a^{6} c d^{4} f^{2} e^{8 i e} + 3840 i a^{6} d^{5} f^{2} e^{8 i e}\right) e^{- 4 i f x} + \left(4608 a^{6} c^{5} f^{2} e^{10 i e} + 29184 i a^{6} c^{4} d f^{2} e^{10 i e} - 76800 a^{6} c^{3} d^{2} f^{2} e^{10 i e} - 101376 i a^{6} c^{2} d^{3} f^{2} e^{10 i e} + 66048 a^{6} c d^{4} f^{2} e^{10 i e} + 16896 i a^{6} d^{5} f^{2} e^{10 i e}\right) e^{- 2 i f x}}{- 24576 i a^{9} c^{6} f^{3} e^{12 i e} + 147456 a^{9} c^{5} d f^{3} e^{12 i e} + 368640 i a^{9} c^{4} d^{2} f^{3} e^{12 i e} - 491520 a^{9} c^{3} d^{3} f^{3} e^{12 i e} - 368640 i a^{9} c^{2} d^{4} f^{3} e^{12 i e} + 147456 a^{9} c d^{5} f^{3} e^{12 i e} + 24576 i a^{9} d^{6} f^{3} e^{12 i e}} & \text{for}\: - 24576 i a^{9} c^{6} f^{3} e^{12 i e} + 147456 a^{9} c^{5} d f^{3} e^{12 i e} + 368640 i a^{9} c^{4} d^{2} f^{3} e^{12 i e} - 491520 a^{9} c^{3} d^{3} f^{3} e^{12 i e} - 368640 i a^{9} c^{2} d^{4} f^{3} e^{12 i e} + 147456 a^{9} c d^{5} f^{3} e^{12 i e} + 24576 i a^{9} d^{6} f^{3} e^{12 i e} \neq 0 \\x \left(- \frac{c^{3} + 5 i c^{2} d - 11 c d^{2} - 15 i d^{3}}{8 a^{3} c^{4} + 32 i a^{3} c^{3} d - 48 a^{3} c^{2} d^{2} - 32 i a^{3} c d^{3} + 8 a^{3} d^{4}} + \frac{c^{3} e^{6 i e} + 3 c^{3} e^{4 i e} + 3 c^{3} e^{2 i e} + c^{3} + 5 i c^{2} d e^{6 i e} + 13 i c^{2} d e^{4 i e} + 11 i c^{2} d e^{2 i e} + 3 i c^{2} d - 11 c d^{2} e^{6 i e} - 21 c d^{2} e^{4 i e} - 13 c d^{2} e^{2 i e} - 3 c d^{2} - 15 i d^{3} e^{6 i e} - 11 i d^{3} e^{4 i e} - 5 i d^{3} e^{2 i e} - i d^{3}}{8 a^{3} c^{4} e^{6 i e} + 32 i a^{3} c^{3} d e^{6 i e} - 48 a^{3} c^{2} d^{2} e^{6 i e} - 32 i a^{3} c d^{3} e^{6 i e} + 8 a^{3} d^{4} e^{6 i e}}\right) & \text{otherwise} \end{cases} - \frac{i d^{4} \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{a^{3} f \left(c - i d\right) \left(c + i d\right)^{4}}"," ",0,"x*(-c**3 - 5*I*c**2*d + 11*c*d**2 + 15*I*d**3)/(-8*a**3*c**4 - 32*I*a**3*c**3*d + 48*a**3*c**2*d**2 + 32*I*a**3*c*d**3 - 8*a**3*d**4) + Piecewise((((512*a**6*c**5*f**2*exp(6*I*e) + 2560*I*a**6*c**4*d*f**2*exp(6*I*e) - 5120*a**6*c**3*d**2*f**2*exp(6*I*e) - 5120*I*a**6*c**2*d**3*f**2*exp(6*I*e) + 2560*a**6*c*d**4*f**2*exp(6*I*e) + 512*I*a**6*d**5*f**2*exp(6*I*e))*exp(-6*I*f*x) + (2304*a**6*c**5*f**2*exp(8*I*e) + 13056*I*a**6*c**4*d*f**2*exp(8*I*e) - 29184*a**6*c**3*d**2*f**2*exp(8*I*e) - 32256*I*a**6*c**2*d**3*f**2*exp(8*I*e) + 17664*a**6*c*d**4*f**2*exp(8*I*e) + 3840*I*a**6*d**5*f**2*exp(8*I*e))*exp(-4*I*f*x) + (4608*a**6*c**5*f**2*exp(10*I*e) + 29184*I*a**6*c**4*d*f**2*exp(10*I*e) - 76800*a**6*c**3*d**2*f**2*exp(10*I*e) - 101376*I*a**6*c**2*d**3*f**2*exp(10*I*e) + 66048*a**6*c*d**4*f**2*exp(10*I*e) + 16896*I*a**6*d**5*f**2*exp(10*I*e))*exp(-2*I*f*x))/(-24576*I*a**9*c**6*f**3*exp(12*I*e) + 147456*a**9*c**5*d*f**3*exp(12*I*e) + 368640*I*a**9*c**4*d**2*f**3*exp(12*I*e) - 491520*a**9*c**3*d**3*f**3*exp(12*I*e) - 368640*I*a**9*c**2*d**4*f**3*exp(12*I*e) + 147456*a**9*c*d**5*f**3*exp(12*I*e) + 24576*I*a**9*d**6*f**3*exp(12*I*e)), Ne(-24576*I*a**9*c**6*f**3*exp(12*I*e) + 147456*a**9*c**5*d*f**3*exp(12*I*e) + 368640*I*a**9*c**4*d**2*f**3*exp(12*I*e) - 491520*a**9*c**3*d**3*f**3*exp(12*I*e) - 368640*I*a**9*c**2*d**4*f**3*exp(12*I*e) + 147456*a**9*c*d**5*f**3*exp(12*I*e) + 24576*I*a**9*d**6*f**3*exp(12*I*e), 0)), (x*(-(c**3 + 5*I*c**2*d - 11*c*d**2 - 15*I*d**3)/(8*a**3*c**4 + 32*I*a**3*c**3*d - 48*a**3*c**2*d**2 - 32*I*a**3*c*d**3 + 8*a**3*d**4) + (c**3*exp(6*I*e) + 3*c**3*exp(4*I*e) + 3*c**3*exp(2*I*e) + c**3 + 5*I*c**2*d*exp(6*I*e) + 13*I*c**2*d*exp(4*I*e) + 11*I*c**2*d*exp(2*I*e) + 3*I*c**2*d - 11*c*d**2*exp(6*I*e) - 21*c*d**2*exp(4*I*e) - 13*c*d**2*exp(2*I*e) - 3*c*d**2 - 15*I*d**3*exp(6*I*e) - 11*I*d**3*exp(4*I*e) - 5*I*d**3*exp(2*I*e) - I*d**3)/(8*a**3*c**4*exp(6*I*e) + 32*I*a**3*c**3*d*exp(6*I*e) - 48*a**3*c**2*d**2*exp(6*I*e) - 32*I*a**3*c*d**3*exp(6*I*e) + 8*a**3*d**4*exp(6*I*e))), True)) - I*d**4*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(a**3*f*(c - I*d)*(c + I*d)**4)","A",0
1089,1,382,0,33.035634," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**2,x)","- \frac{i a^{3} \left(c - 3 i d\right) \left(c + i d\right) \log{\left(e^{2 i f x} + \frac{i a^{3} c^{2} - \frac{a^{3} c d \left(c - 3 i d\right) \left(c + i d\right)}{\left(c - i d\right)^{2}} + a^{3} c d + \frac{i a^{3} d^{2} \left(c - 3 i d\right) \left(c + i d\right)}{\left(c - i d\right)^{2}} + 2 i a^{3} d^{2}}{i a^{3} c^{2} e^{2 i e} + 2 a^{3} c d e^{2 i e} + i a^{3} d^{2} e^{2 i e}} \right)}}{d^{2} f \left(c - i d\right)^{2}} + \frac{i a^{3} \log{\left(\frac{i a^{3} c^{2} + 2 a^{3} c d + i a^{3} d^{2}}{i a^{3} c^{2} e^{2 i e} + 2 a^{3} c d e^{2 i e} + i a^{3} d^{2} e^{2 i e}} + e^{2 i f x} \right)}}{d^{2} f} + \frac{- 2 i a^{3} c^{2} + 4 a^{3} c d + 2 i a^{3} d^{2}}{i c^{3} d f + c^{2} d^{2} f + i c d^{3} f + d^{4} f + \left(i c^{3} d f e^{2 i e} + 3 c^{2} d^{2} f e^{2 i e} - 3 i c d^{3} f e^{2 i e} - d^{4} f e^{2 i e}\right) e^{2 i f x}}"," ",0,"-I*a**3*(c - 3*I*d)*(c + I*d)*log(exp(2*I*f*x) + (I*a**3*c**2 - a**3*c*d*(c - 3*I*d)*(c + I*d)/(c - I*d)**2 + a**3*c*d + I*a**3*d**2*(c - 3*I*d)*(c + I*d)/(c - I*d)**2 + 2*I*a**3*d**2)/(I*a**3*c**2*exp(2*I*e) + 2*a**3*c*d*exp(2*I*e) + I*a**3*d**2*exp(2*I*e)))/(d**2*f*(c - I*d)**2) + I*a**3*log((I*a**3*c**2 + 2*a**3*c*d + I*a**3*d**2)/(I*a**3*c**2*exp(2*I*e) + 2*a**3*c*d*exp(2*I*e) + I*a**3*d**2*exp(2*I*e)) + exp(2*I*f*x))/(d**2*f) + (-2*I*a**3*c**2 + 4*a**3*c*d + 2*I*a**3*d**2)/(I*c**3*d*f + c**2*d**2*f + I*c*d**3*f + d**4*f + (I*c**3*d*f*exp(2*I*e) + 3*c**2*d**2*f*exp(2*I*e) - 3*I*c*d**3*f*exp(2*I*e) - d**4*f*exp(2*I*e))*exp(2*I*f*x))","B",0
1090,1,156,0,3.533476," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)","- \frac{2 i a^{2} \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)^{2}} + \frac{2 a^{2} c + 2 i a^{2} d}{i c^{3} f + c^{2} d f + i c d^{2} f + d^{3} f + \left(i c^{3} f e^{2 i e} + 3 c^{2} d f e^{2 i e} - 3 i c d^{2} f e^{2 i e} - d^{3} f e^{2 i e}\right) e^{2 i f x}}"," ",0,"-2*I*a**2*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d)**2) + (2*a**2*c + 2*I*a**2*d)/(I*c**3*f + c**2*d*f + I*c*d**2*f + d**3*f + (I*c**3*f*exp(2*I*e) + 3*c**2*d*f*exp(2*I*e) - 3*I*c*d**2*f*exp(2*I*e) - d**3*f*exp(2*I*e))*exp(2*I*f*x))","B",0
1091,1,144,0,3.558884," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)","\frac{2 i a d}{i c^{3} f + c^{2} d f + i c d^{2} f + d^{3} f + \left(i c^{3} f e^{2 i e} + 3 c^{2} d f e^{2 i e} - 3 i c d^{2} f e^{2 i e} - d^{3} f e^{2 i e}\right) e^{2 i f x}} - \frac{i a \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)^{2}}"," ",0,"2*I*a*d/(I*c**3*f + c**2*d*f + I*c*d**2*f + d**3*f + (I*c**3*f*exp(2*I*e) + 3*c**2*d*f*exp(2*I*e) - 3*I*c*d**2*f*exp(2*I*e) - d**3*f*exp(2*I*e))*exp(2*I*f*x)) - I*a*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d)**2)","B",0
1092,1,515,0,27.606586," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)","- \frac{2 i d^{3}}{i a c^{5} f - a c^{4} d f + 2 i a c^{3} d^{2} f - 2 a c^{2} d^{3} f + i a c d^{4} f - a d^{5} f + \left(i a c^{5} f e^{2 i e} + a c^{4} d f e^{2 i e} + 2 i a c^{3} d^{2} f e^{2 i e} + 2 a c^{2} d^{3} f e^{2 i e} + i a c d^{4} f e^{2 i e} + a d^{5} f e^{2 i e}\right) e^{2 i f x}} + \frac{x \left(- c - 5 i d\right)}{- 2 a c^{3} - 6 i a c^{2} d + 6 a c d^{2} + 2 i a d^{3}} + \begin{cases} \frac{i e^{- 2 i f x}}{4 a c^{2} f e^{2 i e} + 8 i a c d f e^{2 i e} - 4 a d^{2} f e^{2 i e}} & \text{for}\: 4 a c^{2} f e^{2 i e} + 8 i a c d f e^{2 i e} - 4 a d^{2} f e^{2 i e} \neq 0 \\x \left(- \frac{i c - 5 d}{2 i a c^{3} - 6 a c^{2} d - 6 i a c d^{2} + 2 a d^{3}} + \frac{- c e^{2 i e} - c - 5 i d e^{2 i e} - i d}{- 2 a c^{3} e^{2 i e} - 6 i a c^{2} d e^{2 i e} + 6 a c d^{2} e^{2 i e} + 2 i a d^{3} e^{2 i e}}\right) & \text{otherwise} \end{cases} + \frac{i d^{2} \left(3 c - i d\right) \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{a f \left(c - i d\right)^{2} \left(c + i d\right)^{3}}"," ",0,"-2*I*d**3/(I*a*c**5*f - a*c**4*d*f + 2*I*a*c**3*d**2*f - 2*a*c**2*d**3*f + I*a*c*d**4*f - a*d**5*f + (I*a*c**5*f*exp(2*I*e) + a*c**4*d*f*exp(2*I*e) + 2*I*a*c**3*d**2*f*exp(2*I*e) + 2*a*c**2*d**3*f*exp(2*I*e) + I*a*c*d**4*f*exp(2*I*e) + a*d**5*f*exp(2*I*e))*exp(2*I*f*x)) + x*(-c - 5*I*d)/(-2*a*c**3 - 6*I*a*c**2*d + 6*a*c*d**2 + 2*I*a*d**3) + Piecewise((I*exp(-2*I*f*x)/(4*a*c**2*f*exp(2*I*e) + 8*I*a*c*d*f*exp(2*I*e) - 4*a*d**2*f*exp(2*I*e)), Ne(4*a*c**2*f*exp(2*I*e) + 8*I*a*c*d*f*exp(2*I*e) - 4*a*d**2*f*exp(2*I*e), 0)), (x*(-(I*c - 5*d)/(2*I*a*c**3 - 6*a*c**2*d - 6*I*a*c*d**2 + 2*a*d**3) + (-c*exp(2*I*e) - c - 5*I*d*exp(2*I*e) - I*d)/(-2*a*c**3*exp(2*I*e) - 6*I*a*c**2*d*exp(2*I*e) + 6*a*c*d**2*exp(2*I*e) + 2*I*a*d**3*exp(2*I*e))), True)) + I*d**2*(3*c - I*d)*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(a*f*(c - I*d)**2*(c + I*d)**3)","A",0
1093,1,967,0,70.610947," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)","- \frac{2 i d^{4}}{a^{2} c^{6} f + 2 i a^{2} c^{5} d f + a^{2} c^{4} d^{2} f + 4 i a^{2} c^{3} d^{3} f - a^{2} c^{2} d^{4} f + 2 i a^{2} c d^{5} f - a^{2} d^{6} f + \left(a^{2} c^{6} f e^{2 i e} + 3 a^{2} c^{4} d^{2} f e^{2 i e} + 3 a^{2} c^{2} d^{4} f e^{2 i e} + a^{2} d^{6} f e^{2 i e}\right) e^{2 i f x}} + \frac{x \left(- c^{2} - 6 i c d + 17 d^{2}\right)}{- 4 a^{2} c^{4} - 16 i a^{2} c^{3} d + 24 a^{2} c^{2} d^{2} + 16 i a^{2} c d^{3} - 4 a^{2} d^{4}} + \begin{cases} \frac{\left(4 i a^{2} c^{3} f e^{2 i e} - 12 a^{2} c^{2} d f e^{2 i e} - 12 i a^{2} c d^{2} f e^{2 i e} + 4 a^{2} d^{3} f e^{2 i e}\right) e^{- 4 i f x} + \left(16 i a^{2} c^{3} f e^{4 i e} - 80 a^{2} c^{2} d f e^{4 i e} - 112 i a^{2} c d^{2} f e^{4 i e} + 48 a^{2} d^{3} f e^{4 i e}\right) e^{- 2 i f x}}{64 a^{4} c^{5} f^{2} e^{6 i e} + 320 i a^{4} c^{4} d f^{2} e^{6 i e} - 640 a^{4} c^{3} d^{2} f^{2} e^{6 i e} - 640 i a^{4} c^{2} d^{3} f^{2} e^{6 i e} + 320 a^{4} c d^{4} f^{2} e^{6 i e} + 64 i a^{4} d^{5} f^{2} e^{6 i e}} & \text{for}\: 64 a^{4} c^{5} f^{2} e^{6 i e} + 320 i a^{4} c^{4} d f^{2} e^{6 i e} - 640 a^{4} c^{3} d^{2} f^{2} e^{6 i e} - 640 i a^{4} c^{2} d^{3} f^{2} e^{6 i e} + 320 a^{4} c d^{4} f^{2} e^{6 i e} + 64 i a^{4} d^{5} f^{2} e^{6 i e} \neq 0 \\x \left(- \frac{c^{2} + 6 i c d - 17 d^{2}}{4 a^{2} c^{4} + 16 i a^{2} c^{3} d - 24 a^{2} c^{2} d^{2} - 16 i a^{2} c d^{3} + 4 a^{2} d^{4}} + \frac{c^{2} e^{4 i e} + 2 c^{2} e^{2 i e} + c^{2} + 6 i c d e^{4 i e} + 8 i c d e^{2 i e} + 2 i c d - 17 d^{2} e^{4 i e} - 6 d^{2} e^{2 i e} - d^{2}}{4 a^{2} c^{4} e^{4 i e} + 16 i a^{2} c^{3} d e^{4 i e} - 24 a^{2} c^{2} d^{2} e^{4 i e} - 16 i a^{2} c d^{3} e^{4 i e} + 4 a^{2} d^{4} e^{4 i e}}\right) & \text{otherwise} \end{cases} - \frac{2 d^{3} \left(2 c - i d\right) \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{a^{2} f \left(c - i d\right)^{2} \left(c + i d\right)^{4}}"," ",0,"-2*I*d**4/(a**2*c**6*f + 2*I*a**2*c**5*d*f + a**2*c**4*d**2*f + 4*I*a**2*c**3*d**3*f - a**2*c**2*d**4*f + 2*I*a**2*c*d**5*f - a**2*d**6*f + (a**2*c**6*f*exp(2*I*e) + 3*a**2*c**4*d**2*f*exp(2*I*e) + 3*a**2*c**2*d**4*f*exp(2*I*e) + a**2*d**6*f*exp(2*I*e))*exp(2*I*f*x)) + x*(-c**2 - 6*I*c*d + 17*d**2)/(-4*a**2*c**4 - 16*I*a**2*c**3*d + 24*a**2*c**2*d**2 + 16*I*a**2*c*d**3 - 4*a**2*d**4) + Piecewise((((4*I*a**2*c**3*f*exp(2*I*e) - 12*a**2*c**2*d*f*exp(2*I*e) - 12*I*a**2*c*d**2*f*exp(2*I*e) + 4*a**2*d**3*f*exp(2*I*e))*exp(-4*I*f*x) + (16*I*a**2*c**3*f*exp(4*I*e) - 80*a**2*c**2*d*f*exp(4*I*e) - 112*I*a**2*c*d**2*f*exp(4*I*e) + 48*a**2*d**3*f*exp(4*I*e))*exp(-2*I*f*x))/(64*a**4*c**5*f**2*exp(6*I*e) + 320*I*a**4*c**4*d*f**2*exp(6*I*e) - 640*a**4*c**3*d**2*f**2*exp(6*I*e) - 640*I*a**4*c**2*d**3*f**2*exp(6*I*e) + 320*a**4*c*d**4*f**2*exp(6*I*e) + 64*I*a**4*d**5*f**2*exp(6*I*e)), Ne(64*a**4*c**5*f**2*exp(6*I*e) + 320*I*a**4*c**4*d*f**2*exp(6*I*e) - 640*a**4*c**3*d**2*f**2*exp(6*I*e) - 640*I*a**4*c**2*d**3*f**2*exp(6*I*e) + 320*a**4*c*d**4*f**2*exp(6*I*e) + 64*I*a**4*d**5*f**2*exp(6*I*e), 0)), (x*(-(c**2 + 6*I*c*d - 17*d**2)/(4*a**2*c**4 + 16*I*a**2*c**3*d - 24*a**2*c**2*d**2 - 16*I*a**2*c*d**3 + 4*a**2*d**4) + (c**2*exp(4*I*e) + 2*c**2*exp(2*I*e) + c**2 + 6*I*c*d*exp(4*I*e) + 8*I*c*d*exp(2*I*e) + 2*I*c*d - 17*d**2*exp(4*I*e) - 6*d**2*exp(2*I*e) - d**2)/(4*a**2*c**4*exp(4*I*e) + 16*I*a**2*c**3*d*exp(4*I*e) - 24*a**2*c**2*d**2*exp(4*I*e) - 16*I*a**2*c*d**3*exp(4*I*e) + 4*a**2*d**4*exp(4*I*e))), True)) - 2*d**3*(2*c - I*d)*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(a**2*f*(c - I*d)**2*(c + I*d)**4)","A",0
1094,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1095,1,374,0,8.236220," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**3,x)","- \frac{4 i a^{3} \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)^{3}} + \frac{- 6 a^{3} c^{2} - 12 i a^{3} c d + 6 a^{3} d^{2} + \left(- 8 a^{3} c^{2} e^{2 i e} - 8 a^{3} d^{2} e^{2 i e}\right) e^{2 i f x}}{- i c^{5} f - c^{4} d f - 2 i c^{3} d^{2} f - 2 c^{2} d^{3} f - i c d^{4} f - d^{5} f + \left(- 2 i c^{5} f e^{2 i e} - 6 c^{4} d f e^{2 i e} + 4 i c^{3} d^{2} f e^{2 i e} - 4 c^{2} d^{3} f e^{2 i e} + 6 i c d^{4} f e^{2 i e} + 2 d^{5} f e^{2 i e}\right) e^{2 i f x} + \left(- i c^{5} f e^{4 i e} - 5 c^{4} d f e^{4 i e} + 10 i c^{3} d^{2} f e^{4 i e} + 10 c^{2} d^{3} f e^{4 i e} - 5 i c d^{4} f e^{4 i e} - d^{5} f e^{4 i e}\right) e^{4 i f x}}"," ",0,"-4*I*a**3*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d)**3) + (-6*a**3*c**2 - 12*I*a**3*c*d + 6*a**3*d**2 + (-8*a**3*c**2*exp(2*I*e) - 8*a**3*d**2*exp(2*I*e))*exp(2*I*f*x))/(-I*c**5*f - c**4*d*f - 2*I*c**3*d**2*f - 2*c**2*d**3*f - I*c*d**4*f - d**5*f + (-2*I*c**5*f*exp(2*I*e) - 6*c**4*d*f*exp(2*I*e) + 4*I*c**3*d**2*f*exp(2*I*e) - 4*c**2*d**3*f*exp(2*I*e) + 6*I*c*d**4*f*exp(2*I*e) + 2*d**5*f*exp(2*I*e))*exp(2*I*f*x) + (-I*c**5*f*exp(4*I*e) - 5*c**4*d*f*exp(4*I*e) + 10*I*c**3*d**2*f*exp(4*I*e) + 10*c**2*d**3*f*exp(4*I*e) - 5*I*c*d**4*f*exp(4*I*e) - d**5*f*exp(4*I*e))*exp(4*I*f*x))","B",0
1096,1,389,0,8.208028," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)","- \frac{2 i a^{2} \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)^{3}} + \frac{2 a^{2} c^{2} + 6 i a^{2} c d - 4 a^{2} d^{2} + \left(2 a^{2} c^{2} e^{2 i e} + 4 i a^{2} c d e^{2 i e} + 6 a^{2} d^{2} e^{2 i e}\right) e^{2 i f x}}{i c^{5} f + c^{4} d f + 2 i c^{3} d^{2} f + 2 c^{2} d^{3} f + i c d^{4} f + d^{5} f + \left(2 i c^{5} f e^{2 i e} + 6 c^{4} d f e^{2 i e} - 4 i c^{3} d^{2} f e^{2 i e} + 4 c^{2} d^{3} f e^{2 i e} - 6 i c d^{4} f e^{2 i e} - 2 d^{5} f e^{2 i e}\right) e^{2 i f x} + \left(i c^{5} f e^{4 i e} + 5 c^{4} d f e^{4 i e} - 10 i c^{3} d^{2} f e^{4 i e} - 10 c^{2} d^{3} f e^{4 i e} + 5 i c d^{4} f e^{4 i e} + d^{5} f e^{4 i e}\right) e^{4 i f x}}"," ",0,"-2*I*a**2*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d)**3) + (2*a**2*c**2 + 6*I*a**2*c*d - 4*a**2*d**2 + (2*a**2*c**2*exp(2*I*e) + 4*I*a**2*c*d*exp(2*I*e) + 6*a**2*d**2*exp(2*I*e))*exp(2*I*f*x))/(I*c**5*f + c**4*d*f + 2*I*c**3*d**2*f + 2*c**2*d**3*f + I*c*d**4*f + d**5*f + (2*I*c**5*f*exp(2*I*e) + 6*c**4*d*f*exp(2*I*e) - 4*I*c**3*d**2*f*exp(2*I*e) + 4*c**2*d**3*f*exp(2*I*e) - 6*I*c*d**4*f*exp(2*I*e) - 2*d**5*f*exp(2*I*e))*exp(2*I*f*x) + (I*c**5*f*exp(4*I*e) + 5*c**4*d*f*exp(4*I*e) - 10*I*c**3*d**2*f*exp(4*I*e) - 10*c**2*d**3*f*exp(4*I*e) + 5*I*c*d**4*f*exp(4*I*e) + d**5*f*exp(4*I*e))*exp(4*I*f*x))","B",0
1097,1,355,0,8.241145," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)","- \frac{i a \log{\left(\frac{- i c + d}{- i c e^{2 i e} - d e^{2 i e}} + e^{2 i f x} \right)}}{f \left(c - i d\right)^{3}} + \frac{4 i a c d - 2 a d^{2} + \left(4 i a c d e^{2 i e} + 4 a d^{2} e^{2 i e}\right) e^{2 i f x}}{i c^{5} f + c^{4} d f + 2 i c^{3} d^{2} f + 2 c^{2} d^{3} f + i c d^{4} f + d^{5} f + \left(2 i c^{5} f e^{2 i e} + 6 c^{4} d f e^{2 i e} - 4 i c^{3} d^{2} f e^{2 i e} + 4 c^{2} d^{3} f e^{2 i e} - 6 i c d^{4} f e^{2 i e} - 2 d^{5} f e^{2 i e}\right) e^{2 i f x} + \left(i c^{5} f e^{4 i e} + 5 c^{4} d f e^{4 i e} - 10 i c^{3} d^{2} f e^{4 i e} - 10 c^{2} d^{3} f e^{4 i e} + 5 i c d^{4} f e^{4 i e} + d^{5} f e^{4 i e}\right) e^{4 i f x}}"," ",0,"-I*a*log((-I*c + d)/(-I*c*exp(2*I*e) - d*exp(2*I*e)) + exp(2*I*f*x))/(f*(c - I*d)**3) + (4*I*a*c*d - 2*a*d**2 + (4*I*a*c*d*exp(2*I*e) + 4*a*d**2*exp(2*I*e))*exp(2*I*f*x))/(I*c**5*f + c**4*d*f + 2*I*c**3*d**2*f + 2*c**2*d**3*f + I*c*d**4*f + d**5*f + (2*I*c**5*f*exp(2*I*e) + 6*c**4*d*f*exp(2*I*e) - 4*I*c**3*d**2*f*exp(2*I*e) + 4*c**2*d**3*f*exp(2*I*e) - 6*I*c*d**4*f*exp(2*I*e) - 2*d**5*f*exp(2*I*e))*exp(2*I*f*x) + (I*c**5*f*exp(4*I*e) + 5*c**4*d*f*exp(4*I*e) - 10*I*c**3*d**2*f*exp(4*I*e) - 10*c**2*d**3*f*exp(4*I*e) + 5*I*c*d**4*f*exp(4*I*e) + d**5*f*exp(4*I*e))*exp(4*I*f*x))","B",0
1098,1,824,0,95.611739," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)","\frac{x \left(- c - 7 i d\right)}{- 2 a c^{4} - 8 i a c^{3} d + 12 a c^{2} d^{2} + 8 i a c d^{3} - 2 a d^{4}} + \frac{- 8 c^{2} d^{3} - 6 i c d^{4} - 2 d^{5} + \left(- 8 c^{2} d^{3} e^{2 i e} + 8 i c d^{4} e^{2 i e}\right) e^{2 i f x}}{a c^{8} f + 2 i a c^{7} d f + 2 a c^{6} d^{2} f + 6 i a c^{5} d^{3} f + 6 i a c^{3} d^{5} f - 2 a c^{2} d^{6} f + 2 i a c d^{7} f - a d^{8} f + \left(2 a c^{8} f e^{2 i e} + 8 a c^{6} d^{2} f e^{2 i e} + 12 a c^{4} d^{4} f e^{2 i e} + 8 a c^{2} d^{6} f e^{2 i e} + 2 a d^{8} f e^{2 i e}\right) e^{2 i f x} + \left(a c^{8} f e^{4 i e} - 2 i a c^{7} d f e^{4 i e} + 2 a c^{6} d^{2} f e^{4 i e} - 6 i a c^{5} d^{3} f e^{4 i e} - 6 i a c^{3} d^{5} f e^{4 i e} - 2 a c^{2} d^{6} f e^{4 i e} - 2 i a c d^{7} f e^{4 i e} - a d^{8} f e^{4 i e}\right) e^{4 i f x}} + \begin{cases} \frac{i e^{- 2 i f x}}{4 a c^{3} f e^{2 i e} + 12 i a c^{2} d f e^{2 i e} - 12 a c d^{2} f e^{2 i e} - 4 i a d^{3} f e^{2 i e}} & \text{for}\: 4 a c^{3} f e^{2 i e} + 12 i a c^{2} d f e^{2 i e} - 12 a c d^{2} f e^{2 i e} - 4 i a d^{3} f e^{2 i e} \neq 0 \\x \left(- \frac{c + 7 i d}{2 a c^{4} + 8 i a c^{3} d - 12 a c^{2} d^{2} - 8 i a c d^{3} + 2 a d^{4}} + \frac{- i c e^{2 i e} - i c + 7 d e^{2 i e} + d}{- 2 i a c^{4} e^{2 i e} + 8 a c^{3} d e^{2 i e} + 12 i a c^{2} d^{2} e^{2 i e} - 8 a c d^{3} e^{2 i e} - 2 i a d^{4} e^{2 i e}}\right) & \text{otherwise} \end{cases} + \frac{2 i d^{2} \left(3 c^{2} - 2 i c d - d^{2}\right) \log{\left(\frac{i c - d}{i c e^{2 i e} + d e^{2 i e}} + e^{2 i f x} \right)}}{a f \left(c - i d\right)^{3} \left(c + i d\right)^{4}}"," ",0,"x*(-c - 7*I*d)/(-2*a*c**4 - 8*I*a*c**3*d + 12*a*c**2*d**2 + 8*I*a*c*d**3 - 2*a*d**4) + (-8*c**2*d**3 - 6*I*c*d**4 - 2*d**5 + (-8*c**2*d**3*exp(2*I*e) + 8*I*c*d**4*exp(2*I*e))*exp(2*I*f*x))/(a*c**8*f + 2*I*a*c**7*d*f + 2*a*c**6*d**2*f + 6*I*a*c**5*d**3*f + 6*I*a*c**3*d**5*f - 2*a*c**2*d**6*f + 2*I*a*c*d**7*f - a*d**8*f + (2*a*c**8*f*exp(2*I*e) + 8*a*c**6*d**2*f*exp(2*I*e) + 12*a*c**4*d**4*f*exp(2*I*e) + 8*a*c**2*d**6*f*exp(2*I*e) + 2*a*d**8*f*exp(2*I*e))*exp(2*I*f*x) + (a*c**8*f*exp(4*I*e) - 2*I*a*c**7*d*f*exp(4*I*e) + 2*a*c**6*d**2*f*exp(4*I*e) - 6*I*a*c**5*d**3*f*exp(4*I*e) - 6*I*a*c**3*d**5*f*exp(4*I*e) - 2*a*c**2*d**6*f*exp(4*I*e) - 2*I*a*c*d**7*f*exp(4*I*e) - a*d**8*f*exp(4*I*e))*exp(4*I*f*x)) + Piecewise((I*exp(-2*I*f*x)/(4*a*c**3*f*exp(2*I*e) + 12*I*a*c**2*d*f*exp(2*I*e) - 12*a*c*d**2*f*exp(2*I*e) - 4*I*a*d**3*f*exp(2*I*e)), Ne(4*a*c**3*f*exp(2*I*e) + 12*I*a*c**2*d*f*exp(2*I*e) - 12*a*c*d**2*f*exp(2*I*e) - 4*I*a*d**3*f*exp(2*I*e), 0)), (x*(-(c + 7*I*d)/(2*a*c**4 + 8*I*a*c**3*d - 12*a*c**2*d**2 - 8*I*a*c*d**3 + 2*a*d**4) + (-I*c*exp(2*I*e) - I*c + 7*d*exp(2*I*e) + d)/(-2*I*a*c**4*exp(2*I*e) + 8*a*c**3*d*exp(2*I*e) + 12*I*a*c**2*d**2*exp(2*I*e) - 8*a*c*d**3*exp(2*I*e) - 2*I*a*d**4*exp(2*I*e))), True)) + 2*I*d**2*(3*c**2 - 2*I*c*d - d**2)*log((I*c - d)/(I*c*exp(2*I*e) + d*exp(2*I*e)) + exp(2*I*f*x))/(a*f*(c - I*d)**3*(c + I*d)**4)","A",0
1099,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \sqrt{c + d \tan{\left(e + f x \right)}}\, dx + \int \left(- 3 \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*sqrt(c + d*tan(e + f*x)), x) + Integral(-3*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-3*I*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x))","F",0
1102,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-2*I*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(-sqrt(c + d*tan(e + f*x)), x))","F",0
1103,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx + \int \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*sqrt(c + d*tan(e + f*x)), x) + Integral(sqrt(c + d*tan(e + f*x))*tan(e + f*x), x))","F",0
1104,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral(sqrt(c + d*tan(e + f*x))/(tan(e + f*x) - I), x)/a","F",0
1105,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\sqrt{c + d \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(sqrt(c + d*tan(e + f*x))/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
1106,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\sqrt{c + d \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}{a^{3}}"," ",0,"I*Integral(sqrt(c + d*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
1107,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int i c \sqrt{c + d \tan{\left(e + f x \right)}}\, dx + \int \left(- 3 c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx + \int \left(- 3 i c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int \left(- 3 i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*c*sqrt(c + d*tan(e + f*x)), x) + Integral(-3*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-3*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4, x) + Integral(-3*I*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(-3*I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x))","F",0
1108,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \left(- c \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx + \int c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 2 i c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-c*sqrt(c + d*tan(e + f*x)), x) + Integral(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-2*I*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(-2*I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x))","F",0
1109,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))**(3/2),x)","i a \left(\int \left(- i c \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx + \int c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*c*sqrt(c + d*tan(e + f*x)), x) + Integral(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x))","F",0
1110,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{c \sqrt{c + d \tan{\left(e + f x \right)}}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(c*sqrt(c + d*tan(e + f*x))/(tan(e + f*x) - I), x) + Integral(d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
1111,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{c \sqrt{c + d \tan{\left(e + f x \right)}}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{d \sqrt{c + d \tan{\left(e + f x \right)}} \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(c*sqrt(c + d*tan(e + f*x))/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
1112,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{c \sqrt{c + d \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 \frac{d \sqrt{c + d \tan{\left(e + f x \right)}} \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(c*sqrt(c + d*tan(e + f*x))/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(d*sqrt(c + d*tan(e + f*x))*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
1113,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx + \int \left(- 3 c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{5}{\left(e + f x \right)}\, dx + \int \left(- 3 i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 3 i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\right)\, dx + \int \left(- 6 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx + \int 2 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int \left(- 6 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*c**2*sqrt(c + d*tan(e + f*x)), x) + Integral(-3*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-3*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**5, x) + Integral(-3*I*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-3*I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4, x) + Integral(-6*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4, x) + Integral(2*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(-6*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x))","F",0
1114,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \left(- c^{2} \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx + \int c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx + \int \left(- 2 i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- 2 i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\right)\, dx + \int \left(- 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx + \int 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 4 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-c**2*sqrt(c + d*tan(e + f*x)), x) + Integral(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4, x) + Integral(-2*I*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(-2*I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-4*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x))","F",0
1115,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))**(5/2),x)","i a \left(\int \left(- i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}}\right)\, dx + \int c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx + \int d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\right)\, dx + \int 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"I*a*(Integral(-I*c**2*sqrt(c + d*tan(e + f*x)), x) + Integral(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3, x) + Integral(-I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2, x) + Integral(-2*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x), x))","F",0
1116,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \left(\int \frac{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx + \int \frac{2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}{\tan{\left(e + f x \right)} - i}\, dx\right)}{a}"," ",0,"-I*(Integral(c**2*sqrt(c + d*tan(e + f*x))/(tan(e + f*x) - I), x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2/(tan(e + f*x) - I), x) + Integral(2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)/(tan(e + f*x) - I), x))/a","F",0
1117,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx + \int \frac{2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \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(c**2*sqrt(c + d*tan(e + f*x))/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x) + Integral(2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x))/a**2","F",0
1118,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \left(\int \frac{c^{2} \sqrt{c + d \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 \frac{d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \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}\, dx + \int \frac{2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \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(c**2*sqrt(c + d*tan(e + f*x))/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x) + Integral(d**2*sqrt(c + d*tan(e + f*x))*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(2*c*d*sqrt(c + d*tan(e + f*x))*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
1119,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**(1/2),x)","- i a^{3} \left(\int \frac{i}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/sqrt(c + d*tan(e + f*x)), x) + Integral(-3*tan(e + f*x)/sqrt(c + d*tan(e + f*x)), x) + Integral(tan(e + f*x)**3/sqrt(c + d*tan(e + f*x)), x) + Integral(-3*I*tan(e + f*x)**2/sqrt(c + d*tan(e + f*x)), x))","F",0
1120,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**(1/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\right)\, dx + \int \left(- \frac{1}{\sqrt{c + d \tan{\left(e + f x \right)}}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(e + f*x)**2/sqrt(c + d*tan(e + f*x)), x) + Integral(-2*I*tan(e + f*x)/sqrt(c + d*tan(e + f*x)), x) + Integral(-1/sqrt(c + d*tan(e + f*x)), x))","F",0
1121,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**(1/2),x)","i a \left(\int \left(- \frac{i}{\sqrt{c + d \tan{\left(e + f x \right)}}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx\right)"," ",0,"I*a*(Integral(-I/sqrt(c + d*tan(e + f*x)), x) + Integral(tan(e + f*x)/sqrt(c + d*tan(e + f*x)), x))","F",0
1122,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{1}{\sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - i \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx}{a}"," ",0,"-I*Integral(1/(sqrt(c + d*tan(e + f*x))*tan(e + f*x) - I*sqrt(c + d*tan(e + f*x))), x)/a","F",0
1123,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{1}{\sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 i \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx}{a^{2}}"," ",0,"-Integral(1/(sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 2*I*sqrt(c + d*tan(e + f*x))*tan(e + f*x) - sqrt(c + d*tan(e + f*x))), x)/a**2","F",0
1124,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{1}{\sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 3 i \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 3 \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + i \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx}{a^{3}}"," ",0,"I*Integral(1/(sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 3*I*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 3*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + I*sqrt(c + d*tan(e + f*x))), x)/a**3","F",0
1125,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**(3/2),x)","- i a^{3} \left(\int \frac{i}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(-3*tan(e + f*x)/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(tan(e + f*x)**3/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(-3*I*tan(e + f*x)**2/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x))","F",0
1126,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**(3/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\right)\, dx + \int \left(- \frac{1}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(e + f*x)**2/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(-2*I*tan(e + f*x)/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(-1/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x))","F",0
1127,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**(3/2),x)","i a \left(\int \left(- \frac{i}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx\right)"," ",0,"I*a*(Integral(-I/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x) + Integral(tan(e + f*x)/(c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x))","F",0
1128,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**(3/2),x)","- \frac{i \int \frac{1}{c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - i c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx}{a}"," ",0,"-I*Integral(1/(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x) - I*c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x)/a","F",0
1129,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**(3/2),x)","- \frac{\int \frac{1}{c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 i c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 2 i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx}{a^{2}}"," ",0,"-Integral(1/(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 2*I*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x) - c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 2*I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x)/a**2","F",0
1130,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**(3/2),x)","\frac{i \int \frac{1}{c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 3 i c \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 3 c \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + i c \sqrt{c + d \tan{\left(e + f x \right)}} + d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)} - 3 i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 3 d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} + i d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)}}\, dx}{a^{3}}"," ",0,"I*Integral(1/(c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 3*I*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 3*c*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + I*c*sqrt(c + d*tan(e + f*x)) + d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4 - 3*I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 3*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 + I*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)), x)/a**3","F",0
1131,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**(5/2),x)","- i a^{3} \left(\int \frac{i}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx + \int \left(- \frac{3 \tan{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\right)\, dx + \int \frac{\tan^{3}{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx + \int \left(- \frac{3 i \tan^{2}{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(-3*tan(e + f*x)/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(tan(e + f*x)**3/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(-3*I*tan(e + f*x)**2/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x))","F",0
1132,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**(5/2),x)","- a^{2} \left(\int \frac{\tan^{2}{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx + \int \left(- \frac{2 i \tan{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\right)\, dx + \int \left(- \frac{1}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\right)\, dx\right)"," ",0,"-a**2*(Integral(tan(e + f*x)**2/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(-2*I*tan(e + f*x)/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(-1/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x))","F",0
1133,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**(5/2),x)","i a \left(\int \left(- \frac{i}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\right)\, dx + \int \frac{\tan{\left(e + f x \right)}}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx\right)"," ",0,"I*a*(Integral(-I/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x) + Integral(tan(e + f*x)/(c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x))","F",0
1134,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))**(5/2),x)","- \frac{i \int \frac{1}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx}{a}"," ",0,"-I*Integral(1/(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x) - I*c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 2*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x)/a","F",0
1135,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**2/(c+d*tan(f*x+e))**(5/2),x)","- \frac{\int \frac{1}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} - c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 4 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)} - 2 i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx}{a^{2}}"," ",0,"-Integral(1/(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 2*I*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x) - c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 4*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4 - 2*I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x)/a**2","F",0
1136,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**3/(c+d*tan(f*x+e))**(5/2),x)","\frac{i \int \frac{1}{c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 3 i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} - 3 c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + i c^{2} \sqrt{c + d \tan{\left(e + f x \right)}} + 2 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)} - 6 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} - 6 c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)} + 2 i c d \sqrt{c + d \tan{\left(e + f x \right)}} \tan{\left(e + f x \right)} + d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{5}{\left(e + f x \right)} - 3 i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)} - 3 d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)} + i d^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}}\, dx}{a^{3}}"," ",0,"I*Integral(1/(c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 3*I*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 - 3*c**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + I*c**2*sqrt(c + d*tan(e + f*x)) + 2*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4 - 6*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 - 6*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2 + 2*I*c*d*sqrt(c + d*tan(e + f*x))*tan(e + f*x) + d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**5 - 3*I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**4 - 3*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**3 + I*d**2*sqrt(c + d*tan(e + f*x))*tan(e + f*x)**2), x)/a**3","F",0
1137,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(5/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)*sqrt(c + d*tan(e + f*x)), x)","F",0
1138,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+I*a*tan(f*x+e))**(3/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(c + d*tan(e + f*x)), x)","F",0
1139,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(1/2),x)","\int \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*sqrt(c + d*tan(e + f*x)), x)","F",0
1140,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
1141,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
1142,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
1143,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(c+d*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1144,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(c+d*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(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)*(c + d*tan(e + f*x))**(3/2), x)","F",0
1145,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(3/2),x)","\int \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(c + d*tan(e + f*x))**(3/2), x)","F",0
1146,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
1147,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
1148,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
1149,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)*(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1150,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)*(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(5/2),x)","\int \sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))*(c + d*tan(e + f*x))**(5/2), x)","F",0
1152,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/sqrt(I*a*(tan(e + f*x) - I)), x)","F",0
1153,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(I*a*(tan(e + f*x) - I))**(3/2), x)","F",0
1154,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(I*a*(tan(e + f*x) - I))**(5/2), x)","F",0
1155,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(c+d*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}}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)/sqrt(c + d*tan(e + f*x)), x)","F",0
1156,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(c+d*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}}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)/sqrt(c + d*tan(e + f*x)), x)","F",0
1157,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))/sqrt(c + d*tan(e + f*x)), x)","F",0
1158,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(e + f*x) - I))*sqrt(c + d*tan(e + f*x))), x)","F",0
1159,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(3/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
1160,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+I*a*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(5/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
1161,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(c+d*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(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
1162,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(c+d*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(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
1163,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))/(c + d*tan(e + f*x))**(3/2), x)","F",0
1164,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(e + f*x) - I))*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1165,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(3/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1166,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(5/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1167,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(5/2)/(c+d*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(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(5/2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
1168,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(3/2)/(c+d*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(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**(3/2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
1169,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(I*a*(tan(e + f*x) - I))/(c + d*tan(e + f*x))**(5/2), x)","F",0
1170,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\sqrt{i a \left(\tan{\left(e + f x \right)} - i\right)} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(I*a*(tan(e + f*x) - I))*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1171,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(3/2)*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1172,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{\frac{5}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((I*a*(tan(e + f*x) - I))**(5/2)*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1173,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e))**n,x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(c + d*tan(e + f*x))**n, x)","F",0
1174,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**3*(c+d*tan(f*x+e))**n,x)","- i a^{3} \left(\int i \left(c + d \tan{\left(e + f x \right)}\right)^{n}\, dx + \int \left(- 3 \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx + \int \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(c + d*tan(e + f*x))**n, x) + Integral(-3*(c + d*tan(e + f*x))**n*tan(e + f*x), x) + Integral((c + d*tan(e + f*x))**n*tan(e + f*x)**3, x) + Integral(-3*I*(c + d*tan(e + f*x))**n*tan(e + f*x)**2, x))","F",0
1175,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**2*(c+d*tan(f*x+e))**n,x)","- a^{2} \left(\int \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx + \int \left(- \left(c + d \tan{\left(e + f x \right)}\right)^{n}\right)\, dx\right)"," ",0,"-a**2*(Integral((c + d*tan(e + f*x))**n*tan(e + f*x)**2, x) + Integral(-2*I*(c + d*tan(e + f*x))**n*tan(e + f*x), x) + Integral(-(c + d*tan(e + f*x))**n, x))","F",0
1176,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))**n,x)","i a \left(\int \left(- i \left(c + d \tan{\left(e + f x \right)}\right)^{n}\right)\, dx + \int \left(c + d \tan{\left(e + f x \right)}\right)^{n} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(c + d*tan(e + f*x))**n, x) + Integral((c + d*tan(e + f*x))**n*tan(e + f*x), x))","F",0
1177,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((c + d*tan(e + f*x))**n/(tan(e + f*x) - I), x)/a","F",0
1178,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{n}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((c + d*tan(e + f*x))**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
1179,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**n/(a+I*a*tan(f*x+e))**3,x)","\frac{i \int \frac{\left(c + d \tan{\left(e + f x \right)}\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}{a^{3}}"," ",0,"I*Integral((c + d*tan(e + f*x))**n/(tan(e + f*x)**3 - 3*I*tan(e + f*x)**2 - 3*tan(e + f*x) + I), x)/a**3","F",0
1180,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e))**3,x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(c + d*tan(e + f*x))**3, x)","F",0
1181,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e))**2,x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(c + d*tan(e + f*x))**2, x)","F",0
1182,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e)),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(c + d*tan(e + f*x)), x)","F",0
1183,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e)),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/(c + d*tan(e + f*x)), x)","F",0
1184,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e))**2,x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/(c + d*tan(e + f*x))**2, x)","F",0
1185,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e))**3,x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/(c + d*tan(e + f*x))**3, x)","F",0
1186,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e))**(3/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*(c + d*tan(e + f*x))**(3/2), x)","F",0
1187,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m*(c+d*tan(f*x+e))**(1/2),x)","\int \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m*sqrt(c + d*tan(e + f*x)), x)","F",0
1188,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/sqrt(c + d*tan(e + f*x)), x)","F",0
1189,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/(c + d*tan(e + f*x))**(3/2), x)","F",0
1190,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))**m/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((I*a*(tan(e + f*x) - I))**m/(c + d*tan(e + f*x))**(5/2), x)","F",0
1191,1,240,0,0.465980," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e)),x)","\begin{cases} a^{3} c x + \frac{a^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 a^{2} b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a^{2} b d x + \frac{3 a^{2} b d \tan{\left(e + f x \right)}}{f} - 3 a b^{2} c x + \frac{3 a b^{2} c \tan{\left(e + f x \right)}}{f} - \frac{3 a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 a b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} c \tan^{2}{\left(e + f x \right)}}{2 f} + b^{3} d x + \frac{b^{3} d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{3} d \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{3} \left(c + d \tan{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c*x + a**3*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*a**2*b*c*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a**2*b*d*x + 3*a**2*b*d*tan(e + f*x)/f - 3*a*b**2*c*x + 3*a*b**2*c*tan(e + f*x)/f - 3*a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*a*b**2*d*tan(e + f*x)**2/(2*f) - b**3*c*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*c*tan(e + f*x)**2/(2*f) + b**3*d*x + b**3*d*tan(e + f*x)**3/(3*f) - b**3*d*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))**3*(c + d*tan(e)), True))","A",0
1192,1,143,0,0.298759," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e)),x)","\begin{cases} a^{2} c x + \frac{a^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 2 a b d x + \frac{2 a b d \tan{\left(e + f x \right)}}{f} - b^{2} c x + \frac{b^{2} c \tan{\left(e + f x \right)}}{f} - \frac{b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*x + a**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + a*b*c*log(tan(e + f*x)**2 + 1)/f - 2*a*b*d*x + 2*a*b*d*tan(e + f*x)/f - b**2*c*x + b**2*c*tan(e + f*x)/f - b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*d*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e)), True))","A",0
1193,1,73,0,0.180699," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x)","\begin{cases} a c x + \frac{a d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - b d x + \frac{b d \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x + a*d*log(tan(e + f*x)**2 + 1)/(2*f) + b*c*log(tan(e + f*x)**2 + 1)/(2*f) - b*d*x + b*d*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e)), True))","A",0
1194,1,524,0,0.944844," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{i c f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{c f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i c}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{d f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i d f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{d}{2 b f \tan{\left(e + f x \right)} - 2 i b f} & \text{for}\: a = - i b \\- \frac{i c f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{c f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i c}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{d f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i d f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{d}{2 b f \tan{\left(e + f x \right)} + 2 i b f} & \text{for}\: a = i b \\\frac{x \left(c + d \tan{\left(e \right)}\right)}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{c x + \frac{d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{2 a c f x}{2 a^{2} f + 2 b^{2} f} - \frac{2 a d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} f + 2 b^{2} f} + \frac{a d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f + 2 b^{2} f} + \frac{2 b c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} f + 2 b^{2} f} - \frac{b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f + 2 b^{2} f} + \frac{2 b d f x}{2 a^{2} f + 2 b^{2} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (I*c*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) + c*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) + I*c/(2*b*f*tan(e + f*x) - 2*I*b*f) + d*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) - I*d*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) - d/(2*b*f*tan(e + f*x) - 2*I*b*f), Eq(a, -I*b)), (-I*c*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + c*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) - I*c/(2*b*f*tan(e + f*x) + 2*I*b*f) + d*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + I*d*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) - d/(2*b*f*tan(e + f*x) + 2*I*b*f), Eq(a, I*b)), (x*(c + d*tan(e))/(a + b*tan(e)), Eq(f, 0)), ((c*x + d*log(tan(e + f*x)**2 + 1)/(2*f))/a, Eq(b, 0)), (2*a*c*f*x/(2*a**2*f + 2*b**2*f) - 2*a*d*log(a/b + tan(e + f*x))/(2*a**2*f + 2*b**2*f) + a*d*log(tan(e + f*x)**2 + 1)/(2*a**2*f + 2*b**2*f) + 2*b*c*log(a/b + tan(e + f*x))/(2*a**2*f + 2*b**2*f) - b*c*log(tan(e + f*x)**2 + 1)/(2*a**2*f + 2*b**2*f) + 2*b*d*f*x/(2*a**2*f + 2*b**2*f), True))","A",0
1195,1,2878,0,1.896857," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{c x + \frac{d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f}}{a^{2}} & \text{for}\: b = 0 \\\frac{c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = - i b \\\frac{c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = i b \\\frac{x \left(c + d \tan{\left(e \right)}\right)}{\left(a + b \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 a^{3} c f x}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{a^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} d}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{2 a^{2} b c f x \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{4 a^{2} b c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b c}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{4 a^{2} b d f x}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{a^{2} b d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a b^{2} c f x}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{4 a b^{2} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 a b^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{4 a b^{2} d f x \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{2 a b^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{2 a b^{2} d}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 b^{3} c f x \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{2 b^{3} c}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} + \frac{2 b^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} - \frac{b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} f + 2 a^{4} b f \tan{\left(e + f x \right)} + 4 a^{3} b^{2} f + 4 a^{2} b^{3} f \tan{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((c*x + d*log(tan(e + f*x)**2 + 1)/(2*f))/a**2, Eq(b, 0)), (c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, -I*b)), (c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, I*b)), (x*(c + d*tan(e))/(a + b*tan(e))**2, Eq(f, 0)), (2*a**3*c*f*x/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a**3*d*log(a/b + tan(e + f*x))/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + a**3*d*log(tan(e + f*x)**2 + 1)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 2*a**3*d/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 2*a**2*b*c*f*x*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 4*a**2*b*c*log(a/b + tan(e + f*x))/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a**2*b*c*log(tan(e + f*x)**2 + 1)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a**2*b*c/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 4*a**2*b*d*f*x/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a**2*b*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + a**2*b*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a*b**2*c*f*x/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 4*a*b**2*c*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*a*b**2*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 4*a*b**2*d*f*x*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 2*a*b**2*d*log(a/b + tan(e + f*x))/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 2*a*b**2*d/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*b**3*c*f*x*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - 2*b**3*c/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) + 2*b**3*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)) - b**3*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*f + 2*a**4*b*f*tan(e + f*x) + 4*a**3*b**2*f + 4*a**2*b**3*f*tan(e + f*x) + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)), True))","A",0
1196,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1197,1,445,0,0.831678," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**2,x)","\begin{cases} a^{3} c^{2} x + \frac{a^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - a^{3} d^{2} x + \frac{a^{3} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{3 a^{2} b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 6 a^{2} b c d x + \frac{6 a^{2} b c d \tan{\left(e + f x \right)}}{f} - \frac{3 a^{2} b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 a^{2} b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - 3 a b^{2} c^{2} x + \frac{3 a b^{2} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{3 a b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 a b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} + 3 a b^{2} d^{2} x + \frac{a b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 a b^{2} d^{2} \tan{\left(e + f x \right)}}{f} - \frac{b^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 2 b^{3} c d x + \frac{2 b^{3} c d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 b^{3} c d \tan{\left(e + f x \right)}}{f} + \frac{b^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{b^{3} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{3} \left(c + d \tan{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**2*x + a**3*c*d*log(tan(e + f*x)**2 + 1)/f - a**3*d**2*x + a**3*d**2*tan(e + f*x)/f + 3*a**2*b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 6*a**2*b*c*d*x + 6*a**2*b*c*d*tan(e + f*x)/f - 3*a**2*b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*a**2*b*d**2*tan(e + f*x)**2/(2*f) - 3*a*b**2*c**2*x + 3*a*b**2*c**2*tan(e + f*x)/f - 3*a*b**2*c*d*log(tan(e + f*x)**2 + 1)/f + 3*a*b**2*c*d*tan(e + f*x)**2/f + 3*a*b**2*d**2*x + a*b**2*d**2*tan(e + f*x)**3/f - 3*a*b**2*d**2*tan(e + f*x)/f - b**3*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*c**2*tan(e + f*x)**2/(2*f) + 2*b**3*c*d*x + 2*b**3*c*d*tan(e + f*x)**3/(3*f) - 2*b**3*c*d*tan(e + f*x)/f + b**3*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*d**2*tan(e + f*x)**4/(4*f) - b**3*d**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**3*(c + d*tan(e))**2, True))","A",0
1198,1,258,0,0.492212," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**2,x)","\begin{cases} a^{2} c^{2} x + \frac{a^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - a^{2} d^{2} x + \frac{a^{2} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{a b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 4 a b c d x + \frac{4 a b c d \tan{\left(e + f x \right)}}{f} - \frac{a b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{a b d^{2} \tan^{2}{\left(e + f x \right)}}{f} - b^{2} c^{2} x + \frac{b^{2} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} + b^{2} d^{2} x + \frac{b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{2} d^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*x + a**2*c*d*log(tan(e + f*x)**2 + 1)/f - a**2*d**2*x + a**2*d**2*tan(e + f*x)/f + a*b*c**2*log(tan(e + f*x)**2 + 1)/f - 4*a*b*c*d*x + 4*a*b*c*d*tan(e + f*x)/f - a*b*d**2*log(tan(e + f*x)**2 + 1)/f + a*b*d**2*tan(e + f*x)**2/f - b**2*c**2*x + b**2*c**2*tan(e + f*x)/f - b**2*c*d*log(tan(e + f*x)**2 + 1)/f + b**2*c*d*tan(e + f*x)**2/f + b**2*d**2*x + b**2*d**2*tan(e + f*x)**3/(3*f) - b**2*d**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e))**2, True))","A",0
1199,1,143,0,0.300148," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**2,x)","\begin{cases} a c^{2} x + \frac{a c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - a d^{2} x + \frac{a d^{2} \tan{\left(e + f x \right)}}{f} + \frac{b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 b c d x + \frac{2 b c d \tan{\left(e + f x \right)}}{f} - \frac{b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*x + a*c*d*log(tan(e + f*x)**2 + 1)/f - a*d**2*x + a*d**2*tan(e + f*x)/f + b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*b*c*d*x + 2*b*c*d*tan(e + f*x)/f - b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + b*d**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e))**2, True))","A",0
1200,1,1040,0,1.334628," ","integrate((c+d*tan(f*x+e))**2/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{2}}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{c^{2} x + \frac{c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - d^{2} x + \frac{d^{2} \tan{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{c^{2} f x \tan{\left(e + f x \right)}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{i c^{2} f x}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{c^{2}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{2 i c d f x \tan{\left(e + f x \right)}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{2 c d f x}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{2 i c d}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{d^{2} f x \tan{\left(e + f x \right)}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{i d^{2} f x}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{i d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{d^{2}}{- 2 i b f \tan{\left(e + f x \right)} - 2 b f} & \text{for}\: a = - i b \\\frac{c^{2} f x \tan{\left(e + f x \right)}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{i c^{2} f x}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{c^{2}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{2 i c d f x \tan{\left(e + f x \right)}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{2 c d f x}{2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{2 i c d}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{d^{2} f x \tan{\left(e + f x \right)}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{i d^{2} f x}{2 i b f \tan{\left(e + f x \right)} - 2 b f} + \frac{i d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} - \frac{d^{2}}{2 i b f \tan{\left(e + f x \right)} - 2 b f} & \text{for}\: a = i b \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{2}}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 a^{2} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b f + 2 b^{3} f} + \frac{2 a b c^{2} f x}{2 a^{2} b f + 2 b^{3} f} - \frac{4 a b c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b f + 2 b^{3} f} + \frac{2 a b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b f + 2 b^{3} f} - \frac{2 a b d^{2} f x}{2 a^{2} b f + 2 b^{3} f} + \frac{2 b^{2} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b f + 2 b^{3} f} - \frac{b^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b f + 2 b^{3} f} + \frac{4 b^{2} c d f x}{2 a^{2} b f + 2 b^{3} f} + \frac{b^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b f + 2 b^{3} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**2/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((c**2*x + c*d*log(tan(e + f*x)**2 + 1)/f - d**2*x + d**2*tan(e + f*x)/f)/a, Eq(b, 0)), (c**2*f*x*tan(e + f*x)/(-2*I*b*f*tan(e + f*x) - 2*b*f) - I*c**2*f*x/(-2*I*b*f*tan(e + f*x) - 2*b*f) + c**2/(-2*I*b*f*tan(e + f*x) - 2*b*f) - 2*I*c*d*f*x*tan(e + f*x)/(-2*I*b*f*tan(e + f*x) - 2*b*f) - 2*c*d*f*x/(-2*I*b*f*tan(e + f*x) - 2*b*f) + 2*I*c*d/(-2*I*b*f*tan(e + f*x) - 2*b*f) + d**2*f*x*tan(e + f*x)/(-2*I*b*f*tan(e + f*x) - 2*b*f) - I*d**2*f*x/(-2*I*b*f*tan(e + f*x) - 2*b*f) - I*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*b*f*tan(e + f*x) - 2*b*f) - d**2*log(tan(e + f*x)**2 + 1)/(-2*I*b*f*tan(e + f*x) - 2*b*f) - d**2/(-2*I*b*f*tan(e + f*x) - 2*b*f), Eq(a, -I*b)), (c**2*f*x*tan(e + f*x)/(2*I*b*f*tan(e + f*x) - 2*b*f) + I*c**2*f*x/(2*I*b*f*tan(e + f*x) - 2*b*f) + c**2/(2*I*b*f*tan(e + f*x) - 2*b*f) + 2*I*c*d*f*x*tan(e + f*x)/(2*I*b*f*tan(e + f*x) - 2*b*f) - 2*c*d*f*x/(2*I*b*f*tan(e + f*x) - 2*b*f) - 2*I*c*d/(2*I*b*f*tan(e + f*x) - 2*b*f) + d**2*f*x*tan(e + f*x)/(2*I*b*f*tan(e + f*x) - 2*b*f) + I*d**2*f*x/(2*I*b*f*tan(e + f*x) - 2*b*f) + I*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*b*f*tan(e + f*x) - 2*b*f) - d**2*log(tan(e + f*x)**2 + 1)/(2*I*b*f*tan(e + f*x) - 2*b*f) - d**2/(2*I*b*f*tan(e + f*x) - 2*b*f), Eq(a, I*b)), (x*(c + d*tan(e))**2/(a + b*tan(e)), Eq(f, 0)), (2*a**2*d**2*log(a/b + tan(e + f*x))/(2*a**2*b*f + 2*b**3*f) + 2*a*b*c**2*f*x/(2*a**2*b*f + 2*b**3*f) - 4*a*b*c*d*log(a/b + tan(e + f*x))/(2*a**2*b*f + 2*b**3*f) + 2*a*b*c*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b*f + 2*b**3*f) - 2*a*b*d**2*f*x/(2*a**2*b*f + 2*b**3*f) + 2*b**2*c**2*log(a/b + tan(e + f*x))/(2*a**2*b*f + 2*b**3*f) - b**2*c**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b*f + 2*b**3*f) + 4*b**2*c*d*f*x/(2*a**2*b*f + 2*b**3*f) + b**2*d**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b*f + 2*b**3*f), True))","A",0
1201,1,4258,0,2.139553," ","integrate((c+d*tan(f*x+e))**2/(a+b*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{2}}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{c^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{4 c d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{d^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i d^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{d^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 d^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i d^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = - i b \\\frac{c^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{4 c d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{d^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i d^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{d^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 d^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i d^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = i b \\\frac{c^{2} x + \frac{c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - d^{2} x + \frac{d^{2} \tan{\left(e + f x \right)}}{f}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{2}}{\left(a + b \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\- \frac{a^{4} d^{2}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a^{3} b c^{2} f x}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} b c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a^{3} b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} b c d}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a^{3} b d^{2} f x}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a^{2} b^{2} c^{2} f x \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 a^{2} b^{2} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} b^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} b^{2} c^{2}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{4 a^{2} b^{2} c d f x}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b^{2} c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a^{2} b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} b^{2} d^{2} f x \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b^{2} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a^{2} b^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} b^{2} d^{2}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a b^{3} c^{2} f x}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b^{3} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a b^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{4 a b^{3} c d f x \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b^{3} c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{a b^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b^{3} c d}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a b^{3} d^{2} f x}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{2 a b^{3} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{a b^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{b^{4} c^{2} f x \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{b^{4} c^{2}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{2 b^{4} c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} - \frac{b^{4} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} + \frac{b^{4} d^{2} f x \tan{\left(e + f x \right)}}{a^{5} b f + a^{4} b^{2} f \tan{\left(e + f x \right)} + 2 a^{3} b^{3} f + 2 a^{2} b^{4} f \tan{\left(e + f x \right)} + a b^{5} f + b^{6} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**2/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (c**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c**2*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 4*c*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - d**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*d**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + d**2*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*d**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*d**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, -I*b)), (c**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c**2*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 4*c*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - d**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*d**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + d**2*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*d**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*d**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, I*b)), ((c**2*x + c*d*log(tan(e + f*x)**2 + 1)/f - d**2*x + d**2*tan(e + f*x)/f)/a**2, Eq(b, 0)), (x*(c + d*tan(e))**2/(a + b*tan(e))**2, Eq(f, 0)), (-a**4*d**2/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a**3*b*c**2*f*x/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - 2*a**3*b*c*d*log(a/b + tan(e + f*x))/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a**3*b*c*d*log(tan(e + f*x)**2 + 1)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*a**3*b*c*d/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a**3*b*d**2*f*x/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a**2*b**2*c**2*f*x*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*a**2*b**2*c**2*log(a/b + tan(e + f*x))/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a**2*b**2*c**2*log(tan(e + f*x)**2 + 1)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a**2*b**2*c**2/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 4*a**2*b**2*c*d*f*x/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - 2*a**2*b**2*c*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a**2*b**2*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a**2*b**2*d**2*f*x*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - 2*a**2*b**2*d**2*log(a/b + tan(e + f*x))/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a**2*b**2*d**2*log(tan(e + f*x)**2 + 1)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a**2*b**2*d**2/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a*b**3*c**2*f*x/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*a*b**3*c**2*log(a/b + tan(e + f*x))*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a*b**3*c**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 4*a*b**3*c*d*f*x*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*a*b**3*c*d*log(a/b + tan(e + f*x))/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - a*b**3*c*d*log(tan(e + f*x)**2 + 1)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*a*b**3*c*d/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a*b**3*d**2*f*x/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - 2*a*b**3*d**2*log(a/b + tan(e + f*x))*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + a*b**3*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - b**4*c**2*f*x*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - b**4*c**2/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + 2*b**4*c*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) - b**4*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)) + b**4*d**2*f*x*tan(e + f*x)/(a**5*b*f + a**4*b**2*f*tan(e + f*x) + 2*a**3*b**3*f + 2*a**2*b**4*f*tan(e + f*x) + a*b**5*f + b**6*f*tan(e + f*x)), True))","A",0
1202,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**2/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1203,1,711,0,1.376031," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**3,x)","\begin{cases} a^{3} c^{3} x + \frac{3 a^{3} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a^{3} c d^{2} x + \frac{3 a^{3} c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{a^{3} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{3} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{3 a^{2} b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 9 a^{2} b c^{2} d x + \frac{9 a^{2} b c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{9 a^{2} b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{9 a^{2} b c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 3 a^{2} b d^{3} x + \frac{a^{2} b d^{3} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 a^{2} b d^{3} \tan{\left(e + f x \right)}}{f} - 3 a b^{2} c^{3} x + \frac{3 a b^{2} c^{3} \tan{\left(e + f x \right)}}{f} - \frac{9 a b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{9 a b^{2} c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 9 a b^{2} c d^{2} x + \frac{3 a b^{2} c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{9 a b^{2} c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{3 a b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 a b^{2} d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 a b^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{b^{3} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} c^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + 3 b^{3} c^{2} d x + \frac{b^{3} c^{2} d \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 b^{3} c^{2} d \tan{\left(e + f x \right)}}{f} + \frac{3 b^{3} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 b^{3} c d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 b^{3} c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - b^{3} d^{3} x + \frac{b^{3} d^{3} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{b^{3} d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{b^{3} d^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{3} \left(c + d \tan{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**3*x + 3*a**3*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a**3*c*d**2*x + 3*a**3*c*d**2*tan(e + f*x)/f - a**3*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + a**3*d**3*tan(e + f*x)**2/(2*f) + 3*a**2*b*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 9*a**2*b*c**2*d*x + 9*a**2*b*c**2*d*tan(e + f*x)/f - 9*a**2*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 9*a**2*b*c*d**2*tan(e + f*x)**2/(2*f) + 3*a**2*b*d**3*x + a**2*b*d**3*tan(e + f*x)**3/f - 3*a**2*b*d**3*tan(e + f*x)/f - 3*a*b**2*c**3*x + 3*a*b**2*c**3*tan(e + f*x)/f - 9*a*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 9*a*b**2*c**2*d*tan(e + f*x)**2/(2*f) + 9*a*b**2*c*d**2*x + 3*a*b**2*c*d**2*tan(e + f*x)**3/f - 9*a*b**2*c*d**2*tan(e + f*x)/f + 3*a*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + 3*a*b**2*d**3*tan(e + f*x)**4/(4*f) - 3*a*b**2*d**3*tan(e + f*x)**2/(2*f) - b**3*c**3*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*c**3*tan(e + f*x)**2/(2*f) + 3*b**3*c**2*d*x + b**3*c**2*d*tan(e + f*x)**3/f - 3*b**3*c**2*d*tan(e + f*x)/f + 3*b**3*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*b**3*c*d**2*tan(e + f*x)**4/(4*f) - 3*b**3*c*d**2*tan(e + f*x)**2/(2*f) - b**3*d**3*x + b**3*d**3*tan(e + f*x)**5/(5*f) - b**3*d**3*tan(e + f*x)**3/(3*f) + b**3*d**3*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))**3*(c + d*tan(e))**3, True))","A",0
1204,1,445,0,0.830506," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**3,x)","\begin{cases} a^{2} c^{3} x + \frac{3 a^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a^{2} c d^{2} x + \frac{3 a^{2} c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{a^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{a b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 6 a b c^{2} d x + \frac{6 a b c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 a b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 a b c d^{2} \tan^{2}{\left(e + f x \right)}}{f} + 2 a b d^{3} x + \frac{2 a b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a b d^{3} \tan{\left(e + f x \right)}}{f} - b^{2} c^{3} x + \frac{b^{2} c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 b^{2} c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 b^{2} c d^{2} x + \frac{b^{2} c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 b^{2} c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{b^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*x + 3*a**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a**2*c*d**2*x + 3*a**2*c*d**2*tan(e + f*x)/f - a**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + a**2*d**3*tan(e + f*x)**2/(2*f) + a*b*c**3*log(tan(e + f*x)**2 + 1)/f - 6*a*b*c**2*d*x + 6*a*b*c**2*d*tan(e + f*x)/f - 3*a*b*c*d**2*log(tan(e + f*x)**2 + 1)/f + 3*a*b*c*d**2*tan(e + f*x)**2/f + 2*a*b*d**3*x + 2*a*b*d**3*tan(e + f*x)**3/(3*f) - 2*a*b*d**3*tan(e + f*x)/f - b**2*c**3*x + b**2*c**3*tan(e + f*x)/f - 3*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*b**2*c**2*d*tan(e + f*x)**2/(2*f) + 3*b**2*c*d**2*x + b**2*c*d**2*tan(e + f*x)**3/f - 3*b**2*c*d**2*tan(e + f*x)/f + b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*d**3*tan(e + f*x)**4/(4*f) - b**2*d**3*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e))**3, True))","A",0
1205,1,240,0,0.462175," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**3,x)","\begin{cases} a c^{3} x + \frac{3 a c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a c d^{2} x + \frac{3 a c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{a d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 b c^{2} d x + \frac{3 b c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 b c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + b d^{3} x + \frac{b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b d^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*x + 3*a*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a*c*d**2*x + 3*a*c*d**2*tan(e + f*x)/f - a*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + a*d**3*tan(e + f*x)**2/(2*f) + b*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*b*c**2*d*x + 3*b*c**2*d*tan(e + f*x)/f - 3*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*b*c*d**2*tan(e + f*x)**2/(2*f) + b*d**3*x + b*d**3*tan(e + f*x)**3/(3*f) - b*d**3*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e))**3, True))","A",0
1206,1,1712,0,2.022998," ","integrate((c+d*tan(f*x+e))**3/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{3}}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{i c^{3} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{c^{3} f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i c^{3}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 c^{2} d f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 i c^{2} d f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 c^{2} d}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 i c d^{2} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 c d^{2} f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 i c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 i c d^{2}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 d^{3} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 i d^{3} f x}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 d^{3} \tan^{2}{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 d^{3}}{2 b f \tan{\left(e + f x \right)} - 2 i b f} & \text{for}\: a = - i b \\- \frac{i c^{3} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{c^{3} f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i c^{3}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 c^{2} d f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 i c^{2} d f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 c^{2} d}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 i c d^{2} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 c d^{2} f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 i c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 i c d^{2}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 d^{3} f x \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 i d^{3} f x}{2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 d^{3} \tan^{2}{\left(e + f x \right)}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 d^{3}}{2 b f \tan{\left(e + f x \right)} + 2 i b f} & \text{for}\: a = i b \\\frac{c^{3} x + \frac{3 c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 c d^{2} x + \frac{3 c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{d^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{3}}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{2 a^{3} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{6 a^{2} b c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 a^{2} b d^{3} \tan{\left(e + f x \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 a b^{2} c^{3} f x}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{6 a b^{2} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{3 a b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{6 a b^{2} c d^{2} f x}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{a b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 b^{3} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{b^{3} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{6 b^{3} c^{2} d f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{3 b^{3} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 b^{3} d^{3} f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 b^{3} d^{3} \tan{\left(e + f x \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**3/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (I*c**3*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) + c**3*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) + I*c**3/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*c**2*d*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) - 3*I*c**2*d*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) - 3*c**2*d/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*I*c*d**2*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*c*d**2*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) - 3*I*c*d**2*log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x) - 2*I*b*f) - 3*I*c*d**2/(2*b*f*tan(e + f*x) - 2*I*b*f) - 3*d**3*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*I*d**3*f*x/(2*b*f*tan(e + f*x) - 2*I*b*f) + I*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*f*tan(e + f*x) - 2*I*b*f) + d**3*log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x) - 2*I*b*f) + 2*d**3*tan(e + f*x)**2/(2*b*f*tan(e + f*x) - 2*I*b*f) + 3*d**3/(2*b*f*tan(e + f*x) - 2*I*b*f), Eq(a, -I*b)), (-I*c**3*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + c**3*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) - I*c**3/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*c**2*d*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*I*c**2*d*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) - 3*c**2*d/(2*b*f*tan(e + f*x) + 2*I*b*f) - 3*I*c*d**2*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*c*d**2*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*I*c*d**2*log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*I*c*d**2/(2*b*f*tan(e + f*x) + 2*I*b*f) - 3*d**3*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) - 3*I*d**3*f*x/(2*b*f*tan(e + f*x) + 2*I*b*f) - I*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*f*tan(e + f*x) + 2*I*b*f) + d**3*log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x) + 2*I*b*f) + 2*d**3*tan(e + f*x)**2/(2*b*f*tan(e + f*x) + 2*I*b*f) + 3*d**3/(2*b*f*tan(e + f*x) + 2*I*b*f), Eq(a, I*b)), ((c**3*x + 3*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*c*d**2*x + 3*c*d**2*tan(e + f*x)/f - d**3*log(tan(e + f*x)**2 + 1)/(2*f) + d**3*tan(e + f*x)**2/(2*f))/a, Eq(b, 0)), (x*(c + d*tan(e))**3/(a + b*tan(e)), Eq(f, 0)), (-2*a**3*d**3*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + 6*a**2*b*c*d**2*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + 2*a**2*b*d**3*tan(e + f*x)/(2*a**2*b**2*f + 2*b**4*f) + 2*a*b**2*c**3*f*x/(2*a**2*b**2*f + 2*b**4*f) - 6*a*b**2*c**2*d*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + 3*a*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) - 6*a*b**2*c*d**2*f*x/(2*a**2*b**2*f + 2*b**4*f) - a*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) + 2*b**3*c**3*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) - b**3*c**3*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) + 6*b**3*c**2*d*f*x/(2*a**2*b**2*f + 2*b**4*f) + 3*b**3*c*d**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) - 2*b**3*d**3*f*x/(2*a**2*b**2*f + 2*b**4*f) + 2*b**3*d**3*tan(e + f*x)/(2*a**2*b**2*f + 2*b**4*f), True))","A",0
1207,1,6730,0,3.312671," ","integrate((c+d*tan(f*x+e))**3/(a+b*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{3}}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{c^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c^{3} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c^{3} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c^{3} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i c^{3}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i c^{2} d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 c^{2} d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i c^{2} d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i c^{2} d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 c d^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{6 i c d^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 c d^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{9 c d^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 i c d^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i d^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 d^{3} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i d^{3} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 i d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{5 i d^{3} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 d^{3}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = - i b \\\frac{c^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c^{3} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{c^{3} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{c^{3} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i c^{3}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i c^{2} d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 c^{2} d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i c^{2} d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i c^{2} d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 c d^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 i c d^{2} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 c d^{2} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{9 c d^{2} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{6 i c d^{2}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i d^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 d^{3} f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i d^{3} f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{4 i d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{5 i d^{3} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 d^{3}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = i b \\\frac{c^{3} x + \frac{3 c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 c d^{2} x + \frac{3 c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{d^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{3}}{\left(a + b \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 a^{5} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{5} d^{3}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{4} b c d^{2}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{4} b d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} b^{2} c^{3} f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{3} b^{2} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{3 a^{3} b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{3} b^{2} c^{2} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{3} b^{2} c d^{2} f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{3} b^{2} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{a^{3} b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} b^{2} d^{3}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{2} b^{3} c^{3} f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 a^{2} b^{3} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b^{3} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{2} b^{3} c^{3}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{12 a^{2} b^{3} c^{2} d f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{3} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{3 a^{2} b^{3} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{3} c d^{2} f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{12 a^{2} b^{3} c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{3} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{3} c d^{2}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 a^{2} b^{3} d^{3} f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{3} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{a^{2} b^{3} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 a b^{4} c^{3} f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 a b^{4} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 a b^{4} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{12 a b^{4} c^{2} d f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{4} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{3 a b^{4} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{4} c^{2} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{4} c d^{2} f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{12 a b^{4} c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{4} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 a b^{4} d^{3} f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{a b^{4} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 b^{5} c^{3} f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 b^{5} c^{3}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 b^{5} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{3 b^{5} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 b^{5} c d^{2} f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{b^{5} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**3/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (c**3*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c**3*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c**3*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c**3*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*c**3/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*c**2*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*c**2*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*c**2*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*c**2*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*c*d**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 6*I*c*d**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*c*d**2*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 9*c*d**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*I*c*d**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*d**3*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*d**3*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*d**3*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*I*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*d**3*log(tan(e + f*x)**2 + 1)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 5*I*d**3*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*d**3/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, -I*b)), (c**3*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c**3*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - c**3*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + c**3*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*c**3/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*c**2*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*c**2*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*c**2*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*c**2*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*c*d**2*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*I*c*d**2*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*c*d**2*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 9*c*d**2*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 6*I*c*d**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*d**3*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*d**3*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*d**3*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 4*I*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*d**3*log(tan(e + f*x)**2 + 1)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 5*I*d**3*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*d**3/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, I*b)), ((c**3*x + 3*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*c*d**2*x + 3*c*d**2*tan(e + f*x)/f - d**3*log(tan(e + f*x)**2 + 1)/(2*f) + d**3*tan(e + f*x)**2/(2*f))/a**2, Eq(b, 0)), (x*(c + d*tan(e))**3/(a + b*tan(e))**2, Eq(f, 0)), (2*a**5*d**3*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*a**5*d**3/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**4*b*c*d**2/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*a**4*b*d**3*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*a**3*b**2*c**3*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**3*b**2*c**2*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 3*a**3*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a**3*b**2*c**2*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**3*b**2*c*d**2*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a**3*b**2*d**3*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - a**3*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*a**3*b**2*d**3/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*a**2*b**3*c**3*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*a**2*b**3*c**3*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*a**2*b**3*c**3*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*a**2*b**3*c**3/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 12*a**2*b**3*c**2*d*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**2*b**3*c**2*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 3*a**2*b**3*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**2*b**3*c*d**2*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 12*a**2*b**3*c*d**2*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a**2*b**3*c*d**2*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 6*a**2*b**3*c*d**2/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*a**2*b**3*d**3*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a**2*b**3*d**3*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - a**2*b**3*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*a*b**4*c**3*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*a*b**4*c**3*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*a*b**4*c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 12*a*b**4*c**2*d*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a*b**4*c**2*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 3*a*b**4*c**2*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a*b**4*c**2*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a*b**4*c*d**2*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 12*a*b**4*c*d**2*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*a*b**4*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*a*b**4*d**3*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + a*b**4*d**3*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*b**5*c**3*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*b**5*c**3/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*b**5*c**2*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 3*b**5*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*b**5*c*d**2*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + b**5*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)), True))","A",0
1208,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**3/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1209,1,2516,0,3.610578," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{4}}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\- \frac{a^{4} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{i a^{4} f x}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{a^{4}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{4 i a^{3} b f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{4 a^{3} b f x}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{4 i a^{3} b}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{6 a^{2} b^{2} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 i a^{2} b^{2} f x}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 i a^{2} b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 a^{2} b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 a^{2} b^{2}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{12 i a b^{3} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{12 a b^{3} f x}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{4 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{4 i a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{8 i a b^{3} \tan^{2}{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{12 i a b^{3}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{3 b^{4} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{3 i b^{4} f x}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{2 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{2 b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{i b^{4} \tan^{3}{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{b^{4} \tan^{2}{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{3 b^{4}}{2 i d f \tan{\left(e + f x \right)} + 2 d f} & \text{for}\: c = - i d \\- \frac{a^{4} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{i a^{4} f x}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{a^{4}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{4 i a^{3} b f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{4 a^{3} b f x}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{4 i a^{3} b}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{6 a^{2} b^{2} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{6 i a^{2} b^{2} f x}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{6 i a^{2} b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 a^{2} b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{6 a^{2} b^{2}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{12 i a b^{3} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{12 a b^{3} f x}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{4 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{4 i a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{8 i a b^{3} \tan^{2}{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{12 i a b^{3}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{3 b^{4} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{3 i b^{4} f x}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} + \frac{2 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{2 b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{i b^{4} \tan^{3}{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{b^{4} \tan^{2}{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} - \frac{3 b^{4}}{- 2 i d f \tan{\left(e + f x \right)} + 2 d f} & \text{for}\: c = i d \\\frac{a^{4} x + \frac{2 a^{3} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 6 a^{2} b^{2} x + \frac{6 a^{2} b^{2} \tan{\left(e + f x \right)}}{f} - \frac{2 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{2 a b^{3} \tan^{2}{\left(e + f x \right)}}{f} + b^{4} x + \frac{b^{4} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{4} \tan{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{4}}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 a^{4} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 a^{4} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{a^{4} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{8 a^{3} b c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{4 a^{3} b c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{8 a^{3} b d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{12 a^{2} b^{2} c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{12 a^{2} b^{2} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{6 a^{2} b^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{8 a b^{3} c^{3} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{8 a b^{3} c^{2} d^{2} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{4 a b^{3} c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{8 a b^{3} d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{8 a b^{3} d^{4} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 b^{4} c^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 b^{4} c^{3} d \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{b^{4} c^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 b^{4} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 b^{4} c d^{3} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{b^{4} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{b^{4} d^{4} \tan^{2}{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**4/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (-a**4*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) + I*a**4*f*x/(2*I*d*f*tan(e + f*x) + 2*d*f) - a**4/(2*I*d*f*tan(e + f*x) + 2*d*f) + 4*I*a**3*b*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 4*a**3*b*f*x/(2*I*d*f*tan(e + f*x) + 2*d*f) - 4*I*a**3*b/(2*I*d*f*tan(e + f*x) + 2*d*f) - 6*a**2*b**2*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 6*I*a**2*b**2*f*x/(2*I*d*f*tan(e + f*x) + 2*d*f) + 6*I*a**2*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 6*a**2*b**2*log(tan(e + f*x)**2 + 1)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 6*a**2*b**2/(2*I*d*f*tan(e + f*x) + 2*d*f) - 12*I*a*b**3*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) - 12*a*b**3*f*x/(2*I*d*f*tan(e + f*x) + 2*d*f) - 4*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 4*I*a*b**3*log(tan(e + f*x)**2 + 1)/(2*I*d*f*tan(e + f*x) + 2*d*f) + 8*I*a*b**3*tan(e + f*x)**2/(2*I*d*f*tan(e + f*x) + 2*d*f) + 12*I*a*b**3/(2*I*d*f*tan(e + f*x) + 2*d*f) + 3*b**4*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) - 3*I*b**4*f*x/(2*I*d*f*tan(e + f*x) + 2*d*f) - 2*I*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*d*f*tan(e + f*x) + 2*d*f) - 2*b**4*log(tan(e + f*x)**2 + 1)/(2*I*d*f*tan(e + f*x) + 2*d*f) + I*b**4*tan(e + f*x)**3/(2*I*d*f*tan(e + f*x) + 2*d*f) - b**4*tan(e + f*x)**2/(2*I*d*f*tan(e + f*x) + 2*d*f) - 3*b**4/(2*I*d*f*tan(e + f*x) + 2*d*f), Eq(c, -I*d)), (-a**4*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - I*a**4*f*x/(-2*I*d*f*tan(e + f*x) + 2*d*f) - a**4/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 4*I*a**3*b*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 4*a**3*b*f*x/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 4*I*a**3*b/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 6*a**2*b**2*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 6*I*a**2*b**2*f*x/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 6*I*a**2*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 6*a**2*b**2*log(tan(e + f*x)**2 + 1)/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 6*a**2*b**2/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 12*I*a*b**3*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 12*a*b**3*f*x/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 4*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 4*I*a*b**3*log(tan(e + f*x)**2 + 1)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 8*I*a*b**3*tan(e + f*x)**2/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 12*I*a*b**3/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 3*b**4*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 3*I*b**4*f*x/(-2*I*d*f*tan(e + f*x) + 2*d*f) + 2*I*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 2*b**4*log(tan(e + f*x)**2 + 1)/(-2*I*d*f*tan(e + f*x) + 2*d*f) - I*b**4*tan(e + f*x)**3/(-2*I*d*f*tan(e + f*x) + 2*d*f) - b**4*tan(e + f*x)**2/(-2*I*d*f*tan(e + f*x) + 2*d*f) - 3*b**4/(-2*I*d*f*tan(e + f*x) + 2*d*f), Eq(c, I*d)), ((a**4*x + 2*a**3*b*log(tan(e + f*x)**2 + 1)/f - 6*a**2*b**2*x + 6*a**2*b**2*tan(e + f*x)/f - 2*a*b**3*log(tan(e + f*x)**2 + 1)/f + 2*a*b**3*tan(e + f*x)**2/f + b**4*x + b**4*tan(e + f*x)**3/(3*f) - b**4*tan(e + f*x)/f)/c, Eq(d, 0)), (x*(a + b*tan(e))**4/(c + d*tan(e)), Eq(f, 0)), (2*a**4*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + 2*a**4*d**4*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - a**4*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 8*a**3*b*c*d**3*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + 4*a**3*b*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) + 8*a**3*b*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 12*a**2*b**2*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 12*a**2*b**2*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + 6*a**2*b**2*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 8*a*b**3*c**3*d*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + 8*a*b**3*c**2*d**2*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) - 4*a*b**3*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 8*a*b**3*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 8*a*b**3*d**4*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) + 2*b**4*c**4*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 2*b**4*c**3*d*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) + b**4*c**2*d**2*tan(e + f*x)**2/(2*c**2*d**3*f + 2*d**5*f) + 2*b**4*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) - 2*b**4*c*d**3*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) - b**4*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) + b**4*d**4*tan(e + f*x)**2/(2*c**2*d**3*f + 2*d**5*f), True))","A",0
1210,1,1712,0,2.047352," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{3}}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a^{3} x + \frac{3 a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a b^{2} x + \frac{3 a b^{2} \tan{\left(e + f x \right)}}{f} - \frac{b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{c} & \text{for}\: d = 0 \\\frac{i a^{3} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{a^{3} f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i a^{3}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 a^{2} b f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 i a^{2} b f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 a^{2} b}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 i a b^{2} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 a b^{2} f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 i a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 i a b^{2}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 b^{3} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 i b^{3} f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 b^{3} \tan^{2}{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 b^{3}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} & \text{for}\: c = - i d \\- \frac{i a^{3} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{a^{3} f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i a^{3}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 a^{2} b f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 i a^{2} b f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 a^{2} b}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 i a b^{2} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 a b^{2} f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 i a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 i a b^{2}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 b^{3} f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 i b^{3} f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 b^{3} \tan^{2}{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 b^{3}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{3}}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 a^{3} c d^{2} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 a^{3} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{a^{3} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{6 a^{2} b c d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{3 a^{2} b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{6 a^{2} b d^{3} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{6 a b^{2} c^{2} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{6 a b^{2} c d^{2} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{3 a b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 b^{3} c^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 b^{3} c^{2} d \tan{\left(e + f x \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{b^{3} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 b^{3} d^{3} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 b^{3} d^{3} \tan{\left(e + f x \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**3/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), ((a**3*x + 3*a**2*b*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a*b**2*x + 3*a*b**2*tan(e + f*x)/f - b**3*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*tan(e + f*x)**2/(2*f))/c, Eq(d, 0)), (I*a**3*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) + a**3*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) + I*a**3/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*a**2*b*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) - 3*I*a**2*b*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) - 3*a**2*b/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*I*a*b**2*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*a*b**2*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) - 3*I*a*b**2*log(tan(e + f*x)**2 + 1)/(2*d*f*tan(e + f*x) - 2*I*d*f) - 3*I*a*b**2/(2*d*f*tan(e + f*x) - 2*I*d*f) - 3*b**3*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*I*b**3*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) + I*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) + b**3*log(tan(e + f*x)**2 + 1)/(2*d*f*tan(e + f*x) - 2*I*d*f) + 2*b**3*tan(e + f*x)**2/(2*d*f*tan(e + f*x) - 2*I*d*f) + 3*b**3/(2*d*f*tan(e + f*x) - 2*I*d*f), Eq(c, -I*d)), (-I*a**3*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + a**3*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) - I*a**3/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*a**2*b*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*I*a**2*b*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) - 3*a**2*b/(2*d*f*tan(e + f*x) + 2*I*d*f) - 3*I*a*b**2*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*a*b**2*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*I*a*b**2*log(tan(e + f*x)**2 + 1)/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*I*a*b**2/(2*d*f*tan(e + f*x) + 2*I*d*f) - 3*b**3*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) - 3*I*b**3*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) - I*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + b**3*log(tan(e + f*x)**2 + 1)/(2*d*f*tan(e + f*x) + 2*I*d*f) + 2*b**3*tan(e + f*x)**2/(2*d*f*tan(e + f*x) + 2*I*d*f) + 3*b**3/(2*d*f*tan(e + f*x) + 2*I*d*f), Eq(c, I*d)), (x*(a + b*tan(e))**3/(c + d*tan(e)), Eq(f, 0)), (2*a**3*c*d**2*f*x/(2*c**2*d**2*f + 2*d**4*f) + 2*a**3*d**3*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) - a**3*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 6*a**2*b*c*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) + 3*a**2*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) + 6*a**2*b*d**3*f*x/(2*c**2*d**2*f + 2*d**4*f) + 6*a*b**2*c**2*d*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) - 6*a*b**2*c*d**2*f*x/(2*c**2*d**2*f + 2*d**4*f) + 3*a*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 2*b**3*c**3*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) + 2*b**3*c**2*d*tan(e + f*x)/(2*c**2*d**2*f + 2*d**4*f) - b**3*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 2*b**3*d**3*f*x/(2*c**2*d**2*f + 2*d**4*f) + 2*b**3*d**3*tan(e + f*x)/(2*c**2*d**2*f + 2*d**4*f), True))","A",0
1211,1,1040,0,1.345688," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{2}}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a^{2} x + \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - b^{2} x + \frac{b^{2} \tan{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\\frac{a^{2} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{i a^{2} f x}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{a^{2}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{2 i a b f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{2 a b f x}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{2 i a b}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{b^{2} f x \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{i b^{2} f x}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{i b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{b^{2}}{- 2 i d f \tan{\left(e + f x \right)} - 2 d f} & \text{for}\: c = - i d \\\frac{a^{2} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{i a^{2} f x}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{a^{2}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{2 i a b f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{2 a b f x}{2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{2 i a b}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{b^{2} f x \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{i b^{2} f x}{2 i d f \tan{\left(e + f x \right)} - 2 d f} + \frac{i b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} - \frac{b^{2}}{2 i d f \tan{\left(e + f x \right)} - 2 d f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{2}}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 a^{2} c d f x}{2 c^{2} d f + 2 d^{3} f} + \frac{2 a^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{a^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{4 a b c d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} + \frac{2 a b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} + \frac{4 a b d^{2} f x}{2 c^{2} d f + 2 d^{3} f} + \frac{2 b^{2} c^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{2 b^{2} c d f x}{2 c^{2} d f + 2 d^{3} f} + \frac{b^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**2/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), ((a**2*x + a*b*log(tan(e + f*x)**2 + 1)/f - b**2*x + b**2*tan(e + f*x)/f)/c, Eq(d, 0)), (a**2*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) - 2*d*f) - I*a**2*f*x/(-2*I*d*f*tan(e + f*x) - 2*d*f) + a**2/(-2*I*d*f*tan(e + f*x) - 2*d*f) - 2*I*a*b*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) - 2*d*f) - 2*a*b*f*x/(-2*I*d*f*tan(e + f*x) - 2*d*f) + 2*I*a*b/(-2*I*d*f*tan(e + f*x) - 2*d*f) + b**2*f*x*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) - 2*d*f) - I*b**2*f*x/(-2*I*d*f*tan(e + f*x) - 2*d*f) - I*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*I*d*f*tan(e + f*x) - 2*d*f) - b**2*log(tan(e + f*x)**2 + 1)/(-2*I*d*f*tan(e + f*x) - 2*d*f) - b**2/(-2*I*d*f*tan(e + f*x) - 2*d*f), Eq(c, -I*d)), (a**2*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) - 2*d*f) + I*a**2*f*x/(2*I*d*f*tan(e + f*x) - 2*d*f) + a**2/(2*I*d*f*tan(e + f*x) - 2*d*f) + 2*I*a*b*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) - 2*d*f) - 2*a*b*f*x/(2*I*d*f*tan(e + f*x) - 2*d*f) - 2*I*a*b/(2*I*d*f*tan(e + f*x) - 2*d*f) + b**2*f*x*tan(e + f*x)/(2*I*d*f*tan(e + f*x) - 2*d*f) + I*b**2*f*x/(2*I*d*f*tan(e + f*x) - 2*d*f) + I*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*d*f*tan(e + f*x) - 2*d*f) - b**2*log(tan(e + f*x)**2 + 1)/(2*I*d*f*tan(e + f*x) - 2*d*f) - b**2/(2*I*d*f*tan(e + f*x) - 2*d*f), Eq(c, I*d)), (x*(a + b*tan(e))**2/(c + d*tan(e)), Eq(f, 0)), (2*a**2*c*d*f*x/(2*c**2*d*f + 2*d**3*f) + 2*a**2*d**2*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) - a**2*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f) - 4*a*b*c*d*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) + 2*a*b*c*d*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f) + 4*a*b*d**2*f*x/(2*c**2*d*f + 2*d**3*f) + 2*b**2*c**2*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) - 2*b**2*c*d*f*x/(2*c**2*d*f + 2*d**3*f) + b**2*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f), True))","A",0
1212,1,524,0,0.949864," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{i a f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{a f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i a}{2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{b f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i b f x}{2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{b}{2 d f \tan{\left(e + f x \right)} - 2 i d f} & \text{for}\: c = - i d \\- \frac{i a f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{a f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i a}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{b f x \tan{\left(e + f x \right)}}{2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i b f x}{2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{b}{2 d f \tan{\left(e + f x \right)} + 2 i d f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right)}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{a x + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f}}{c} & \text{for}\: d = 0 \\\frac{2 a c f x}{2 c^{2} f + 2 d^{2} f} + \frac{2 a d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} f + 2 d^{2} f} - \frac{a d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f + 2 d^{2} f} - \frac{2 b c \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} f + 2 d^{2} f} + \frac{b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f + 2 d^{2} f} + \frac{2 b d f x}{2 c^{2} f + 2 d^{2} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (I*a*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) + a*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) + I*a/(2*d*f*tan(e + f*x) - 2*I*d*f) + b*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) - 2*I*d*f) - I*b*f*x/(2*d*f*tan(e + f*x) - 2*I*d*f) - b/(2*d*f*tan(e + f*x) - 2*I*d*f), Eq(c, -I*d)), (-I*a*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + a*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) - I*a/(2*d*f*tan(e + f*x) + 2*I*d*f) + b*f*x*tan(e + f*x)/(2*d*f*tan(e + f*x) + 2*I*d*f) + I*b*f*x/(2*d*f*tan(e + f*x) + 2*I*d*f) - b/(2*d*f*tan(e + f*x) + 2*I*d*f), Eq(c, I*d)), (x*(a + b*tan(e))/(c + d*tan(e)), Eq(f, 0)), ((a*x + b*log(tan(e + f*x)**2 + 1)/(2*f))/c, Eq(d, 0)), (2*a*c*f*x/(2*c**2*f + 2*d**2*f) + 2*a*d*log(c/d + tan(e + f*x))/(2*c**2*f + 2*d**2*f) - a*d*log(tan(e + f*x)**2 + 1)/(2*c**2*f + 2*d**2*f) - 2*b*c*log(c/d + tan(e + f*x))/(2*c**2*f + 2*d**2*f) + b*c*log(tan(e + f*x)**2 + 1)/(2*c**2*f + 2*d**2*f) + 2*b*d*f*x/(2*c**2*f + 2*d**2*f), True))","A",0
1213,1,8050,0,25.244710," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\frac{2 a f x}{2 a^{2} f + 2 b^{2} f} + \frac{2 b \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} f + 2 b^{2} f} - \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f + 2 b^{2} f}}{c} & \text{for}\: d = 0 \\\frac{\frac{2 c f x}{2 c^{2} f + 2 d^{2} f} + \frac{2 d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} f + 2 d^{2} f} - \frac{d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} f + 2 d^{2} f}}{a} & \text{for}\: b = 0 \\\frac{i c^{2} f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{c^{2} f x}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{i c^{2}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 c d f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{2 i c d f x}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{i d^{2} f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{d^{2} f x}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{2 i d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{i d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{i d^{2}}{2 b c^{3} f \tan{\left(e + f x \right)} - 2 i b c^{3} f + 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} - 2 i b c d^{2} f + 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} & \text{for}\: a = - i b \\- \frac{i c^{2} f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{c^{2} f x}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{i c^{2}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 c d f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 i c d f x}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{i d^{2} f x \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{d^{2} f x}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{2 i d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} + \frac{i d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} - \frac{i d^{2}}{2 b c^{3} f \tan{\left(e + f x \right)} + 2 i b c^{3} f - 2 i b c^{2} d f \tan{\left(e + f x \right)} + 2 b c^{2} d f + 2 b c d^{2} f \tan{\left(e + f x \right)} + 2 i b c d^{2} f - 2 i b d^{3} f \tan{\left(e + f x \right)} + 2 b d^{3} f} & \text{for}\: a = i b \\\frac{c^{3} d f x}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} + \frac{c^{2} d^{2} f x \tan{\left(e + f x \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} + \frac{2 c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{c^{2} d^{2}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{c d^{3} f x}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} + \frac{2 c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{d^{4} f x \tan{\left(e + f x \right)}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} - \frac{d^{4}}{b c^{5} f + b c^{4} d f \tan{\left(e + f x \right)} + 2 b c^{3} d^{2} f + 2 b c^{2} d^{3} f \tan{\left(e + f x \right)} + b c d^{4} f + b d^{5} f \tan{\left(e + f x \right)}} & \text{for}\: a = \frac{b c}{d} \\\frac{i a^{2} f x \tan{\left(e + f x \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{a^{2} f x}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{i a^{2}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} - \frac{2 a b f x \tan{\left(e + f x \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{2 i a b f x}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{i b^{2} f x \tan{\left(e + f x \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{b^{2} f x}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} - \frac{2 b^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{2 i b^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} - \frac{i b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} + \frac{i b^{2}}{2 a^{3} d f \tan{\left(e + f x \right)} - 2 i a^{3} d f + 2 i a^{2} b d f \tan{\left(e + f x \right)} + 2 a^{2} b d f + 2 a b^{2} d f \tan{\left(e + f x \right)} - 2 i a b^{2} d f + 2 i b^{3} d f \tan{\left(e + f x \right)} + 2 b^{3} d f} & \text{for}\: c = - i d \\\frac{a^{2} f x \tan{\left(e + f x \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{i a^{2} f x}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{a^{2}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} - \frac{2 i a b f x \tan{\left(e + f x \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{2 a b f x}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{b^{2} f x \tan{\left(e + f x \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{i b^{2} f x}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} - \frac{2 i b^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{2 b^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{i b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} + \frac{b^{2}}{2 i a^{3} d f \tan{\left(e + f x \right)} - 2 a^{3} d f + 2 a^{2} b d f \tan{\left(e + f x \right)} + 2 i a^{2} b d f + 2 i a b^{2} d f \tan{\left(e + f x \right)} - 2 a b^{2} d f + 2 b^{3} d f \tan{\left(e + f x \right)} + 2 i b^{3} d f} & \text{for}\: c = i d \\\frac{x}{\left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right)} & \text{for}\: f = 0 \\\frac{2 a^{2} c d f x}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} + \frac{2 a^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} - \frac{a^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} - \frac{2 a b c^{2} f x}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} - \frac{2 a b d^{2} f x}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} - \frac{2 b^{2} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} + \frac{b^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} + \frac{2 b^{2} c d f x}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} - \frac{2 b^{2} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} + \frac{2 b^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} c^{2} d f + 2 a^{3} d^{3} f - 2 a^{2} b c^{3} f - 2 a^{2} b c d^{2} f + 2 a b^{2} c^{2} d f + 2 a b^{2} d^{3} f - 2 b^{3} c^{3} f - 2 b^{3} c d^{2} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((2*a*f*x/(2*a**2*f + 2*b**2*f) + 2*b*log(a/b + tan(e + f*x))/(2*a**2*f + 2*b**2*f) - b*log(tan(e + f*x)**2 + 1)/(2*a**2*f + 2*b**2*f))/c, Eq(d, 0)), ((2*c*f*x/(2*c**2*f + 2*d**2*f) + 2*d*log(c/d + tan(e + f*x))/(2*c**2*f + 2*d**2*f) - d*log(tan(e + f*x)**2 + 1)/(2*c**2*f + 2*d**2*f))/a, Eq(b, 0)), (I*c**2*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + c**2*f*x/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + I*c**2/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*c*d*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + 2*I*c*d*f*x/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + I*d**2*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + d**2*f*x/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + 2*I*d**2*log(c/d + tan(e + f*x))/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - I*d**2*log(tan(e + f*x)**2 + 1)/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + I*d**2/(2*b*c**3*f*tan(e + f*x) - 2*I*b*c**3*f + 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) - 2*I*b*c*d**2*f + 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f), Eq(a, -I*b)), (-I*c**2*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + c**2*f*x/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - I*c**2/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*c*d*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*I*c*d*f*x/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - I*d**2*f*x*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + d**2*f*x/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - 2*I*d**2*log(c/d + tan(e + f*x))/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) + I*d**2*log(tan(e + f*x)**2 + 1)/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f) - I*d**2/(2*b*c**3*f*tan(e + f*x) + 2*I*b*c**3*f - 2*I*b*c**2*d*f*tan(e + f*x) + 2*b*c**2*d*f + 2*b*c*d**2*f*tan(e + f*x) + 2*I*b*c*d**2*f - 2*I*b*d**3*f*tan(e + f*x) + 2*b*d**3*f), Eq(a, I*b)), (c**3*d*f*x/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) + c**2*d**2*f*x*tan(e + f*x)/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) + 2*c**2*d**2*log(c/d + tan(e + f*x))/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - c**2*d**2*log(tan(e + f*x)**2 + 1)/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - c**2*d**2/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - c*d**3*f*x/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) + 2*c*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - c*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - d**4*f*x*tan(e + f*x)/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)) - d**4/(b*c**5*f + b*c**4*d*f*tan(e + f*x) + 2*b*c**3*d**2*f + 2*b*c**2*d**3*f*tan(e + f*x) + b*c*d**4*f + b*d**5*f*tan(e + f*x)), Eq(a, b*c/d)), (I*a**2*f*x*tan(e + f*x)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + a**2*f*x/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + I*a**2/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) - 2*a*b*f*x*tan(e + f*x)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + 2*I*a*b*f*x/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + I*b**2*f*x*tan(e + f*x)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + b**2*f*x/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) - 2*b**2*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + 2*I*b**2*log(a/b + tan(e + f*x))/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) - I*b**2*log(tan(e + f*x)**2 + 1)/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f) + I*b**2/(2*a**3*d*f*tan(e + f*x) - 2*I*a**3*d*f + 2*I*a**2*b*d*f*tan(e + f*x) + 2*a**2*b*d*f + 2*a*b**2*d*f*tan(e + f*x) - 2*I*a*b**2*d*f + 2*I*b**3*d*f*tan(e + f*x) + 2*b**3*d*f), Eq(c, -I*d)), (a**2*f*x*tan(e + f*x)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + I*a**2*f*x/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + a**2/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) - 2*I*a*b*f*x*tan(e + f*x)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + 2*a*b*f*x/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + b**2*f*x*tan(e + f*x)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + I*b**2*f*x/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) - 2*I*b**2*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + 2*b**2*log(a/b + tan(e + f*x))/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + I*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) - b**2*log(tan(e + f*x)**2 + 1)/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f) + b**2/(2*I*a**3*d*f*tan(e + f*x) - 2*a**3*d*f + 2*a**2*b*d*f*tan(e + f*x) + 2*I*a**2*b*d*f + 2*I*a*b**2*d*f*tan(e + f*x) - 2*a*b**2*d*f + 2*b**3*d*f*tan(e + f*x) + 2*I*b**3*d*f), Eq(c, I*d)), (x/((a + b*tan(e))*(c + d*tan(e))), Eq(f, 0)), (2*a**2*c*d*f*x/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) + 2*a**2*d**2*log(c/d + tan(e + f*x))/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) - a**2*d**2*log(tan(e + f*x)**2 + 1)/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) - 2*a*b*c**2*f*x/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) - 2*a*b*d**2*f*x/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) - 2*b**2*c**2*log(a/b + tan(e + f*x))/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) + b**2*c**2*log(tan(e + f*x)**2 + 1)/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) + 2*b**2*c*d*f*x/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) - 2*b**2*d**2*log(a/b + tan(e + f*x))/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f) + 2*b**2*d**2*log(c/d + tan(e + f*x))/(2*a**3*c**2*d*f + 2*a**3*d**3*f - 2*a**2*b*c**3*f - 2*a**2*b*c*d**2*f + 2*a*b**2*c**2*d*f + 2*a*b**2*d**3*f - 2*b**3*c**3*f - 2*b**3*c*d**2*f), True))","A",0
1214,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1215,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1216,1,8928,0,5.559506," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{4}}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a^{4} x + \frac{2 a^{3} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 6 a^{2} b^{2} x + \frac{6 a^{2} b^{2} \tan{\left(e + f x \right)}}{f} - \frac{2 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{2 a b^{3} \tan^{2}{\left(e + f x \right)}}{f} + b^{4} x + \frac{b^{4} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{4} \tan{\left(e + f x \right)}}{f}}{c^{2}} & \text{for}\: d = 0 \\\frac{a^{4} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{4} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{4} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{4} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{4}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i a^{3} b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 a^{3} b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i a^{3} b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i a^{3} b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 a^{2} b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{12 i a^{2} b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{6 a^{2} b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{18 a^{2} b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{12 i a^{2} b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{12 i a b^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{24 a b^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{12 i a b^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{16 i a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{8 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{20 i a b^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{16 a b^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{9 b^{4} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{18 i b^{4} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{9 b^{4} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 b^{4} \tan^{3}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{19 b^{4} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{14 i b^{4}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = - i d \\\frac{a^{4} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{4} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{4} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{4} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{4}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i a^{3} b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 a^{3} b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i a^{3} b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i a^{3} b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 a^{2} b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{12 i a^{2} b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{6 a^{2} b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{18 a^{2} b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{12 i a^{2} b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{12 i a b^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{24 a b^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{12 i a b^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{16 i a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{8 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{20 i a b^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{16 a b^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{9 b^{4} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{18 i b^{4} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{9 b^{4} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{8 b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 b^{4} \tan^{3}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{19 b^{4} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{14 i b^{4}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{4}}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{a^{4} c^{3} d^{3} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{a^{4} c^{2} d^{4} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a^{4} c^{2} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} c^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} c^{2} d^{4}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} c d^{5} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a^{4} c d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} c d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} d^{6} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{a^{4} d^{6}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{4 a^{3} b c^{3} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} b c^{3} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} b c^{3} d^{3}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{8 a^{3} b c^{2} d^{4} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{4 a^{3} b c^{2} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} b c^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{8 a^{3} b c d^{5} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} b c d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} b c d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} b c d^{5}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} b d^{6} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} b d^{6} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{2} c^{4} d^{2}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{2} c^{3} d^{3} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{2} c^{2} d^{4} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{12 a^{2} b^{2} c^{2} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{2} c^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b^{2} c^{2} d^{4}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{2} c d^{5} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{12 a^{2} b^{2} c d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{2} c d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b^{2} d^{6} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a b^{3} c^{5} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a b^{3} c^{5} d}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a b^{3} c^{4} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{12 a b^{3} c^{3} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 a b^{3} c^{3} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{4 a b^{3} c^{3} d^{3}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{8 a b^{3} c^{2} d^{4} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{12 a b^{3} c^{2} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 a b^{3} c^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{8 a b^{3} c d^{5} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a b^{3} c d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 a b^{3} d^{6} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 b^{4} c^{6} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 b^{4} c^{6}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{2 b^{4} c^{5} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{4 b^{4} c^{4} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{b^{4} c^{4} d^{2} \tan^{2}{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{3 b^{4} c^{4} d^{2}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{b^{4} c^{3} d^{3} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{4 b^{4} c^{3} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{b^{4} c^{2} d^{4} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{b^{4} c^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{2 b^{4} c^{2} d^{4} \tan^{2}{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{b^{4} c^{2} d^{4}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{b^{4} c d^{5} f x}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{b^{4} c d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} - \frac{b^{4} d^{6} f x \tan{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} + \frac{b^{4} d^{6} \tan^{2}{\left(e + f x \right)}}{c^{5} d^{3} f + c^{4} d^{4} f \tan{\left(e + f x \right)} + 2 c^{3} d^{5} f + 2 c^{2} d^{6} f \tan{\left(e + f x \right)} + c d^{7} f + d^{8} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**4/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), ((a**4*x + 2*a**3*b*log(tan(e + f*x)**2 + 1)/f - 6*a**2*b**2*x + 6*a**2*b**2*tan(e + f*x)/f - 2*a*b**3*log(tan(e + f*x)**2 + 1)/f + 2*a*b**3*tan(e + f*x)**2/f + b**4*x + b**4*tan(e + f*x)**3/(3*f) - b**4*tan(e + f*x)/f)/c**2, Eq(d, 0)), (a**4*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**4*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**4*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**4*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**4/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*a**3*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*a**3*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*a**3*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*a**3*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*a**2*b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 12*I*a**2*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 6*a**2*b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 18*a**2*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 12*I*a**2*b**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 12*I*a*b**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 24*a*b**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 12*I*a*b**3*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 16*I*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 8*a*b**3*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 20*I*a*b**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 16*a*b**3/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 9*b**4*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 18*I*b**4*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 9*b**4*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*b**4*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*b**4*tan(e + f*x)**3/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 19*b**4*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 14*I*b**4/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, -I*d)), (a**4*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**4*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**4*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**4*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**4/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*a**3*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*a**3*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*a**3*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*a**3*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*a**2*b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 12*I*a**2*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 6*a**2*b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 18*a**2*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 12*I*a**2*b**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 12*I*a*b**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 24*a*b**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 12*I*a*b**3*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 16*I*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 8*a*b**3*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 20*I*a*b**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 16*a*b**3/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 9*b**4*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 18*I*b**4*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 9*b**4*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 8*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*b**4*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*b**4*tan(e + f*x)**3/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 19*b**4*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 14*I*b**4/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, I*d)), (x*(a + b*tan(e))**4/(c + d*tan(e))**2, Eq(f, 0)), (a**4*c**3*d**3*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + a**4*c**2*d**4*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a**4*c**2*d**4*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*c**2*d**4*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*c**2*d**4/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*c*d**5*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a**4*c*d**5*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*c*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*d**6*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - a**4*d**6/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 4*a**3*b*c**3*d**3*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a**3*b*c**3*d**3*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a**3*b*c**3*d**3/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 8*a**3*b*c**2*d**4*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 4*a**3*b*c**2*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a**3*b*c**2*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 8*a**3*b*c*d**5*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a**3*b*c*d**5*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*a**3*b*c*d**5*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a**3*b*c*d**5/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a**3*b*d**6*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*a**3*b*d**6*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 6*a**2*b**2*c**4*d**2/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 6*a**2*b**2*c**3*d**3*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 6*a**2*b**2*c**2*d**4*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 12*a**2*b**2*c**2*d**4*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 6*a**2*b**2*c**2*d**4*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 6*a**2*b**2*c**2*d**4/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 6*a**2*b**2*c*d**5*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 12*a**2*b**2*c*d**5*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 6*a**2*b**2*c*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 6*a**2*b**2*d**6*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a*b**3*c**5*d*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a*b**3*c**5*d/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a*b**3*c**4*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 12*a*b**3*c**3*d**3*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*a*b**3*c**3*d**3*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 4*a*b**3*c**3*d**3/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 8*a*b**3*c**2*d**4*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 12*a*b**3*c**2*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*a*b**3*c**2*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 8*a*b**3*c*d**5*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a*b**3*c*d**5*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*a*b**3*d**6*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*b**4*c**6*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*b**4*c**6/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 2*b**4*c**5*d*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 4*b**4*c**4*d**2*log(c/d + tan(e + f*x))/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + b**4*c**4*d**2*tan(e + f*x)**2/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 3*b**4*c**4*d**2/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + b**4*c**3*d**3*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - 4*b**4*c**3*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + b**4*c**2*d**4*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - b**4*c**2*d**4*log(tan(e + f*x)**2 + 1)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + 2*b**4*c**2*d**4*tan(e + f*x)**2/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - b**4*c**2*d**4/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - b**4*c*d**5*f*x/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - b**4*c*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) - b**4*d**6*f*x*tan(e + f*x)/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)) + b**4*d**6*tan(e + f*x)**2/(c**5*d**3*f + c**4*d**4*f*tan(e + f*x) + 2*c**3*d**5*f + 2*c**2*d**6*f*tan(e + f*x) + c*d**7*f + d**8*f*tan(e + f*x)), True))","A",0
1217,1,6730,0,3.357862," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{3}}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i a^{2} b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 a^{2} b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i a^{2} b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i a^{2} b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 a b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{6 i a b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 a b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{9 a b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 i a b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i b^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 b^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i b^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{5 i b^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 b^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = - i d \\\frac{a^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i a^{2} b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 a^{2} b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i a^{2} b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i a^{2} b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 a b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 i a b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 a b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{9 a b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{6 i a b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i b^{3} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 b^{3} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i b^{3} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{5 i b^{3} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 b^{3}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = i d \\\frac{a^{3} x + \frac{3 a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 a b^{2} x + \frac{3 a b^{2} \tan{\left(e + f x \right)}}{f} - \frac{b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{c^{2}} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{3}}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 a^{3} c^{3} d^{2} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 a^{3} c^{2} d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} c^{2} d^{3}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} c d^{4} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 a^{3} c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} d^{5} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 a^{3} d^{5}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{3 a^{2} b c^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b c^{3} d^{2}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{12 a^{2} b c^{2} d^{3} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a^{2} b c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{3 a^{2} b c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{12 a^{2} b c d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{3 a^{2} b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b c d^{4}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a^{2} b d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{3 a^{2} b d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a b^{2} c^{4} d}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a b^{2} c^{3} d^{2} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a b^{2} c^{2} d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{12 a b^{2} c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{2} c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{6 a b^{2} c^{2} d^{3}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{2} c d^{4} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{12 a b^{2} c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{2} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 a b^{2} d^{5} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 b^{3} c^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 b^{3} c^{5}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 b^{3} c^{4} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 b^{3} c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{b^{3} c^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 b^{3} c^{3} d^{2}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 b^{3} c^{2} d^{3} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 b^{3} c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{b^{3} c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 b^{3} c d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{b^{3} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{b^{3} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**3/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (a**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**3*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**3/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*a**2*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*a**2*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*a**2*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*a**2*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*a*b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 6*I*a*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*a*b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 9*a*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*I*a*b**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*b**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*b**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*b**3*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*b**3*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 5*I*b**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*b**3/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, -I*d)), (a**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**3*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**3/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*a**2*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*a**2*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*a**2*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*a**2*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*a*b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*I*a*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*a*b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 9*a*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 6*I*a*b**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*b**3*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*b**3*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*b**3*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*b**3*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 5*I*b**3*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*b**3/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, I*d)), ((a**3*x + 3*a**2*b*log(tan(e + f*x)**2 + 1)/(2*f) - 3*a*b**2*x + 3*a*b**2*tan(e + f*x)/f - b**3*log(tan(e + f*x)**2 + 1)/(2*f) + b**3*tan(e + f*x)**2/(2*f))/c**2, Eq(d, 0)), (x*(a + b*tan(e))**3/(c + d*tan(e))**2, Eq(f, 0)), (2*a**3*c**3*d**2*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*a**3*c**2*d**3*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*a**3*c**2*d**3*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*c**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*c**2*d**3/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*c*d**4*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*a**3*c*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*c*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*d**5*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*a**3*d**5/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a**2*b*c**3*d**2*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 3*a**2*b*c**3*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a**2*b*c**3*d**2/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 12*a**2*b*c**2*d**3*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a**2*b*c**2*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 3*a**2*b*c**2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 12*a**2*b*c*d**4*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a**2*b*c*d**4*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 3*a**2*b*c*d**4*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a**2*b*c*d**4/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a**2*b*d**5*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 3*a**2*b*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a*b**2*c**4*d/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a*b**2*c**3*d**2*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a*b**2*c**2*d**3*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 12*a*b**2*c**2*d**3*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a*b**2*c**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 6*a*b**2*c**2*d**3/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a*b**2*c*d**4*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 12*a*b**2*c*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a*b**2*c*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*a*b**2*d**5*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*b**3*c**5*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*b**3*c**5/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*b**3*c**4*d*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*b**3*c**3*d**2*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - b**3*c**3*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*b**3*c**3*d**2/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*b**3*c**2*d**3*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*b**3*c**2*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - b**3*c**2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*b**3*c*d**4*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + b**3*c*d**4*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + b**3*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)), True))","A",0
1218,1,4258,0,2.154134," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{2}}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 a b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = - i d \\\frac{a^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 a b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{b^{2} f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i b^{2} f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{b^{2} f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 b^{2} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i b^{2}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = i d \\\frac{a^{2} x + \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - b^{2} x + \frac{b^{2} \tan{\left(e + f x \right)}}{f}}{c^{2}} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{2}}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{a^{2} c^{3} d f x}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{a^{2} c^{2} d^{2} f x \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a^{2} c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} c^{2} d^{2}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} c d^{3} f x}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a^{2} c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} d^{4} f x \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a^{2} d^{4}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{2 a b c^{3} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{a b c^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b c^{3} d}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{4 a b c^{2} d^{2} f x}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{2 a b c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{a b c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{4 a b c d^{3} f x \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a b c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b c d^{3}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{2 a b d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{a b d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{b^{2} c^{4}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{b^{2} c^{3} d f x}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{b^{2} c^{2} d^{2} f x \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{2 b^{2} c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{b^{2} c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{b^{2} c^{2} d^{2}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{b^{2} c d^{3} f x}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} - \frac{2 b^{2} c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{b^{2} c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} + \frac{b^{2} d^{4} f x \tan{\left(e + f x \right)}}{c^{5} d f + c^{4} d^{2} f \tan{\left(e + f x \right)} + 2 c^{3} d^{3} f + 2 c^{2} d^{4} f \tan{\left(e + f x \right)} + c d^{5} f + d^{6} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**2/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (a**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**2*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*a*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*b**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, -I*d)), (a**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a**2*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*a*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - b**2*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*b**2*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + b**2*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*b**2*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*b**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, I*d)), ((a**2*x + a*b*log(tan(e + f*x)**2 + 1)/f - b**2*x + b**2*tan(e + f*x)/f)/c**2, Eq(d, 0)), (x*(a + b*tan(e))**2/(c + d*tan(e))**2, Eq(f, 0)), (a**2*c**3*d*f*x/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + a**2*c**2*d**2*f*x*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a**2*c**2*d**2*log(c/d + tan(e + f*x))/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*c**2*d**2*log(tan(e + f*x)**2 + 1)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*c**2*d**2/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*c*d**3*f*x/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a**2*c*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*c*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*d**4*f*x*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a**2*d**4/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - 2*a*b*c**3*d*log(c/d + tan(e + f*x))/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + a*b*c**3*d*log(tan(e + f*x)**2 + 1)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a*b*c**3*d/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 4*a*b*c**2*d**2*f*x/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - 2*a*b*c**2*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + a*b*c**2*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 4*a*b*c*d**3*f*x*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a*b*c*d**3*log(c/d + tan(e + f*x))/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a*b*c*d**3*log(tan(e + f*x)**2 + 1)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a*b*c*d**3/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + 2*a*b*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - a*b*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - b**2*c**4/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - b**2*c**3*d*f*x/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - b**2*c**2*d**2*f*x*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - 2*b**2*c**2*d**2*log(c/d + tan(e + f*x))/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + b**2*c**2*d**2*log(tan(e + f*x)**2 + 1)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - b**2*c**2*d**2/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + b**2*c*d**3*f*x/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) - 2*b**2*c*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + b**2*c*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)) + b**2*d**4*f*x*tan(e + f*x)/(c**5*d*f + c**4*d**2*f*tan(e + f*x) + 2*c**3*d**3*f + 2*c**2*d**4*f*tan(e + f*x) + c*d**5*f + d**6*f*tan(e + f*x)), True))","A",0
1219,1,2878,0,1.912840," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = - i d \\\frac{a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right)}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{a x + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f}}{c^{2}} & \text{for}\: d = 0 \\\frac{2 a c^{3} f x}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{2 a c^{2} d f x \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{4 a c^{2} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a c^{2} d}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a c d^{2} f x}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{4 a c d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 a d^{3}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 b c^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{2 b c^{3}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{4 b c^{2} d f x}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{2 b c^{2} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{b c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{4 b c d^{2} f x \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{2 b c d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{2 b c d^{2}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} + \frac{2 b d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} - \frac{b d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} f + 2 c^{4} d f \tan{\left(e + f x \right)} + 4 c^{3} d^{2} f + 4 c^{2} d^{3} f \tan{\left(e + f x \right)} + 2 c d^{4} f + 2 d^{5} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*a/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, -I*d)), (a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - a*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*a/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, I*d)), (x*(a + b*tan(e))/(c + d*tan(e))**2, Eq(f, 0)), ((a*x + b*log(tan(e + f*x)**2 + 1)/(2*f))/c**2, Eq(d, 0)), (2*a*c**3*f*x/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 2*a*c**2*d*f*x*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 4*a*c**2*d*log(c/d + tan(e + f*x))/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*c**2*d*log(tan(e + f*x)**2 + 1)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*c**2*d/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*c*d**2*f*x/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 4*a*c*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*d**3*f*x*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*a*d**3/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*b*c**3*log(c/d + tan(e + f*x))/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + b*c**3*log(tan(e + f*x)**2 + 1)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 2*b*c**3/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 4*b*c**2*d*f*x/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - 2*b*c**2*d*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + b*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 4*b*c*d**2*f*x*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 2*b*c*d**2*log(c/d + tan(e + f*x))/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 2*b*c*d**2/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) + 2*b*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)) - b*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*f + 2*c**4*d*f*tan(e + f*x) + 4*c**3*d**2*f + 4*c**2*d**3*f*tan(e + f*x) + 2*c*d**4*f + 2*d**5*f*tan(e + f*x)), True))","A",0
1220,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1221,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1222,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1223,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1224,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1225,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1226,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
1227,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1228,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
1229,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**3,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{3} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*sqrt(c + d*tan(e + f*x)), x)","F",0
1230,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**2,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*sqrt(c + d*tan(e + f*x)), x)","F",0
1231,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e)),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x)), x)","F",0
1232,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e)),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(a + b*tan(e + f*x)), x)","F",0
1233,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**2,x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(a + b*tan(e + f*x))**2, x)","F",0
1234,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**3,x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(a + b*tan(e + f*x))**3, x)","F",0
1235,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(c + d*tan(e + f*x))**(3/2), x)","F",0
1236,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(3/2), x)","F",0
1237,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2), x)","F",0
1238,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e)),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x)), x)","F",0
1239,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x))**2, x)","F",0
1240,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**3,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x))**3, x)","F",0
1241,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**(5/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(c + d*tan(e + f*x))**(5/2), x)","F",0
1242,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**(5/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(5/2), x)","F",0
1243,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**(5/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2), x)","F",0
1244,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e)),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x)), x)","F",0
1245,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**2, x)","F",0
1246,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**3,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**3, x)","F",0
1247,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{4}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**4/sqrt(c + d*tan(e + f*x)), x)","F",0
1248,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3/sqrt(c + d*tan(e + f*x)), x)","F",0
1249,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2/sqrt(c + d*tan(e + f*x)), x)","F",0
1250,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{a + b \tan{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))/sqrt(c + d*tan(e + f*x)), x)","F",0
1251,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e)),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right) \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))), x)","F",0
1252,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**2,x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**2*sqrt(c + d*tan(e + f*x))), x)","F",0
1253,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{4}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**4/(c + d*tan(e + f*x))**(3/2), x)","F",0
1254,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3/(c + d*tan(e + f*x))**(3/2), x)","F",0
1255,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2/(c + d*tan(e + f*x))**(3/2), x)","F",0
1256,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{a + b \tan{\left(e + f x \right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))/(c + d*tan(e + f*x))**(3/2), x)","F",0
1257,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1258,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1259,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**4/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{4}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**4/(c + d*tan(e + f*x))**(5/2), x)","F",0
1260,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3/(c + d*tan(e + f*x))**(5/2), x)","F",0
1261,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2/(c + d*tan(e + f*x))**(5/2), x)","F",0
1262,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{a + b \tan{\left(e + f x \right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))/(c + d*tan(e + f*x))**(5/2), x)","F",0
1263,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1264,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1265,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**(5/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)*sqrt(c + d*tan(e + f*x)), x)","F",0
1266,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*sqrt(c + d*tan(e + f*x)), x)","F",0
1267,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(1/2),x)","\int \sqrt{a + b \tan{\left(e + f x \right)}} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x)), x)","F",0
1268,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/sqrt(a + b*tan(e + f*x)), x)","F",0
1269,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(a + b*tan(e + f*x))**(3/2), x)","F",0
1270,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))/(a + b*tan(e + f*x))**(5/2), x)","F",0
1271,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(c+d*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(3/2), x)","F",0
1272,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(3/2),x)","\int \sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2), x)","F",0
1273,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/sqrt(a + b*tan(e + f*x)), x)","F",0
1274,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x))**(3/2), x)","F",0
1275,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x))**(5/2), x)","F",0
1276,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)/(a+b*tan(f*x+e))**(7/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)/(a + b*tan(e + f*x))**(7/2), x)","F",0
1277,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(5/2),x)","\int \sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2), x)","F",0
1279,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/sqrt(a + b*tan(e + f*x)), x)","F",0
1280,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**(3/2), x)","F",0
1281,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**(5/2), x)","F",0
1282,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)/(a+b*tan(f*x+e))**(7/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)/(a + b*tan(e + f*x))**(7/2), x)","F",0
1283,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)/sqrt(c + d*tan(e + f*x)), x)","F",0
1284,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)/sqrt(c + d*tan(e + f*x)), x)","F",0
1285,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))/sqrt(c + d*tan(e + f*x)), x)","F",0
1286,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(e + f x \right)}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))), x)","F",0
1287,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(3/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
1288,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(5/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
1289,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(7/2)/(c+d*tan(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1290,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
1291,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
1292,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))/(c + d*tan(e + f*x))**(3/2), x)","F",0
1293,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1294,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1295,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(5/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
1296,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(9/2)/(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(7/2)/(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
1299,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
1300,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))/(c + d*tan(e + f*x))**(5/2), x)","F",0
1301,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1302,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1303,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{1}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(1/((a + b*tan(e + f*x))**(5/2)*(c + d*tan(e + f*x))**(5/2)), x)","F",0
1304,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1305,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**3,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))**3, x)","F",0
1306,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**2,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))**2, x)","F",0
1307,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e)),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x)), x)","F",0
1308,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m, x)","F",0
1309,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e)),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m}}{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m/(c + d*tan(e + f*x)), x)","F",0
1310,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e))**2,x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m/(c + d*tan(e + f*x))**2, x)","F",0
1311,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e))**3,x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m/(c + d*tan(e + f*x))**3, x)","F",0
1312,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**(3/2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))**(3/2), x)","F",0
1313,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**m,x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \sqrt{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*sqrt(c + d*tan(e + f*x)), x)","F",0
1314,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m/sqrt(c + d*tan(e + f*x)), x)","F",0
1315,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m/(c + d*tan(e + f*x))**(3/2), x)","F",0
1316,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m/(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+I*a*tan(f*x+e))**m,x)","\int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \left(i a \left(\tan{\left(e + f x \right)} - i\right)\right)^{m}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n*(I*a*(tan(e + f*x) - I))**m, x)","F",0
1318,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+I*a*tan(f*x+e))**3,x)","- i a^{3} \left(\int i \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}\, dx + \int \left(- 3 \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx + \int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan^{3}{\left(e + f x \right)}\, dx + \int \left(- 3 i \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-I*a**3*(Integral(I*(c*(d*tan(e + f*x))**p)**n, x) + Integral(-3*(c*(d*tan(e + f*x))**p)**n*tan(e + f*x), x) + Integral((c*(d*tan(e + f*x))**p)**n*tan(e + f*x)**3, x) + Integral(-3*I*(c*(d*tan(e + f*x))**p)**n*tan(e + f*x)**2, x))","F",0
1319,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+I*a*tan(f*x+e))**2,x)","- a^{2} \left(\int \left(- \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}\right)\, dx + \int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 i \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*(Integral(-(c*(d*tan(e + f*x))**p)**n, x) + Integral((c*(d*tan(e + f*x))**p)**n*tan(e + f*x)**2, x) + Integral(-2*I*(c*(d*tan(e + f*x))**p)**n*tan(e + f*x), x))","F",0
1320,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+I*a*tan(f*x+e)),x)","i a \left(\int \left(- i \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}\right)\, dx + \int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \tan{\left(e + f x \right)}\, dx\right)"," ",0,"I*a*(Integral(-I*(c*(d*tan(e + f*x))**p)**n, x) + Integral((c*(d*tan(e + f*x))**p)**n*tan(e + f*x), x))","F",0
1321,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n/(a+I*a*tan(f*x+e)),x)","- \frac{i \int \frac{\left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}}{\tan{\left(e + f x \right)} - i}\, dx}{a}"," ",0,"-I*Integral((c*(d*tan(e + f*x))**p)**n/(tan(e + f*x) - I), x)/a","F",0
1322,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n/(a+I*a*tan(f*x+e))**2,x)","- \frac{\int \frac{\left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}}{\tan^{2}{\left(e + f x \right)} - 2 i \tan{\left(e + f x \right)} - 1}\, dx}{a^{2}}"," ",0,"-Integral((c*(d*tan(e + f*x))**p)**n/(tan(e + f*x)**2 - 2*I*tan(e + f*x) - 1), x)/a**2","F",0
1323,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+b*tan(f*x+e))**m,x)","\int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n*(a + b*tan(e + f*x))**m, x)","F",0
1324,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+b*tan(f*x+e))**3,x)","\int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{3}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n*(a + b*tan(e + f*x))**3, x)","F",0
1325,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+b*tan(f*x+e))**2,x)","\int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)^{2}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n*(a + b*tan(e + f*x))**2, x)","F",0
1326,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n*(a+b*tan(f*x+e)),x)","\int \left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n} \left(a + b \tan{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n*(a + b*tan(e + f*x)), x)","F",0
1327,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n/(a+b*tan(f*x+e)),x)","\int \frac{\left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n/(a + b*tan(e + f*x)), x)","F",0
1328,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))**p)**n/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(c \left(d \tan{\left(e + f x \right)}\right)^{p}\right)^{n}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c*(d*tan(e + f*x))**p)**n/(a + b*tan(e + f*x))**2, x)","F",0
